Norton Sound Red King Crab Stock Assessment April 30, 2013

Draft - Norton Sound Red King Crab Stock Assessment April 30, 2013

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Norton Sound Red King Crab Stock Assessment for the fishing year 2013/14

Toshihide Hamazaki1 and Jie Zheng 2 Alaska Department of Fish and Game Commercial Fisheries Division

1333 Raspberry Rd., Anchorage, AK 99518-1565 Phone: 907-267-2158

Email: [email protected] 2P.O. Box 115526, Juneau, AK 99811-5526

Phone : 907-465-6102 Email : [email protected]

Executive Summary

1. Stock. Red king crab, Paralithodes camtschaticus, in Norton Sound, Alaska.

2. Catches. This stock supports three main fisheries: summer commercial, winter commercial, and winter subsistence fisheries. Of those, the summer commercial fishery accounts for more than 90% of total harvest. Summer commercial fishery started in 1977, and its catch quickly reached a peak in the late 1970s with retained catch of over 2.9 million pounds. Since 1982, retained catches have been below 0.5 million pounds, averaging 0.275 million pounds, including several low years in the 1990s. As the crab population rebounds, retained catches have been increasing. For past several years, retained catch is around 0.4 million pounds.

3. Stock Biomass. Estimated mature male biomass (MMB) shows an increasing trend since

1997, and an historic low in 1982 following a crash from the peak in 1977. However, uncertainty in historical biomass is great, which is in part by infrequent trawl surveys (every 3 to 5 years) and limited winter pot survey.

4. Recruitment. Model estimated recruitment was weak during the late 1970s and high during

the early 1980s with a slight downward trend from 1983 to 1993. Estimated recruitment has been highly variable but on an increasing trend in recent years.

5. Management performance.

Status and catch specifications (million lbs.)

Year MSST Biomass (MMB)

GHLRetained

Catch Total Catch

OFL ABC

2009/10 1.54A 5.83 0.38 0.40 0.43 0.71A 2010/11 1.56B 5.44 0.40 0.42 0.46 0.73B 2011/12 1.56C 4.70 0.36 0.40 0.43 0.66C 0.59 2012/13 1.78D 4.59 0.47 0.47 0.47 0.53D 0.48 2013/14


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GHLRetained

Catch Total Catch

OFL ABC

2013/14a 2.06 5.00 0.58 0.52 2013/14b 1.83 5.03 0.71 0.64 2013/14c 1.37 4.77 0.81 0.73

Status and catch specifications (1000t)


GHLRetained

Catch Total Catch OFL

ABC

2009/10 0.70A 2.64 0.17 0.18 0.20 0.32A 2010/11 0.71B 2.47 0.18 0.19 0.21 0.33B 2011/12 0.71C 2.13 0.16 0.18 0.20 0.30C 0.27 2012/13 0.80D 2.08 0.21 0.21 0.21 0.24D 0.22 2013/14 TBD TBD TBD


GHLRetained

Catch Total Catch

OFL ABC

2013/14a 0.93 2.27 0.26 0.24 2013/14b 0.83 2.28 0.32 0.29 2013/14c 0.62 2.16 0.37 0.33

Notes: MSST was calculated as BMSY/2 A-Calculated from the assessment reviewed by the Crab Plan Team in May 2009 B-Calculated from the assessment reviewed by the Crab Plan Team in May 2010 C-Calculated from the assessment reviewed by the Crab Plan Team in May 2011 D-Calculated from the assessment reviewed by the Crab Plan Team in May 2012 E-Calculated from the assessment reviewed by the Crab Plan Team in May 2013 Biomass in millions of pounds

Year Tier BMSY Current MMB

B/BMSY (MMB)

FOFL

Years to define BMSY

M 1-Buffer ABC

2009/10 4a 3.07 5.83 1.9 0.18 1983-2009 0.18 2010/11 4a 3.12 5.44 1.7 0.18 1983-2010 0.18 2011/12 4a 2.97 4.70 1.6 0.18 1983-2011 0.18 0.9 0.59 2012/13 4a 3.51 4.25 1.2 0.18 1980-2012 0.18 0.9 0.48 2013/14 4a 1980-2013 0.9

Candidate OFL and ABC million lb. Parenthesis indicates standard deviation


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Model B2013 BMSY B/ BMSY Legal male

biomass M FOFL OFL

ABC (0.9×OFL)

S3-1 5.00

(0.98) 4.12 1.21 3.55 (0.48) 0.18 0.18

0.577 (0.08)

0.519

S3-6 5.03

(0.96) 3.73 1.35 3.31 (0.50) 0.24 0.24 0.708 (0.11)

0.637

S3-7 4.77

(1.00) 3.95 1.20 3.12 (0.49) 0.30 0.30

0.808 (0.13)

0.727

Biomass in 1000t

Year Tier BMSY Current MMB

B/BMSY (MMB)

FOFL

Years to define BMSY

M 1-Buffer ABC

2009/10 4a 1.39 2.64 1.9 0.18 1983-2009 0.18 2010/11 4a 1.42 2.47 1.7 0.18 1983-2010 0.18 2011/12 4a 1.35 2.18 1.6 0.18 1983-2011 0.18 0.9 0.27 2012/13 4a 1.59 1.93 1.2 0.18 1980-2012 0.18 0.9 0.22 2013/14 4a 0.9

Candidate OFL and ABC 1000t. Parenthesis indicates standard deviation

Model B2013 BMSY B/ BMSY Legal male

biomass M FOFL OFL

ABC (0.9×OFL)

S3-1 2.27

(0.44) 1.86 1.22 1.61 (0.22) 0.18 0.18

0.26 (0.04)

0.24

S3-6 2.31

(0.44) 1.66 1.39 1.40 (0.23) 0.24 0.24

0.32 (0.05)

0.29

S3-7 2.20

(0.45) 1.73 1.30 1.42 (0.22) 0.30 0.30

0.367 (0.06)

0.33


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6. Probability Density Function of the OFL

S3-1 S3-6 S3-7

OFL profile. CV of the OFL was assumed to be 0.2.

7. The basis for the ABC recommendation For Tier 4 stocks, the default maximum ABC is based on P*=49% that is essentially identical to the OFL. Accounting for uncertainties in assessment and model results, the SSC chose to use 90% OFL (10% Buffer) for the Norton Sound red king crab stock in 2011. For 2013 analyses, we chose 90% OFL (10% Buffer) which was million lb because of remained uncertainties in the model.

8. A summary of the results of any rebuilding analyses. N/A

A. Summary of Major Changes in 2012

1. Changes to the management of the fishery:

In March 2012, the board of fish adopted a revised GHL: (1) 0% harvest rate of legal crab when estimated legal biomass < 1.25 million lbs; (2) ≤ 7% of legal male abundance when the estimated legal biomass falls within the range 1.25-2.0 million lbs; (3) ≤ 13% of legal male abundance when the estimated legal biomass falls within the range 2.0-3.0 million lbs; and (3) ≤ 15% of legal male when estimated legal biomass >3.0 million lbs.


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2. Changes to the input data

a. Data update: the 2011/12 winter pot survey, 2012 summer commercial fishery, 2011/2012 winter commercial and subsistence catch finalized

b. New Data: 2012 summer commercial fishery observer data, standardized commercial catch CPUE and CV.

c. Revised data: 1976-1991 NMFS survey NSRKC crab abundance estimates were revised based on original survey data.

d. Dropped data: 1981-85 summer pot survey data were dropped because of the lack of raw data and unverifiable abundance estimates.

3. Changes to the assessment methodology: Following model modification were evaluated

a. See Appendix A for model modification.

4. Changes to the assessment results.

B. Response to SSC and CPT Comments

CPT Review May 7-10, 2012 The team had the following comments:

1. Lack of bycatch data. The CPT requests that some data on bycatch be collected in conjunction with the NPRB project recently funded.

Author response: In 2012 limited summer commercial fishery observer data were collected. The data were included in the model. Further continuation of observer program depends upon availability of funding.

2. Length composition data have been downweighted, but there still is apparent conflict within the model. This is a possible indication of model mis-specification.

Author response: Since specifics of the “apparent conflict” were lacking, it is difficult to respond. See response for not fitting earlier abundance data.


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3. There is a need for better justification for the higher natural mortality on animals in the largest length bin (none of the models address dome vs. asymptotic M).

Author response: We re-examined dome shaped vs. constant M =0.24 and 0.30 (Scenario 0 vs. S1-6, S1-6). We did not evaluate asymptotic M. Constant M increased fit to trawl survey abundance and trawl length composition, and observer and winter pot length composition, but reduced fit to commercial catch length composition. Further, projected crab abundance was lower by 4-11%. Additional effects are lower molting probability for larger length classes, and reducing retrospective bias and error. As for calculation of OFL and ABC, constant M assumptions will increase of OFL proportion

))exp(1( OFLF For M = 0.18, it is 0.165, whereas it is 0.213 and 0.259, respectively for M =

0.24 and 0.30. This will result in an increase of OFL by 20-60% from that of M = 0.18.

4. Model does not fit early data, and it was suggested to start prospective analysis in 75, 76, 77, …

Author response: Possible reasons for the model not fitting earlier data are related to assessment crab population model structure: assumption of constant M and constant growth-per-molt. Recent (1996-2012) data show that the crab population has been increasing gradually (average 3% per year) at about 10% of harvest rate, and OFL harvest rate of 16.5%. However, during 1976-1982 periods, especially from 1979 to 1982 estimated total (CL > 73mm) crab abundance increased from 0.9 million to 2.09 million, more than 2 times, under the harvest rate of 50-60% (Table 3). This cannot be explained by the current population model structure. Consequently, the model estimated abundance was higher than observed during those years. This discrepancy can be partially solved by 1) further down weighting length composition data and thus increasing weight of trawl survey (scenario S1-3), 2) assuming less than 1.0 for survey Q (S1-4) (i.e., trawl survey underestimated true crab abundance), 3) time variant growth-per-molt matrix, 4) density-dependent growth/mortality, 5) inclusion of environmental changes, or combinations of all. In this iteration, we evaluated only the first two alternative scenarios. Those alternative model scenarios resulted in better fit of historical data; however, those still will meet an identical model criticisms on the lack of empirical/scientific justification of the model changes (e.g., is there any empirical evidence supporting that historical trawl surveys underestimated true abundance, that historical trawl length compositions are biased, that growth-per-molt changed over time, that density-dependent growth/mortality occurring, or that Norton Sound environmental conditions changed to affect crab population dynamics?). Due to the absence of historical data in Norton Sounds, those uncertainties could not be easily resolved. Simultaneously, prospective analyses show that those historical uncertainties about true historical population dynamics had little influences on population trends of 1996 to present. Another influence of a model better fitting to historical data is calculation of BMSY proc that is an average 82-present modeled biomass for the Norton Sound red king crab. For this, all model scenarios resulted in B/ BMSY proc > 1, suggesting that model misfits to historical data would not affect assessment of recent data.


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5. Use the derivative checker to verify that the objective function is differentiable.

Author response: We verified that the objective function is differentiable.

6. Plot histograms for effective sample sizes for the compositional data.

Author response: Implemented

SSC Review on June 4-6, 2012 The current model assumes that selectivity of the trawl survey follows a sigmoid function and Q was estimated 1.0 for length classes 3 through 5. The SSC asks the author to review this assumption given the results of recent studies of trawl survey Q for Bristol Bay red king crab, snow crab and Tanner crab. Author response: We relaxed the trawl survey selectivity function to estimate all length classes with 1.0 for length classes 5 and 6. However, this relaxation did not change the shape of trawl selectivity. Selectivity of all length classes was still estimated to 1.0 or closer. Under a direction of the CPT, we also included evaluated the assumption of survey Q = 1.0 for trawl surveys (i.e., estimated survey abundance is accurate). Holding survey Q=1 for NMFS resulted in greater than 1 Q for ADF&G surveys (i.e., ADF&G trawl surveys OVERESTIMATE crab abundance). Oppositely, holding survey Q=1 for AD&G survey resulted in less than 1 Q for NMFS surveys (i.e., NMFS trawl surveys UNDERESTIMATE crab abundance). Given that overestimation of ADF&G survey abundance is unlikely, we incorporated estimation of NOAA survey Q in the current assessment model.

C. Introduction

1. Species: red king crab (Paralithodes camtschaticus) in Norton Sound, Alaska.

2. General Distribution: Norton Sound red king crab is one of the northernmost red king crab populations that can support a commercial fishery (Powell et al. 1983). It is distributed throughout Norton Sound with a westward limit of 167-168o W. longitude with depths less than 30 m and summer bottom temperatures above 4oC. The Norton Sound red king crab management area consists of two units: Norton Sound Section (Q3) and Kotzebue Section


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(Q4) (Menard et al. 2011). The Norton Sound Section (Q3) consists of all waters in Registration Area Q north of the latitude of Cape Romanzof, east of the International Dateline, and south of 66°N latitude (Figure 1). The Kotzebue Section (Q4) lies immediately north of the Norton Sound Section and includes Kotzebue Sound. Commercial fisheries have not occurred regularly in the Kotzebue Section. This report deals with the Norton Sound Section of the Norton Sound red king crab management area.

3. Evidence of stock structure: Thus far, no studies have been made on possible stock separation within the putative stock known as Norton Sound red king crab.

4. Life history characteristics relevant to management: One of the unique life-history traits of Norton Sound red king crab is that they spend their entire lives in shallow water since Norton Sound is generally less than 40 m in depth. Distribution and migration patterns of Norton Sound red king crab have not been well studied. Based on the 1976-2006 trawl surveys, red king crab in Norton Sound are found in areas with a mean depth range of 19 ± 6 (SD) m and bottom temperatures of 7.4 ± 2.5 (SD) oC during the summer. Norton Sound red king crab are consistently abundant offshore of Nome.

Norton Sound red king crab migrate between deeper offshore waters during molting/feeding and inshore shallow waters during the mating period. Timing of the inshore mating migration is unknown; but is assumed to be during March-June. Offshore migration is considered to begin in May-July. Trawl surveys show that crab distribution is dynamic. Recent surveys show high abundance on the southeast side of the Sound, offshore of Stebbins and Saint Michael.

5. Brief management history: Norton Sound red king crab fisheries consist of commercial and subsistence fisheries. The commercial red king crab fishery started in 1977 and occurs in summer (June – August) and in winter (December – May) (Menard et al. 2011). The majority of red king crab are harvested by the summer commercial fisheries, whereas the majority of the winter harvest is in the subsistence fishery occurring near the coast (Table 2).

Summer Commercial Fishery

Summer commercial crab fishery started in 1977. A large-vessel summer commercial crab fishery existed in the Norton Sound Section from 1977 through 1990. No summer commercial fishery occurred in 1991 because there was no staff to manage the fishery. In March 1993, the Alaska Board of Fisheries (BOF) limited participation in the fishery to small boats. Then on June 27, 1994, a super-exclusive designation went into effect for the fishery. This designation stated that a vessel registered for the Norton Sound crab fishery may not be used to take king crabs in any other registration areas during that registration year. A vessel moratorium was put into place before the 1996 season. This was intended to precede a license limitation program. In 1998, Community Development Quota (CDQ) groups were allocated a portion of the summer harvest; however, no CDQ harvest occurred until the 2000 season. On January 1, 2000 the North Pacific License Limitation Program (LLP) went into effect for the Norton Sound crab fishery. The program dictates that a vessel which exceeds 32 feet in length overall must hold a valid crab license issued under the LLP by the National Marine Fisheries Service. Regulation changes and location of buyers resulted in harvest distribution moving eastward in Norton Sound in the mid-1990s. In the Norton Sound, a


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legal crab is defined as ≥ 4-3/4 inch carapace width (CW, Menard et al. 2011; equivalent to ≥ 124 mm carapace length [CL]). Since 2005, commercial buyers started accepting only legal crabs of ≥ 5 inch carapace.

Not all Norton Sound area is open for commercial fisheries. Since beginning of the commercial fisheries in 1977, inland waters near Nome area has been closed for summer commercial crab fishery, possibly to protect crab nursery grounds (Figure 2). Extent of closed water changed throughout history. Appendix E shows historical harvest by Stat area.

CDQ Fishery

The Norton Sound and Lower Yukon CDQ groups divide the CDQ allocation. Only fishers designated by the Norton Sound and Lower Yukon CDQ groups are allowed to participate in this portion of the king crab fishery. Fishers are required to have a CDQ fishing permit from the Commercial Fisheries Entry Commission (CFEC) and register their vessel with the Alaska Department of Fish and Game (ADF&G) before they make their first delivery. Fishers operate under authority of the CDQ group and each CDQ group decides how their crab quota is to be harvested. During the March 2002 BOF meeting, new regulations were adopted that affected the CDQ crab fishery and relaxed closed-water boundaries in eastern Norton Sound and waters west of Sledge Island. At its March 2008, the BOF changed the start date of the Norton Sound open-access portion of the fishery to be opened by emergency order and as early as June 15. The CDQ fishery may open at any time (as soon as ice is out), by emergency order. It is possible that the fishery starts BEFORE determination of OFL and ABC.

Winter Commercial Fishery

The Norton Sound winter commercial fishery is a small fishery using hand lines and pots through the nearshore ice. Approximately 10 permit holders participated in this fishery harvesting, on average 2,500 crabs during 1978-2009 (Menard 2011). The winter commercial fishery catch is influenced not only by crab abundance, but also by changes in near shore crab distribution, and ice conditions.

Subsistence Fishery

The Norton Sound subsistence crab fishery mainly occurs during winter using hand lines and pots through the nearshore ice. Average annual subsistence harvest was 5,300 crabs (1978-2007). Subsistence harvesters need to obtain a permit before fishing and record daily effort and catch. There is no size limit in the subsistence fishery. The subsistence fishery catch is influenced not only by crab abundance, but also by changes in distribution, changes in gear (e.g., more use of pots instead of hand lines since 1980s), and ice conditions (e.g., reduced catch due to unstable ice conditions: 1987-88, 1988-89, 1992-93, 2000-01, 2003-04, 2004-05, and 2006-07).


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6. Brief description of the annual ADF&G harvest strategy

Since 1997 Norton Sound red king crab have been managed based on a guideline harvest limit (GHL). Detailed history of GHL determination methods are unknown. Since 1999, GHL is determined by a prediction model and the model estimated predicted biomass: (1) 0% harvest rate of legal crab when estimated legal biomass < 1.5 million lbs; (2) ≤ 5% of legal male abundance when the estimated legal biomass falls within the range 1.5-2.5 million lbs; and (3) ≤ 10% of legal male when estimated legal biomass >2.5 million lbs.

In 2012 the Alaska Board of Fisheries adopted a revised GHL: (1) 0% harvest rate of legal crab when estimated legal biomass < 1.25 million lbs; (2) ≤ 7% of legal male abundance when the estimated legal biomass falls within the range 1.25-2.0 million lbs; (3) ≤ 13% of legal male abundance when the estimated legal biomass falls within the range 2.0-3.0 million lbs; and (3) ≤ 15% of legal male when estimated legal biomass >3.0 million lbs.

Year Notable historical management changes 1976 The abundance survey started 1977 Large vessel commercial fisheries began 1991 Fishery closed due to staff constraints 1994 Super exclusive designation into effect. The end of large vessel commercial fishery operation.

Participation limited to small boats. The majority of commercial fishery subsequently shifted to east of 164oW line.

1998 Community Development Quota (CDQ) allocation into effect 1999 Guideline Harvest Limit (GHL) into effect 2000 North Pacific License Limitation Program (LLP) into effect. 2002 Change in closed water boundaries (Figure 2) 2005 Commercially accepted legal crab size changed from ≥ 4-3/4 inch CW to ≥ 5 inch CW 2006 The Statistical area Q3 section expanded (Figure 1) 2008 Start date of the open access fishery changed from July1 to after June 15 by emergency order.

Pot configuration requirement: at least 4 escape rings (>4½ inch diameter) per pot located within one mesh of the bottom of the pot, or at least ½ of the vertical surface of a square pot or sloping side-wall surface of a conical or pyramid pot with mesh size > 6½ inches.

2012 Board of fisheries adopted a revised GHL

7. Summary of the history of the BMSY.

NSRKC is a tier4a crab stock, and direct estimation of the BMSY is not possible. BMSY is calculated as mean model estimated mature male biomass (MMB) from 1980 to present. Choice of this period was based on a belief that PDO shift occurred in 1976-77 could have changed the productivity.

D. Data

1. Summary of new information:


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1. Standardized summer commercial fishery cpue and standard deviation was calculated (Bishop 2013) and included in the model

2. Harvests of 2012 summer commercial fishery, and 2011/2012 winter commercial and subsistence fisheries, were updated. For winter 2012/13 harvest data, 2011/2012 winter harvest data were used.

3. 2012 summer commercial fishery observer discard data were included.

2. Available survey, catch, and tagging data

Data Years Data Types Tables

Summer trawl survey 76,79,82,85,88,91,96, 99, 02,06,08,10,11

Abundance and proportion by length and shell condition

3,5, Appendix B, E

Summer pot survey 80-82,85 Abundance and proportion by length and shell condition

3, 8, Appendix C, Not used for assessment

Winter pot survey 81-87, 89-91,93,95-00,02-12

Proportion by length and shell condition

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Summer preseason survey 95 Proportion by length and shell condition

Not used for assessment

Summer commercial fishery

76-90,92-12 Harvest, effort, standardized CPUE, and proportion by length and shell condition

1,4, Appendix E, Bishop et al (2013)

Observer data 87-90,92,94, 2012 Proportion by length and shell condition (sub-legal only)

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Winter commercial and subsistence fishery

76-11 The Number of crab harvested 2

Tagging 80-11 Used to create a growth increment matrix

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1. Summer commercial fishery and winter commercial and subsistence catch, (ADF&G 1976-2011) (Tables 1 and 2).

2. Discards of sublegal males (observer data) from the summer fishery (ADF&G 1987-90,

1992, 1994, 2012). The survey was opportunistic, and the number of crab discarded was not recorded. Continuation of summer commercial discards observer data depend upon future funding. Only catch-at-length and shell condition of sub-legal male were recorded (Table 8). In Norton Sound, no other crab, groundfish, or shellfish fisheries exist.

Fishery Data

availability Directed pot fishery (males) Summer commercial

Winter commercial/subsistence summer

commercial Directed pot fishery (females) None Bycatch in other crab fisheries Does not exist NA

Bycatch in ground pot Does not exist NA


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Bycatch in ground fish trawl Does not exist NA Bycatch in the scallop fishery Does not exist NA 3. Catch at length data for summer commercial fisheries (Table 4). 4. Survey abundance estimates:

1. Triennial Trawl Survey Triennial trawl surveys were conducted by the NMFS (1976-1991, 2010) and by the ADF&G (1996-2011) (Table 3). The NMFS survey was conducted using the 83-112 Eastern Otter Trawl, whereas the ADF&G survey was conducted using the 400 Eastern Otter Trawl. In both surveys, survey design was based on 10×10nm square, except for the NMFS survey in 2010 where survey grid was 20×20nm. Abundance of crabs were estimated by area-swept methods (Alverson and Pereyra 1969; see Appendix B). While the assessment model is based on crab population of ≥ 74mm CL, none of surveys have reported abundance of crab ≥ 74mm CL. NMFS survey reported crab abundance of ≥ 100 mm CL, 0-100 mm CL, and all sizes during 1991 periods, and ≥ 90 mm CL, 0 - 89 mm CL, and all sizes during 1985periods. On the other hand, ADF&G survey reported crab abundance of legal size (≥ 4 ¾ inch CW). To estimate abundance of ≥ 74mm CL crab, we re-estimated abundance of ≥ 74mm CL crab from original raw trawl survey data for ADF&G trawl survey. For 1976-1991 NMFS survey, we took two approaches for estimation of historical NMFS trawl abundances: 1) Indirect method based on published report (See Appendix B).

2. Summer pot survey

Summer pot surveys were conducted in 1980-1982 and 1985 by ADF&G. The pot survey crab abundance estimates were based on Petersen Mark-recapture method. Before fisheries season, crabs were captured throughout Norton Sound, tagged and released. The tagged crabs were recaptured by commercial crab fisheries, from which crab abundance was estimated. Details of procedures and estimates of abundances, however, were lacking except for 1985 (Brannian 1986), and original raw data were presumed lost. Hence, abundance of ≥ 74mm CL crab was estimated from published legal crab abundance and the proportion of length crab (See Appendix C). At the 2013 CPT meeting, it was discussed that all observed data should be reproducible from original data. Because the raw data do not exist, summer pot survey data were dropped from assessment model.

3. Survey catch-at-length data available include: Summer commercial catch (1977-2011) (Table

4), triennial Trawl survey (Table 5) and winter pot survey (Table 6). Other miscellaneous data include: summer commercial catch observer survey (1987-90, 92, 94) (Table 7), summer pot survey (1980-82, 85: Dropped) (Table 8), and summer preseason survey (1995) (Not included for the assessment model).


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4. Other miscellaneous data: None.

5. Growth-per-molt (Table 9), estimated from tagging data (1991-2007).

6. Proportion of legal size crab, estimated from trawl survey data (Table 10).

E. Analytic Approach

1. History of the modeling approach.

The Norton Sound red king crab stock was assessed using a length-based synthesis model (Zheng et al. 1998). The model was updated in 2009-2010 to provide information for the federal OFL. At the May 2010 CPT meeting, seven alternative models were presented: 1) based on 2009 model reviewed by Punt (University of Washington), 2) model 1 and including bycatch mortality, 3) model 2 with weight of fishing effort increased from 5 to 20; 4) model 3 with fishery selectivity for the last length group from 0.6 to being estimated from the model, 5) model 3 and reduce the maximum effective sample size for commercial catch and winter surveys from 200 to 100, 6) model 5 with M for the last length group increased from the default 0.18 to 0.288, and 7) model 6 with M increased to 0.34. The CPT and subsequent SSC recommended using the Model 6 for the 2010/11 iteration. During 2011 NPFMC meeting in June, SSC was concerned high hindcast prediction error and bias (i.e., model predicted crab abundance for assessment year tend to be higher than “actual/model reconstructed” abundance, which resulted in higher exploitation rate, than anticipated at the time of an assessment. The SSC, directed assessment authors to revise the model and reduce hindcast prediction error.

2. Model Description

a. Description of overall modeling approach:

The model is a male-only size structured model that combines multiple sources of survey, catch, and mark-recovery data using a maximum likelihood approach to estimate abundance, recruitment, catchability of the commercial pot gear, and parameters for selectivity and molting probabilities (See Appendix A for full model description).

b-f. See Appendix A. g. Critical assumptions of the model:

i. Male crab mature at CL length 94mm.

Bases for this assumption have not been located. No formal study has been conducted to test this assumption.


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ii. Instantaneous natural mortality M is 0.18 for all length classes, except for the last length group (> 123mm) where M =0.648 (0.18 × 3.6) (Zheng et al. 1998). M is constant over time.

This mortality is based on Bristol Bay red king crab, estimated with a maximum age 25 and the 1% rule (Zheng 2005), and was adopted for NSRKC by CPT. The assumption of the higher M for the last length group is based not on biological data, but rather a working hypothesis attempting to explain the lower than model predicted proportion of this group in summer commercial fisheries (Figures 10, 13). It is possible, that the last length group moved into areas inaccessible to commercial fisheries (CPT review 2010). However, this does not explain the low proportion observed in the summer trawl survey, when all of the Norton Sound Area was surveyed. In addition, lowering the catch selectivity did not result in lower log likelihood than increasing the mortality (CPT 2010).

2013 Model Alternatives:

M=0.24 for all length classes

M=0.30 for all length classes

The above alternative M were derived from likelihood profile analyses (Appendix D1)

iii. Trawl survey selectivity is a logistic function with 1.0 for length classes 5-6.

This assumption was not based on biological/mechanistic data and reasoning, but rather an attempt to improve model fit.

iv. Winter pot survey selectivity is a dome shaped function: 1.0 for length classes, a logistic function for length classes 1-4, 1.0 for length class 5, and model estimate for the last length group.

This assumption is based on a belief (but no empirical data) that very large crab less representative in near shore area where the winter surveys occur. This assumption improves the model fit and reduces the bias in the bubble plot.

v. Summer commercial fisheries selectivity is an asymptotic logistic function of 1.0 at the length class 5 and 6. It has two curves: before 1993, and 1993-present, reflecting changes in fishing vessel composition and pot configuration.

vi. Winter commercial and subsistence fishery selectivity and length-shell conditions are the same as those of the winter pot survey.

Winter commercial king crab pots can be any dimension (5AAC 34.925(d)). No data exists about crab pot configuration of commercial or subsistence crab fishery gears. However, because commercial fishers are also subsistence fishers, it is reasonable to assume that the commercial fishers used crab pots that they also used for subsistence harvest, and hence both fisheries have the same selectivity.

vii. Growth increments are is a function of length and are constant over time.

viii. Molting probabilities are an inverse logistic function of length for males.

ix. A summer fishing season for the directed fishery is short.

x. Discards handling mortality is assumed to be 20%. No empirical estimate is available.


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xi. Annual retained catch is measured without error.

xii. All legal size crabs (≥ 4-3/4 inch CW) are taken to the commercial dock.

xiii. Since 2005, all commercially acceptable size crabs ( ≥ 5 inch CW) are taken to

the commercial dock.

xiv. All sublegal size crab or commercially unacceptable size crab (< 5 inch CW, since 2005) are discarded.

xv. Length compositions have a multinomial error structure, and abundance has a log-normal error structure.

h. Changes of assumptions since last assessment:

Following model modifications were made since 2012:

1. Standardized commercial catch cpue and standard error (Bishop 2013) was incorporated into the model. Consequently, likelihood for effort was replaced with likelihood for standardized cpue.

2. Based on 2013 CPT modeling workshop. 1980-1985 summer pot survey was eliminated from the model.

i. Code validation. Model code is reviewed at CPT modeling workshop in 2013, and is available from the authors.

3. Model Selection and Evaluation

a. Description of alternative model configurations. See Appendix D for the rationale of selecting candidate alternative models and results

Three alternative model configurations were evaluated:

0. Baseline 2013 model: standardized CPUE data 1. S3-1: 1) No Summer pot survey (abundance, length comp) data, 2) estimate

survey q for 1976-1991 NMFS survey, 3) maximum sample size = 20. 2. S3-6: 1) No Summer pot survey (abundance, length comp) data, 2) estimate

survey q for 1976-1991 NMFS survey, 3) maximum sample size = 20, 4) M = 0.24 for all length classes

3. S3-7: 1) No Summer pot survey (abundance, length comp) data, 2) estimate survey q for 1976-1991 NMFS survey, 3) maximum sample size = 20, 4) M = 0.30 for all length classes


16

b. Evaluation of alternative models results

Log-likelihood

LL TR SP CPUE TRL SPL WPL SCL RE OBL Base 77.87 11.41 0.99 -16.29 3.94 5.38 27.35 32.31 0.29 12.38 S3-1 20.78 5.95 -19.29 1.01 12.93 14.66 0.32 5.38 S3-6 21.45 6.09 -18.78 0.83 11.54 16.21 0.39 5.17 S3-7 19.00 5.71 -19.13 0.20 11.70 15.15 0.33 5.05

Mean bias

Mean error

Prospective Legal abundance

Base 0.150 0.146 1612.59 (43.2) S3-1 0.061 0.040 1618.64 (39.7) S3-6 0.026 0.013 1575.77 (38.8) S3-7 -0.022 -0.043 1482.58 (21.8)

c. Selection of best models:

Comparing alternative model scenarios, following trends were observed (See Appendix D1 D2 for details).

1) All alternative model scenarios (except for S1-4) decreased retrospective hindcast

error and bias. 2) Constant M = 0.24 and 0.3 increased fit to 1976-1979 trawl abundance, but resulted

in lower projected legal abundance. 3) Change of survey Q indicates that historical NMFS abundance is underestimated, or

that current ADF&G abundance is overestimated. 4) Lowering of effective sample size resulted in better fit of trawl abundance and CPUE. 5) Removing CPUE data generated in mixed results on model fit. 6) Regardless alternative model scenarios (except for S1-4), results of prospective

analyses were similar, or that uncertainties of historical abundance (1976-1991) do not seem affect model performance of recent (1996-2012) abundance trajectory.

d. Parameter estimates:

See Table 11

e. Model selection criteria.


17

Results of alternative models were evaluated using following criteria: 1) lower total negative log-likelihoods, and 2) consistent prospective abundance results, and 3) low mean retrospective prediction bias and error.

Prospective analyses consist of systematically removing first n year’s data consecutively (e.g., 1976, 1976-1977, 1976-1978, …), fitting a model to the reduced data sets, and examine predicted model abundance (e.g., 2013 model predicted legal abundance). If the model is greatly influenced by a set of initial data, the predicted abundance would change greatly. On the other hand, retrospective analyses consist of systematically removing last n year’s data consecutively (e.g., 2012, 2012-2011, 2012-2010, …), fitting a model to the reduced data sets, and examine predicted model abundance (hindcast predicted abundance) (e.g., 2012, 2011, 2010, …) with that of complete data set (reconstructed abundance).

From hindcast predicted and reconstructed legal crab abundance, hindcast error for each year was calculated as

Ei = (ypi - yi)/ypi, mean hindcast error (ΣEi)/n

Mean hindcast bias (1-β) was calculated by regressing reconstructed legal crab abundance with hindcast predicted abundance as

yi = β ypi.

In these two measures, a better model should have lower mean hindcast error and mean bias (close to 0). Positive values indicate that predicted abundance tends to be higher than hindcast abundance.

f. Residual analysis. See Figures S3-1, S3-6, S3-7

g. Model evaluation: See Appendix D2

4. Results

1. Effective sample sizes and weighting factors.

Effective sample sizes were calculated as

2,,,, )ˆ()ˆ1(ˆly

llyly

lly PPPPn

Where lyP , and lyP ,ˆ are observed and estimated length compositions in year y and length

group l, respectively. Estimated effective sample sizes vary greatly overtime.

Following weights were used


18

Data Weighting Factor

Recruitment 0.01

Maximum sample size for length proportion:

Survey data Sample size

Summer commercial, winter pot, and summer observer

minimum of 0.1× actual sample size or 10

Summer trawl and pot survey minimum of 0.5× actual sample size or 20

2. Tables of estimates.

Model Parameter estimates (Table 11).

a. Most of parameters were estimated with CV of around 30%. Notable exception was recruitment parameter for 1978 and 1979 (log_R78, log_R79), trawl selectivity parameter (log_ϕst and log_ωst), and winter pot survey selectivity (log_ωsw). For 1978 and 1979, estimates were close to zero reflecting extremely low proportion of < 94mm crab observed in 1979 trawl survey (Table 5, Figure 3,4). The high CVs for those selectivity parameters are an artifact because the estimated selectivity was 1.0 for those cases. In asymptotic logistic function, multitudes of parameter combinations can result in 1.0, so that model was not able to converge into single parameter. The parameter p4 hit the bound of 1.0. This shows that commercial buyer’s preference of purchasing only ≥ 5 inch CW legal crab (as opposed to 4 ¾ inch CW legal crab), did not seem to change fishing behavior (i.e., discarding <5 inch CW legal crabs).

b. Abundance and biomass time series are provided in Table 12 and Figure 4.

c. Recruitment time series are in Table 12 and Figure 4.

d. Time series of catch/biomass are in Table 13

e. Selectivities, molting probabilities, and proportions of legal crabs by length are provided in Table 10.

3. Graphs of estimates.

a. Estimated male abundances (recruits, legal, and total) are plotted in Figures 4.

b. Time series of catch and harvest rates are plotted in Figure 5.

c. Harvest rate are plotted against mature male biomass in Figure 6.

d. Estimated and observed catch effort was plotted in Figure 7.

e. Molting probability and catch selectivity in Figure 8


19

4. Evaluation of the fit to the data

a. Fits to observed and model predicted catches. Not applicable. Catch is assumed to be measured without error

b. Model fits to survey numbers (Figure 4a).

The majority of model estimated abundances of total crabs were within the 95% confidence interval of the survey observed abundance, except for 1976 and 1979, where model estimates was higher than the observed abundance.

c. Model fits to catch and survey proportions by length (Figures S3-1-3 through S3-6-6, S3-6-3 through S3-1-6, S3-7-3 through S3-7-6).

A residual plot for the commercial catch showed that the model tended to overestimate catches of largest length class and thus underestimate crab sizes of (4 and 5). Residuals of winter pot survey showed the model tended to overestimate (negative residuals) the proportion of large length classes (>103 mm). However, during 1991-1995, the pattern was reversed.

Plots of summer trawl, pot, and observer data did not seem show noticeable patterns. Similar to the winter pot survey, the model tended to overestimate proportion of large length classes. This tendency was most prominent during the last 3 trawl surveys.

d. Marginal distribution for the fits to the composition data: (Figure 8 ). e. Plots of implied versus input effective sample sizes and time-series of implied effective

sample size (Figures S3-1-2, S3-6-2, S3-7-2). f. Tables of RMSEs for the indices:

RMSE was calculated as

21 ))ln()(ln( predobsRMSE n

Indices S3-1 S3-6 S3-7 Trawl survey 0.262 0.264 0.259 CPUE 0.490 0.506 0.501

h. QQ plots and histograms of residuals: Figure S3-1-1, S3-6-1, S3-7-1,


20

5. Retrospective and prospective analyses.

See Figure 10 and 11

6. Uncertainty and sensitivity analyses.

F. Calculation of the OFL

1. Specification of the Tier level and stock status.

The Norton Sound red king crab stock is currently placed in Tier 4 (NPFMC 2007). It is not possible to estimate the spawner-recruit relationship, but some abundance and harvest estimates are available to build a computer simulation model that capture the essential population dynamics. Whereas tier 4 stocks are assumed to have reliable estimates of current survey biomass and instantaneous M, the estimates for the Norton Sound red king crab stock uncertain. Survey biomass is based on triennial trawl surveys with CVs ranging 15-42% (Table 4). The natural mortality of 18% adopted by the CPT (2010) is based on Bristol Bay red king crab with the maximum age 25 and the 1% rule (Zheng 2005); however, no data are available to support the assumption of a maximum age 25 for the Norton Sound red king crab.

The OFL is estimated by the FMSY proxy, BMSY proxy, and estimated legal male abundance and biomass:

,1/, proxMSYOFL BBwhenMF (1)

,1/25.0 ,9.0/)1.0/( proxprox MSYMSYOFL BBwhenBBMF (2)

,25.0/,0& proxMSYOFL BBwhenFfisherydirectedmortalitybycatchF (3)

where B is a mature male biomass (MMB), BMSY proxy is average mature male biomass over a specified time period. M = 0.18 and = 1.

For Norton Sound red king crab, MMB is defined as CL > 94 mm.

OFL was calculated for retained catch and total male catch. The retained OFL is based on legal crab biomass catchable to summer commercial pot fisheries (Legal_B):

lllsl,sl,sl

wmLSON=BLegal ,,, )(_

BLegalFOFL OFLretained _))exp(1(


21

The total male OFL is

hmwmLSONFOFLOFL lllsl,sl,s

lOFLretainedtotalmales )1()())exp(1( ,,,

where Ns,l and Os,l are summer abundances of newshell and oldshell crabs in length class l in the terminal year, Ll is the proportion of legal males in length class l, Ss,l is summer commercial catch selectivity, wml is average weight in length class l and hm is handling mortality rate

For the selection of the BMSY proxy, default data used are survey MMB. However, for the Norton Sound red king crab stock, only available survey MMB data are triennial trawl surveys, 11 years of data during 37 years period. Instead, we used the model estimated MMB for calculation of BMSY proxy from 1980 to present.

Predicted legal male and mature male biomass in 2013 are:

Legal male biomass: Model S3-1: 3.55 million lb with a standard deviation of 0.48 million lb. Model S3-6: 3.31 million lb with a standard deviation of 0.50 million lb. Model S3-7: 3.12 million lb with a standard deviation of 0.49 million lb.

Mature male biomass: Model S3-1: 5.00 million lb with a standard deviation of 0.98 million lb. Model S3-6: 5.03 million lb with a standard deviation of 0.96 million lb. Model S3-7: 4.77 million lb with a standard deviation of 1.00 million lb.

Candidate OFL and ABC million lb. Parenthesis indicates standard deviation

Model B2013 BMSY Legal male

biomass M FOFL OFL

ABC (0.9×OFL)

S3-1 5.00 (0.98) 4.12 3.55 (0.48) 0.18 0.18 0.577 (0.08) 0.519

S3-6 5.03 (0.96) 3.73 3.31 (0.50) 0.24 0.24 0.708 (0.11) 0.637

S3-7 4.77 (1.00) 3.95 3.12 (0.49) 0.30 0.30 0.808 (0.13) 0.727

In all three models, estimated mature male biomass of 2013 was higher than estimated BMSY proxy. Hence, FOFL was the same as M.

Retained OFL for legal male crab is Model S3-1: 0.58 million lb. Model S3-6: 0.71 million lb. Model S3-7: 0.81 million lb.


22

Difference in OFL derived from difference in M.

G. Calculation of the ABC

1. Specification of the probability distribution of the OFL.

Probability distribution of the OFL was determined based on the CPT recommendation in January 2012 as follows: Tier 4 crab stocks Calculation of a distribution for the OFL for Tier 4 stocks involves repeating four steps (detailed below). The aim is to have the median of the distribution for the OFL equal the point estimate (so that P*=0.5 implies that the ABC equals to the point estimate of the OFL). The proposed steps are: (a) Sample current MMB from a normal distribution with mean given by the point estimate of current MMB and CV equal to the sampling CV. (b)The BMSY proxy is the average MMB over a pre-specified set of years. Uncertainty in the BMSY proxy only accounts for uncertainty in MMB for the years for which it is assumed the stock was “at BMSY” and not uncertainty in the years concerned. For each of the years used when defining the BMSY proxy, sample MMB from a distribution with mean given by its point estimate and CV equal to the sampling CV. The pseudo BMSY proxy is then the average of the samples values. (c)Sample M from a normal distribution with mean equal to the assumed M and CV equal to an assumed CV (e.g. 0.2). (d)Compute the OFL. Form a cumulative distribution for the OFL from the sampled values. Find the median of this distribution. Using normal quantiles to rescale the distribution so that the median equals the OFL (similar to a bias-corrected bootstrap).

For the Norton Sound red king crab, calculation of OFL was based on summer commercial retained legal male biomass. For calculation of the ABC, default percentile is P* = 49; however, for the Norton Sound Stock the NPFMC adopted 10% buffer of OFL (i.e., ABC = 0.9×OFL) in 2012.

Retained ABC for legal male crab is Model S3-1: 0.52 million lb. Model S3-6: 0.64 million lb. Model S3-7: 0.73 million lb.

H. Rebuilding Analyses

Not applicable

I. Data Gaps and Research Priorities The model suggests that historical NMFS survey underestimated historical crab abundances. In


23

this assessment, NMFS abundances were estimated from published reports in ad hoc manner; however, it is more appropriate re-estimating the survey abundance original survey data. The major data gaps of the Norton Sound red king crab are: spatially and temporarily consistent estimate of abundance, length frequency of discards from fisheries, and estimates of the instantaneous natural mortality. In addition, life-history of the Norton Sound red king crab stock is poorly understood. This includes size at maturity, natural mortality rate, timing and locations of reproduction, location of females during summer.

Acknowledgments

We thank all CPT modeling workshop attendants for critical review of the assessment model and suggestions for improvements and diagnoses.

References

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evaluation of exploratory fishing methods and analytical approaches to stock size and yield forecasts. J. Fish. Res. Board Can. 26:1985-2001.

Bishop, G., M.S.M. Siddeek, J. Zheng, and T. Hamazaki. 2013. Summary Report: Norton Sound red king crab CPUE standardization. Unpublished manuscript. Alaska Depart of Fish and Game, Division of Commercial Fisheries, Juneau.

Brannian, L. K. 1987. Population assessment survey for red king crab (Paralithodes camtschatica) in Norton Sound, Alaska, 1985. Alaska Department of Fish and Game, Technical Data Report No. 214, Juneau.

Fournier, D., and C.P. Archibald. 1982. A general theory for analyzing catch at age data. Can. J. Fish. Aquat. Sci. 39:1195-1207.

Fournier, D.A., H.J. Skaug, J. Ancheta, J. Ianelli, A. Magnusson, M.N. Maunder, A. Nielsen, and J. Sibert. 2012. AD Model Builder: using automatic differentiation for statistical inference of highly parameterized complex nonlinear models. Optimization Methods and Software 27:233-249.

Menard, J., J. Soong, and S. Kent 2011. 2009 Annual Management Report Norton Sound, Port Clarence, and Kotzebue. Fishery Management Report No. 11-46.

Methot, R.D. 1989. Synthetic estimates of historical abundance and mortality for northern anchovy. Amer. Fish. Soc. Sym. 6:66-82.

NPFMC/NMFS 2010. Environmental assessment for proposed amendments 38 and 39 to the fishery management plan for the Bering Sea and Aleutian Islands king and tanner crabs to


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comply with the annual catch limit requirements (Amendment 38) and to revise the rebuilding plan for the EBS snow crab (Amendment 39). NPFMC AGENDA C-3, October 2010.

http://www.fakr.noaa.gov/npfmc/PDFdocuments/conservation_issues/ACL/CrabACL910.pdf

Powell, G.C., R. Peterson, and L. Schwarz. 1983. The red king crab, Paralithodes camtschatica (Tilesius), in Norton Sound, Alaska: History of biological research and resource utilization through 1982. Alaska Dept. Fish and Game, Inf. Leafl. 222. 103 pp.

Schwarz, L. 1984. Norton Sound section of the Bering Sea 1983 king crab fishery report to the Board of Fisheries. Alaska Department of Fish and Game, Division of Commercial Fisheries, Region III: Shellfish Report No. 5, Anchorage.

Stevens, B.G., and R. A. MacIntosh. 1986. Analysis of crab data from the 1985 NMFS survey of the northeast Bering Sea and Norton Sound. National Marine Fisheries Service, Northwest and Alaska Fisheries Center, NWAFC Processed Report 86-16. September 1986.

Stevens, B.G. 1989. Analysis of crab data from the 1988 NMFS survey of Norton Sound and the northeast Bering Sea. National Marine Fisheries Service, Northwest and Alaska Fisheries Center, unpublished report. February 1989.

Stevens, B.G. 1992. Results of the 1991 NMFS survey of red king crab in Norton Sound. National Marine Fisheries Service, Alaska Fisheries Science Center, unpublished memorandum to the State of Alaska. May 1992.

Soong, J. 2007. Norton Sound winter red king crab studies, 2007. Alaska Department of Fish and Game, Fishery Data Series No. 07-53, Anchorage.

Soong, J. 2008. Analysis of red king crab data from the 2008 Alaska Department of Fish and Game trawl survey of Norton Sound. Alaska Department of Fish and Game, Fishery Data Series No. 08-58, Anchorage.

Wolotira, R.J., Jr., T.M. Sample, and M. Morin, Jr. 1977. Demersal fish and shellfish resources of Norton Sound, the southeastern Chukchi Sea, and adjacent waters in the baseline year 1976. National Marine Fisheries Service, Northwest and Alaska Fisheries Center, Processed Report. October 1977.

Zheng, J. 2005. A review of natural mortality estimation for crab stocks: data-limited for every stock? Pages 595-612 in G.H. Kruse, V.F. Gallucci, D.E. Hay, R.I. Perry, R.M. Peterman, T.C. Shirley, P.D. Spencer, B. Wilson, and D. Woodby (eds.). Fisheries Assessment and Management in Data-limite Situation. Alaska Sea Grant College Program, AK-SG-05-02, Fairbanks.

Zheng, J., G.H. Kruse, and L. Fair. 1998. Use of multiple data sets to assess red king crab, Paralithodes camtschaticus, in Norton Sound, Alaska: A length-based stock synthesis approach. Pages 591-612 In Fishery Stock Assessment Models, edited by F. Funk, T.J.


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Quinn II, J. Heifetz, J.N. Ianelli, J.E. Powers, J.F. Schweigert, P.J. Sullivan, and C.-I. Zhang, Alaska Sea Grant College Program Report No. AK-SG-98-01, University of Alaska Fairbanks

Table 1. Historical summer commercial red king crab fishery economic performance, Norton Sound Section, eastern Bering Sea, 1977-2012.

Guideline Commercial Harvest Harvest (lb) a,

b

Level Open Total Number (incl. Total Pots Season Length Year (lbs) b Access CDQ Harvest Vessels Permits Landings Registered Pulls CPUE SD Days Dates

1977 c 0.52 195,877 7 7 13 5,457 NA NA 60 c 1978 3.00 2.09 660,829 8 8 54 10,817 16.78 2.94 60 6/07-8/151979 3.00 2.93 970,962 34 34 76 34,773 9.2 1.61 16 7/15-7/311980 1.00 1.19 329,778 9 9 50 11,199 11.8 2.07 16 7/15-7/311981 2.50 1.38 376,313 36 36 108 33,745 3.7 0.66 38 7/15-8/221982 0.50 0.23 63,949 11 11 33 11,230 1.4 0.25 23 8/09-9/011983 0.30 0.37 132,205 23 23 26 3,583 11,195 3.5 0.62 3.8 8/01-8/051984 0.40 0.39 139,759 8 8 21 1,245 9,706 6.6 1.16 13.6 8/01-8/151985 0.45 0.43 146,669 6 6 72 1,116 13,209 3.5 0.61 21.7 8/01-8/231986 0.42 0.48 162,438 3 3 578 4,284 10.5 1.84 13 8/01-8/251987 0.40 0.33 103,338 9 9 1,430 10,258 2.9 0.50 11 8/01-8/121988 0.20 0.24 76,148 2 2 360 2,350 NA NA 9.9 8/01-8/111989 0.20 0.25 79,116 10 10 2,555 5,149 6.0 1.05 3 8/01-8/041990 0.20 0.19 59,132 4 4 1,388 3,172 6.8 1.19 4 8/01-8/05

1991 0.34 0 No Summer Fishery 1992 0.34 0.07 24,902 27 27 2,635 5,746 2.0 0.35 2 8/01-8/031993 0.34 0.33 115,913 14 20 208 560 7,063 5.6 0.98 52 7/01-8/281994 0.34 0.32 108,824 34 52 407 1,360 11,729 4.9 0.86 31 7/01-7/311995 0.34 0.32 105,967 48 81 665 1,900 18,782 2.7 0.47 67 7/01-9/051996 0.34 0.22 74,752 41 50 264 1,640 10,453 3.3 0.58 57 7/01-9/031997 0.08 0.09 32,606 13 15 100 520 2,982 4.7 0.83 44 7/01-8/131998 0.08 0.03 0.00 10,661 8 11 50 360 1,639 3.9 0.68 65 7/01-9/031999 0.08 0.02 0.00 8,734 10 9 53 360 1,630 3.7 0.64 66 7/01-9/042000 0.33 0.29 0.01 111,728 15 22 201 560 6,345 8.0 1.40 91 7/01- 9/292001 0.30 0.28 0.00 98,321 30 37 319 1,200 11,918 4.3 0.75 97 7/01- 9/092002 0.24 0.24 0.01 86,666 32 49 201 1,120 6,491 8.6 1.50 77 6/15-9/032003 0.25 0.25 0.01 93,638 25 43 236 960 8,494 6.3 1.10 68 6/15-8/242004 0.35 0.31 0.03 120,289 26 39 227 1,120 8,066 9.1 1.60 51 6/15-8/082005 0.37 0.37 0.03 138,926 31 42 255 1,320 8,867 8.4 1.47 73 6/15-8/272006 0.45 0.42 0.03 150,358 28 40 249 1,120 8,867 8.8 1.55 68 6/15-8/222007 0.32 0.29 0.02 110,344 38 30 251 1,200 9,118 7.3 1.28 52 6/15-8/172008 0.41 0.36 0.03 143,337 23 30 248 920 8,721 8.9 1.56 73 6/23-9/032009 0.38 0.37 0.03 143,485 22 27 359 920 11,934 5.3 0.93 98 6/15-9/202010 0.40 0.39 0.03 149,822 23 32 286 1,040 9,698 7.6 1.33 58 6/28-8/242011 0.36 0.37 0.03 141,626 24 25 173 1,040 6,808 10.8 1.89 33 6/28-7/302012 0.47 0.44 0.03 161,113 29 29 289 1,200 10,041 8.4 1.47 72 6/29-9/08

a Deadloss included in total. b Millions of pounds. c Information not available.

Table 2. Historical winter commercial and subsistence red king crab fishery economic performance, Norton Sound Section, eastern Bering Sea, 1977-2011.

Commercial Subsistence

Yeara # of

Fishers

# of Crab Harvested

Winterb

Permits Total Crab Average Permit Fished Issued Returned Fished Caughtc Retainedd

1978 37 9,625 1977/78 290 206 149 e 12,506 84 1979 1f 221f 1978/79 48 43 38 e 224 6 1980 1f 22f 1979/80 22 14 9 e 213 24 1981 0 0 1980/81 51 39 23 e 360 16 1982 1f 17f 1981/82 101 76 54 e 1,288 24 1983 5 549 1982/83 172 106 85 e 10,432 123 1984 8 856 1983/84 222 183 143 15,923 11,220 78 1985 9 1,168 1984/85 203 166 132 10,757 8,377 63

1985/86 5 2,168 1985/86 136 133 107 10,751 7,052 66 1986/87 7 1,040 1986/87 138 134 98 7,406 5,772 59 1987/88 10 425 1987/88 71 58 40 3,573 2,724 68 1988/89 5 403 1988/89 139 115 94 7,945 6,126 65 1989/90 13 3,626 1989/90 136 118 107 16,635 12,152 114 1990/91 11 3,800 1990/91 119 104 79 9,295 7,366 93 1991/92 13 7,478 1991/92 158 105 105 15,051 11,736 112 1992/93 8 1,788 1992/93 88 79 37 1,193 1,097 30 1993/94 25 5,753 1993/94 118 95 71 4,894 4,113 58 1994/95 42 7,538 1994/95 166 131 97 7,777 5,426 56 1995/96 9 1,778 1995/96 84 44 35 2,936 1,679 48 1996/97 2f 83f 1996/97 38 22 13 1,617 745 57 1997/98 5 984 1997/98 94 73 64 20,327 8,622 135 1998/99 5 2,714 1998/99 95 80 71 10,651 7,533 106

1999/2000 10 3,045 1999/2000 98 64 52 9,816 5,723 107 2000/01 3 1,098 2000/01 50 27 12 366 256 21 2001/02 11 2,591 2001/02 114 61 45 5,119 2,177 48 2002/03 13 6,853 2002/03 107 70 61 9,052 4,140 68

2003/04g 2 522 2003/04g 96 77 41 1,775 1,181 29 2004/05 4 2,091 2004/05 170 98 58 6,484 3,973 112 2005/06 1f 75f 2005/06 98 97 67 2,083 1,239 18 2006/07 8 3,313 2006/07 129 127 116 21,444 10,690 92 2007/08 9 5,796 2007/08 139 137 108 18,621 9,485 88 2008/09 7 4,951 2008/09 105 105 70 6,971 4,752 68 2009/10 10 4,834 2009/10 125 123 85 9,004 7,044 83 2010/11 5 3,365 2010/11 148 148 95 9,183 6,640 70 2011/12 35 9,157 2011/12 204 204 138 11,341 7,311 53 2012/13

a Prior to 1985 the winter commercial fishery occurred from January 1 - April 30. As of March 1985, fishing may occur from November 15 - May 15. b The winter subsistence fishery occurs during months of two calendar years (as early as December, through May). c The number of crab actually caught; some may have been returned. d The number of crab Retained is the number of crab caught and kept. e Information not available. f Confidential under AS 16.05.815. g Confidentiality was waived by the fishers. h Prior to 2005, permits were only given out of the Nome ADF&G office. Starting with the 2004-5 season, permits were given out in Elim, Golovin, Shaktoolik, and White Mountain.

Table 3. Summary of triennial trawl survey Norton Sound male red king crab abundance estimates. Trawl survey abundance estimate is based on 10×10 nmil2 grid, except for 2010 (20×20 nmil2). See Appendix for details

Survey coverage Abundance ≥74 mm

Year Dates Survey Agency

Survey method

surveyed stations

Stations w/

NSRKC

n mile2

covered CV

1976 9/02 - 9/05 NMFS Trawl 103 62 10260 4219.6 0.355 1979 7/26 - 8/05 NMFS Trawl 85 22 8421 901.0 0.270 1980 7/04 - 7/14 ADFG Pots 2092.3 N/A 1981 6/28 - 7/14 ADFG Pots 2153.4 N/A 1982 7/06 - 7/20 ADFG Pots 1140.5 N/A 1982 9/05 - 9/11 NMFS Trawl 58 37 5721 2325.0 0.294 1985 7/01 - 7/14 ADFG Pots 2320.4 0.083 1985 9/16 -10/01 NMFS Trawl 78 49 7688 2905.8 0.308 1988 8/16 - 8/30 NMFS Trawl 78 41 7721 2311.5 0.327 1991 8/22 - 8/30 NMFS Trawl 52 38 5183 2211.4 0.402 1996 8/07 - 8/18 ADFG Trawl 50 30 4938 1264.7 0.317 1999 7/28 - 8/07 ADFG Trawl 53 31 5221 2276.1 0.194 2002 7/27 - 8/06 ADFG Trawl 57 37 5621 1747.6 0.125 2006 7/25 - 8/08 ADFG Trawl 101 45 10008 2549.7 0.288 2008 7/24 - 8/11 ADFG Trawl 74 44 7330 2707.1 0.164 2010a 7/27 - 8/09 NMFS Trawl 35 15 13749 2041.0 0.455 2011 7/18 - 8/15 ADFG Trawl 65 34 6447 2701.7 0.133

Table 4. Summer commercial catch size/shell composition. Sizes in this and Tables 5-10 and 12 are mm carapace length. Legal size (4.75 inch carapace width is approximately equal to 124 mm carapace length.

New Shell Old Shell Year Sample 74-83 84-93 94-103 104-113 114-123 124+ 74-83 84-93 94-103 104-113 114-123 124+ 1977 1549 0 0 0.0032 0.4196 0.3422 0.1220 0 0 0 0.0626 0.040 0.01031978 389 0 0 0.0103 0.1851 0.473 0.3059 0 0 0 0.0051 0.0103 0.01031979 1660 0 0 0.0253 0.2325 0.3831 0.3217 0 0 0 0.0253 0.0006 0.01141980 1068 0 0 0.0037 0.0983 0.3062 0.5543 0 0 0 0.0028 0.0112 0.02341981 1748 0 0 0.0039 0.0734 0.1541 0.5090 0 0 0 0.0045 0.0504 0.20461982 1093 0 0 0.0421 0.1921 0.1647 0.5050 0 0 0.0037 0.0128 0.022 0.05761983 802 0 0 0.0387 0.4127 0.3579 0.0973 0 0 0.0037 0.0362 0.010 0.04361984 963 0 0 0.0966 0.4195 0.2804 0.0717 0 0 0.0104 0.0654 0.0488 0.00731985 2691 0 0.0004 0.0643 0.3122 0.3716 0.1747 0 0 0.0026 0.0334 0.0312 0.00971986 1138 0 0 0.029 0.3559 0.3937 0.1353 0 0 0.0018 0.0202 0.0378 0.02641987 1542 0 0 0.0166 0.1788 0.2912 0.3798 0 0 0.0025 0.0267 0.0650 0.03931988 1522 0.0007 0 0.0237 0.2004 0.3003 0.2181 0 0 0.0059 0.0644 0.0972 0.08941989 2595 0 0 0.0127 0.1643 0.3185 0.2148 0 0 0.0042 0.0555 0.1215 0.10841990 1289 0 0 0.0147 0.1435 0.3468 0.3251 0 0 0.0008 0.0372 0.0737 0.05821991 1992 2566 0 0 0.0172 0.201 0.2662 0.2244 0 0 0.0027 0.0792 0.1292 0.0801993 1813 0 0 0.0142 0.2312 0.3939 0.263 0 0 0.0004 0.0173 0.0437 0.03621994 404 0 0 0.0248 0.0941 0.0817 0.0891 0 0 0.0248 0.1881 0.25 0.24751995 1174 0 0 0.0392 0.2615 0.2853 0.207 0 0 0.0077 0.0486 0.0741 0.07671996 787 0 0 0.0318 0.2236 0.2389 0.141 0 0 0.014 0.1194 0.136 0.09531997 1198 0 0 0.0292 0.3656 0.3414 0.1244 0 0 0.0033 0.0559 0.0417 0.03841998 1055 0 0 0.0284 0.2332 0.2427 0.1071 0 0 0.0218 0.1118 0.1431 0.11181999 561 0 0 0.0026 0.2434 0.2698 0.3836 0 0 0 0 0.0423 0.05822000 17213 0 0 0.0194 0.2991 0.3917 0.1249 0 0 0.0028 0.0531 0.0654 0.04362001 20030 0 0 0.0243 0.2232 0.3691 0.2781 0 0 0.0008 0.0241 0.0497 0.03042002 5198 0 0 0.0442 0.2341 0.2814 0.3253 0 0 0.0046 0.0282 0.0419 0.04022003 5220 0 0 0.0232 0.3680 0.3197 0.1523 0 0 0.0011 0.0218 0.0465 0.06742004 9605 0 0 0.0087 0.3811 0.3880 0.1395 0 0 0.0004 0.0255 0.0347 0.02212005 5360 0 0 0.0022 0.2539 0.4709 0.1823 0 0 0 0.0205 0.0451 0.0252006 6707 0 0 0.0021 0.1822 0.3484 0.199 0 0 0.0003 0.0498 0.1375 0.08072007 6125 0 0 0.0111 0.3574 0.3407 0.1714 0 0 0.0008 0.0247 0.0573 0.03662008 5766 0 0 0.0047 0.3512 0.3476 0.0668 0 0 0.0014 0.0895 0.0928 0.04612009 6026 0 0 0.0105 0.3445 0.3294 0.1339 0 0 0.0012 0.0768 0.0795 0.02422010 5902 0 0 0.0053 0.3855 0.3617 0.1095 0 0 0.0019 0.0546 0.0546 0.02712011 2552 0 0 0.0043 0.3170 0.3969 0.1387 0 0 0.0020 0.0611 0.0588 0.02122012 5056 0 0 0.0026 0.2421 0.4620 0.2067 0 0 0.0002 0.0259 0.0423 0.0182

Table 5. Summer Trawl Survey size/shell composition

New Shell Old Shell Year Sample 74-83 84-93 94-103 104-113 114-123 124+ 74-83 84-93 94-103 104-113 114-123 124+ 1976 1311 0.0214 0.1053 0.1915 0.3455 0.1831 0.0290 0.0046 0.0114 0.0252 0.032 0.0366 0.0145 1979 133 0.0151 0.0075 0.0301 0.0752 0.0827 0.0602 0 0.0075 0.0301 0.1203 0.3835 0.188 1982 256 0.0898 0.2031 0.2891 0.2109 0.0352 0.0078 0 0.0156 0.0195 0.043 0.0234 0.0625 1985 311 0.1190 0.2122 0.1865 0.1768 0.0643 0.0193 0 0 0.0193 0.0514 0.0868 0.0643 1988 306 0.2255 0.1405 0.1536 0.1275 0.0686 0.0392 0 0.0065 0.0131 0.0392 0.0882 0.0980 1991 250 0.0967 0.0223 0.0372 0.0743 0.0409 0.0223 0.0706 0.0297 0.0967 0.197 0.1747 0.1375 1996 196 0.2959 0.1786 0.1224 0.0816 0.0051 0.0153 0.0051 0.0357 0.0459 0.0612 0.0612 0.0918 1999 274 0.0109 0.1058 0.2993 0.2701 0.1314 0.0401 0 0.0036 0.0292 0.0511 0.0401 0.0182 2002 230 0.1261 0.1435 0.1565 0.0304 0.0348 0.0348 0.0304 0.0739 0.1087 0.0957 0.0913 0.0739 2006 208 0.3235 0.2614 0.1405 0.0752 0.0458 0.0294 0 0 0.0196 0.0458 0.0458 0.0131 2008 242 0.1743 0.2407 0.1286 0.112 0.0332 0.029 0.0083 0.0498 0.0705 0.0954 0.0125 0.0456 2010 68 0.1202 0.1366 0.2077 0.1257 0.1093 0.0437 0.0109 0.0328 0.082 0.071 0.0383 0.0219 2011 320 0.1282 0.0989 0.1282 0.2051 0.1612 0.0476 0.0037 0.0147 0.0256 0.0989 0.0513 0.0366

Table 6. Winter pot survey size/shell composition

New Shell Old Shell

Year Sample 74-83 84-93 94-103

104-113 114-123 124+ 74-83 84-9394-103

104-113

114-123 124+

1981/82 243 0.1481 0.3374 0.3169 0.1029 0.0288 0.0247 0 0 0.0041 0.0082 0.0082 0.0206 1982/83 2520 0.0855 0.2824 0.2854 0.2155 0.0706 0.0085 0 0 0.004 0.0194 0.0097 0.0189 1983/84 1655 0.1638 0.2626 0.2291 0.1502 0.0601 0.0057 0 0 0.0178 0.065 0.0329 0.0127 1984/85 773 0.0932 0.2589 0.3618 0.1586 0.057 0.0097 0 0 0.0065 0.0291 0.0239 0.0013 1985/86 568 0.1276 0.1831 0.2553 0.2025 0.0863 0.0132 0 0 0.015 0.0607 0.044 0.0123 1986/87 144 0.0556 0.1597 0.1944 0.0694 0.0417 0 0 0 0.0417 0.2986 0.1111 0.0278 1987/88 1988/89 492 0.1341 0.1514 0.1352 0.1941 0.1758 0.0346 0 0 0.002 0.0528 0.0854 0.0346 1989/90 2072 0.0495 0.2075 0.2616 0.1795 0.1221 0.0726 0 0 0.001 0.0263 0.056 0.0239 1990/91 1281 0.0125 0.0921 0.2857 0.2678 0.096 0.0109 0 0 0.0039 0.0265 0.1163 0.0882 1992/93 181 0.0055 0.0331 0.0552 0.1271 0.116 0.0276 0 0 0.0166 0.1934 0.2707 0.1547 1993/94 1994/95 850 0.0588 0.08 0.0988 0.2576 0.2341 0.0847 0 0 0.0035 0.0329 0.0718 0.0776 1995/96 776 0.1214 0.1835 0.1733 0.1022 0.0599 0.0265 0 0 0.0181 0.1214 0.1242 0.0695 1996/97 1582 0.2297 0.2351 0.1189 0.1568 0.1216 0.0676 0 0 0 0.0189 0.027 0.0243 1997/98 399 0.1395 0.4136 0.2653 0.0544 0.0236 0.0034 0 0 0.0238 0.0317 0.017 0.0272 1998/99 882 0.0192 0.1168 0.3566 0.3605 0.0838 0.0154 0 0 0.01 0.0223 0.0069 0.0085 1999/00 1308 0.0885 0.1062 0.1646 0.3345 0.1788 0.0372 0 0 0.0018 0.0513 0.023 0.0142 2000/01 2001/02 832 0.3136 0.2763 0.1761 0.0681 0.0668 0.0501 0 0 0.0077 0.0051 0.0154 0.0064 2002/03 826 0.0994 0.2236 0.2994 0.1801 0.0559 0.0261 0 0 0.0224 0.0273 0.0261 0.0273 2003/04 286 0.0175 0.1643 0.2622 0.3462 0.1119 0.0105 0 0 0.0175 0.021 0.014 0.0245 2004/05 406 0.0741 0.1407 0.1827 0.2173 0.1852 0.0765 0 0 0.0025 0.0395 0.0593 0.0173 2005/06 512 0.1406 0.2266 0.209 0.1563 0.0547 0.0215 0 0 0.0176 0.043 0.0742 0.0352 2006/07 160 0.1486 0.2095 0.3784 0.1419 0.0473 0 0 0 0.0068 0.0203 0.0405 0 2007/08 3482 0.1898 0.3219 0.1703 0.1479 0.0672 0.0083 0 0 0.0359 0.0339 0.0155 0.0092 2008/09 526 0.0706 0.1336 0.3511 0.2023 0.084 0.0134 0 0 0.0019 0.0382 0.0992 0.0057 2009/10 581 0.047 0.1357 0.2157 0.2452 0.113 0.0191 0 0 0.0591 0.1009 0.0539 0.0104 2010/11 597 0.0786 0.1368 0.2103 0.1744 0.1333 0.0513 0 0.0120 0.0325 0.1128 0.0462 0.0120 2011/12 676 0.1155 0.2340 0.1945 0.1246 0.1292 0.0456 0.0030 0.0030 0.0912 0.0532 0.0532 0.0350 2012/13

Table 7. Summer commercial1987-1994, 2012 observer survey (Sub legal crab only)

New Shell Old Shell

Year Sample 74-83 84-93 94-103 104-113 114-123 124+ 74-83 84-93 94-103 104-113 114-123 124+ 1987 1076 0.2026 0.3625 0.3522 0.0344 0 0 0 0 0.0437 0.0046 0 0 1988 712 0.052 0.184 0.4831 0.139 0 0 0 0 0.0969 0.0449 0 0 1989 911 0.2492 0.3392 0.2371 0.0274 0 0 0 0 0.1196 0.0274 0 0 1990 459 0.2702 0.3203 0.3028 0.0414 0 0 0 0 0.0588 0.0065 0 0 1992 515 0.2175 0.3592 0.332 0.0369 0 0 0 0 0.0447 0.0097 0 0 1994 726 0.1556 0.303 0.1736 0.0262 0 0 0 0 0.2824 0.0592 0 0 2012 738 0.1396 0.2398 0.4106 0.1314 0.0122 0 0.0027 0.0027 0.0298 0.0285 0.0014 0.0014

Table 8. Summer Pot Survey size/shell composition

New Shell Old Shell

Year Sample 74-83 84-93 94-103 104-113 114-123 124+ 74-83 84-93 94-103 104-113 114-123 124+ 1980 3619 0.0288 0.0241 0.0444 0.0956 0.2286 0.4575 0 0 0.0003 0.0072 0.0506 0.0627 1981 4588 0.2095 0.1899 0.0699 0.0642 0.0845 0.2398 0 0 0.0010 0.0048 0.0339 0.1024 1982 6354 0.1678 0.2220 0.2717 0.1190 0.0411 0.1129 0 0 0.0025 0.0145 0.0157 0.0328 1985 9900 0.1471 0.2088 0.2467 0.1385 0.1356 0.0644 0 0 0.0063 0.0283 0.0202 0.0040

Table 9. Growth matrix (proportion of crabs molting from a given pre-molt carapace length range into post-molt length ranges) for Norton Sound male red king crab. Length is measured as mm CL. Results are derived from mark-recapture and winter tagging data from 1980 to 2007. Pre-molt Post-molt Length Class Length Class

Mean weight (lb)

74-83

84-93

94-103

104-113

114-123

124+

74-83 0.854 0 0.33 0.67 0 0 0 84-93 1.210 0 0 0.56 0.44 0 0

94-103 1.652 0 0 0 0.76 0.24 0 104-113 2.187 0 0 0 0.18 0.61 0.21 114-123 2.825 0 0 0 0 0.33 0.67

124+ 3.697 0 0 0 0 0 1.00

Table 10. Estimated selectivities, molting probabilities, and proportions of legal crabs by length (mm CL) class for Norton Sound male red king crab. S3-1

Selectivity

Length Class

Proportion of Legal

Summer Trawl

Winter Pot

Summer Fishery Molting Probability 77-92 93-11

74 - 83 0.00 1.00 0.61 0.15 0.02 1.00 84 - 93 0.00 1.00 1.00 0.24 0.08 0.88 94 - 103 0.26 1.00 1.00 0.40 0.28 0.77 104 - 113 0.97 1.00 1.00 0.63 0.67 0.68 114 - 123 0.99 1.00 1.00 1.00 1.00 0.59

124+ 1.00 1.00 0.37 1.00 1.00 0.51

S3-6 Selectivity

Length Class

Proportion of Legal

Summer Trawl

Winter Pot


74 - 83 0.00 0.94 0.58 0.14 0.02 1.00 84 - 93 0.00 0.95 1.00 0.23 0.07 0.86 94 - 103 0.26 0.97 1.00 0.38 0.23 0.68 104 - 113 0.97 0.98 1.00 0.60 0.59 0.48 114 - 123 0.99 1.00 1.00 1.00 1.00 0.30

124+ 1.00 1.00 0.46 1.00 1.00 0.18

S3-7 Selectivity

Length Class

Proportion of Legal

Summer Trawl

Winter Pot


74 - 83 0.00 0.87 0.42 0.11 0.02 1.00 84 - 93 0.00 0.90 0.89 0.19 0.06 0.88 94 - 103 0.26 0.94 0.99 0.33 0.23 0.77 104 - 113 0.97 0.97 1.00 0.57 0.62 0.68 114 - 123 0.99 1.00 1.00 1.00 1.00 0.59

124+ 1.00 1.00 0.41 1.00 1.00 0.51

Table 11. Summary of parameter estimates for a length-based stock synthesis population model of Norton Sound red king crab.

S3-1 S3-6 S3-7 name value std.dev value std.dev value std.dev

log_q1 -6.97 0.21 -6.70 0.18 -7.43 0.26 log_q2 -6.73 0.13 -6.66 0.14 -6.66 0.13

log_N76 8.93 0.13 8.78 0.07 9.58 0.23 log_mean 6.18 0.13 6.08 0.15 6.91 0.13 log_R77 -0.37 1.89 -2.07 3.67 1.13 0.50 log_R78 -2.23 3.27 -2.34 2.88 -1.92 2.81 log_R79 -2.60 1.69 -2.65 1.68 -2.44 1.63 log_R80 -0.26 1.11 -0.24 1.45 -0.18 0.81 log_R81 1.28 0.37 1.44 0.40 1.18 0.36 log_R82 0.52 0.44 0.50 0.48 0.73 0.38 log_R83 0.87 0.47 0.85 0.52 1.12 0.40 log_R84 1.19 0.36 1.09 0.40 1.44 0.33 log_R85 0.59 0.45 0.48 0.46 0.87 0.40 log_R86 0.45 0.50 0.15 0.58 0.96 0.39 log_R87 0.39 0.39 0.23 0.42 0.80 0.34 log_R88 0.11 0.38 0.02 0.40 0.31 0.36 log_R89 0.39 0.36 0.30 0.39 0.54 0.32 log_R90 0.10 0.39 0.05 0.42 0.23 0.34 log_R91 -0.84 0.60 -0.86 0.63 -0.77 0.50 log_R92 -0.37 0.53 -0.27 0.56 -0.54 0.45 log_R93 -1.65 1.39 -1.89 1.91 -1.24 0.69 log_R94 -0.01 0.42 0.12 0.48 -0.37 0.37 log_R95 -0.58 0.60 -0.52 0.71 -0.67 0.42 log_R96 0.06 0.33 0.27 0.35 -0.37 0.31 log_R97 0.47 0.38 0.70 0.42 0.09 0.34 log_R98 0.70 0.30 0.82 0.35 0.52 0.25 log_R99 -2.18 1.44 -2.07 1.46 -2.03 1.20 log_R00 -0.55 0.71 -0.46 0.78 -0.53 0.53 log_R01 0.57 0.36 0.73 0.40 0.15 0.34 log_R02 0.38 0.33 0.53 0.35 0.00 0.29 log_R03 0.60 0.42 0.75 0.46 0.49 0.34 log_R04 -1.14 1.51 -1.14 1.74 -0.81 0.81 log_R05 0.12 0.45 0.30 0.50 -0.16 0.39 log_R06 0.87 0.27 1.12 0.29 0.43 0.25 log_R07 0.26 0.48 0.50 0.53 0.02 0.37 log_R08 0.91 0.29 1.11 0.32 0.47 0.26 log_R09 0.74 0.38 0.82 0.45 0.58 0.28 log_R10 0.09 0.46 0.22 0.49 -0.19 0.38 log_R11 0.19 0.41 0.37 0.42 -0.23 0.37 log_R12 0.92 0.62 1.09 0.63 0.37 0.61

a1 -0.61 1.92 -1.17 1.83 -0.35 1.92 a2 1.13 1.26 0.56 1.10 1.40 1.26 a3 1.90 1.15 1.35 0.98 2.05 1.16 a4 2.35 1.13 2.00 0.96 2.23 1.15 a5 1.61 1.18 1.43 1.01 1.50 1.20 r1 0.61 0.06 0.61 0.05 0.60 0.06

log_ -4.13 0.16 -2.65 0.32 -2.98 0.65 log_ 0.55 0.26 4.62 0.07 5.00 0.00

log_st -1.39 324.66 -5.50 0.00 -4.13 1.00 log_st 1.68 1323.90 0.51 0.79 3.00 0.00 log_sw 0.60 298.54 0.60 299.21 -1.45 0.61 log_sw 4.36 0.91 4.36 0.87 4.38 0.02

Sw6 0.37 0.11 0.47 0.14 0.41 0.12 log_1 -3.00 0.00 -2.98 0.23 -2.89 0.21 log_1 5.08 0.50 5.50 0.07 5.50 1.10 log_2 -1.95 0.27 -2.01 0.28 -1.92 0.25 log_2 4.67 0.04 4.70 0.05 4.69 0.04 advar 0.07 0.03 0.07 0.02 0.07 0.03

q 0.70 0.13 0.88 0.14 0.41 0.10 p4 1.00 0.00 1.00 0.00 1.00 0.00

Table 12. Annual abundance estimates (million crabs) and mature male biomass (MMB, million lbs) for Norton Sound red king crab estimated by length-based analysis from 1976-2011. S3-1

Abundance Legal (≥ 104 mm) MMB

Year Recruits Total

(≥ 74 mm) Matures

(≥ 94 mm) Abundance S.D Biomass S.D Biomass S.D. 1976 1.03 7.96 6.94 5.04 0.95 12.08 2.47 14.57 2.47 1977 0.24 6.04 5.80 5.26 0.71 13.91 1.97 15.08 2.03 1978 0.12 4.40 4.28 4.34 0.49 12.34 1.49 12.91 1.42 1979 0.05 2.79 2.74 2.88 0.32 8.61 1.02 8.84 1.02 1980 0.41 1.74 1.33 1.41 0.23 4.33 0.71 4.42 0.72 1981 2.11 3.07 0.96 0.85 0.16 2.56 0.48 2.80 0.55 1982 1.25 2.85 1.60 0.84 0.19 2.01 0.49 3.06 0.69 1983 1.49 3.36 1.86 1.31 0.27 3.16 0.67 4.02 0.83 1984 1.93 4.06 2.12 1.58 0.31 3.92 0.79 4.86 0.98 1985 1.22 3.78 2.57 1.92 0.37 4.81 0.94 6.05 1.14 1986 0.92 3.41 2.49 2.14 0.41 5.53 1.07 6.47 1.23 1987 0.88 3.12 2.25 2.10 0.40 5.59 1.09 6.34 1.20 1988 0.69 2.77 2.09 1.99 0.37 5.43 1.03 6.10 1.12 1989 0.84 2.72 1.88 1.83 0.33 5.08 0.93 5.63 1.00 1990 0.71 2.52 1.80 1.67 0.28 4.65 0.81 5.25 0.88 1991 0.33 2.03 1.70 1.56 0.25 4.33 0.70 4.85 0.76 1992 0.41 1.85 1.44 1.40 0.21 3.96 0.60 4.27 0.62 1993 0.18 1.46 1.28 1.18 0.16 3.41 0.48 3.70 0.51 1994 0.56 1.52 0.96 0.90 0.13 2.62 0.38 2.78 0.40 1995 0.41 1.34 0.93 0.72 0.10 2.05 0.30 2.37 0.34 1996 0.64 1.49 0.85 0.66 0.10 1.79 0.27 2.06 0.30 1997 1.04 1.98 0.94 0.67 0.10 1.76 0.26 2.15 0.31 1998 1.33 2.60 1.26 0.84 0.12 2.13 0.29 2.70 0.39 1999 0.28 1.97 1.69 1.13 0.14 2.83 0.35 3.59 0.40 2000 0.35 1.77 1.42 1.23 0.14 3.24 0.37 3.55 0.39 2001 1.05 2.21 1.16 1.02 0.12 2.83 0.34 3.09 0.38 2002 0.94 2.32 1.38 0.98 0.12 2.65 0.31 3.22 0.37 2003 1.29 2.78 1.49 1.10 0.12 2.86 0.31 3.47 0.34 2004 0.39 2.17 1.77 1.25 0.13 3.21 0.32 3.92 0.44 2005 0.70 2.15 1.46 1.22 0.16 3.25 0.40 3.60 0.45 2006 1.47 2.84 1.37 1.08 0.14 2.94 0.39 3.36 0.43 2007 1.04 2.77 1.73 1.15 0.14 2.96 0.38 3.76 0.46 2008 1.51 3.31 1.79 1.31 0.16 3.35 0.40 4.00 0.48 2009 1.46 3.54 2.08 1.46 0.16 3.71 0.42 4.61 0.48 2010 0.81 3.08 2.27 1.66 0.17 4.24 0.43 5.14 0.52 2011 0.77 2.80 2.04 1.68 0.18 4.43 0.48 5.05 0.54 2012 1.39 3.23 1.83 1.56 0.17 4.22 0.47 4.76 0.51 2013 1.25 3.27 2.02 1.56 0.26 4.13 0.61 5.00 0.98

S3-6 Abundance Legal (≥ 104 mm) MMB

Year Recruits Total

(≥ 74 mm) Matures


S3-7 Abundance Legal (≥ 104 mm) MMB

Year Recruits Total

(≥ 74 mm) Matures


Table 13. Summary of catch and bycatch (million lbs) for Norton Sound red king crab. The bycatch (discards) is estimated from the model. Summer commercial catches are from ADF&G fish ticket database during 1985-2009 and from Menard et al. (2011) during 1977 to 1984. Winter commercial and subsistence catches are from ADF&G permit reporting and average weight of 2.5 lbs for the winter commercial catch and 2.0 lbs for the subsistence catch were assumed to estimate total weight. S3-1

Year Summer Winter Subsistence Bycatch/ discards

Total Catch/MMB

1977 0.52 0.024 0.025 0.004 0.57 0.04 1978 2.09 0.001 0.000 0.007 2.10 0.16 1979 2.93 0.000 0.000 0.008 2.94 0.33 1980 1.19 0.000 0.001 0.005 1.20 0.27 1981 1.38 0.000 0.003 0.037 1.42 0.51 1982 0.23 0.001 0.021 0.009 0.26 0.09 1983 0.37 0.002 0.022 0.011 0.41 0.10 1984 0.39 0.003 0.017 0.012 0.42 0.09 1985 0.43 0.005 0.014 0.011 0.46 0.08 1986 0.48 0.003 0.012 0.008 0.50 0.08 1987 0.33 0.001 0.005 0.005 0.34 0.05 1988 0.24 0.001 0.012 0.003 0.26 0.04 1989 0.25 0.009 0.024 0.003 0.29 0.05 1990 0.19 0.010 0.015 0.003 0.22 0.04 1991 0 0.019 0.023 0.000 0.04 0.01 1992 0.07 0.004 0.002 0.001 0.08 0.02 1993 0.33 0.014 0.008 0.002 0.35 0.10 1994 0.32 0.019 0.011 0.002 0.35 0.13 1995 0.32 0.004 0.003 0.003 0.33 0.14 1996 0.22 0.000 0.001 0.002 0.22 0.11 1997 0.09 0.002 0.017 0.001 0.11 0.05 1998 0.03 0.007 0.015 0.001 0.05 0.02 1999 0.02 0.008 0.011 0.000 0.04 0.01 2000 0.3 0.003 0.001 0.002 0.31 0.09 2001 0.28 0.006 0.004 0.002 0.29 0.09 2002 0.25 0.017 0.008 0.003 0.28 0.09 2003 0.26 0.001 0.002 0.004 0.27 0.08 2004 0.34 0.005 0.008 0.004 0.36 0.09 2005 0.4 0.000 0.002 0.003 0.41 0.11 2006 0.45 0.008 0.021 0.005 0.48 0.14 2007 0.31 0.014 0.019 0.005 0.35 0.09 2008 0.39 0.012 0.010 0.005 0.42 0.10 2009 0.4 0.012 0.014 0.006 0.43 0.09 2010 0.42 0.008 0.013 0.005 0.45 0.09 2011 0.4 0.011 0.018 0.004 0.43 0.09 2012 0.47 0.011 0.018 0.005 0.50 0.11

S3-6


Total Catch/MMB

1977 0.52 0.024 0.025 0.004 0.57 0.05 1978 2.09 0.001 0.000 0.008 2.10 0.20 1979 2.93 0.000 0.000 0.008 2.94 0.40 1980 1.19 0.000 0.001 0.005 1.20 0.32 1981 1.38 0.000 0.003 0.037 1.42 0.57 1982 0.23 0.001 0.021 0.010 0.26 0.09 1983 0.37 0.002 0.022 0.012 0.41 0.11 1984 0.39 0.003 0.017 0.012 0.42 0.10 1985 0.43 0.005 0.014 0.011 0.46 0.10 1986 0.48 0.003 0.012 0.009 0.50 0.10 1987 0.33 0.001 0.005 0.005 0.34 0.07 1988 0.24 0.001 0.012 0.003 0.26 0.06 1989 0.25 0.009 0.024 0.003 0.29 0.07 1990 0.19 0.010 0.015 0.003 0.22 0.05 1991 0 0.019 0.023 0.000 0.04 0.01 1992 0.07 0.004 0.002 0.001 0.08 0.02 1993 0.33 0.014 0.008 0.002 0.35 0.11 1994 0.32 0.019 0.011 0.002 0.35 0.13 1995 0.32 0.004 0.003 0.003 0.33 0.14 1996 0.22 0.000 0.001 0.002 0.22 0.11 1997 0.09 0.002 0.017 0.001 0.11 0.05 1998 0.03 0.007 0.015 0.001 0.05 0.02 1999 0.02 0.008 0.011 0.000 0.04 0.01 2000 0.3 0.003 0.001 0.002 0.31 0.09 2001 0.28 0.006 0.004 0.002 0.29 0.10 2002 0.25 0.017 0.008 0.003 0.28 0.09 2003 0.26 0.001 0.002 0.004 0.27 0.08 2004 0.34 0.005 0.008 0.004 0.36 0.09 2005 0.4 0.000 0.002 0.003 0.41 0.11 2006 0.45 0.008 0.021 0.005 0.48 0.14 2007 0.31 0.014 0.019 0.005 0.35 0.09 2008 0.39 0.012 0.010 0.006 0.42 0.10 2009 0.4 0.012 0.014 0.006 0.43 0.09 2010 0.42 0.008 0.013 0.005 0.45 0.09 2011 0.4 0.011 0.018 0.004 0.43 0.09 2012 0.47 0.011 0.018 0.005 0.50 0.11

S3-7


Total Catch/MMB

1977 0.52 0.024 0.025 0.004 0.57 0.04 1978 2.09 0.001 0.000 0.007 2.10 0.18 1979 2.93 0.000 0.000 0.008 2.94 0.37 1980 1.19 0.000 0.001 0.006 1.20 0.30 1981 1.38 0.000 0.003 0.037 1.42 0.53 1982 0.23 0.001 0.021 0.008 0.26 0.08 1983 0.37 0.002 0.022 0.011 0.40 0.10 1984 0.39 0.003 0.017 0.012 0.42 0.09 1985 0.43 0.005 0.014 0.010 0.46 0.08 1986 0.48 0.003 0.012 0.008 0.50 0.09 1987 0.33 0.001 0.005 0.005 0.34 0.06 1988 0.24 0.001 0.012 0.003 0.26 0.05 1989 0.25 0.009 0.024 0.003 0.29 0.06 1990 0.19 0.010 0.015 0.003 0.22 0.05 1991 0 0.019 0.023 0.000 0.04 0.01 1992 0.07 0.004 0.002 0.001 0.08 0.02 1993 0.33 0.014 0.008 0.002 0.35 0.10 1994 0.32 0.019 0.011 0.002 0.35 0.13 1995 0.32 0.004 0.003 0.003 0.33 0.14 1996 0.22 0.000 0.001 0.002 0.22 0.10 1997 0.09 0.002 0.017 0.001 0.11 0.05 1998 0.03 0.007 0.015 0.001 0.05 0.02 1999 0.02 0.008 0.011 0.000 0.04 0.01 2000 0.3 0.003 0.001 0.002 0.31 0.09 2001 0.28 0.006 0.004 0.002 0.29 0.10 2002 0.25 0.017 0.008 0.003 0.28 0.09 2003 0.26 0.001 0.002 0.004 0.27 0.08 2004 0.34 0.005 0.008 0.004 0.36 0.09 2005 0.4 0.000 0.002 0.003 0.41 0.11 2006 0.45 0.008 0.021 0.006 0.49 0.14 2007 0.31 0.014 0.019 0.006 0.35 0.09 2008 0.39 0.012 0.010 0.007 0.42 0.10 2009 0.4 0.012 0.014 0.007 0.43 0.09 2010 0.42 0.008 0.013 0.005 0.45 0.09 2011 0.4 0.011 0.018 0.004 0.43 0.09 2012 0.47 0.011 0.018 0.005 0.50 0.11

Figure 1. King crab fishing districts and sections of Statistical Area Q.

Figure 2. Closed water regulations in effect for the Norton Sound commercial crab fishery.

Figure 3. Observed length compositions 1976-2012.

1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

0.0

0.4

0.8

Commercial Harvest

1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

0.0

0.4

0.8

Winter Pot Survey

1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

0.0

0.4

0.8

Summter Trawl Survey

1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

0.0

0.4

0.8

Summter Observer Survey

1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 2009 2012

0.0

0.4

0.8 6

54321

Summter Pot Survey

1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124

Figure 4a. Estimated abundance of total (crabs ≥ 74 mm CL) male from 1976-2012.

1975 1980 1985 1990 1995 2000 2005 2010

02

46

8

Year

To

tal C

rab

Ab

un

da

nce

(m

illio

n)

S3-1S3-6S3-7

Trawl survey crab abundance

Figure 4b. Estimated abundance of legal male from 1976-2012.

1980 1990 2000 2010

01

23

45

6

Year

Ab

un

da

nce

(m

illio

n c

rab

s)

S3-1S3-6S3-7

Trawl survey Legal crab abundance

Figure 4c. Estimated abundance of leg recruits from 1976-2012.

1975 1980 1985 1990 1995 2000 2005 2010

01

23

45

6

Year

Ab

un

da

nce

(m

illio

n c

rab

s)

S3-1S3-6S3-7

Trawl survey Recruit crab abundance

Figure 5. Total catch and predicted harvest rate time series.

1975 1980 1985 1990 1995 2000 2005 2010

0.0

0.2

0.4

0.6

0.8

1.0

Year

To

tal C

atc

h (

mill

ion

)

0.0

0.1

0.2

0.3

0.4

Est

ima

ted

ha

rve

st r

ate

Total CatchEstimated Harvest Rate

Total catch & Estimated harvest rate

Figure 6. harvest rate vs. MMB

0 5 10 15

0.0

0.1

0.2

0.3

0.4

0.5

S3-1

0 5 10 150.

00.

10.

20.

30.

40.

5

S3-6

0 5 10 15

0.0

0.1

0.2

0.3

0.4

0.5

S3-7

Figure 7. Comparison of observed and estimated summer fishing standardized CPUE 1977-2012.

1975 1980 1985 1990 1995 2000 2005 2010

01

23

45

67

Year

Sta

nd

ard

ize

d C

PU

E

ObservedS3-1S3-6S3-7

Summer commercial standardized cpue

Figure 8. Molting probability and selectivity and trawl/pot selectivity.

80 90 100 110 120 130

0.0

0.2

0.4

0.6

0.8

1.0

Molting Probability

80 90 100 110 120 130

0.0

0.2

0.4

0.6

0.8

1.0

Trawl Selectivity

80 90 100 110 120 130

0.0

0.2

0.4

0.6

0.8

1.0

Winter pot Selectivity

80 90 100 110 120 130

0.0

0.2

0.4

0.6

0.8

1.0

Commercial 77-92 Selectivity

80 90 100 110 120 130

0.0

0.2

0.4

0.6

0.8

1.0

Commercial 93-12 Selectivity

Figure 9. Cumulative frequency of length classes between observed and modeled.

80 90 100 110 120 130

0.0

0.2

0.4

0.6

0.8

1.0

Commercial Harvest

80 90 100 110 120 130

0.2

0.4

0.6

0.8

1.0

Winter Pot Survey

80 90 100 110 120 130

0.2

0.4

0.6

0.8

1.0

Trawl Survey

80 90 100 110 120 130

0.2

0.4

0.6

0.8

1.0

Summer Observer

S3-1 S3-6 S3-7

Figure 10. Prospective Analysis. S3-1 S3-6 S3-7

Figure 11. Retrospective Analysis.

Figures S3-1

Figure S3-1-1: Histogram and Q-Q plot of trawl and standardized cpue.

Trawl survey Residuals

-1000 -500 0 500 1000

01

23

45

-1.5 -0.5 0.5 1.5

-100

0-5

000

500

Normal Q-Q Plot

2000 3000 4000 5000

-100

0-5

000

500

Commercial CPUE Residuals

-3 -2 -1 0 1 2 3

05

1015

-2 -1 0 1 2

-3-2

-10

12

Normal Q-Q Plot

0.5 1.0 1.5 2.0 2.5 3.0 3.5

-3-2

-10

12

Residuals Histogram Q-Q Plot

Figure S3-1-2: Histogram and plot of implied vs. effective sample size.

Trawl survey

50 100 150

02

46

0 5 10 15 20

050

150

Trawl survey

1975 1985 1995 2005

5015

0

Commercial Catch

0 1000 2000 3000 4000

010

25

0 2 4 6 8 10

020

00

Commercial Catch

1980 1990 2000 2010

020

00

Winter pot survey

0 50 150 250 350

04

8

0 2 4 6 8 10

010

025

0

Winter pot survey

1980 1990 2000 2010

5020

0

Observer survey

20 40 60 80 120

0.0

0.4

0.8

0 2 4 6 8 10

040

100

Observer survey

1990 2000 2010

2060

120

Effective sample size: Input Size vs. Implied

Figure S3-1-3: Predicted vs. observed length class proportion for commercial catch

1 2 3 4 5 6

0.0

0.3

0.6

1977

1 2 3 4 5 6

0.0

0.3

0.6

1978

1 2 3 4 5 6

0.0

0.3

0.6

1979

1 2 3 4 5 6

0.0

0.3

0.6

1980

1 2 3 4 5 6

0.0

0.3

0.6

1981

1 2 3 4 5 6

0.0

0.3

0.6

1982

1 2 3 4 5 6

0.0

0.3

0.6

1983

1 2 3 4 5 6

0.0

0.3

0.6

1984

1 2 3 4 5 6

0.0

0.3

0.6

1985

1 2 3 4 5 6

0.0

0.3

0.6

1986

1 2 3 4 5 6

0.0

0.3

0.6

1987

1 2 3 4 5 6

0.0

0.3

0.6

1988

1 2 3 4 5 6

0.0

0.3

0.6

1989

1 2 3 4 5 6

0.0

0.3

0.6

1990

1 2 3 4 5 6

0.0

0.3

0.6

1992

1 2 3 4 5 6

0.0

0.3

0.6

1993

1 2 3 4 5 6

0.0

0.3

0.6

1994

1 2 3 4 5 6

0.0

0.3

0.6

1995

1 2 3 4 5 6

0.0

0.3

0.6

1996

1 2 3 4 5 6

0.0

0.3

0.6

1997

1 2 3 4 5 6

0.0

0.3

0.6

1998

1 2 3 4 5 6

0.0

0.3

0.6

1999

1 2 3 4 5 6

0.0

0.3

0.6

2000

1 2 3 4 5 6

0.0

0.3

0.6

2001

1 2 3 4 5 6

0.0

0.3

0.6

2002

1 2 3 4 5 6

0.0

0.3

0.6

2003

1 2 3 4 5 6

0.0

0.3

0.6

2004

1 2 3 4 5 6

0.0

0.3

0.6

2005

1 2 3 4 5 6

0.0

0.3

0.6

2006

1 2 3 4 5 60.

00.

30.

6

2007

1 2 3 4 5 6

0.0

0.3

0.6

2008

1 2 3 4 5 6

0.0

0.3

0.6

2009

1 2 3 4 5 6

0.0

0.3

0.6

2010

1 2 3 4 5 6

0.0

0.3

0.6

2011

1 2 3 4 5 6

0.0

0.3

0.6

2012

commercial harvest length: observed vs predicted

1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124

Figure S3-1-4: Predicted vs. observed length class proportion for winter pot survey

1 2 3 4 5 6

0.0

0.2

0.4 1981

1 2 3 4 5 6

0.0

0.2

0.4 1982

1 2 3 4 5 6

0.0

0.2

0.4 1983

1 2 3 4 5 6

0.0

0.2

0.4 1984

1 2 3 4 5 6

0.0

0.2

0.4 1985

1 2 3 4 5 6

0.0

0.2

0.4 1986

1 2 3 4 5 6

0.0

0.2

0.4 1988

1 2 3 4 5 6

0.0

0.2

0.4 1989

1 2 3 4 5 6

0.0

0.2

0.4 1990

1 2 3 4 5 6

0.0

0.2

0.4 1992

1 2 3 4 5 6

0.0

0.2

0.4 1994

1 2 3 4 5 6

0.0

0.2

0.4 1995

1 2 3 4 5 6

0.0

0.2

0.4 1996

1 2 3 4 5 6

0.0

0.2

0.4 1997

1 2 3 4 5 6

0.0

0.2

0.4 1998

1 2 3 4 5 6

0.0

0.2

0.4 1999

1 2 3 4 5 6

0.0

0.2

0.4 2001

1 2 3 4 5 6

0.0

0.2

0.4 2002

1 2 3 4 5 6

0.0

0.2

0.4 2003

1 2 3 4 5 6

0.0

0.2

0.4 2004

1 2 3 4 5 6

0.0

0.2

0.4 2005

1 2 3 4 5 6

0.0

0.2

0.4 2006

1 2 3 4 5 6

0.0

0.2

0.4 2007

1 2 3 4 5 6

0.0

0.2

0.4 2008

1 2 3 4 5 6

0.0

0.2

0.4 2009

1 2 3 4 5 6

0.0

0.2

0.4 2010

1 2 3 4 5 6

0.0

0.2

0.4 2011

Winter pot length: observed vs predicted

1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124

Figure S3-1-5: Predicted vs. observed length class proportion for trawl survey and commercial observer.

1 2 3 4 5 6

0.0

0.2

0.4 1976

1 2 3 4 5 6

0.0

0.2

0.4 1979

1 2 3 4 5 6

0.0

0.2

0.4 1982

1 2 3 4 5 6

0.0

0.2

0.4 1985

1 2 3 4 5 6

0.0

0.2

0.4 1988

1 2 3 4 5 6

0.0

0.2

0.4 1991

1 2 3 4 5 6

0.0

0.2

0.4 1996

1 2 3 4 5 6

0.0

0.2

0.4 1999

1 2 3 4 5 6

0.0

0.2

0.4 2002

1 2 3 4 5 6

0.0

0.2

0.4 2006

1 2 3 4 5 6

0.0

0.2

0.4 2008

1 2 3 4 5 6

0.0

0.2

0.4 2010

1 2 3 4 5 6

0.0

0.2

0.4 2011

Trawl length: observed vs predicted

1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124

1 2 3 4 5 6

0.0

0.2

0.4 1987

1 2 3 4 5 6

0.0

0.2

0.4 1988

1 2 3 4 5 6

0.0

0.2

0.4 1989

1 2 3 4 5 6

0.0

0.2

0.4 1990

1 2 3 4 5 6

0.0

0.2

0.4 1992

1 2 3 4 5 6

0.0

0.2

0.4 1994

1 2 3 4 5 6

0.0

0.2

0.4 2012

Observer length: observed vs predicted

1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124

Figure S3-1-6: Bubble plots of length class proportion.

1975 1980 1985 1990 1995 2000 2005 2010

13

5

Commercial Harvest

1975 1980 1985 1990 1995 2000 2005 2010

13

5

Winter Pot Survey

1975 1980 1985 1990 1995 2000 2005 2010

13

5

Trawl Survey

1975 1980 1985 1990 1995 2000 2005 2010

13

5

Observer Survey

1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124

S3-6



-1500 -500 0 500 1000

01

23

4

-1.5 -0.5 0.5 1.5

-100

0-5

000

500

Normal Q-Q Plot

2000 4000 6000

-100

0-5

000

500


-4 -3 -2 -1 0 1 2 3

05

1015

-2 -1 0 1 2

-4-3

-2-1

01

2

Normal Q-Q Plot

1 2 3 4

-4-3

-2-1

01

2



Trawl survey

0 100 200 300 400 500

02

4

0 5 10 15 20

020

040

0

Trawl survey

1975 1985 1995 2005

100

300

Commercial Catch

0 50 150 250 350

04

812

0 2 4 6 8 10

015

030

0

Commercial Catch

1980 1990 2000 2010

015

030

0

Winter pot survey

0 50 150 250 350

04

812

0 2 4 6 8 10

015

030

0

Winter pot survey

1980 1990 2000 2010

015

030

0

Observer survey

20 40 60 80 100

0.0

0.4

0.8

0 2 4 6 8 10

040

80

Observer survey

1990 2000 2010

2060

100



1 2 3 4 5 6

0.0

0.3

0.6

1977

1 2 3 4 5 6

0.0

0.3

0.6

1978

1 2 3 4 5 6

0.0

0.3

0.6

1979

1 2 3 4 5 6

0.0

0.3

0.6

1980

1 2 3 4 5 6

0.0

0.3

0.6

1981

1 2 3 4 5 6

0.0

0.3

0.6

1982

1 2 3 4 5 6

0.0

0.3

0.6

1983

1 2 3 4 5 6

0.0

0.3

0.6

1984

1 2 3 4 5 6

0.0

0.3

0.6

1985

1 2 3 4 5 6

0.0

0.3

0.6

1986

1 2 3 4 5 6

0.0

0.3

0.6

1987

1 2 3 4 5 6

0.0

0.3

0.6

1988

1 2 3 4 5 6

0.0

0.3

0.6

1989

1 2 3 4 5 6

0.0

0.3

0.6

1990

1 2 3 4 5 6

0.0

0.3

0.6

1992

1 2 3 4 5 6

0.0

0.3

0.6

1993

1 2 3 4 5 6

0.0

0.3

0.6

1994

1 2 3 4 5 6

0.0

0.3

0.6

1995

1 2 3 4 5 6

0.0

0.3

0.6

1996

1 2 3 4 5 6

0.0

0.3

0.6

1997

1 2 3 4 5 6

0.0

0.3

0.6

1998

1 2 3 4 5 6

0.0

0.3

0.6

1999

1 2 3 4 5 6

0.0

0.3

0.6

2000

1 2 3 4 5 6

0.0

0.3

0.6

2001

1 2 3 4 5 6

0.0

0.3

0.6

2002

1 2 3 4 5 6

0.0

0.3

0.6

2003

1 2 3 4 5 6

0.0

0.3

0.6

2004

1 2 3 4 5 6

0.0

0.3

0.6

2005

1 2 3 4 5 6

0.0

0.3

0.6

2006

1 2 3 4 5 60.

00.

30.

6

2007

1 2 3 4 5 6

0.0

0.3

0.6

2008

1 2 3 4 5 6

0.0

0.3

0.6

2009

1 2 3 4 5 6

0.0

0.3

0.6

2010

1 2 3 4 5 6

0.0

0.3

0.6

2011

1 2 3 4 5 6

0.0

0.3

0.6

2012


1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124


1 2 3 4 5 6

0.0

0.2

0.4 1981

1 2 3 4 5 6

0.0

0.2

0.4 1982

1 2 3 4 5 6

0.0

0.2

0.4 1983

1 2 3 4 5 6

0.0

0.2

0.4 1984

1 2 3 4 5 6

0.0

0.2

0.4 1985

1 2 3 4 5 6

0.0

0.2

0.4 1986

1 2 3 4 5 6

0.0

0.2

0.4 1988

1 2 3 4 5 6

0.0

0.2

0.4 1989

1 2 3 4 5 6

0.0

0.2

0.4 1990

1 2 3 4 5 6

0.0

0.2

0.4 1992

1 2 3 4 5 6

0.0

0.2

0.4 1994

1 2 3 4 5 6

0.0

0.2

0.4 1995

1 2 3 4 5 6

0.0

0.2

0.4 1996

1 2 3 4 5 6

0.0

0.2

0.4 1997

1 2 3 4 5 6

0.0

0.2

0.4 1998

1 2 3 4 5 6

0.0

0.2

0.4 1999

1 2 3 4 5 6

0.0

0.2

0.4 2001

1 2 3 4 5 6

0.0

0.2

0.4 2002

1 2 3 4 5 6

0.0

0.2

0.4 2003

1 2 3 4 5 6

0.0

0.2

0.4 2004

1 2 3 4 5 6

0.0

0.2

0.4 2005

1 2 3 4 5 6

0.0

0.2

0.4 2006

1 2 3 4 5 6

0.0

0.2

0.4 2007

1 2 3 4 5 6

0.0

0.2

0.4 2008

1 2 3 4 5 6

0.0

0.2

0.4 2009

1 2 3 4 5 6

0.0

0.2

0.4 2010

1 2 3 4 5 6

0.0

0.2

0.4 2011


1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124


1 2 3 4 5 6

0.0

0.2

0.4 1976

1 2 3 4 5 6

0.0

0.2

0.4 1979

1 2 3 4 5 6

0.0

0.2

0.4 1982

1 2 3 4 5 6

0.0

0.2

0.4 1985

1 2 3 4 5 6

0.0

0.2

0.4 1988

1 2 3 4 5 6

0.0

0.2

0.4 1991

1 2 3 4 5 6

0.0

0.2

0.4 1996

1 2 3 4 5 6

0.0

0.2

0.4 1999

1 2 3 4 5 6

0.0

0.2

0.4 2002

1 2 3 4 5 6

0.0

0.2

0.4 2006

1 2 3 4 5 6

0.0

0.2

0.4 2008

1 2 3 4 5 6

0.0

0.2

0.4 2010

1 2 3 4 5 6

0.0

0.2

0.4 2011


1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124

1 2 3 4 5 6

0.0

0.2

0.4 1987

1 2 3 4 5 6

0.0

0.2

0.4 1988

1 2 3 4 5 6

0.0

0.2

0.4 1989

1 2 3 4 5 6

0.0

0.2

0.4 1990

1 2 3 4 5 6

0.0

0.2

0.4 1992

1 2 3 4 5 6

0.0

0.2

0.4 1994

1 2 3 4 5 6

0.0

0.2

0.4 2012


1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124


1975 1980 1985 1990 1995 2000 2005 2010

13

5

Commercial Harvest

1975 1980 1985 1990 1995 2000 2005 2010

13

5

Winter Pot Survey

1975 1980 1985 1990 1995 2000 2005 2010

13

5

Trawl Survey

1975 1980 1985 1990 1995 2000 2005 2010

13

5

Observer Survey

1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124

S3-7



-1500 -500 0 500 1000

01

23

45

67

-1.5 -0.5 0.5 1.5

-100

0-5

000

500

Normal Q-Q Plot

2000 4000 6000

-100

0-5

000

500


-4 -3 -2 -1 0 1 2 3

05

1015

-2 -1 0 1 2

-4-3

-2-1

01

2

Normal Q-Q Plot

1 2 3 4

-4-3

-2-1

01

2



Trawl survey

0 200 400 600

0.0

1.5

3.0

0 5 10 15 20

030

060

0

Trawl survey

1975 1985 1995 2005

100

400

700

Commercial Catch

0 100 200 300 400

04

812

0 2 4 6 8 10

020

040

0

Commercial Catch

1980 1990 2000 2010

020

040

0

Winter pot survey

0 200 400 600 800 1000

05

15

0 2 4 6 8 10

040

080

0

Winter pot survey

1980 1990 2000 2010

040

080

0

Observer survey

20 40 60 80 120

0.0

0.4

0.8

0 2 4 6 8 10

050

150 Observer survey

1990 2000 2010

2080

140



1 2 3 4 5 6

0.0

0.3

0.6

1977

1 2 3 4 5 6

0.0

0.3

0.6

1978

1 2 3 4 5 6

0.0

0.3

0.6

1979

1 2 3 4 5 6

0.0

0.3

0.6

1980

1 2 3 4 5 6

0.0

0.3

0.6

1981

1 2 3 4 5 6

0.0

0.3

0.6

1982

1 2 3 4 5 6

0.0

0.3

0.6

1983

1 2 3 4 5 6

0.0

0.3

0.6

1984

1 2 3 4 5 6

0.0

0.3

0.6

1985

1 2 3 4 5 6

0.0

0.3

0.6

1986

1 2 3 4 5 6

0.0

0.3

0.6

1987

1 2 3 4 5 6

0.0

0.3

0.6

1988

1 2 3 4 5 6

0.0

0.3

0.6

1989

1 2 3 4 5 6

0.0

0.3

0.6

1990

1 2 3 4 5 6

0.0

0.3

0.6

1992

1 2 3 4 5 6

0.0

0.3

0.6

1993

1 2 3 4 5 6

0.0

0.3

0.6

1994

1 2 3 4 5 6

0.0

0.3

0.6

1995

1 2 3 4 5 6

0.0

0.3

0.6

1996

1 2 3 4 5 6

0.0

0.3

0.6

1997

1 2 3 4 5 6

0.0

0.3

0.6

1998

1 2 3 4 5 6

0.0

0.3

0.6

1999

1 2 3 4 5 6

0.0

0.3

0.6

2000

1 2 3 4 5 6

0.0

0.3

0.6

2001

1 2 3 4 5 6

0.0

0.3

0.6

2002

1 2 3 4 5 6

0.0

0.3

0.6

2003

1 2 3 4 5 6

0.0

0.3

0.6

2004

1 2 3 4 5 6

0.0

0.3

0.6

2005

1 2 3 4 5 6

0.0

0.3

0.6

2006

1 2 3 4 5 60.

00.

30.

6

2007

1 2 3 4 5 6

0.0

0.3

0.6

2008

1 2 3 4 5 6

0.0

0.3

0.6

2009

1 2 3 4 5 6

0.0

0.3

0.6

2010

1 2 3 4 5 6

0.0

0.3

0.6

2011

1 2 3 4 5 6

0.0

0.3

0.6

2012


1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124


1 2 3 4 5 6

0.0

0.2

0.4 1981

1 2 3 4 5 6

0.0

0.2

0.4 1982

1 2 3 4 5 6

0.0

0.2

0.4 1983

1 2 3 4 5 6

0.0

0.2

0.4 1984

1 2 3 4 5 6

0.0

0.2

0.4 1985

1 2 3 4 5 6

0.0

0.2

0.4 1986

1 2 3 4 5 6

0.0

0.2

0.4 1988

1 2 3 4 5 6

0.0

0.2

0.4 1989

1 2 3 4 5 6

0.0

0.2

0.4 1990

1 2 3 4 5 6

0.0

0.2

0.4 1992

1 2 3 4 5 6

0.0

0.2

0.4 1994

1 2 3 4 5 6

0.0

0.2

0.4 1995

1 2 3 4 5 6

0.0

0.2

0.4 1996

1 2 3 4 5 6

0.0

0.2

0.4 1997

1 2 3 4 5 6

0.0

0.2

0.4 1998

1 2 3 4 5 6

0.0

0.2

0.4 1999

1 2 3 4 5 6

0.0

0.2

0.4 2001

1 2 3 4 5 6

0.0

0.2

0.4 2002

1 2 3 4 5 6

0.0

0.2

0.4 2003

1 2 3 4 5 6

0.0

0.2

0.4 2004

1 2 3 4 5 6

0.0

0.2

0.4 2005

1 2 3 4 5 6

0.0

0.2

0.4 2006

1 2 3 4 5 6

0.0

0.2

0.4 2007

1 2 3 4 5 6

0.0

0.2

0.4 2008

1 2 3 4 5 6

0.0

0.2

0.4 2009

1 2 3 4 5 6

0.0

0.2

0.4 2010

1 2 3 4 5 6

0.0

0.2

0.4 2011


1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124


1 2 3 4 5 6

0.0

0.2

0.4 1976

1 2 3 4 5 6

0.0

0.2

0.4 1979

1 2 3 4 5 6

0.0

0.2

0.4 1982

1 2 3 4 5 6

0.0

0.2

0.4 1985

1 2 3 4 5 6

0.0

0.2

0.4 1988

1 2 3 4 5 6

0.0

0.2

0.4 1991

1 2 3 4 5 6

0.0

0.2

0.4 1996

1 2 3 4 5 6

0.0

0.2

0.4 1999

1 2 3 4 5 6

0.0

0.2

0.4 2002

1 2 3 4 5 6

0.0

0.2

0.4 2006

1 2 3 4 5 6

0.0

0.2

0.4 2008

1 2 3 4 5 6

0.0

0.2

0.4 2010

1 2 3 4 5 6

0.0

0.2

0.4 2011


1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124

1 2 3 4 5 6

0.0

0.2

0.4 1987

1 2 3 4 5 6

0.0

0.2

0.4 1988

1 2 3 4 5 6

0.0

0.2

0.4 1989

1 2 3 4 5 6

0.0

0.2

0.4 1990

1 2 3 4 5 6

0.0

0.2

0.4 1992

1 2 3 4 5 6

0.0

0.2

0.4 1994

1 2 3 4 5 6

0.0

0.2

0.4 2012


1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124


1975 1980 1985 1990 1995 2000 2005 2010

13

5

Commercial Harvest

1975 1980 1985 1990 1995 2000 2005 2010

13

5

Winter Pot Survey

1975 1980 1985 1990 1995 2000 2005 2010

13

5

Trawl Survey

1975 1980 1985 1990 1995 2000 2005 2010

13

5

Observer Survey

1: 74-83, 2: 84-93, 3: 94-103, 4: 104-113, 5: 114-123, 6: >124

Appendix A. Description of the Norton Sound Red King Crab Model a. Model description.

The model is an extension of the length-based model developed by Zheng et al. (1998) for Norton Sound red king crab. The model has 6 length classes with model parameters estimated by the maximum likelihood method. The model estimates abundances of crabs with CL 74 mm and with 10-mm length intervals because few crabs with CL <74 mm were caught during surveys or fisheries and there were relatively small sample sizes for trawl and winter pot surveys. The model was made for newshell and oldshell male crabs separately, but assumed they have the same molting probability and natural mortality. In this model year starts July 1st to June 30th of the following year.

Initial pre-fishery summer crab abundance on July 1st 1976

Abundance of the initial pre-fishery population was estimated as a stochastic process around the mean, B1:

),0(~, 211 1Bt NeBB t (1)

The length proportion of the first year was calculated as

)exp(1

)exp(1

11 for )exp(1

)exp(

1

1

1

1

1

1

n

ii

n

ii

n

n

ii

ii

a

ap

,..,n-ia

ap

(2)

Abundance of crab length class was is a multiplication of the first year abundance. In this it was assumed no oldshell crab exist for the first year.

11,, BpN ils (3) Where

Ns,l,1 , Os,l,1 : summer abundances of newshell and oldshell crabs in length class l in the first year. pn : proportion of the neswshell crab pn,l : conditional proportion of l-th length neswshell crab, pn,0 =0 po,l : conditional proportion of l-th length oldwshell crab, po,0 = po,1 =0

Summer crab abundance on July 1st

Summer crab abundance of the t-th year new and old shell of l-th length class before the summer commercial fishery, is the survivors of winter crab from fishery and natural mortality

e)PCPC-O(=O

e)PCPC-N(=Nl

l

M0.417-tl,optptl,owtwtl,wtl,s

M0.417-tl,nptptl,nwtwtl,wtl,s

ˆˆ

ˆˆ

1,,1,1,,,1,,

1,,1,1,,,1,,

(4)

where

Ns,l,t , Os,l,t : summer abundances of newshell and oldshell crabs in length class l in year t Nw,l,t, Ow,l,t :winter abundances of newshell and oldshell crabs in length class l in year t Cw,t, Cp,t : total winter and subsistence catches in year t, Pw,n,l,t, Pp,n,l,t : Length proportion of winter and subsistence catches for newshell crabs for length class l in year t Pw,o,l,t, Pp,o,l,t : length compositions of winter and subsistence catches for oldshell crabs in length class l in year t Ml : instantaneous natural mortality in length class l, constant for all sizes and shell conditions 0.417 : proportion of the year from Feb. 1 to July 1 is 5 months, or 0.417 Winter crab abundance on February 1st

Abundance of newshell crab of the t-th year and l-th length class (Nw,l,t ), is a population that molted to become l-th length class minus l-th length class harvested by summer commercial fishery and discards, the combined result of growth, molting probability, summer commercial harvests, mortality, and recruitment from the summer population:

R+]em)D)P+P(CeON(G[ = N tl,My-0.583-

tlt,lost,lnsts,My

t,lst,lsl,l

l=l

=ltl,w

lc

l

lc )(,',,,,,,, ˆˆ)(

1

(5)

Winter abundance of oldshell crabs Os,l,t is the non-molting portion of survivors of crabs from summer:

e)m-(1] D)P+P(CeON[ = O lc

l

lc My0.583--tltlostl,nsts,

Mytl,stl,stl,w

)(,,,,,,,,, ˆˆ)( (6)

where

Gl’, l : a growth matrix representing the expected proportion of crabs molting from length class l’ to length class l (independently estimated outside of the assessment model frame), Cs,t : total summer catch in year t (assumed to be accurate without error), Ps,n,l,t , Ps,o,l,t : Compositions of summer catch for newshell and oldshell crabs in length class l in year t, Dl,t : discards of length class l in year t, ml : molting probability in length class l, yc : the time in year from July 1 to the mid-point of the summer fishery 0.583: Proportion of the year from July 1 to Feb. 1 is 7 months, or 0.583 year Rl,t: recruitment into length class l in year t.

Discards

In summer commercial fisheries, sublegal males (<4.75 inch CW and <5.0 inch CW since 2005) are not retained, but are sorted and discarded. Those discarded crabs are subject to handling mortality. Due to lack of data, we assumed discards mortality to be 0.2.

Discards of length class l in year t from the commercial pot fishery were estimated as:

l

ltlstlstsllstlstlstl LONChmL SON=D ])(/[)1()( ,,,,,,,,,,, (7)

where hm: handling mortality rate assumed to be 0.2 Ll : the proportion of legal males in length class l. Reflecting the change of commercial acceptable crab size since 2005, proportion of legal males in the length class 4, was calculated as p4L4. Where p4 is the proportion of commercially acceptable crab among legal crab of the length class 4. p4

was estimated from the model. Ss,l : Selectivity of the summer commercial fishery. Molting Probability Molting probability for length class l, ml, was calculated using a reverse logistic function fitted as a function of length and time (Balsiger's 1974)

e+1

1-1 = m

i-l )( (8)

where and are parameters, and i is the mid-length of length class l. ml was re-scaled such that m1 = 1.

Trawl net and pot selectivity Selectivity of length class l for summer commercial fishery ( Ss,l ), summer trawl survey ( Sst,l ), summer pot survey (Sp,l ), winter pot survey (Sw,l ), and summer trawl survey were assumed to be an asymptotic logistic function with parameters and , where i is the mid-length of the length class l.

e+1

1 = S i-l )(

(9)

Selectivity of S1-4 were re-scaled such that S5 = S6 =1.

For summer commercial fisheries, two sets of parameters (1, 1), (2, 2) were estimated: 1) before 1993, and 2) 1933 to present reflecting changes in fisheries, and crab pot configurations.

For winter pot survey and winter harvest, selectivity (Sw,l) was estimated for the first 2 length classes, the length classes 3-5 were assumed to be 1, and Sw,6 was directly estimated from the model. This resulted in the model taking a dorm shaped selectivity.

Estimation of Recruitment

We modeled recruitment of year t, Rt, as a stochastic process around the mean, R0:

),0(~, 20 Rtt NeRR t (10)

Rt was assumed to come from only length classes 1 (R1,t) and 2 (R2,t) , and was calculated as

Rr)(1 = R

Rr=R

tt,

tt,

2

1 (11)

where r is a parameter with a value less than or equal to 1. Rl,t = 0 when l 3. Observation model Estimates of survey abundances Summer trawl survey abundance Abundance of t-th year trawl survey was estimated by subtracting population of July 1st abundance minus summer commercial fisheries harvested by before trawl survey, multiplied by selectivity of trawl.

llst

Mylslsst

l

Myytct,lost,lnsts,

My

lsttlstlstst

SeON=B

Se)PP+P(CeON=B

lst

lcstlc

,)(

1,,1,,1,

)(,,,,, ,,,,,,

)(ˆ

]ˆˆ)[(ˆ

(12)

Where yst : the time in year from July 1 to the mid-point of the summer trawl survey. (yst > yc: Trawl survey starts after opening of commercial fisheries) Pc,t : proportion of summer commercial crab harvested before the survey.

Summer pot survey abundance (Removed from likelihood components) Abundance of t-th year pot survey was estimated as

l

Mylptlstlstp SeON=B lp ])[(ˆ,,,,,, (13)

Where yp : the time in year from July 1 to the mid-point of the summer trawl survey.

Estimation of summer commercial cpue Summer commercial fishing cpue (ft) was calculated as a product of catchability coefficient q and mean exploitable abundance minus one half of summer catch, Ct.

)CA(qf ttt 5.0ˆ i (14)

Because fishing fleet and pot limit configuration changed in 1993 and 2008, q1 is for fishing efforts before 1993, q2 is from 1994 to present.

Estimates of length composition Winter commercial catch Length compositions of winter commercial catch (Pw,n,l,t, Pw,o,l,t) for length l in year t were estimated from the winter population, winter pot selectivity, and proportion of legal crabs for each length class as:

]LS)ON[(LSO=P

]LS)ON[(LSN=P

lllwtl,wtl,wllwtl,wtl,ow

lllwtl,wtl,wllwtl,wtl,nw

3,,,,,,,

3,,,,,,,

/ˆ

/ˆ

(15)

Winter subsistence catch Subsistence fishery does not have a size limit; however, crabs of size smaller than length class 3 are generally not retained. Hence, we assumed proportion of length composition l = 1 and 2 as 0, and estimated length compositions (l ≥ 3) as follows

3,,,,,,,

3,,,,,,,

/ˆ

/ˆ

llwtl,wtl,wlwtl,wtl,op

llwtl,wtl,wlwtl,wtl,np

]S)ON[(SO=P

]S)ON[(SN=P (16)

Winter pot survey

The above equations were also used to calculate length compositions of winter pot survey for newshell and oldshell crabs, Psw,n,l,t and Psw,o,l,t (l 1).

llwtl,wtl,wlwtl,wtl,osw

llwtl,wtl,wlwtl,wtl,nsw

]S)ON[(SO=P

]S)ON[(SN=P

,,,,,,,

,,,,,,,

/ˆ

/ˆ

(17)

Summer commercial catch Length compositions of the summer commercial catch for new and old shell crabs Ps,n,l,t and Ps,o,l,t, were calculated based on summer population, selectivity, and legal abundance;

ALSO =P

ALSN =P

tllstl,stl,os

tllstl,stl,ns

/ˆ

/ˆ

,,,,

,,,, (18)

Where At is exploitable legal abundance in year t, estimated as

l

llstl,stl,st ]LS)ON[(A ,,, (19)

Observer discards

Length/shell compositions of Observer discards in 87-90, 92, 94, and 2012 were estimated as

)]L(1S)ON[()L(1SO=P

)]L(1S)ON[()L(1SN=P

lllstl,stl,sllstl,stl,ob

lllstl,stl,sllstl,stl,nb

,,,,,,,

,,,,,,,

/ˆ

/ˆ (20)

Summer trawl survey

Some trawl surveys occurred during the molting period, and thus we combined the length compositions of newshell and oldshell crabs as one single shell condition, Pst,l,t, and were estimated as

l

lsttl,stl,slsttl,stl,st ]S)ON[(SN =P ,,,,,,, /ˆ (21)

Summer pre-season survey (1976) (Removed from likelihood)

The same selectivity for the summer commercial fishery was applied to the summer pre-season survey, resulting in estimated length compositions for both newshell and oldshell crabs as:

]S)ON[(SO =P

] S)ON[(SN =P

llstl,stl,slstl,stl,osf

llstl,stl,slstl,stl,nsf

,,,,,,,

,,,,,,,

/ˆ

/ˆ

(22)

This was not incorporated into likelihood calculation because of one year data.

Summer pot survey (1980-82, 85) (Removed from likelihood)

The length/shell condition compositions of summer pot survey were estimated as

llsptl,stl,slsptl,stl,osp

llsptl,stl,slsptl,stl,nsp

]S)ON[(SO =P

]S)ON[(SN =P

,,,,,,,

,,,,,,,

/ˆ

/ˆ

(23)

b. Software used: AD Model Builder (Fournier et al. 2012).

c. Likelihood components.

Under assumptions that measurement errors of annual total survey abundances and summer commercial fishing efforts follow lognormal distributions and each type of length composition

has a multinomial error structure (Fournier and Archibald 1982; Methot 1989), the log-likelihood function is:

1

2

,,

,,

6

1,,,,

6

1,,,

5

}(ˆ)(

ˆ

[ˆ[(

ttR

nt

1=t

2t

2t

2tt

2t

2t

nt

1=t

2ti,

2titi

nt

1=ttli

l

ltlitli

l

ltliti

i

=i

W

))ln(w1)ln(CV/(2)]+fln(-)+f[ln()ln(w1)ln(CV{-(1/2)ln(

1))ln(CV/(2)]+Bln(-)+B[ln(q

)])}+Pln( P-)]+Pln( PK{

i

i

i

1

(24)

1where i: length/shell compositions of :

1 triennial summer trawl survey 2 summer pot survey (1980-82, 85): Removed 3 annual winter pot survey 4 summer commercial fishery 5 observer bycatch during the summer fishery

ni: the number of years in which data set i is available Ki,t: the effective sample size of length/shell compositions for data set i in year t Pi,l,t : observed and estimated length compositions for data set i, length class l, and year t

In this, while observation and estimation were made for oldshell and newshell separately, both were combined for likelihood calculations.

: a constant equal to 0.001 CV : coefficient of variation for the survey abundance. CV for summer pot survey was assumed 0.34 Bi,k,t: observed and estimated annual total abundances for data set i and year t Wf : the weighting factor of the summer fishing effort ft : observed and estimated summer fishing cpue w2

t: extra variance factor WR : the weighting factor of recruitment. It is generally believed that total annual commercial crab catches in Alaska are fairly accurately reported. Thus, no measurement error was imposed on total annual catch. Variances for total survey abundances and summer fishing effort were not estimated; rather, we used weighting factors to reflect these variances.

e. Parameter estimation framework:

i. Parameters Estimated Independently

The following parameters were estimated independently: natural mortality (M =0.18),

proportions of legal males by length group, and the growth matrix.

Natural mortality was based on an assumed maximum age, tmax, and the 1% rule (Zheng 2005):

,

where p is the proportion of animals that reach the maximum age and is assumed to be 0.01 for the 1% rule (Shepherd and Breen 1992, Clarke et al. 2003). The maximum age of 25, which was used to estimate M for U.S. federal overfishing limits for red king crab stocks (NPFMC 2007) results in an estimated M of 0.18. Among the 199 recovered crabs from the tagging returns during 1991-2007 in Norton Sound, the longest time at liberty was 6 years and 4 months from a crab tagged at 85 mm CL. The crab was below the mature size and was likely less than 6 years old when tagged. Therefore, the maximum age from tagging data is about 12, which does not support the maximum age of 25 chosen by the CPT.

Proportions of legal males (CW > 4.75 inches) by length group were estimated from the ADF&G trawl data 1996-2011 (Table 8).

Mean growth increment per molt, standard deviation for each pre-molt length class, and the growth matrix (Table 8), were estimated from tagging surveys conducted in summer 1981-1985, and winter 1981-present. In summer 1981-1985 study legal and sublegal males captured by the survey pots were tagged, and in the1981-present winter survey, sublegal males were tagged. All tagged crabs were recaptured by summer and winter commercial/subsistence fisheries.

ii. Parameters Estimated Conditionally

Estimated parameters are listed in Table 5. Selectivity and molting probabilities based on these estimated parameters are summarized in Table 4 (also in the primary document).

A likelihood approach was used to estimate parameters, which include fishing catchability, parameters for selectivities of survey and fishing gears and for molting probabilities, recruits each year (except the first and the last years), and total abundance in the first year (Table 5).

Crabs usually aggregate, and this increases the uncertainty in survey estimates of abundance. To reduce the effect of aggregation, annual total sample sizes for summer trawl and pot survey data sets were reduced to 50% and all other sample sizes were reduced to 10%. Also, annual effective sample sizes were capped at 200 for summer trawl and pot surveys and 100 for the other data to avoid overweighting the data with a large sample size (Fournier and Archibald 1982). Weighting factors represent prior assumptions about the accuracy or the variances of the observed data or random variables. WR was set to be 0.01.

To reduce the number of parameters, we assumed that length and shell compositions from the first year (1976) summer trawl survey data approximated the true relative compositions. Abundances by length and shell condition in all other years were computed recursively from abundances by length and shell condition in the first year and by annual recruitment, catch, and model parameters. Initial parameter estimates were an educated guess based on observation

max/)ln( tpM

and current knowledge.

f. Definition of model outputs.

i. Mature Male Biomass (MMB): defined as those 94 mm carapace length and above (size classes 3 to 6). The mean weights for size classes 1-6 are 0.854, 1.210, 1.652, 2.187, 2.825 and 3.697 lbs.

ii. Projected Legal Male Biomass for OFL calculation: defined as the number of crab on July 1st 2012 of size class greater than 94mm (Nsl+Osl), multiplied by commercial pot selectivity(Ssl), proportion of legal crab (Ll), and mean weight lb (wml)

lllsl,sl,sl

wmLSON=BLegal ,,, )(_

iii. Recruitment: the number of males of the length classes 1 and 2.

Appendix B: Estimation of 1976-1991 NMFS and 1996-present trawl survey abundance

1976-1991 NMFS trawl survey abundance

In the indirect method, reported numbers were estimated from published reports and archived memos. Published abundance consisted of 0-100mm, 100-125mm, >125mm, and total for 1976-1979, and 0-90mm, 90-104mm, >104mm, and total for 1985-1991. For 1982, abundance was not reported formally, but estimates were produced for each length classes.

For 1976 – 1979 abundance of ≥74mm crab was estimated by adding abundance of ≥ 100mm and abundance of < 100mm multiplied by the proportion of 74-99mm among crabs of 0-99mm CL.

997410010074 PNNN

Where P74-99 is the proportion of 74-99mm among crabs of 0-99mm CL.

Similarly abundance of ≥74mm crab in 1985-1991 was estimated by adding abundance of ≥ 90mm and abundance of < 90mm multiplied by the proportion of 74-89mm among crabs of 0-89mm CL.

8974909074 PNNN

For 1982 abundance was calculated by summing abundance estimates of >74mm crabs.

CVs of the indirect method were substituted with those calculated from the original raw data.

abundance Proportion Estimated abundance

Year >100mm <100mm 74-99 mm ≥74 mm Data source

1976 3119.8 1171.2 0.939 4219.6 Wolotira et al 1977 1979 762.0 178.7 0.778 901.0 Sample and Wolotira 1985 1982 2325.0 Archived output file 1987

> 90 mm < 90mm 74-89mm 1985 2111.0 1354.0 0.587 2905.8 Stevens and MacIntosh 1986 1988 1607.0 1395.0 0.505 2311.5 Stevens 1989 1991 1771.0 1355.0 0.325 2211.4 Stevens 1992

1976

1979

1982

1985

1988

1991

1996-2011 ADF&G trawl survey abundance

In the ADF&G trawl survey, only one tow was conducted for each station. Second tow was conducted when the first tow caught more than 6 crabs or the first tow was unsuccessful. The survey stations were

Abundance of (CL > 73mm) red king crab at j-th station ( jN ) was estimated as:

j

jjj

a

AnN ^

. (1)

Where nj is the number of (CL > 73mm) crab captured, aj is a towed area computed by multiplying the width of the net mouth opening (0.00658 nmi) with the distance trawled (generally around 1.0 nmi), and Aj is an area of station (generally 100nmi2). Surveyed stations were stratified into single-towed and multiple-towed stations. For single-towed stations, the total crab abundance, sN , was estimated as the sum of estimated

station abundances:

^^ j

js NN . (2)

The variance of sN^

was estimated as:

1

)ˆˆ()

^(

2

n

NNnNV jj

s (3)

where n was the number of stations trawled.

For multiple-towed stations, stratum r, crab abundance per station, )(^

rjN , was estimated as the average abundance of tows for station j:

jrj NN ˆ^)(

. (4)

Total crab abundance for stratum r, ^

rN was estimated as the sum of estimated station abundances:

j

rjr NN )(ˆ^ . (5)

The variance of rN^

was estimated as:

)ˆ(^

)( )(j

rjr NVNV , (6)

where

1

)ˆˆ()

^(V

2)(

)(

n

NNnN rjj

rj

, (7)

where n was the number of tows at station j, and assuming independent estimates for each station. Total abundance of red king crab was a sum of abundance estimates for the 2 strata:

rs NNN^^^ .

(8)

Assuming independent estimates for the 2 strata, the variance of the estimated total red king crab abundance was estimated as:

)ˆ()ˆ(^

)( rs NVNVNV . (9)

Re-estimation 1976-1991 NMFS trawl survey data:

Under the direction of the CPT workshop, re-estimation of 1976-1991 trawl survey was directed. Despite both NMFS and ADF&G used identical survey data, re-estimated crab abundance differed considerably between ADF&G (using method above), and MMFS re-estimates. Overall, AD&G re-estimates are closer to original NMFS report, whereas NMFS re-estimate showed higher estimates for 1979, 1982, 1988, and 1991. At the moment of current assessment period, these discrepancies have not been resolved, and further investigations are needed. Under this circumstance, we elected to use ad hoc estimates of crab abundance from the original published report with CV of NMFS re-estimate.

Estimated Total Crab male abundance.

Year NMFS Report

NMFS Re-estimate

ADF&G Re-estimate

1976 4291.0 4343.0 4214.81979 940.6 1584.6 1153.71982 4065.0 9269.6 3487.01985 3465.0 2637.1 2758.61988 3002.0 5888.0 3029.91991 3126.0 4464.5 3116.5

Estimated Crab male abundance (CL > 74mm).

Current NMFS Re-estimate ADF&G Re-estimate Year Assessment Abundance CV Abundance CV

1976 4219.6 4247.5 0.31 4119.5 0.321979 901.0 1417.2 0.20 1007.8 0.251982 2325.0 5583.5 0.29 2107.7 0.251985 2905.8 2306.3 0.25 2411.9 0.271988 2311.5 4526.7 0.29 2336.5 0.301991 2211.4 3132.5 0.43 2200.0 0.35

Appendix C: Reconstruction of ADF&G Summer pot survey abundance

In the indirect method, reported numbers were estimated from published reports Brannian (1988)

The proportion of length class was estimated form original trawl length frequency data.

For 1980 – 1982 abundance, only legal crab abundance was available. Abundance of ≥74mm crab was estimated by expanding abundance of legal crab with the ratio of ≥74mm crab to legal crab, as follows

legal

sulegallegallegal P

PPNN 74,

74

Where Plegal is the proportion of legal crab and Psublegal,>74 is the proportion of sublegal crab of ≥74mm CL.

For 1985 abundance, abundance of both legal and sublegal crab was available. Hence, abundance of ≥74mm crab was estimated as

7474 PsNNN sublegallegal

where Ps>74 is the proportion of crab of ≥74mm CL among sublegal crab.

Estimated abundance of 1985 ≥74mm crab using the first method was reasonably closer.

Since CV of the pot survey were missing (1980-1982) or too small (1985), we employed cv = 0.34 that was an average CV of trawl survey

Abundance Proportion

Year Sublegal Legal Legal Sublegal >74mm

>74mm: Legal ratio

Estimated Abundance

1980 NA 1900.000 0.88 0.09 1.10 2092.303 1981 NA 1285.195 0.53 0.36 1.68 2153.407 1982 NA 353.273 0.28 0.64 3.23 1140.582 1985 1600.668 907.579 0.88 2320.381

0.43 0.50 2.16 1960.449

Appendix D1: Likelihood profile Analyses

The assumptions of high mortality and low trawl selectivity of the length class 6 (M=0.64) was intended to improve the model fit under the assumption of M= 0.18. At the reasonable range of M 0.1 – 0.5, total likelihood was minimized at M = 0.3-0.36, as well as commercial cpue, trawl length proportion, recruits. On the other hand, likelihood of trawl survey and winter pot survey was minimized at 0.22-0.26 range. Based on those results we assess M =0.24 and M =0.3 as an alternative model scenario.

Figure D1: weight sensitivity M changed 0.1 to 0.5 (x-axis) and corresponding likelihood components.

Appendix D2: Alternative Model Scenario Selection

For 2013 Assessment, we examined following model scenarios. All the model scenarios are in direct response to the CPT modeling workshop and SSC comments 2012.

0. Baseline 2013 model: Use standardized CPUE data, unrestricted net/pot selectivity functions, estimate of first year length composition

1: drop summer pot abundance & length comp data 2: drop CPUE data 3: estimate q of NMFS trawl surveys (1976-1991) 4: estimate q of ADF&G trawl surveys (1996-2011) 5: reduce length maximum n to 20 6: change M to 0.24

0.2 0.3 0.4 0.5

8090

100

110

Total negative log likelihood

0.2 0.3 0.4 0.5

1012

1416

Trawl survey

0.2 0.3 0.4 0.5

1.2

1.6

2.0

Pot survey

0.2 0.3 0.4 0.5

-16.

5-1

5.5

Commercial cpue

0.2 0.3 0.4 0.5

46

810

12

Trawl size

0.2 0.3 0.4 0.5

56

78

910

Summer Pot size

0.2 0.3 0.4 0.5

2527

2931

Winter Pot size

0.2 0.3 0.4 0.5

3035

4045

Summer Commercial size

0.2 0.3 0.4 0.5

0.3

0.4

0.5

0.6

recruits

0.2 0.3 0.4 0.5

11.5

12.5

13.5

14.5

Observer size

0.2 0.3 0.4 0.5

01

23

45

67

Total negative log likelihood

Trawl surveyCommercial cpueTrawl sizeWinter Pot sizeSummer Commercial sizerecruitsObserver size

7: change M to 0.30

Rationales

Scenario 1: Drop summer pot abundance and length composition data Scenario 2: Drop standardized CPUE data At the workshop, validity of input data was discussed, especially regarding to summer pot survey abundance data and standardized commercial crab catch CPUE. The scenario 1 and 2 examine the influence of those data on overall model fits.

Scenario 3: Estimate q of NMFS trawl surveys (1976-1991) Scenario 4: Estimate q of ADF&G trawl surveys (1996-2011) The model assumes that the trawl survey q be 1.0, validity of which was questioned. Especially, because survey coverage of NMFS surveys were generally larger than that of ADF&G (See Appendix E), validity of q = 1 for ADF&G survey was questioned.

Scenario 5: Reduce maximum sample size to 20 The 2012 assessment model lowered maximum sample size from 200 to 50; however, because the model did not fit well in earlier trawl abundance data and the majority of assessment data are length composition, further reduction of sample size was suggested. Scenario 6: Change M to 0.24 Scenario 7: Change M to 0.30 The 2012 assessment model assumes M = 0.18 for length classes 1-5 and 0.648 (i.e., 3.6 times higher) for the length class 6. This assumption was not based on biological evidence but rather an attempt to fit the model to data. CPT and SSC requested to review this assumption by conducting a likelihood profile analyses. Likelihood profile analyses (Appendix D) showed alternative M of 0.24 and 0.30 as candidate. Table 1. Alternative model configurations. Blank cell means that model configuration is the same as base model

Alt Summer

Pot survey

CPUE Q

NOAA Q

ADF&G

Max N

M

Base + + 1 1 50 0.18 S1-1 - S1-2 - S1-3 est S1-4 est S1-5 20 S1-6 0.24

S1-7 0.30 S2-1 - - S2-2 - est S2-3 - 20 S2-4 - 0.24 S2-5 - 0.30 S3-1 - est 20 S3-2 - est 0.24 S3-3 - est 0.30 S3-4 - 20 0.24 S3-5 - 20 0.30 S3-6 - est 20 0.24 S3-7 - est 20 0.30 S4-1 - - 20 S4-2 - - 20 0.24 S4-3 - - 20 0.30 S4-4 - - est S4-5 - - est 20 S4-6 - - est 20 0.24 S4-7 - - est 20 0.30

+: included, -: excluded, est: estimated. Among the seven alternative scenarios, scenarios S1-1, S1-3, S1-5, and S1-6 resulted in better fit to the trawl data. Removal of summer pot survey data and subsequent improvement of trawl abundance (TR) and length (TRL) data suggests data conflicts in length composition data between trawl and pot surveys. Estimating NMFS survey q (S1-3) resulted in estimate of q < 1, or that historical NMFS survey underestimated crab abundance. This may be caused by the fact that NMFS survey was conducted after the majority of fishery (though survey timing was incorporated in the model), or that NMFS trawl gear may not be as efficient as ADF&G trawl gear. Also, as expected, reduction of the maximum sample size (S1-5) increased fit of trawls abundance and CPUE. Changing M = 0.24 (S1-6) improved fit of trawl abundance, but this increased conflicts for summer commercial catch data. For other scenarios, removing CPUE data (S1-2) resulted lower fit of trawl data, and estimate of q for ADF&G (S1-4) resulted greater than 1 or that ADF&G trawl surveys overestimated crab abundance. Because this is unlikely, we dropped this scenario for further consideration. Finally, changing M=0.3 (S1-7) did not particularly improve fit of individual component; however, it had the best overall fit. Among each likelihood components, catch length composition (WPL, SCL, OBL) were not affected by choices of scenarios, except when M was fixed for all size classes (S1-6, S1-7). The other characteristics of constant M is an elimination of high recruits in 1976 and low molting probability that indicates slow growth (Figures ). Because the Norton Sound Red King crab is the northern most population, it is reasonable to assume that their growth rate is slower and their mortality is higher than those of southern population (e.g. Bristol Bay red king crab). Retrospective analyses showed that constant M scenario had better estimates. Overall, all model scenarios considered did not change fits of length composition, but resulted in improvement in fit of trawl survey data, especially on historical (1976-1991) trawl survey data. However, prospective analyses showed all model scenarios resulted in consistent and similar projected estimates. This suggests that majority of model improvements are made for fit of historical trawl data; however, those improvements had little impacts on fitting of recent (1996-2012) data. As for

differences of model scenarios on prediction bias and error, retrospective analyses suggests that constant M (M=0.24, 0.30) and removing CPUE seem to reduce bias/error. Considering all those above factors, we selected S3-1, S3-6, S3-7 as a candidate model.

Table 2. Likelihood components of alternative model scenarios. Bold type number show likelihood value 2 units lower than baseline or among the scenario groups.

LL TR SP CPUE TRL SPL WPL SCL RE OBL Mean bias

Mean error

Projected Legal abundance

Base 77.87 11.41 0.99 -16.29 3.94 5.38 27.35 32.31 0.29 12.38 0.150 0.146 1612.59 (43.2) S1-1 69.87 9.94 -17.33 2.44 27.91 33.68 0.33 12.70 0.111 0.107 1616.28 (42.3) S1-2 96.65 12.32 0.86 3.21 4.73 26.74 32.18 0.28 12.32 0.128 0.145 1618.62 (33.9) S1-3 76.54 9.53 1.48 -16.65 5.34 5.34 27.50 32.54 0.28 12.60 0.109 0.103 1604.44 (37.1) S1-4 76.62 11.83 0.99 -15.26 3.40 4.89 26.47 32.52 0.28 12.50 0.346 0.303 896.05 (84.2) S1-5 28.22 9.42 1.32 -18.78 1.70 2.91 12.66 13.64 0.29 5.06 0.120 0.100 1599.86 (32.8) S1-6 79.77 9.50 1.44 -16.37 3.50 7.42 25.10 36.89 0.36 11.91 0.080 0.077 1552.10 (24.1) S1-7 74.65 10.00 1.32 -16.73 2.61 6.27 25.26 34.04 0.28 11.60 0.033 0.030 1443.88 (20.7) S2-1 85.33 10.66 1.47 27.27 33.07 0.34 12.52 0.108 0.123 1601.80 (17.8) S2-2 68.09 8.06 -17.47 2.63 27.92 33.65 0.33 12.97 0.100 0.090 1641.35 (27.4) S2-3 22.70 7.73 -19.50 1.00 13.02 14.94 0.32 5.18 0.101 0.084 1615.37 (34.3) S2-4 68.46 8.75 -17.47 1.47 24.99 36.85 0.38 12.15 0.066 0.064 1531.82 (21.2) S2-5 64.71 9.18 -17.47 0.33 26.13 34.48 0.30 11.76 0.014 0.009 1428.33 (16.5) S3-1 20.78 5.95 -19.29 1.01 12.93 14.66 0.32 5.38 0.061 0.040 1618.64 (39.7) S3-2 68.28 8.38 -17.16 1.56 25.89 37.00 0.39 12.24 0.059 0.057 1567.40 (38.9) S3-3 63.38 7.74 -17.43 0.35 25.70 37.74 0.31 11.96 -0.013 -0.020 1439.31 (14.6) S3-4 21.78 6.56 -18.88 0.74 11.65 16.24 0.38 5.08 0.038 0.027 1564.09 (8.8) S3-5 20.31 7.01 -19.36 0.16 12.00 15.28 0.31 4.89 0.005 -0.009 1481.51 (13.7) S3-6 21.45 6.09 -18.78 0.83 11.54 16.21 0.39 5.17 0.026 0.013 1575.77 (38.8) S3-7 19.00 5.71 -19.13 0.20 11.70 15.15 0.33 5.05 -0.022 -0.043 1482.58 (21.8) S4-1 40.38 7.70 0.65 11.84 14.72 0.33 5.14 0.051 0.065 1622.18 (29.8) S4-2 39.24 6.56 0.28 11.18 15.85 0.38 4.99 -0.006 0.007 1566.98 (34.7) S4-3 37.96 6.91 0.22 11.27 14.90 0.31 4.78 -0.037 -0.026 1467.91 (33.4) S4-4 83.58 7.82 1.67 27.36 33.53 0.33 12.86 0.008 0.091 1624.54 (37.5) S4-5 37.98 4.64 1.03 11.73 14.80 0.33 5.45 0.014 0.022 1624.50 (27.7) S4-6 38.39 5.24 0.46 11.12 16.07 0.40 5.10 -0.027 -0.018 1566.98 (34.7) S4-7 35.83 4.35 0.06 10.83 15.25 0.33 5.01 -0.142 -0.147 1467.91 (33.4)

1975 1980 1985 1990 1995 2000 2005 2010

02

46

8

Year

To

tal C

rab

Ab

un

da

nce

(m

illio

n)

BASES1-1S1-2S1-3S1-4S1-5S1-6S1-7


1975 1980 1985 1990 1995 2000 2005 2010

02

46

8

Year

To

tal C

rab

Ab

un

da

nce

(m

illio

n)

BASES2-1S2-2S2-3S2-4S2-5


1975 1980 1985 1990 1995 2000 2005 2010

02

46

8

Year

To

tal C

rab

Ab

un

da

nce

(m

illio

n)

BASES4-1S4-2S4-3S4-4S4-5S4-6S4-7


Appendix E: Trawl Survey Location and CPUE. Larger circle indicate higher CPUE. The smallest dots indicate 0 CPUE.

1976 1979 1982

1985 1988 1991

1996 1999 2002

2006 2008 2010

2011

Appendix : Summer Commercial Catch locations 1977 1978 1979

1980 1981 1982

1983 1984 1985

1986 1987 1988

1989 1990 1992

1993 1994 1995

1996 1997 1998

1999 2000 2001

2002 2003 2004

2005 2006 2007

2008 2009 2010

2011 2012 2013

2005 2006 2007

2008 2009 2010

2011 2012 2013

SummaryReport:NortonSoundRedKingCrabCPUE

Standardization

Gretchen Bishop,

M.S.M. Siddeek,

Jie Zheng, and

Toshihide Hamazaki

Alaska Department of Fish and Game

Division of Commercial Fisheries

P.O. Box 115526; Juneau, Alaska 99811-5526

[email protected]; [email protected]; [email protected];

[email protected]

Report prepared for Crab Plan Team Meeting: April 30, 2013

Abstract

Although summer commercial fishery CPUE data is currently used in stock assessment for the red king

crab fishery in Norton Sound, changes in vessel size, fishery timing, and harvest location over the 34-year

history of the fishery compromise the utility of CPUE data as an index of population size. We used

generalized linear modeling with lognormal distribution to standardize this data. We modeled the

relationship between the natural log of CPUE in numbers as a function of Year, Modified Statistical Area,

Week of Year, Vessel Length Overall, and Permit Fishery to produce standardized CPUE indices for the

Norton Sound red king crab fishery 1977–1992 and 1993–2012 time series. For the 1977–1992 time

series, standardized CPUE showed little difference from arithmetic CPUE while for the 1993–2012 series,

standardized CPUE was greater than arithmetic CPUE before but less than after 2003. However,

standardized CPUE was no less variable than arithmetic CPUE, and only a slightly better predictor of

biomass estimates. The real test of the utility of standardized CPUE indices will be if their incorporation

into the stock synthesis model reduces bias and variability of crab population estimates. Given that this is

a first generation effort to standardize these indices, we suggest ways to refine the model by incorporating

Norton Sound red king crab CPUE standardization

2

additional explanatory variables and interactions. We also suggest that data collection be expanded to

include pot size and soak time and that interactions be incorporated through the use of GLMM.

Introduction

The necessity of utilizing fishery-dependent data and the tendency for fishermen to constantly improve

their methods is not unique to Norton Sound. Data-poor or “difficult to assess” fisheries which have

experienced large management changes that confound interpretation of fishery CPUE data abound

worldwide. Stock assessment scientists working on data-poor fisheries have pioneered methods to

standardize CPUE data; the most common is generalized linear modeling, or GLM (Maunder and Punt

2004). This method involves linking CPUE data with an assumed distribution to a suite of explanatory

variables with a link function that serves to linearize the relationship, most commonly a log link; or in

other words, modeling the natural log of CPUE as a function of a linear combination of a suite of

explanatory variables (Quinn 1987). The method is commonly employed for tuna (Punsley and Nakano

1992; Rodríguez-Marín 2003; Tsou and Yeh 1991) and several other fisheries without fishery-

independent surveys, but invertebrate fisheries, with their lack of age data, are a prime candidate. One

example of an application is the CPUE standardization used for the rock lobster fishery in New Zealand

(Maunder and Starr 1995; Starr 2012). The Norton Sound red king crab fishery is thought to be a good

candidate for CPUE standardization for many of these same reasons.

Gathering information for stock assessment of the red king crab fishery in Norton Sound entails several

challenges. Its location, away from major population centers and in the Arctic, makes stock assessment

work expensive and difficult, which has resulted in inconsistent and variable fishery-independent survey

data collection. Trawl surveys have been conducted only approximately triennially (Soong 2008; Soong

and Hamazaki 2012), and were supplemented by four pot surveys conducted from 1980 through 1985

(Hamazaki and Zheng 2011). The fact that there are three different fisheries for red king crab in Norton

Sound, each with distinct user groups, methods, fishing areas, and seasons, renders harvest and effort data

more variable. A winter subsistence fishery has long been operated by dropping pots through holes in

shorefast shelf ice offshore Nome from January through April and requires a harvest permit (Lean and

Brennan 1996). There is also a winter commercial fishery from November 15 through May 15 which

employs similar methods. The summer commercial fishery, which began in 1977 (Menard et al. 2012)

occurs in the open waters of Norton Sound from June 15 through September 30, but primarily in July and

August. These challenges combine to render the fishery somewhat data-poor.


3

In addition to being data-poor, this fishery has undergone many management changes (Table 2), some,

but not all, of which we have data to describe. The most notable management changes have been to pot

limits, vessel size, season timing (Month of Year, Week of Year), statistical area distribution of harvest

(Modified Statistical Area), and fishery permit structure (Permit Fishery). The vessel pot limit was

reduced in 1993 from 100 to 40 for vessels less than 125 ft or 50 for vessels greater than 125 ft in length.

Reductions in pot limit are usually associated with shortened soak time, as vessels adjust their fishing

strategy to maintain catch levels (Johnson 1985; Briand et al. 2001). Soak time affects pot CPUE and pots

have an optimal soak time above or below which CPUE is reduced (Zhou and Shirley 1997; Pengilly and

Tracy 1998; Briand et al. 2001). We have no data on soak time, however. Vessel size was effectively

reduced in 1994 when the fishery was designated superexclusive, prohibiting vessels fishing Norton

Sound from participating in other red king crab fisheries during the same season. Vessel size affects

CPUE positively, as larger boats can fish in stormier weather with less competition and pull larger pots.

Although smaller vessels often fish smaller pots, we have no data on pot size. The season timing has

moved progressively earlier; the start date changed first from August 1 to July 1 in 1993, and then from

July 1 to June 15 in 2002 (Appendix A1). Season timing influences crab CPUE in several ways, first

through crab distribution, as crab move offshore out of the the closed area and become available to the

fleet late in the summer season (Powell et al. 1983), and second through their behavior, as crab

catchability is reduced before and after the molt for most species (Miller 1990). Molting of red king crab

in Norton Sound occurs in September (Stevens and Macintosh 1986) for legal male red king crab in

Norton Sound. These factors act in opposite ways on crab CPUE, movement suggests CPUE should be

higher for later start dates while proximity to molt timing would dictate a decrease at the end of the

season. Fishing does not always begin immediately upon season start date, particularly since the start date

has been moved earlier in recent years. The summer fishery start date has been influenced by herring

fishery timing, and crab market conditions (Menard et al. 2012). Finally, there has been a large

southeasterly shift in the Modified Statistical Area distribution of the summer fishery harvest in Norton

Sound (Figures 1 and 2). As discussed above, this change in harvest distribution coincided with an earlier

season start and decreased vessel size. Together, these large management changes have degraded the

utility of CPUE as an index of population size.

Although the biggest management changes occurred in 1993 and 1994, additional smaller changes

continued thereafter, and some of these also affect crab CPUE. New permit types with different

management regimes were created in 1998, with the establishment of a Community Development Quota

(CDQ) program (CDQ are distinct harvest quotas allocated to local communities and designed to provide


4

economic benefits by assuring their ability to participate in the fishing industry.). The first CDQ fishery

was conducted in 2000. Permit type affects CPUE in several ways; there are separate permit types for

vessel sizes greater or less than 60 ft, and for CDQ fisheries (Appendix A3). CDQ permit types have

separate GHLs and sometimes, but not always, separate season timing. In 2002, the Alaska Board of

Fisheries (BOF) adjusted start dates for the CDQ fishery from after to concurrent with the open access

fishery and established a second “clean-up” CDQ season, these actions should have increased CPUE for

CDQ permit type by providing fishing opportunity before removal of most of the GHL and exclusive

access after the regular season. Also in 2002, processors stopped buying crabs with carapace width (CW)

smaller than 5 in, although the legal size limit remained 4 ¾-in CW, this effectively reduced the saleable

population size and hence reduced CPUE; however, we have not included a variable for size limit in the

current analysis. The changes to section boundaries and closed waters in 2006 and 2010 don’t impact

areas of crab aggregation and are thus unlikely to have affected crab CPUE. Insufficient information is

available to assess the impact of the 2008 BOF adoption of an escape ring or escape mesh requirement.

Depending on crab density, pot configuration and escape ring size relative to crab legal size, escape rings

can either increase CPUE through reducing gear saturation (Miller 1977), or reduce CPUE by allowing

legal crabs to escape. For these reasons, we have not included a variable for escape rings. Several

adjustments to harvest strategy (a reduction in threshold and increase in harvest rate) were made in 2012

(Howard and Hamazaki 2012), and might affect CPUE. These smaller, post-1994 management changes

further obfuscate the use of CPUE data as an index of abundance, we have included some, but additional

explanatory variables may be required in the future.

Despite the dubious quality of summer fishery CPUE data, the data-poor nature of the Norton Sound red

king crab fishery has made it necessary to utilize fishery-dependent data in addition to survey data for

stock assessment. In all, nine types of data are used for stock assessment: 1) triennial summer trawl

survey population estimates, 2) occasional summer pot survey population estimates, 3) winter pot survey

size and shell condition, 4) summer preseason survey size and shell condition, 5) summer observer

program bycatch size and shell composition, 6) summer commercial fishery CPUE and size and shell

composition, 7) winter commercial fishery harvest, 8) winter subsistence fishery harvest, and 9) tagging

growth data (Hamazaki and Zheng 2011). These data are input to a length-based stock synthesis model

(Zheng et al. 1998) to produce legal biomass estimates. The patchwork nature of stock assessment data

for this fishery gives summer commercial fishery CPUE data an unusually important role as the “glue,”

unifying disparate data units of variable quality. Summer commercial fishery CPUE data is able to

perform this function because it is annually collected, spatially extensive, abundant data.


5

Thus, the primary objective of this analysis was to review the utility of standardizing Norton Sound

summer red king crab fishery CPUE data to eliminate variability associated with changes in crab

catchability induced by changes in fishing methods, management strategy and the environment using

GLM based on the lognormal distribution. Specifically, we modeled the response of CPUE in terms of

number per pot to six predictor variables: Year, Vessel, Permit Fishery, Month of Year, Week of Year, and

Modified Statistical Area. We also investigated the utility of including interactions between these

explanatory variables. The use of standardized Norton Sound red king crab CPUE as input to the stock

synthesis model to estimate population size is being investigated.

A secondary objective was to review data currently collected by management and make recommendations

for future data collection protocols.

Methods

Preliminarydataprocessing

The primary unit of commercial fishery harvest data in the State of Alaska is a fish ticket. Fish tickets are

a legal document, required by Alaska Administrative Code [5 AAC 39.130] for each delivery and sale of

fish or invertebrates by a commercial permit holder to a processor. Fish tickets must contain certain

variables, the nine fish ticket variables important to this analysis are: Landing Date, Fish Ticket Number,

Vessel ADF&G Number, Permit Fishery, Statistical Area(s) fished, Pounds of Crab, Number of Crab,

Delivery Code, and Effort (Table 3). A fish ticket record may consist of only a single line of data if only

one Statistical Area was fished and no harvest was retained for personal use or of multiple lines of data if

several Statistical Areas were fished and crabs were retained for personal use as well as delivered for

commercial sale. The primary, and thus most accurate, unit of measure on a fish ticket is pounds, as this is

the basis of the payment to the permit holder.

Three main problems with fish ticket harvest data were addressed in preliminary data processing: a need

to combine personal use and commercial harvest (because personal use harvest generally did not have

associated Effort), Effort missing for other reasons, Number of Crab missing, and Number of Crab

inaccurate. First, to combine harvest retained for personal use with commercial harvest, we summarized

data by Year, Fish Ticket Number, and Statistical Area. Second, all records with missing Effort values

were deleted. (Respectively n=118, 12.8% for 1977–1992, and n=1282, 19.7% for 1993–2012 were


6

missing.) Third, all records with Number of Crab missing (respectively n=8, 1.0% for 1977–1992, and

n=6, 0.1% for 1993–2012) were deleted. Fourth, records with Number of Crab inaccurate were deleted.

To determine when Number of Crab was inaccurate, we created a new variable, Mean Crab Weight. We

then calculated the 2nd and 98th quartiles of Mean Crab Weight, and deleted records for which Mean Crab

Weight was outside the 2nd and 98th quartile range. This was respectively n=32, 4.0% for 1977–1992, and

n=210, 4.0% for 1993–2012.

In addition to the above, we computed several new variables to the harvest data set. The first was the

response variable Catch per Unit Effort (CPUE), which was computed as Number of Crab divided by

Effort in terms of pot lifts for each Fish Ticket Number and Statistical Area. CPUE was log-transformed

to normalize the distribution. To describe changes in season timing, we created variables for Month of

Year (MOY) and Week of Year (WOY) from Landing Date. In order to improve the design matrix, we

grouped the 25 Statistical Areas into Modified Statistical Area (MSA) with four levels (Figure 1,

Appendix A4).

The final set of model input variables included the single response variable, CPUE in terms of number per

pot, and six explanatory variables: Year, Vessel, Permit Fishery, Month of Year, Week of Year, and

Modified Statistical Area. Variables were selected for specific purposes. Year in the data set was

measured from January 1 to December 31 and included the 36-year time series 1977–2012. Because of

the extensive management changes, we were unsure of being able to effectively standardize the complete

time series. For this reason, two discrete time series were modeled: before (1977–1992) and after (1993–

2012) the large change in management regime that occurred in 1993. Year is a proxy for recruitment

strength and its inclusion in the model was mandatory as it was necessary to extract annual indices of

abundance. There are 119 Vessel levels in the 1977–1992, and 131 in the 1993–2012 time series. The

predictive ability of Vessel is a function of size, horse power, skipper, seaworthiness, and electronics.

There are 6 levels of Permit Fishery (Appendix A3). Permit Fishery is useful because of its unique vessel

and management characteristics such as vessel size, and season timing and duration. There are 4 Month of

Year factor levels, June through September, and 16 Week of Year factor levels, ranging from the second

week in June through the fourth week in September. Except for the first and last Week of Year, weeks are

seven days in length, beginning on Sunday and ending on Saturday, and overlap months. The predictive

abilities of Month of Year and Week of Year are a function of molt timing, crab distribution, and

cumulative fishery removals. Modified Statistical Area is important because the clumped distribution of


7

red king crab (Dew 1990) strongly influenced by habitat preferences and life history events, means that

CPUE is highly spatially variable.

Since many vessels had only a few years or a few deliveries, we limited the data to a subset of those

vessels having long-term records. To do this, we investigated different arbitrarily selected data subset

criteria. For 1977–1992, this consisted of twelve subsets of vessels having a minimum of two, three, five,

or seven deliveries over a minimum of three, five, or seven years, while for the 1993–2012 time series it

consisted of nine subsets of vessels having a minimum of three, five, or seven deliveries over a minimum

of three, five, or seven years. The number of vessels or pounds of harvest included in the data subset

declined with increasingly stringent selection criteria (Appendices B1 and B2). Data subsets included

from 0 to 63 vessels and 0.0% to 89.4% of the harvest over the respective time series (Appendix B1 and

B2 and Appendix A2). We selected the criteria of a minimum of two deliveries for three years for 1977–

1992 because stricter criteria contained unacceptably small proportions of harvest. For the 1993–2012

time series we were able to investigate subsets of vessels having three deliveries over three, five, or seven

years as all of these subsets contained substantial proportions of the harvest (Appendix A2).

After selecting subset criteria, we compared the CPUE of data subsets to the whole using Z-tests to

understand the effects of subsetting the data (Appendix B3). We also examined the spatial distribution of

effort for data included and not included in subsets using two-way contingency tables (Appendices A5–

A8). Next, we determined the significance of the contingency table by calculating the Chi-square statistic

(Zar 1996). Significance of cell-specific differences in expected values was not determined. The strength

of the contingency table association was determined by calculating Cramers V (Zar 1996). Examination

of these subsets showed that for the 1977–1992 time series even the most inclusive criteria of two years

with three deliveries reduced the harvest included to only 29.2% of the total (Appendix A2). In contrast,

for the 1993–2012 time series, the criteria of three deliveries over three, five, or seven years included

59.0–88.0% of the harvest (Appendix A2).

For each time series, exploratory analyses of the single response and six explanatory variables were

conducted. First, pairwise scatter plots, Spearman’s rank correlation coefficient (Zar 1996) (Spearman’s

rho––a non-parametric measure of statistical dependence), and frequency histograms were plotted to

evaluate collinearity between explanatory variables, strength and linearity of relationships between

response and explanatory variables, and normality of distributions. Note that although Spearman’s rho is

appropriate only for continuous and ordinal numeric variables, R nonetheless calculates it for strictly


8

categorical variables (Vessel, Permit Fishery, and Modified Statistical Area) as well; these results must be

disregarded. Second, Akaike Information Criterion (AIC) (Akaike 1974) were calculated for pairwise

relationships of the response with each explanatory variable to assess their relative predictive ability.

Theoryandequations

Let denote the observed CPUE, U0 the reference CPUE, Pij a factor i at level j, and let Xij take a value

of 1 when the jth level of the factor Pij is present and 0 when it is not. If observation error ijk, of k is

normally distributed with mean 0 and standard deviation σ, then the lognormal distribution of (Quinn

and Deriso 1999), can be denoted as:

∏ ∏ , (1)

or

ln ln ∑ ∑ ln .

By substituting ln to β0 and ln(Pij ) to βij, we then obtain an additive GLM lognormal error

distribution of :

ln ∑ ∑ . (2)

For selection of the best model, we used a forward step-wise selection procedure. After selection of the

best model, we calculate standardized CPUE. To do this we first divide coefficients by their geometric

mean to obtain canonical coefficients:

. (3)

We then exponentiate the result to obtain the non-log space canonical coefficients:

. (4)


9

Finally, we subtract the year coefficient reference level to obtain standardized CPUE Uj for each year

level j as:

. (5)

Eliminating all factors but Year in the GLM, but otherwise following Equations 2 and 3, 4, and 5 above

gives an estimate of the base year CPUE index.

If we let denote the catch and the effort, in pot lifts, for each delivery i in year y, then the

arithmetic CPUE can be calculated as:

∑

∑ , (6)

the geometric mean of the arithmetic CPUE as:

∏ , (7)

and the scaled arithmetic CPUE for each year level j as:

′ . (8)

Analyses

A forward stepwise GLM fitting algorithm was used to select explanatory variables from the full variable

set to the model. We assumed the null model to include only Year, and the full variable set to include the

six factor variables: Year, Vessel, Permit Fishery, Month of Year, and Modified Statistical Area and Week

of Year. First, a GLM was fit for each explanatory variable against the natural log of CPUE and an AIC

generated for the fit. The explanatory variable whose fit produced the lowest AIC was then added to the

model. This was repeated, accumulating explanatory variables and increasing the model degrees of

freedom until the increase in R2 for the final iteration was less than 0.01.


10

Several approaches to dealing with interactions have been used in fitting GLMs designed to produce

annual estimates of standardized fishery CPUE. The first and most common is to ignore interactions

altogether (Starr 2012; Vignaux 1994), a second is to include interactions in the selection process, but to

sequentially remove variables which exhibit strong interactions with Year and re-run the selection process

(Zuur et al. 2010). A third approach is to average CPUE over the interacting variable (Maunder and Punt

2004), and finally, if it is thought that random processes are responsible for the interaction, interactions

with Year can be included as random terms in a generalized linear mixed model (GLMM) (Maunder and

Punt 2004). In this analysis the first approach was taken. However, for the preferred models only, a two-

stage process was used to determine the necessity of including interactions in future improved models.

The first stage consisted of the stepwise variable selection described above and the second stage of

offering the variables selected in the first stage to the stepwise selection process along with their second-

order interactions.

After the GLM was fitted, generalized variance inflation factors (GVIF) (Faraway 2006) were calculated

for preferred models. GVIF indicate the degree to which variance of model parameter estimates is being

inflated as a result of multicollinearity. A threshold of GVIF > 3 was used to decide when to remove

multicollinear variables from the model.

Diagnostics were conducted (for models without interactions only) to check assumptions, look for

outliers, and check model choice. First, Pearson residuals were plotted against each variable in or out of

the model to assess independence of observations. Second, residuals were plotted against the linear

predictor to assess homogeneity of variance and goodness of fit of the model. Thirdly, a QQ plot was

made to test the assumption of normal distribution of residuals. QQ plots are constructed by plotting

residuals against their theoretical computed value if they were normally distributed, and should coincide

with or be parallel to the line y = x. Plots were constructed to allow graphic examination of interaction of

each explanatory variable with Year. Component + Residual plots were constructed to show the

independent influence of each explanatory variable on CPUE. Finally, four plots were made to detect

influential outliers. First hat values, DFFits, and Cooks distance (Faraway 2006) were plotted versus fitted

values and then studentized residuals were plotted against hat values, where data point diameter is

proportional to Cooks Distance.

Finally, interannual trends in standardized, base year, and scaled arithmetic CPUE were plotted.


11

We coded in the open-source programming language R to process data, and used two R scripts obtained

from Paul Starr for stepwise model selection and CPUE index calculation (Appendix E). R notation is

used in some of the tables and text to describe models.

ChangessinceFebruary2013crabmodelingworkshop

This work was first presented at a Crab Modeling Workshop of the Scientific and Statistical Committee

(SSC) of the Crab Plan Team of the North Pacific Fisheries Management Council in February 2013.

Based upon recommendations by the SSC at this meeting, the following changes have been implemented

in this report.

1.) Previously imputed data for effort and number of crab has been removed.

2.) Data for 1977 has been added.

3.) In order to add 1977 data, it was necessary to remove Commercial Fisheries Entry Commission

(CFEC) data (because this data set begins in 1978). This had provided the variables Owner and

Length Overall. However, this loss was not considered important as these variables are collinear

with Vessel and Vessel has more explanatory power. Furthermore, removing the join to the CFEC

dataset increased the null degrees of freedom as several Vessel had been being eliminated as a

result of having missing Owner data.

4.) We removed the link to Management Data for Season Start Date and ceased calculating the

variable Day of Season based upon SSC recommendation. This variable was also highly collinear

with the stronger Week of Year and had not been selected to the model.

5.) We removed the 1978–2012 time series per SSC recommendation because of excessive

management changes over this time period.

6.) We added more stringent filtering criteria (3 deliveries in 5 years and 3 deliveries in 7 years) for

the 1993–2012 time series.

7.) We included additional diagnostics from the ‘Car’ package including interaction plots,

component plus residual plots, and influence plots. However, we have not as of yet incorporated

the (http://projects.trophia.com/projects/influ/repository/entry/influ.R.) diagnostics package.

8.) We included tables with stepwise selection of second-order interactions for the preferred models.

The next step should be to incorporate significant substantial interactions into the model using

GLMM.

9.) An error in the data subsetting algorithm was corrected resulting in fewer vessels being included

in subsets.


12

Results

Preliminarydataprocessing

The large management change in 1993 resulted in vessels making more and smaller deliveries each year

and in harvest shifting to the southeast (Figure 2). The subset criteria of vessels having two deliveries a

year for three years was chosen for the 1977–1992 time series because more stringent criteria retained

insufficient data for a well-balanced design matrix (Appendix A2, Appendices B1 and B2). For the 1993–

2012 time series, more stringent subset criteria of three deliveries a year for three, five or seven years

could be applied while still retaining a high proportion of the harvest (Appendix A2, Appendices B1 and

B2).

CPUE did not differ from the full data for most subsets of the 1977–1992 time series, but were very

slightly greater for most subsets of the 1993–2012 time series (Appendix B3).

There was no significant effect of subsetting on the statistical area composition of harvest for the 1977–

1992 time series (Appendix A5, Appendix B4). However, for the 1993–2012 time series, subsetting data

resulted in overrepresenting the Inner and underrepresenting the Outer Modified Statistical Area;

however, the strength of the association, measured by Cramers V, was weak (Appendix A6, Appendix

B4).

Scatter plots for the two time series analyzed exhibited many visual patterns among explanatory variables

and a few with the response variable, log(CPUE). For the 1977–1992 time series the most notable

relationships for log(CPUE) are with Year and with Modified Statistical Area; while Year exhibits

patterns of varying strength with all other explanatory variables. It is also evident that Month of Year and

Week of Year are highly collinear and there also appears to be some collinearity of Month of Year and

Week of Year with Modified Statistical Area (Appendix B5). For the 1993–2012 time series the most

notable relationships for log(CPUE) are with Year and Modified Statistical Area; while Year again

exhibits trends with all other explanatory variables. Once again, Month of Year and Week of Year are

highly collinear (Appendix B6). The many covariations with Year are important because they hinder the

ability to unambiguously extract interannual trends in CPUE. Although Spearman’s rank correlation

coefficient (Spearman’s rho) exceeded the “folk lore” threshold of 0.7 (Briand et al. 2004) only for

correlations between Month of Year, and Week of Year, (Appendices B6 and B7), Spearman’s rho is only

a useful of measure of the strength of relationships for continuous (CPUE) and ordinal numeric (Year,


13

Month of Year, and Week of Year) variables. Thus, patterns with Year can only be visually assessed for

categorical variables (Vessel, Permit Fishery, and Modified Statistical Area).

The three variables having the lowest AICs for both data sets consistently included Year and Vessel; the

third variable was respectively, Week of Year for 1977–1992, and Modified Statistical Area for 1993–

2012 (Appendices A7 and A8).

The value of GVIF ^(1/(2*df)) did not exceed a threshold value of three for any of the variables selected

to the model for either time series (Appendices A9 and A10).

Analyses

1977–1992Dataset

When all six variables, but no interactions, were offered to the stepwise selection Year, Vessel, Modified

Statistical Area, and Week of Year were selected, producing an R2 of 0.702 (Tables 4 and 5). Review of

GVIF found no multicollinearity (Appendix A9) and 13 of 31 or 41.9% of model coefficients were

significant (Appendix C1). Offering these variables and their second order interactions to the model

resulted in addition to the above model of the interaction variables Vessel:Week of Year, Year:Week of

Year, Week of Year:Modified Statistical Area, and Year:Modified Statistical Area and an increase in R2 to

0.886 (Tables 4 and 6).

Consistent with the relatively high R2, model diagnostics indicate little departure from normality, no

excessively influential large outliers, independence of observations, and homogeneity of variance

(Figures 3–6). However, some unexplained variation remains in Year, Vessel, and Week of Year. The

interaction plots are roughly parallel. No Cooks Distance exceeding 1.0 were observed so no influential

data points were eliminated (Figures 3–6).

Standardized CPUE deviated little from scaled arithmetic or base year CPUE except in 1978. CPUE

declined from 1978 through 1982, after which it bounced somewhat erratically (Figure 7). Standard errors

are moderate ( = 0.36) (Appendix D1).

1993–2012Dataset

When all six variables, but no interactions, were offered to the stepwise selection procedure Year, Vessel,

Week of Year, and Modified Statistical Area were selected to the model for all three data subsets (Tables


14

4, 7, 8, and 9); however, review of diagnostics revealed residual patterns with Permit Fishery so it was

added. The model R2 was highest for the data subset having three deliveries for three years and lowest for

the subset of three deliveries for seven years (Tables 4, 7, 8, and 9); however, review of diagnostics

(Figures 8–22) revealed that the subset having three deliveries for five years produced the best fit and it

was selected as the preferred model. Review of GVIF found no multicollinearity (Appendix A10) and, 38

of 79 or 48.1% of coefficients were significant (Appendix C2). Offering the selected variables and their

second order interactions to the model resulted in addition to the model of the interaction variables

Year:Vessel, Vessel:Week of Year, and Year:Week of Year, the loss of Modified Statistical Area and an R2

increase to 0.699 (Tables 4 and 10).

Model diagnostics suggest no significant departure from normality, no excessively large and influential

outliers, homogeneous error distribution, and independence of observations (Figures 15–19). Despite the

relatively low R2, there is very little unexplained variability in the residuals. Interaction plots are messy

but largely parallel. There are no data points with Cooks Distances exceeding one, so no outliers were

removed from the model.

In addition to exhibiting the best fit, the standardized CPUE extracted from the preferred model exhibited

the best smoothing (Figures 12, 17, and 22). Standardized CPUE increased modestly over the 1993–2012

time series and was slightly greater than the base year and scaled arithmetic CPUE prior to 2003 and

slightly less after 2003 (Figure 20). Standard errors were very small ( = 0.06) (Appendix D2).

CPUEmeasurecomparisons

Norton Sound summer commercial red king crab fishery standardized CPUE was only slightly more

useful than arithmetic CPUE in predicting trawl survey legal male population size (Table 11). Likewise

there were no differences in the variance of standardized, base year, and scaled arithmetic CPUEs for

either data set: 1977–1992 (Bartlett’s K2 = 0.8161, df = 2, p = 0.665), 1993–2012 (Bartlett’s K2 = 1.2, df =

2, p = 0.542).

Discussion

We were able to successfully fit generalized linear models for two time series, 1977–1992 and 1993–

2012, identifying useful sets of explanatory variables and producing the first standardized indices of

CPUE for the Norton Sound red king crab summer commercial fishery. Although this standardized index


15

was not less variable than the arithmetic index, it was more closely related to trawl survey population

estimates, suggesting that its use will improve the Norton Sound stock synthesis model.

These benefits are somewhat diminished by the presence of significant and substantial interactions of

explanatory variables with Year, most notably of Week of Year, and Vessel. These interaction terms could

not be included in the loglinear generalized linear model, as this would prevent the extraction of

interannual trends in CPUE. The significance of these interaction terms may be a result of missing

explanatory variables. For example, the significance of the Year:Vessel interaction term may be due to

changes in Vessel catchability due to interannual changes in vessel size, pot configuration, soak time, and

electronics. Likewise, the significance of the Year:Week of Year interaction term is likely a result of the

large interannual variation in season start date. Although anecdotal reports suggest the existence of

information on historic pot configuration (Charlie Lean, personal communication, December 13, 2012),

neither pot configuration nor soak time data were available to this analysis. Pot configuration data could

be collected during registration and soak time through mandatory logbooks. Registration forms do not

currently note pot configuration; however, and logbooks are not required in regulation. Changes in

registration forms would require a simple modification of the form and spreadsheet, but any logbook

requirement would need to be promulgated through an action of the BOF, and might be considered

onerous for this small-boat fishery. Another explanatory variable whose addition could be investigated to

improve model fit is the 2002 change in the size of crab accepted by processors. This would simply

require the inclusion of a dummy variable to denote this change.

Besides acquiring additional explanatory variables, interactions might also be dealt with analytically.

Interactions of explanatory variables with year are a common problem in CPUE standardization and other

investigators have solved the problem by averaging CPUE over interacting variables (Maunder and Punt

2004) or by incorporating interactions as a random effects variable in a Generalized Linear Mixed Model

(Brandão et al. 2004; Ortiz and Arocha 2004).

The interaction of Year with Modified Statistical Area for the 1977–1992 data subset is most likely

caused by interannual shifts in harvest distribution. Because red king crab aggregate (Dew 1990; Taggart

et al. 2008), changes in their distribution are often a result of changes in population size. The fact that

historic survey grounds have also contracted (Soong and Hamazaki 2012) supports this hypothesized

explanation. This suggests that there may have been a larger change in population size than what we

currently describe. This question might be addressed either by using a spatially discrete method to


16

standardize CPUE (Campbell 2004; Quinn et al. 1982), or by expanding the survey to include historic

grounds.

In summary, we identified explanatory variable sets, and developed first-generation models to standardize

Norton Sound red king crab summer commercial fishery data. We also identified data needs and analytic

methods to improve the modeling process.

Acknowledgements

We are thankful for conversations with Joyce Soong, Jim Menard, and Jenefer Bell, who provided

valuable insights into the model, survey, biology, and fishery for red king crab in Norton Sound, for

editorial input from Chris Siddon, and for statistical advice from February 2013 Model workshop

members.


17

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Vignaux, M. 1994. Catch per unit effort (CPUE) analysis of west coast South Island Cook Strait spawning hoki fisheries, 1987-93, New Zealand Fisheries Association Research Document #94/11, Wellington, New Zealand.

Zar, J. H. 1996. Biostatistical analysis, Third edition. Simon & Schluster, Upper Saddle River, NJ. Zheng, J., G. Kruse, and L. Fair. 1998. Using multiple data sets to assess red king crab in Norton Sound,

Alaska: length-based stock synthesis. pp. 591-612, In: Fishery Stock Assessment Models. Alaska Sea Grant College Program, AK-SG-98-01, Anchorage.

Zhou, S., and T. C. Shirley. 1997. A model expressing the relationship between catch and soak time for trap fisheries. North American Journal of Fisheries Management. 17: 482-487.

Zuur, A. F., E. N. Ieno, N. J. Walker, A. A. Saveliev, and G. M. Smith. 2010. Mixed Effects Models and Extensions in Ecology with R, First edition. Springer, Breinigsville, PA.

Tables


19

Table 1. Commercial and subsistence harvest (lbs) of red king crab in Norton Sound by fishery, 1977–

2012 seasons.

Year

Commercial

Subsistence

Total Percent summer

Open access CDQ

Winter Summer Summer Winter 1977 517,787 0 517,787 100.0% 1978 33,909 2,089,674 0 25,012 2,141,036 97.7% 1979 a 641 2,931,672 0 448 NA NA 1980 a 75 753,796 0 426 NA NA 1981 1,382,174 0 720 1,379,734 99.9% 1982 a 228,921 0 2,576 NA NA 1983 368,032 0 20,864 390,269 94.3% 1984 387,427 0 22,440 412,007 94.0% 1985 3,042 427,011 0 16,754 446,685 95.6% 1986 5,015 479,463 0 14,104 498,987 96.1% 1987 2,590 327,121 0 11,544 341,265 95.9% 1988 980 236,688 0 5,448 243,199 97.3% 1989 246,487 0 12,252 259,747 94.9% 1990 9,792 192,831 0 24,304 226,200 85.2% 1991 10,064 0 14,732 24,232 0.0% 1992 21,177 63,557 0 23,472 116,196 63.7% 1993 4,926 335,790 0 2,194 342,454 98.1% 1994 17,214 328,905 0 8,226 350,467 93.5% 1995 25 322,676 0 10,852 352,373 91.6% 1996 5,064 223,471 0 3,358 232,034 96.6% 1997 a 210 92,988 0 1,490 NA NA 1998 2,349 29,684 0 17,244 49,388 60.1% 1999 7,041 23,553 0 15,066 45,404 51.9% 2000 7,894 297,654 14,870 11,446 331,583 94.3% 2001 2,943 288,199 512 291,456 98.9% 2002 6,860 244,376 15,226 7,338 273,417 94.9% 2003 16,827 253,284 13,923 8,280 292,620 91.3% 2004 1,293 314,472 26,274 2,362 344,413 98.9% 2005 5,618 370,744 30,060 7,946 414,053 96.8% 2006 a 218 418,851 32,557 2,478 NA NA 2007 8,023 289,264 23,611 21,380 342,278 91.4% 2008 14,843 364,235 30,900 18,970 428,781 92.2% 2009 12,181 369,462 28,125 9,504 419,439 94.8% 2010 12,028 387,304 30,000 14,088 443,420 94.1% 2011 8,669 373,990 26,851 13,280 422,789 94.8% 2012 b NA 441,080 34,910 NA NA NA

a Confidential data; b Current season incomplete


20

Table 2. Timeline of management actions for the Norton Sound summer commercial red king crab fishery

(Hamazaki and Zheng 2011; Menard et al. 2012).

Year Management action

1977 Summer commercial fishery begins.

1991 Fishery closed due to staff constraints.

1992 Pot limit of 100 becomes effective.

1993 Pot limit 40 for vessels <125 ft and to 50 for vessels >125 ft becomes effective.

1994 Norton Sound red king crab superexclusive designation becomes effective.

1996 Vessel moratorium in preparation for Federal license limitation program effective.

1998 Community Development Quota (CDQ) allocation becomes effective.

1999 Guideline Harvest Limit becomes effective.

1999 Alaska Board of Fisheries (BOF) promulgates new management strategy.

2000 North Pacific License Limitation Program (LLP) becomes effective. Vessels exceeding 32 ft in LOA must hold LLP issued by National Marine Fisheries Service (NMFS).

2000 CDQ groups begin to take a portion of summer harvest quota.

2002 BOF adjusts season start dates for CDQ fishery and provides for a second “clean-up” CDQ fishery.

2002 BOF changes closed water boundaries.

2002 Commercially accepted legal crab size changed from ≥ 4 ¾-in to ≥ 5-in CW.

2006 Norton Sound Section expanded but waters of Norton Sound Section above latitude of Cape Prince of Wales closed.

2008 BOF makes 4 ½ -in escape rings or 6 ½ -in stretch mesh mandatory.

2008 BOF changes start date of open access fishery from June 15 to any time on or after June 15, requirement for herring fishery to be completed before crab season starts removed.

2008 BOF changes commercial size limit for blue king crab in Norton Sound from 5 ½ to 5 inches carapace width.

2010 NMFS closes area above latitude of Cape Prince of Wales.

2012 BOF adjusts harvest strategy.


21

Table 3. List of 16 variables used to calculate other variables, or offered to the generalized linear model

stepwise selection procedure for standardization of Norton Sound summer commercial red king crab

CPUE data through generalized linear modeling.

Variable Description

ADF&G Number Unique 5-digit number assigned to all commercial fishing vessels in the State of Alaska, recoded here to preserve confidentiality, and renamed “Vessel.”

CPUE Number of legal male red king crabs harvested per pot lift, calculated as: Number of Crab divided by Effort.

Effort Number of pot lifts.

Fish Ticket Number Unique 6-digit number assigned to all fish tickets, which are legally required records of deliveries of commercially harvested fish or invertebrates to a processor by a vessel.

Landing Date Date crabs were delivered to a processor.

Mean Crab Weight Calculated as Pounds of Crab divided by Number of Crab.

Modified Statistical Area One of four groups of spatially proximate Statistical Areas, used only for analyses described in this document. See Appendix A 4 for definitions.

Month of Year Month of Landing Date.

Number of Crab Number of legal male red king crab harvested.

Permit Fishery One of six permit categories. See Appendix A 3 for definitions.

Permit Number Unique 5-digit number associated with a permit.

Pounds of Crab Harvested whole pounds of legal male red king crab, includes both commercial and that retained for personal use while commercial fishing. Legally required information on all fish tickets.

Statistical Area Unique 6-digit number associated with a spatially discrete marine area. Legally required information on all fish tickets.

Vessel ADF&G Number recoded to achieve confidentiality, see above.

Week of Year Week of Landing Date, ranging from 1 to 53; a week starts on Sunday and ends on Saturday.

Year Calendar year, ranging from 1977–2012, measured from January 1–December 31.


22

Table 4. Final generalized linear model formulae and associated R2 selected for Norton Sound summer

commercial red king crab fishery from varous data subsets. The dependent variable is ln(CPUE) in

numbers. Preferred models are shown in bold. Notation from the open source programming language R is

used. Abbreviations: YR=Year, VSL= Vessel, MSA=Modified Statistical Area, WOY=Week of Year,

PF=Permit Fishery.

Time series Deliveries Years

Explanatory variables Null dev. Null df

Resid. dev.

Resid. df AIC R2

1977–1992

2 3 ~YR+VSL+MSA +WOY

155.8 155 46.5 125 318 0.702

~YR+VSL+WOY+VSL:WOY+YR:WOY+MSA+WOY:MSA+YR:MSA

155.8 155 17.8 75 268 0.886

1993–2012

3 3 ~YR+VSL+WOY+MSA+PF 2646.2 4274 1528.5 4177 7933 0.422

3 5 ~YR+VSL+WOY +MSA+PF

2061.1 3505 1219.5 3427 6407 0.408

~YR+VSL+ YR:VSL+WOY+ VSL:WOY+ YR:WOY

2061.1 3505 620.6 2656 5581 0.699

3 7 ~YR+VSL+WOY +MSA+PF

1365.9 2601 891.2 2541 4720 0.348

Table 5. Preferred model. Analysis of deviance for stepwise lognormal model selection for generalized

linear modeling of Norton Sound red king crab harvest data. The response variable is log(CPUE). The

variables Year, Vessel, Week of Year, Modified Statistical Area, and Permit Fishery were offered to the

model for selection. Data is from vessels having two deliveries for three years over the time series 1977–

1992. The forward stepwise selection process used a stopping point of R2 difference > 0.01. Notation

from the open source programming language R is used.

Variable

Difference from null in Residual

df R2 Null

deviance Null df Residual deviance

Year -27.45 142 0.555

Vessel -9.92 -5 -37.36 137 0.638

Modified Statistical Area -17.96 -9 -55.32 128 0.676

Week of Year -5.97 -3 -61.30 125 0.702


23

Table 6. Analysis of deviance for two-stage stepwise lognormal model selection for generalized linear

modeling of Norton Sound red king crab harvest data. The response variable is log(CPUE). In the first

stage the variables but no interactions were offered for selection, in the second stage the variables selected

(see Table 4) and their second order interactions were offered. Data is from vessels having two deliveries

for three years over the time series 1977–1992. The forward stepwise selection process used a stopping

point of R2 difference > 0.01. Notation from the open source programming language R is used.

Variable


df R2 Null


Year -27.445 142 0.555

Vessel -9.918 -5 -37.363 137 0.638

Week of Year -17.962 -9 -55.324 128 0.676

Vessel:Week of Year -57.873 -29 -113.198 99 0.802

Year:Week of Year -15.954 -8 -129.152 91 0.848


Week of Year:Modified Statistical Area -15.988 -8 -151.128 80 0.872

Year: Modified Statistical Area -9.987 -5 -161.114 75 0.886

Table 7. Analysis of deviance for stepwise lognormal model selection for generalized linear modeling of

Norton Sound red king crab harvest data. The response variable is log(CPUE). Data is from vessels

having three deliveries for three years over the time series from 1993–2012. The forward stepwise

selection process used a stopping point of R2 difference > 0.01. Notation from the open source

programming language R is used.

Variable


df R2 Null


Year -39.77 4255 0.235

Vessel -111.85 -56 -151.62 4199 0.383

Week of Year -29.98 -15 -181.60 4184 0.415



24

Table 8. Preferred model. Analysis of deviance for stepwise lognormal model selection for generalized

linear modeling of Norton Sound red king crab harvest data. The response variable is log(CPUE). Permit

fishery was added afterwards due to residual patterns. Data is from vessels having three deliveries for five

years over the time series from 1993–2012. The forward stepwise selection process used a stopping point

of R2 difference > 0.01. Notation from the open source programming language R is used.

Variable


df R2 Null


Year -39.77 3486 0.231

Vessel -73.87 -37 -113.64 3449 0.360

Week of Year -29.97 -15 -143.61 3434 0.386


Table 9. Analysis of deviance for stepwise lognormal model selection for generalized linear modeling of

Norton Sound red king crab harvest data. The response variable is log(CPUE). Data is from vessels

having three deliveries for seven years over the time series from 1993–2012. The forward stepwise

selection process used a stopping point of R2 difference > 0.01. Notation from the open source

programming language R is used.

Variable


df R2 Null


Year -37.85 2583 0.154

Vessel -43.86 -22 -81.70 2561 0.297

Week of Year -27.98 -14 -109.68 2547 0.322



25

Table 10. Analysis of deviance for two-stage stepwise lognormal model selection for generalized linear

modeling of Norton Sound red king crab harvest data. The response variable is log(CPUE). In the first

stage variables but no interactions and in the second stage the selected variables (see Table 8) and their

second-order interactions were offered to the model for selection. Data is from vessels having three

deliveries for five years over the time series from 1993–2012. The forward stepwise selection process

used a stopping point of R2 difference > 0.01. Notation from the open source programming language R is

used.

Variable


df R2 Null


Year -39.77 3486 0.231

Vessel -73.87 -37 -113.64 3449 0.360

Year:Vessel -535.83 -268 -649.47 3181 0.531

Week of Year -29.98 -15 -679.45 3166 0.552

Vessel:Week of Year -739.90 -370 -1419.35 2796 0.652

Year:Week of Year -279.95 -140 -1699.30 2656 0.699

Table 11. Results of linear modeling of the trawl and pot survey legal male population estimate for the

Norton Sound red king crab fishery (TS.LM) versus three measures of commercial CPUE: standardized

(CPUE.Std.), base year (CPUE.Base), and scaled arithmetic (CPUE.Arith). The CPUE values can be

found in Appendix D. The population estimates were obtained from Soong and Hamazaki (2012).

Notation from the open source programming language R is used.

Time series Formula Adjusted r2

n F p

1978–1992 TS.LM~CPUE.Std -0.146 5 0.914 0.3831

TS.LM~CPUE.Base 0.075 5 1.485 0.2774

TS.LM~CPUE.Arith -0.040 5 0.769 0.4206 1993–2012 TS.LM~CPUE.Std. -0.163 4 0.299 0.6137

TS.LM~CPUE.Base -0.249 4 0.005 0.9473

TS.LM~CPUE.Arith -0.250 4 0.002 0.9710


26

Figures

Figure 1. Closed area and statistical area boundaries used for reporting commercial harvest information

for red king crab in Registration Area Q, Northern District, Norton Sound Section and boundaries of the

new Modified Statistical Areas used in this analysis.


27

Figure 2. Distribution of effort in deliveries (a) and harvest in pounds (b) by vessel and year, and of

pounds by statistical area and year (c) for the summer commercial red king crab fishery in Norton Sound,

1977–2012. The size of circles is proportional to number of deliveries or pounds.

Deliveries

1975 1980 1985 1990 1995 2000 2005 2010 2015

Ve

ssel

#

0

20000

40000

60000

80000

Pounds

1975 1980 1985 1990 1995 2000 2005 2010 2015

Ves

sel #

0

20000

40000

60000

80000

Year

1975 1980 1985 1990 1995 2000 2005 2010 2015

Sta

tistic

al a

rea

#

610000

620000

630000

640000

650000

660000

670000

680000

690000

Pounds

(a)

(b)

(c)


28

Figure 3. Preferred model. Pearson residuals plotted against variables in the model and fitted values, and

QQ plots for the generalized linear model of: log(CPUE)~Year+Vessel+Modified Statistical Area+Week

of Year. CPUE is in numbers per pot. Data is from the summer commercial fishery for red king crab in

Norton Sound for vessels having two deliveries for three years over the time series from 1977–1992. The

forward stepwise selection process used a stopping point of R2 difference > 0.01.

1977 1979 1981 1983 1985 1987 1990

-2.0

-1.0

0.0

1.0

factor(YR)

Pe

ars

on

re

sid

ua

ls

294

201

324

81

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-1.0

0.0

1.0

factor(VSL)

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ars

on

re

sid

ua

ls

83

81

324

399

27 28 29 30 31 32 33 34 35 36

-2.0

-1.0

0.0

1.0

factor(WOY)

Pe

ars

on

re

sid

ua

ls

324

215254

259201 231

Inner Mid Outer Outer North

-2.0

-1.0

0.0

1.0

factor(MSA)

Pe

ars

on

re

sid

ua

ls

81

324

201

1 2 3 4 5

-2.0

-1.0

0.0

1.0

Linear Predictor

Pe

ars

on

re

sid

ua

ls

-2 -1 0 1 2

-4-2

01

2

Theoretical Quantiles

Sa

mp

le Q

ua

ntil

es


29

Figure 4. Preferred model. Pearson residuals plotted against variables not in the model for the

generalized linear model of: log(CPUE)~Year+Vessel+Modified Statistical Area+Week of Year. CPUE is

in numbers per pot. Data is from the summer commercial fishery for red king crab in Norton Sound for

vessels having two deliveries for three years over the time series from 1977–1992. The forward stepwise

selection process used a stopping point of R2 difference > 0.01.

7 8 9

-5-4

-3-2

-10

12

34

5

Month of Year

Re

sid

ua

ls

K09Q K09Z K09ZE K09ZF K91Q K91Z

-5-4

-3-2

-10

12

34

5

Permit FisheryR

esi

du

als


30

Figure 5. Preferred model. Interaction plots for the generalized linear model of: log(CPUE)~Year+

Vessel+Modified Statistical Area+Week of Year. CPUE is in numbers per pot. Data is from the summer

commercial fishery for red king crab in Norton Sound for vessels having two deliveries for three years

over the time series from 1977–1992. The forward stepwise selection process used a stopping point of R2

difference > 0.01.

01

23

4

Year

ln(C

PU

E, n

o)

1977 1980 1983 1986 1989

NSdata$VSL

ACABAAADAEAF

12

34

Yearln

(CP

UE

, no

)

1977 1980 1983 1986 1989

NSdata$MSA

OuterInnerMidOuter North

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Year

ln(C

PU

E, n

o)

1977 1980 1983 1986 1989

NSdata$PF

K91ZK09QK09ZK09ZEK09ZFK91Q

12

34

5

Year

ln(C

PU

E, n

o)

1977 1980 1983 1986 1989

NSdata$WOY

31272829303233343536


31

Figure 6. Preferred model. Influence plots for the generalized linear model of: log(CPUE)~Year+

Vessel+Modified Statistical Area+Week of Year. CPUE is in numbers per pot. Data is from the summer

commercial fishery for red king crab in Norton Sound for vessels having two deliveries for three years


difference > 0.01.

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

Fitted values

Ha

t-va

lue

s

96

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.5

1.0

1.5

Fitted values|D

FF

its|

46 99

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

00

.02

0.0

40

.06

0.0

80

.10

Fitted values

Co

oks

dis

tan

ce

30 79

0.2 0.4 0.6 0.8 1.0

-4-3

-2-1

01

2

Hat-Values

Stu

de

ntiz

ed

Re

sid

ua

ls

81

201

203

204

217

220

257

294

324

395

396

73


32

Figure 7. Preferred model. Trends in standardized (ST.CPUE), base year (BY.CPUE), and scaled

arithmetic (A.CPUE) catch per unit effort (CPUE) in numbers per pot and their standard errors from the

generalized linear model: log(CPUE)~Year+Vessel+Modified Statistical Area+Week of Year. Data is from

the summer commercial fishery for red king crab in Norton Sound for vessels having two deliveries for

three years over the time series from 1977–1992. The forward stepwise selection process used a stopping

point of R2 difference > 0.01.

1976 1978 1980 1982 1984 1986 1988 1990 1992 1994

0

1

2

3

4

5

Year

Re

lativ

e C

PU

E in

de

x

ST.CPUEBY.CPUEA.CPUE


33

Figure 8. Pearson residuals plotted against variables in the model and fitted values, and QQ plots for the

generalized linear model of: log(CPUE) ~Year+Vessel+Week of Year+Modified Statistical Area+Permit

Fishery. CPUE is in numbers per pot. Data is from the summer commercial fishery for red king crab in

Norton Sound for vessels having three deliveries for three years over the time series from 1993–2012.

The forward stepwise selection process used a stopping point of R2 difference > 0.01.

1993 1996 1999 2002 2005 2008 2011

-2-1

01

2

factor(YR)

Pe

ars

on

re

sid

ua

ls

1155638

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01

2

factor(VSL)

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sid

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ls

75

208294

262

534638692

806

805

883

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2245

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29983023

312732273342

3708

3716

3909

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24 26 28 30 32 34 36 38

-2-1

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2

factor(WOY)

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ars

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ua

ls

3909

1102

2358

1122

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3830

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290

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01

2

factor(MSA)P

ea

rso

n r

esi

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als

27971212

3830

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K09Q K09Z K09ZE K09ZF K91Z

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2

factor(PF)

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ars

on

re

sid

ua

ls

1204

3830

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4808

1155

0.5 1.0 1.5 2.0 2.5 3.0 3.5

-2-1

01

2

Linear Predictor

Pe

ars

on

re

sid

ua

ls

-2 0 2

-4-2

02


Sa

mp

le Q

ua

ntil

es


34

Figure 9. Pearson residuals plotted against variables not in the model for the generalized linear model of:

log(CPUE)~Year+Vessel+Week of Year +Modified Statistical Area+Permit Fishery. CPUE is in numbers

per pot. Data is from the summer commercial fishery for red king crab in Norton Sound for vessels

having three deliveries for three years over the time series from 1993–2012. The forward stepwise

selection process used a stopping point of R2 difference > 0.01.

6 7 8 9

-5-4

-3-2

-10

12

34

5

Month of Year

Re

sid

ua

ls


35

Figure 10. Interaction plots for the generalized linear model of: log(CPUE) ~Year+Vessel+Week of

Year+Modified Statistical Area+Permit Fishery. CPUE is in numbers per pot. Data is from the summer

commercial fishery for red king crab in Norton Sound for vessels having three deliveries for three years


difference > 0.01.

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Year

ln(C

PU

E, n

o)

1993 1996 1999 2002 2005 2008 2011

NSdata$VSL

AQBSBHBNARBTAFAMBBAKCGAOATBQBFANBJAPADABBDAJBAAAAE

1.5

2.0

2.5

3.0

Yearln

(CP

UE

, no

)

1993 1997 2001 2005 2009

NSdata$MSA

InnerMidOuterOuter North

1.5

2.0

2.5

3.0

Year

ln(C

PU

E, n

o)

1993 1996 1999 2002 2005 2008 2011

NSdata$PF

K09ZEK09ZK09QK09ZFK91QK91Z

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Year

ln(C

PU

E, n

o)

1993 1996 1999 2002 2005 2008 2011

NSdata$WOY

36353028312729322624253334373839


36

Figure 11. Influence plots for the generalized linear model of: log(CPUE) ~Year+Vessel+Week of Year+

Modified Statistical Area+Permit Fishery. CPUE is in numbers per pot. Data is from the summer

commercial fishery for red king crab in Norton Sound for vessels having three deliveries for three years


difference > 0.01.

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

Fitted values

Ha

t-va

lue

s

311

6024004

4073

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.5

1.0

1.5

Fitted values|D

FF

its|

602

3938

4004

4071

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

00

.02

0.0

40

.06

0.0

80

.10

Fitted values

Co

oks

dis

tan

ce

0.0 0.1 0.2 0.3 0.4 0.5

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02

Hat-Values

Stu

de

ntiz

ed

Re

sid

ua

ls

75

347

773

788

1155120412122457

4546

46134681

4683


37

Figure 12. Trends in standardized (ST.CPUE), base year (BY.CPUE), and scaled arithmetic (A.CPUE)

catch per unit effort (CPUE) in numbers per pot and their standard errors from the generalized linear

model: log(CPUE) ~Year+Vessel+Week of Year+Modified Statistical Area+Permit Fishery. Data is from

the summer commercial fishery for red king crab in Norton Sound for vessels having three deliveries for

three years over the time series from 1993–2012. The forward stepwise selection process used a stopping

point of R2 difference > 0.01.

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014

0

1

2

3

Year

Re

lativ

e C

PU

E in

de

x



38

Figure 13. Preferred model. Pearson residuals plotted against variables in the model and fitted values,

and QQ plots for the generalized linear model of: log(CPUE) ~Year+Vessel+Week of Year+Modified

Statistical Area+Permit Fishery. CPUE is in numbers per pot. Data is from the summer commercial

fishery for red king crab in Norton Sound for vessels having three deliveries for five years over the time

series from 1993–2012. Permit Fishery was added afterwards due to residual patterns. The forward

stepwise selection process used a stopping point of R2 difference > 0.01.

1993 1996 1999 2002 2005 2008 2011

-2-1

01

2

factor(YR)

Pe

ars

on

re

sid

ua

ls

2998

2245

483745324546

4422262

201617181559

1122

21577512041212

1102

1487

1114

5272457534

3830

AA AD AH AL AO AS AV BA BE BI BL

-2-1

01

2

factor(VSL)

Pe

ars

on

re

sid

ua

ls

75

208294

262

534692

883

936

1122

1212

1225

15591718

1684

2016

2245

2457

2666

2797

2859

2998312732273342

3952

3830

40604332

4356 4709

4837

24 26 28 30 32 34 36 38

-2-1

01

2

factor(WOY)

Pe

ars

on

re

sid

ua

ls

39092358

1122

2797

3830

2457

3260

12041559

2245

2157534

290

75

262

1212

1114


-2-1

01

2

factor(MSA)P

ea

rso

n r

esi

du

als

27971212

3830

1204

262

K09Q K09Z K09ZE K09ZF K91Z

-2-1

01

2

factor(PF)

Pe

ars

on

re

sid

ua

ls

1204

3830

1212

4808

0.5 1.0 1.5 2.0 2.5 3.0 3.5

-2-1

01

2

Linear Predictor

Pe

ars

on

re

sid

ua

ls

-2 0 2

-4-2

02


Sa

mp

le Q

ua

ntil

es


39

Figure 14. Preferred model. Pearson residuals plotted against variables not in the model for the

generalized linear model of: log(CPUE)~Year+Vessel+Week of Year+Modified Statistical Area+Permit

Fishery. CPUE is in numbers per pot. Permit Fishery was added afterwards due to residual patterns. Data

is from the summer commercial fishery for red king crab in Norton Sound for vessels having three

deliveries for five years over the time series from 1993–2012. The forward stepwise selection process

used a stopping point of R2 difference > 0.01.

6 7 8 9

-5-4

-3-2

-10

12

34

5

Month of Year

Re

sid

ua

ls


40

Figure 15. Preferred model. Interaction plots for the generalized linear model of: log(CPUE)

~Year+Vessel+Week of Year+Modified Statistical Area+Permit Fishery. CPUE is in numbers per pot.

Permit fishery was added afterwards due to residual patterns. Data is from the summer commercial


series from 1993–2012. The forward stepwise selection process used a stopping point of R2 difference >

0.01.

1.0

1.5

2.0

2.5

3.0

3.5

4.0

Year

ln(C

PU

E, n

o)

1993 1996 1999 2002 2005 2008 2011

NSdata$VSL

ALBFBCBGAHASAGBMAJANAWAIAXAKACABAUAFARAAADAEAMAOAP

1.5

2.0

2.5

3.0

Yearln

(CP

UE

, no

)

1993 1997 2001 2005 2009

NSdata$MSA

MidInnerOuterOuter North

1.5

2.0

2.5

3.0

Year

ln(C

PU

E, n

o)

1993 1996 1999 2002 2005 2008 2011

NSdata$PF


0.5

1.0

1.5

2.0

2.5

3.0

3.5

Year

ln(C

PU

E, n

o)

1993 1996 1999 2002 2005 2008 2011

NSdata$WOY

36302827293132352425263334373839


41

Figure 16. Preferred model. Influence plots for the generalized linear model of: log(CPUE)

~Year+Vessel+Week of Year+Modified Statistical Area+Permit Fishery. CPUE is in numbers per pot.

Permit Fishery was added afterwards due to residual patterns. Data is from the summer commercial


series from 1993–2012. The forward stepwise selection process used a stopping point of R2 difference >

0.01.

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

Fitted values

Ha

t-va

lue

s

291

3178

32623331

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.5

1.0

1.5

Fitted values|D

FF

its|

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

00

.02

0.0

40

.06

0.0

80

.10

Fitted values

Co

oks

dis

tan

ce

0.0 0.2 0.4 0.6 0.8 1.0

-4-2

02

Hat-Values

Stu

de

ntiz

ed

Re

sid

ua

ls

75

347

534120412122457

3227

4422

4546

4613

4681

4683

1


42

Figure 17. Preferred model. Trends in standardized (ST.CPUE), base year (BY.CPUE), and scaled

arithmetic (A.CPUE) catch per unit effort (CPUE) in numbers per pot and their standard errors from the

generalized linear model: log(CPUE)~Year+Vessel+Week of Year+Modified Statistical Area+Permit

Fishery. Permit Fishery was added afterwards due to residual patterns. Data is from the summer

commercial fishery for red king crab in Norton Sound for vessels having three deliveries for five years


difference > 0.01.

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014

0

1

2

3

Year

Re

lativ

e C

PU

E in

de

x



43

Figure 18. Pearson residuals plotted against variables in the model and fitted values, and QQ plots for the

generalized linear model of: log(CPUE)~Year+Vessel+Week of Year+Modified Statistical Area+Permit

Fishery. Permit Fishery was added afterwards due to residual patterns. CPUE is in numbers per pot. Data

is from the summer commercial fishery for red king crab in Norton Sound for vessels having three

deliveries for seven years over the time series from 1993–2012. The forward stepwise selection process

used a stopping point of R2 difference > 0.01.

1993 1996 2000 2003 2006 2009 2012

-2-1

01

2

factor(YR)

Pe

ars

on

re

sid

ua

ls

32421229

525

17181559

1122

4877512041212

1102

1487

1114

23582457534

3830

AA AC AE AG AI AK AM AO AQ AS AU AW

-2-1

01

2

factor(VSL)

Pe

ars

on

re

sid

ua

ls

75

262

534

883

9361122

1204

1225

15591718

1684

20162457

27973227 3909

3830

4060

4837

24 26 28 30 32 34 36 38

-2-1

01

2

factor(WOY)

Pe

ars

on

re

sid

ua

ls

39092358

1122

2797

3830

2457

3260

12041559

525

534

290

7512121487

1114


-2-1

01

2

factor(MSA)P

ea

rso

n r

esi

du

als

27971212

3830

1204

262

K09Q K09Z K09ZE K09ZF

-2-1

01

2

factor(PF)

Pe

ars

on

re

sid

ua

ls

1546

1204

3830

1212

1.5 2.0 2.5 3.0 3.5

-2-1

01

2

Linear Predictor

Pe

ars

on

re

sid

ua

ls

-3 -2 -1 0 1 2 3

-4-2

02


Sa

mp

le Q

ua

ntil

es


44

Figure 19. Pearson residuals plotted against variables not in the model for the generalized linear model of:

log(CPUE)~Year+Vessel+Week of Year+Modified Statistical Area+Permit Fishery. Permit Fishery was

added afterwards due to residual patterns. CPUE is in numbers per pot. Data is from the summer

commercial fishery for red king crab in Norton Sound for vessels having three deliveries for seven years

over the time series 1993–2012. The forward stepwise selection process used a stopping point of R2

difference > 0.01.

6 7 8 9

-5-4

-3-2

-10

12

34

5

Month of Year

Re

sid

ua

ls


45

Figure 20. Interaction plots for the generalized linear model of: log(CPUE)~Year+Vessel+Week of

Year+Modified Statistical Area+Permit Fishery. Permit Fishery was added afterwards due to residual

patterns. CPUE is in numbers per pot. Data is from the summer commercial fishery for red king crab in

Norton Sound for vessels having three deliveries for seven years over the time series from 1993–2012.


1.0

1.5

2.0

2.5

3.0

3.5

4.0

Year

ln(C

PU

E, n

o)

1993 1996 1999 2002 2005 2008 2011

NSdata$VSL

AKAUARAVAHAOAGAWAJALAIACABAPAFANAAADAEAMAQASAT

1.5

2.0

2.5

3.0

Year

ln(C

PU

E, n

o)

1993 1997 2001 2005 2009

NSdata$MSA

MidInnerOuterOuter North

1.5

2.0

2.5

3.0

Year

ln(C

PU

E, n

o)

1993 1996 1999 2002 2005 2008 2011

NSdata$PF


1.0

1.5

2.0

2.5

3.0

3.5

Year

ln(C

PU

E, n

o)

1993 1996 1999 2002 2005 2008 2011

NSdata$WOY

36302827293132352425263334373839


46

Figure 21. Influence plots for the generalized linear model of: log(CPUE)~Year+Vessel+Week of

Year+Modified Statistical Area+Permit Fishery. Permit Fishery was added afterwards due to residual

patterns. CPUE is in numbers per pot. Data is from the summer commercial fishery for red king crab in

Norton Sound for vessels having three deliveries for seven years over the time series from 1993–2012.


-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.2

0.4

0.6

0.8

1.0

Fitted values

Ha

t-va

lue

s

291 2160

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

0.5

1.0

1.5

Fitted values

|DF

Fits

|

-5 -4 -3 -2 -1 0 1 2 3 4 5

0.0

00

.02

0.0

40

.06

0.0

80

.10

Fitted values

Co

oks

dis

tan

ce

0.0 0.2 0.4 0.6 0.8 1.0

-4-2

02

Hat-Values

Stu

de

ntiz

ed

Re

sid

ua

ls

75

347

53412041212

1487

2457

3227

33603546

4826

4837

4841


47

Figure 22. Trends in standardized (ST.CPUE), base year (BY.CPUE), and scaled arithmetic (A.CPUE)

catch per unit effort (CPUE) in numbers per pot and their standard errors from the generalized linear

model: log(CPUE)~Year+Vessel+Week of Year+Modified Statistical Area+Permit Fishery. Permit

Fishery was added afterwards due to residual patterns. Data is from the summer commercial fishery for

red king crab in Norton Sound for vessels having three deliveries for seven years over the time series

from 1993–2012. The forward stepwise selection process used a stopping point of R2 difference > 0.01.

1992 1994 1996 1998 2000 2002 2004 2006 2008 2010 2012 2014

0

1

2

3

Year

Re

lativ

e C

PU

E in

de

x



48

AppendixA.BackgroundTables

Appendix A 1. Season start and end dates for open access and CDQ permit holders, open access fishing

start and end dates by year for the summer commercial fishery for red king crab in Norton Sound for

1977–2012 seasons (excerpted from Menard et al. 2012).

Year

Open access season start

Open access fishing start

Open access season

end

CDQ season 1

start

CDQ season 1

end

CDQ season 2

start

CDQ season 2

end

Both seasons

end

Season length (days)

1977 7/5/1977 7/5/1977 8/1/1977 NA NA NA NA 8/1/1977 27

1978 6/7/1978 6/7/1978 8/15/1978 NA NA NA NA 8/15/1978 69

1979 7/15/1979 7/15/1979 7/31/1979 NA NA NA NA 7/31/1979 16

1980 7/15/1980 7/15/1980 7/31/1980 NA NA NA NA 7/31/1980 16

1981 7/15/1981 7/15/1981 8/22/1981 NA NA NA NA 8/22/1981 38

1982 8/9/1982 8/9/1982 9/1/1982 NA NA NA NA 9/1/1982 23

1983 8/1/1983 8/1/1983 8/5/1983 NA NA NA NA 8/5/1983 4

1984 8/1/1984 8/1/1984 8/15/1984 NA NA NA NA 8/15/1984 14

1985 8/1/1985 8/1/1985 8/23/1985 NA NA NA NA 8/23/1985 22

1986 8/1/1986 8/12/1986 8/25/1986 NA NA NA NA 8/25/1986 24

1987 8/1/1987 8/1/1987 8/12/1987 NA NA NA NA 8/12/1987 11

1988 8/1/1988 8/1/1988 8/11/1988 NA NA NA NA 8/11/1988 10

1989 8/1/1989 8/1/1989 8/4/1989 NA NA NA NA 8/4/1989 3

1990 8/1/1990 8/1/1990 8/5/1990 NA NA NA NA 8/5/1990 4

1992 8/1/1992 8/1/1992 8/3/1992 NA NA NA NA 8/3/1992 2

1993 7/1/1993 7/8/1993 8/28/1993 NA NA NA NA 8/28/1993 58

1994 7/1/1994 7/1/1994 7/31/1994 NA NA NA NA 7/31/1994 30

1995 7/1/1995 7/1/1995 9/5/1995 NA NA NA NA 9/5/1995 66

1996 7/1/1996 7/9/1996 9/3/1996 NA NA NA NA 9/3/1996 64

1997 7/1/1997 7/9/1997 8/13/1997 NA NA NA NA 8/13/1997 43

1998 7/1/1998 7/15/1998 9/3/1998 NA NA NA NA 9/3/1998 64

1999 7/1/1999 7/1/1999 9/4/1999 NA NA NA NA 9/4/1999 65

2000 7/1/2000 7/1/2000 8/29/2000 9/1/2000 9/29/2000 NA NA 9/29/2000 90

2001 7/1/2001 7/1/2001 9/1/2001 9/1/2001 9/9/2001 NA NA 9/9/2001 70

2002 6/15/2002 6/15/2002 8/6/2002 6/15/2002 6/28/2002 8/9/2002 9/3/2002 9/3/2002 80

2003 6/16/2003 6/16/2003 8/13/2003 6/15/2003 6/28/2003 8/15/2003 8/24/2003 8/24/2003 69


49

Appendix A1. Cont.

Year

Open access season start

Open access fishing start

Open access season

end

CDQ season 1

start

CDQ season 1

end

CDQ season 2

start

CDQ season 2

end

Both seasons

end

Season length (days)

2004 6/15/2004 7/1/2004 8/8/2004 6/15/2004 6/28/2004 NA NA 8/8/2004 54

2005 6/15/2005 7/1/2005 8/15/2005 6/15/2005 6/28/2005 8/17/2005 8/27/2005 8/27/2005 73

2006 6/15/2006 7/1/2006 8/22/2006 6/15/2006 6/28/2006 NA NA 8/22/2006 68

2007 6/15/2007 7/1/2007 8/7/2007 6/15/2007 6/28/2007 NA NA 8/7/2007 53

2008 6/23/2008 6/23/2008 8/18/2008 8/17/2008 9/3/2008 NA NA 9/3/2008 72

2009 6/15/2009 6/15/2009 9/20/2009 6/15/2009 7/28/2009 NA NA 9/20/2009 97

2010 6/28/2010 7/1/2010 8/24/2010 6/28/2010 7/16/2010 NA NA 8/24/2010 57

2011 6/28/2011 7/1/2011 7/30/2011 6/28/2011 7/16/2011 NA NA 7/30/2011 32

2012 6/29/2012 6/29/2012 8/11/2012 6/29/2012 9/9/2012 NA NA 9/9/2012 72


50

Appendix A 2. Harvested pounds included by time series and data subset for Norton Sound summer

commercial red king crab harvest data. Bolding indicates subsets used for the current analysis.

Year subset Deliveries Years Pounds Subset percent

harvest Vessels 1977-1992 1 1 10,632,641 100.0% 119

2 3 3,104,794 29.2% 6

2 5 1,284,301 12.1% 2

2 7 0 0.0% 0

3 3 1,001,638 9.4% 2

3 5 535,540 5.0% 1

3 7 0 0.0% 0

5 3 466,098 4.4% 1

5 5 0 0.0% 0

5 7 0 0.0% 0

7 3 0 0.0% 0

7 5 0 0.0% 0

7 7 0 0.0% 0

1993-2012 1 1 6,077,090 100.0% 131

2 3 5,366,220 88.3% 60

2 5 4,559,239 75.0% 40

2 7 3,583,601 59.0% 23

3 3 5,348,723 88.0% 57

3 5 4,503,676 74.1% 38

3 7 3,583,601 59.0% 23

5 3 5,268,700 86.7% 53

5 5 4,209,343 69.3% 31

5 7 3,301,588 54.3% 20

7 3 5,048,478 83.1% 47

7 5 3,785,198 62.3% 27

7 7 2,999,373 49.4% 17


51

Appendix A 3. Permit fisheries, descriptions, and years with deliveries for Norton Sound summer

commercial red king crab harvest data.

Permit fishery Type Description Years

K09Q Open access KING CRAB , POT GEAR VESSEL UNDER 60', BERING SEA 1994–2002

K09Z Open access KING CRAB , POT GEAR VESSEL UNDER 60', NORTON SOUND 1992–2012

K09ZE CDQ KING CRAB , POT GEAR VESSEL UNDER 60', NORTON SOUND

CDQ, NSEDC 2000–2012

K09ZF CDQ KING CRAB , POT GEAR VESSEL UNDER 60', NORTON SOUND

CDQ, YDFDA 2002–2004

K91Q Open access KING CRAB , POT GEAR VESSEL 60' OR OVER, BERING SEA 1978–1989

K91Z Open access KING CRAB , POT GEAR VESSEL 60' OR OVER, NORTON SOUND 1982–1994

Appendix A 4. Modified statistical area definitions used for analysis of Norton Sound summer

commercial red king crab harvest data.

Modified statistical area Statistical areas included

Inner 616331, 616401, 626331, 626401, 626402

Mid 636330, 636401, 636402, 646301, 646330, 646401, 646402

Outer 656300, 656330, 656401, 656402, 666230, 666300, 666330, 666401

Outer North 666402, 666431, 676300, 676330 ,676400, 676430, 676501, 686330


52

Appendix A 5. Preferred model. Contingency tables comparing the distribution of not included and

included effort by Modified Statistical Area for a subset of Norton Sound red king crab summer

commercial fishery harvest data having two deliveries for three years for 1977–1992 (Pearson’s Chi-

squared(3,733)=3.4 p=0.33; Cramers V=0.14, Z=3.3, p<.001)

Dataset Parameter

Modified statistical area

Row total Inner Mid Outer Outer north

Not included

n 6 24 363 78

471 64.3%

Expected 5.1 24.4 354.7 86.8

Chi squ. cont. 0.1 0.0 0.2 0.9

n row total 1.3% 5.1% 77.1% 16.6%

Included

n 2 14 189 57

262 35.7%

Expected 2.9 13.6 197.3 48.3

Chi squ. cont. 0.3 0.0 0.4 1.6

n row total 0.8% 5.3% 72.1% 21.8%

Column Total

n 8 38 552 135 733

n column total 1.1% 5.2% 75.3% 18.4%

Appendix A 6. Preferred model. Contingency tables comparing the distribution of not included and

included effort by Modified Statistical Area for a subset of Norton Sound red king crab summer

commercial fishery harvest data having three deliveries for five years for 1993–2012 (Pearson’s Chi-

squared(3,5033)=21.9 p<0.0001; Cramers V=0.26, Z=-2.8, p<.01)

Dataset Parameter

Modified statistical area

Row total Inner Mid Outer Outer north

Not included

n 71 306 272 26

675

13.4%

Expected 108.1 296.8 252.9 17.2

Chi squ. cont. 12.7 0.3 1.4 4.6

n row total 10.5% 45.3% 40.3% 3.9%

Included

n 735 1907 1614 102

4358

86.6%

Expected 697.9 1916.2 1633.1 110.8

Chi squ. cont. 2.0 0.0 0.2 0.7

n row total 16.9% 43.8% 37.0% 2.3%

Column

Total

n 806 2213 1886 128 5033

n column total 16.0% 44.0% 37.5% 2.5%


53

Appendix A 7. Akaike Information Criterion (AIC) from linear modeling of log(CPUE) in terms of

number per pot against six explanatory variables from the summer commercial fishery for red king crab in

Norton Sound for 1977–1992. Notation from the open source programming language R is used.

Variable AIC Year 424.5

Vessel 497.9

Week of Year 544.8

Permit Fishery 548.4

Modified Statistical Area 549.4

Month of Year 555.2

Appendix A 8. Akaike Information Criterion (AIC) from linear modeling of log(CPUE) in terms of

number per pot against six explanatory variables from the summer commercial fishery for red king crab in

Norton Sound for 1993–2012. Notation from the open source programming language R is used.

Variable AIC Vessel 8847.1

Year 8981.1

Modified Statistical Area 9889.3

Week of Year 10036.9

Permit Fishery 10053.5

Month of Year 10066.0


54

Appendix A 9. Preferred model. Generalized Variance Inflation Factors (GVIF) for Norton Sound red

king crab harvest data for the linear model: log(CPUE)~Year+Vessel+Modified Statistical Area+Week of

Year. Data is from vessels having two deliveries for three years over the time series from 1977–1992.

GVIF^(1/(2*df)) exceeding three indicate multicollinearity problems. The forward stepwise selection

process used a stopping point of R2 difference > 0.01. Notation from the open source programming

language R is used.

Variable GVIF df GVIF^(1/(2*df)) Year 1213.2 13 1.3

Vessel 12.9 5 1.3

Modified Statistical Area 4.8 3 1.3

Week of Year 263.4 9 1.4

Appendix A 10. Preferred model. Generalized Variance Inflation Factors (GVIF) for Norton Sound red

king crab harvest data from the linear model: log(CPUE)~Year+Vessel+Week of Year+Modified

Statistical Area+Permit Fishery. Data is from vessels having three deliveries for five years over the time

series from 1993–2012. GVIF^(1/(2*df)) exceeding three indicate multicollinearity problems. The

forward stepwise selection process used a stopping point of R2 difference > 0.01. Notation from the open

source programming language R is used.

Variable GVIF df GVIF^(1/(2*df)) Year 27.6 19 1.1

Vessel 63.1 37 1.1

Week of Year 3.5 15 1.0

Modified Statistical Area 3.0 3 1.2

Permit Fishery 3.3 4 1.2


55

AppendixB.BackgroundFigures

Appendix B 1. Number of vessels included in the full (1,1) data set and subsets with varying number of

delivery and year selection criteria for two different time series for the summer commercial red king crab

fishery in Norton Sound.

3 years

1,1 2,3 3,3 5,3 7,3

0

20

40

60

80

100

120

140

1977-1992 1993-2012

5 years

1,1 2,5 3,5 5,5 7,5

No.

ve

sse

ls

0

20

40

60

80

100

120

140

7 years

Deliveries, Years

1,1 2,7 3,7 5,7 7,7

0

20

40

60

80

100

120

140

(a)

(b)

(c)


56

Appendix B 2. Harvest in pounds included in full (1,1) dataset and subsets with varying number of


fishery in Norton Sound.

3 years

1,1 2,3 3,3 5,3 7,3-0

2

4

6

8

10

12

1977-1992 1993-2012

5 years

1,1 2,5 3,5 5,5 7,5

Har

vest

(lb

s*1

06)

-0

2

4

6

8

10

12

7 years

Deliveries, Years

1,1 2,7 3,7 5,7 7,7-0

2

4

6

8

10

12

(a)

(b)

(c)


57

Appendix B 3. CPUE in terms of numbers per pot of the full (1,1) dataset and subsets with varying


fishery in Norton Sound. Results of significant Z-tests of the hypothesis that the subset mean is equal to

that of the full data set are shown in the form of p-values.

3 years

1,1 2,3 3,3 5,3 7,30

10

20

30

40

1977-1992 1993-2012

5 years

1,1 2,5 3,5 5,5 7,5

CP

UE

(n

o./p

ot)

0

10

20

30

40

7 years

Deliveries, Years

1,1 2,7 3,7 5,7 7,70

10

20

30

40

(a)

(b)

(c)

p<0.

001

p<0.

01

p<0.

001

p<0.

0001

p<0.

01

p<0.

001

p<0.

0001

p<0.

0001

p<0.

0001

p<0.

0001

p<0.

0001

p<0.

0001


58

Appendix B 4. Modified Statistical Area composition of harvest in pounds for full (1,1) and subsets with

varying delivery and year selection criteria for two different time series for the summer commercial red

king crab fishery in Norton Sound. Contingency tables are provided in Appendix A.

3 years

1,1 2,3 3,3 5,3 7,30

10

20

30

40

1977-1992 1993-2012

5 years

1,1 2,5 3,5 5,5 7,5

CP

UE

(no

./pot

)

0

10

20

30

40

7 years

Deliveries, Years

1,1 2,7 3,7 5,7 7,70

10

20

30

40

(a)

(b)

(c)

p<0.

001

p<0.

01

p<0.

001

p<0.

0001

p<0.

01

p<0.

001

p<0.

0001

p<0.

0001

p<0.

0001

p<0.

0001

p<0.

0001

p<0.

0001


59

Appendix B 5. Scatter with loess smoother, Spearman’s rank correlation coefficient, and frequency

histogram for variables considered for inclusion in generalized linear modeling to standardize CPUE for

the summer commercial red king crab fishery in Norton Sound. Data is from vessels having two

deliveries for three years over the 1977–1992 time series. The correlation coefficient’s font size is

proportional to the number. Axes are factor levels for variables Year (YR), Vessel (VSL), Permit Fishery

(PF), Month of Year (MOY), Modified Statistical Area (MSA), and values for the continuous variable

log(CPUE in numbers) (L.CPUE.NO).

L.CPUE.NO

2 6 10 14 5.0 5.4 5.8 2 4 6 8 10

01

23

45

26

1014

0.62YR

0.10 0.27

VSL

12

34

56

5.0

5.4

5.8

0.26 0.39 0.08

PF

0.061 0.24 0.067 0.30

MOY

1.0

1.5

2.0

2.5

3.0

24

68

10

0.069 0.046 0.11 0.24 0.87WOY

0 1 2 3 4 5

0.26 0.35

1 2 3 4 5 6

0.17 0.083

1.0 1.5 2.0 2.5 3.0

0.38 0.46

1.0 2.0 3.0 4.01.

02.

03.

04.

0

MSA


60

L.CPUE.NO

5 10 15 20 1 2 3 4 5 6 5 10 15

-11

35

510

1520

0.34

YR

0.043 0.37

VSL

010

2030

12

34

56

0 .041 0.13 0 . 0 3 2

PF

0.072 0.057 0 . 0 0 2 9 0.23

MOY

1.0

2.0

3.0

4.0

510

15

0.076 0 . 0 3 4 0 . 0 0 8 3 0.23 0.85WOY

-1 1 3 5

0.20 0.16

0 10 20 30

0 . 0 1 5 0 .047

1.0 2.0 3.0 4.0

0.066 0.059

1.0 2.0 3.0 4.01.

02.

03.

04.

0

MSA


61

Appendix B 6. Scatter with loess smoother, Spearman’s rank correlation coefficient, and frequency

histogram for variables considered for inclusion in generalized linear modeling to standardize CPUE for

the summer commercial red king crab fishery in Norton Sound. Data is from vessels having three

deliveries for five years over the 1993–2012 time series. The correlation coefficient’s font size is

proportional to the number. The correlation coefficient’s font size is proportional to the number. Axes are

factor levels for variables Year (YR), Vessel (VSL), Permit Fishery (PF), Month of Year (MOY), Week of

Year (WOY), Modified Statistical Area (MSA), and values for the continuous variable log(CPUE in

numbers) (L.CPUE.NO).


62

AppendixC.ModelParameterEstimates

Appendix C 1. Summary for the generalized linear model of: log(CPUE)~Year+Vessel+Modified

Statistical Area+Week of Year. CPUE is in terms of numbers per pot and data is from the Norton Sound

red king crab summer commercial fishery for vessels having two deliveries for three years over the time

series 1977–1992. The forward stepwise selection process used a stopping point of R2 difference > 0.01.

Factor:Level Estimate

Std.

Error t value Pr(>|t|:

Intercept 0.78 0.81 0.96 0.3380

YR:1978 0.76 0.56 1.36 0.1773

YR:1979 -0.03 0.35 -0.09 0.9306

YR:1980 -0.20 0.39 -0.52 0.6068

YR:1981 -1.34 0.36 -3.74 0.0003

YR:1982 -1.74 0.64 -2.72 0.0074

YR:1983 -1.09 0.54 -2.00 0.0476

YR:1984 -0.60 0.60 -1.00 0.3170

YR:1985 -1.33 0.54 -2.47 0.0150

YR:1986 -0.18 0.77 -0.23 0.8164

YR:1987 -1.21 0.72 -1.68 0.0952

YR:1989 -0.24 0.65 -0.38 0.7071

YR:1990 -0.36 0.66 -0.55 0.5857

YR:1992 -2.17 0.60 -3.62 0.0004

VSL:AB 0.03 0.24 0.14 0.8901

VSL:AC 0.51 0.21 2.44 0.0161

VSL:AD 0.85 0.26 3.28 0.0014

VSL:AE 0.01 0.21 0.05 0.9584

VSL:AF 0.33 0.22 1.47 0.1442

MSA:Mid 1.08 0.50 2.13 0.0348

MSA:Outer 0.97 0.48 2.02 0.0452

MSA:Outer North 0.50 0.51 0.98 0.3271

WOY:28 1.71 0.68 2.51 0.0135

WOY:29 1.82 0.70 2.59 0.0108

WOY:30 1.50 0.69 2.16 0.0325

WOY:31 1.25 0.74 1.69 0.0936


63

Appendix C 1. Page 2 of 2.

Factor:Level Estimate

Std.

Error t value Pr(>|t|:

WOY:32 1.45 0.81 1.80 0.0736

WOY:33 1.38 0.82 1.68 0.0946

WOY:34 1.60 0.84 1.90 0.0591

WOY:35 1.37 0.86 1.59 0.1139

WOY:36 2.27 0.88 2.57 0.0114


64

Appendix C 2. Summary for the generalized linear model of: log(CPUE:~Year+Vessel+Week of

Year+Modified Statistical Area+Permit fishery. CPUE is in terms of numbers per pot and data is from the

Norton Sound red king crab summer commercial fishery for vessels having three deliveries for five years

over the time series 1993–2012. The forward stepwise selection process used a stopping point of R2

difference > 0.01.

Factor:Level Estimate Std.

Error t value Pr(>|t|: Intercept 1.85 0.24 7.59 0.00

YR:1994 -0.20 0.13 -1.54 0.12

YR:1995 -0.89 0.13 -6.88 0.00

YR:1996 -0.75 0.14 -5.31 0.00

YR:1997 -0.29 0.15 -1.92 0.06

YR:1998 -0.31 0.17 -1.79 0.07

YR:1999 -0.22 0.17 -1.29 0.20

YR:2000 0.09 0.13 0.71 0.48

YR:2001 -0.62 0.13 -4.70 0.00

YR:2002 0.10 0.13 0.74 0.46

YR:2003 -0.19 0.13 -1.44 0.15

YR:2004 0.18 0.13 1.34 0.18

YR:2005 0.11 0.13 0.84 0.40

YR:2006 0.17 0.13 1.28 0.20

YR:2007 -0.07 0.13 -0.52 0.61

YR:2008 0.17 0.13 1.28 0.20

YR:2009 -0.31 0.13 -2.34 0.02

YR:2010 0.05 0.13 0.35 0.72

YR:2011 0.42 0.13 3.15 0.00

YR:2012 0.10 0.13 0.76 0.45

VSL:AB -0.22 0.09 -2.30 0.02

VSL:AC -0.07 0.08 -0.86 0.39

VSL:AD -0.03 0.08 -0.32 0.75

VSL:AE -0.10 0.11 -0.91 0.36

VSL:AF -0.40 0.09 -4.48 0.00

VSL:AG 0.45 0.08 5.52 0.00

VSL:AH 0.32 0.07 4.32 0.00

VSL:AI 0.08 0.08 0.96 0.34

VSL:AJ 0.07 0.11 0.65 0.52

VSL:AK -0.20 0.10 -2.03 0.04

VSL:AL 0.55 0.08 7.09 0.00

VSL:AM 0.14 0.11 1.25 0.21

VSL:AN 0.16 0.09 1.81 0.07


65

Appendix C2. Page 2 of 3.


Error t value Pr(>|t|: VSL:AO -0.07 0.10 -0.74 0.46

VSL:AP -0.19 0.11 -1.66 0.10

VSL:AQ -0.77 0.11 -6.88 0.00

VSL:AR 0.04 0.08 0.46 0.65

VSL:AS 0.22 0.08 2.65 0.01

VSL:AT 0.23 0.10 2.25 0.02

VSL:AU -0.25 0.09 -2.78 0.01

VSL:AV 0.15 0.10 1.52 0.13

VSL:AW 0.00 0.10 -0.03 0.98

VSL:AX -0.10 0.09 -1.03 0.30

VSL:BA 0.22 0.10 2.34 0.02

VSL:BB -0.19 0.14 -1.38 0.17

VSL:BC 0.43 0.09 5.04 0.00

VSL:BD 0.04 0.09 0.46 0.65

VSL:BE 0.10 0.09 1.10 0.27

VSL:BF 0.22 0.07 3.00 0.00

VSL:BG 0.57 0.09 6.47 0.00

VSL:BH -0.15 0.11 -1.41 0.16

VSL:BI -0.25 0.11 -2.23 0.03

VSL:BJ -0.27 0.12 -2.28 0.02

VSL:BK -0.16 0.09 -1.73 0.08

VSL:BL -0.11 0.12 -0.91 0.36

VSL:BM 0.52 0.11 4.68 0.00

VSL:BN 0.28 0.09 3.01 0.00

WOY:25 0.19 0.13 1.52 0.13

WOY:26 0.25 0.13 1.94 0.05

WOY:27 0.34 0.13 2.69 0.01

WOY:28 0.33 0.13 2.61 0.01

WOY:29 0.37 0.13 2.90 0.00

WOY:30 0.35 0.13 2.72 0.01

WOY:31 0.40 0.13 3.15 0.00

WOY:32 0.47 0.13 3.64 0.00

WOY:33 0.44 0.13 3.31 0.00

WOY:34 0.65 0.13 4.85 0.00

WOY:35 0.68 0.15 4.58 0.00

WOY:36 0.60 0.16 3.75 0.00

WOY:37 1.37 0.17 7.96 0.00

WOY:38 0.86 0.44 1.95 0.05

WOY:39 2.08 0.44 4.68 0.00


66

Appendix C 2. Page 3 of 3.


Error t value Pr(>|t|: MSA:Mid 0.03 0.03 0.99 0.32

MSA:Outer -0.25 0.04 -6.12 0.00

MSA:Outer North -0.48 0.08 -6.22 0.00

PF:K09Z 0.25 0.15 1.63 0.10

PF:K09ZE 0.13 0.16 0.78 0.43

PF:K09ZF 0.42 0.22 1.87 0.06

PF:K91Z 0.25 0.62 0.40 0.69


67

AppendixD.StandardizedCPUEdata

Appendix D 1. Base year, standardized, and scaled arithmetic CPUE indices and their standard error from

the generalized linear model: log(CPUE)~Year+Vessel+Modified Statistical Area+Week of Year. Data is

from the Norton Sound red king crab fishery for the data subset of vessels having two deliveries in three

years from 1977–1992. The forward stepwise selection process used a stopping point of R2 difference >

0.01.

Year

Base year Standardized Scaled arithmetic

CPUE SE CPUE SE CPUE 1977 1.79 0.25 2.01 0.42 1.68

1978 3.17 0.14 4.29 0.30 3.92

1979 1.79 0.19 1.94 0.27 2.15

1980 1.72 0.20 1.64 0.31 1.61

1981 0.65 0.14 0.52 0.27 0.72

1982 0.37 0.20 0.35 0.33 0.35

1983 0.67 0.34 0.68 0.34 0.71

1984 1.29 0.23 1.10 0.29 1.15

1985 0.59 0.19 0.53 0.23 0.63

1986 2.08 0.47 1.68 0.51 1.81

1987 0.64 0.47 0.60 0.47 0.56

1988

1989 1.38 0.47 1.57 0.45 1.20

1990 1.35 0.47 1.39 0.43 1.17

1991

1992 0.19 0.47 0.23 0.45 0.24


68

Appendix D 2. Base year, standardized, and scaled arithmetic CPUE indices and their standard error from

the generalized linear model: log(CPUE)~Year+Vessel+Week of Year+Modified Statistical Area+Permit

fishery. Data is from the Norton Sound red king crab fishery for a subset of vessels having three deliveries

in five years from 1993–2012. The forward stepwise selection process used a stopping point of R2

difference > 0.01.

Year

Base year Standardized Scaled

arithmetic

CPUE SE CPUE SE CPUE 1993 0.97 0.12 1.13 0.12 1.02

1994 0.72 0.06 0.92 0.06 0.71

1995 0.40 0.05 0.46 0.05 0.39

1996 0.56 0.07 0.54 0.07 0.57

1997 0.78 0.09 0.84 0.09 0.93

1998 0.70 0.12 0.83 0.12 0.69

1999 0.52 0.12 0.91 0.12 0.59

2000 1.38 0.05 1.24 0.06 1.42

2001 0.74 0.04 0.61 0.04 0.69

2002 1.20 0.06 1.25 0.05 1.13

2003 0.97 0.05 0.94 0.05 0.93

2004 1.36 0.04 1.35 0.05 1.41

2005 1.34 0.04 1.26 0.04 1.38

2006 1.51 0.04 1.34 0.04 1.45

2007 1.12 0.05 1.06 0.04 1.07

2008 1.53 0.04 1.34 0.05 1.44

2009 1.02 0.04 0.83 0.04 1.02

2010 1.37 0.04 1.18 0.04 1.31

2011 1.89 0.05 1.73 0.05 1.83

2012 1.51 0.04 1.25 0.04 1.47

AppendixE.Rcode

## Note that this version has no imputing and that CFEC and Mngmt data have been removed

## Preliminary data processing

## Norton Sound red king crab fish ticket data preparation prior to analysis

#Datasubsetnameoptionsare:c("77‐92","77‐12","93‐12",)Yrname<‐"93‐12"#Numberofdeliveryoptionsare:c("2","3","5","7")Dlchoice<‐3#Optionsforthenumberofyearswiththespecifiednumberofdeliveriesare:c("3","5","7")Yrchoice<‐7Dataname<‐paste("Yrs",Yrname,"Del",Dlchoice,"Yr",Yrchoice,sep="")##‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐##Summarizerawdataforanalysis#Readdatain(n=7447*59)NSdata<‐read.csv("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Data/NSRKCFT69‐12Summer.csv",header=T)#Eliminateunnecessarydatacolumnsandtheyear1977(78‐12:n=7411*10),(78‐92:n=XX*XX),(93‐12:n=7411)NSdata<‐data.frame(NSdata$BATCH_YEAR,NSdata$SEQ_TICKET_NUMBER,NSdata$PERMIT_FISHERY,NSdata$ADFG_NUMBER,NSdata$DATE_FISHING_BEGAN,NSdata$DATE_LANDED,NSdata$STAT_AREA_1985,NSdata$EFFORT,NSdata$NUMBER_OF_FISH,NSdata$WHOLE_POUNDS)names(NSdata)<‐c("YR","TCKTNM","PF","VSL","DTBGN","DTLND","SA","EFRT","NO.CRB","LB.CRB")#Determineyearsubset(77‐92:n=925),(93‐12:n=6522*10)if(Yrname=="77‐92"){NSdata<‐NSdata[NSdata$YR<1993,]}else{if(Yrname=="93‐12"){NSdata<‐NSdata[NSdata$YR>1992,]}else{if(Yrname=="77‐12"){NSdata<‐NSdata[NSdata$YR>1976,]}}}#DesignatesomedatacolumnsasfactorialNSdata$YR<‐as.factor(NSdata$YR)NSdata$VSL<‐as.factor(NSdata$VSL)NSdata$PF<‐as.factor(NSdata$PF)NSdata$SA<‐as.factor(NSdata$SA)NSdata$DTLND<‐as.Date(NSdata$DTLND,"%m/%d/%Y")NSdata$DTBGN<‐as.Date(NSdata$DTBGN,"%m/%d/%Y")NSdata$EFRT<‐as.numeric(NSdata$EFRT)NSdata$LB.CRB<‐as.numeric(NSdata$LB.CRB)NSdata$NO.CRB<‐as.numeric(NSdata$NO.CRB)#Replaceblankeffortwith0andsummarizebyyear,ticketnumber,andstatareaand(77‐92:n=807*10),(93‐12:n=5291*10)NSdata$EFRT[is.na(NSdata$EFRT)]<‐0NSdata<‐aggregate(x=NSdata[,c("EFRT","NO.CRB","LB.CRB")],by=list(NSdata$YR,NSdata$VSL,NSdata$TCKTNM,NSdata$SA,NSdata$PF,NSdata$DTLND,NSdata$DTBGN),FUN=sum)names(NSdata)<‐c("YR","VSL","TCKTNM","SA","PF","DTLND","DTBGN","EFRT","NO.CRB","LB.CRB")#DeleterecordswhereMNWTeither<2%quantileor>98%quantileormissing(78‐92,n=788)


70

#FirsteliminaterowswhereNO.CRB=0orEFRT=0NSdata<‐NSdata[NSdata$NO.CRB>0&NSdata$EFRT>0,]MNWT<‐numeric(dim(NSdata)[1])#Nextcalculatedelivery‐specificmeanweightfor(iin1:dim(NSdata)[1]){if(NSdata$NO.CRB[i]>0){MNWT[i]<‐NSdata$LB.CRB[i]/NSdata$NO.CRB[i]}else{MNWT[i]<‐NA}}NSdata<‐(cbind(NSdata,MNWT))#Thencalculate2%and98%quantilesq2<‐quantile(NSdata$MNWT,.02,na.rm=TRUE)q98<‐quantile(NSdata$MNWT,.98,na.rm=TRUE)#ComputevectorofYear‐specificmeanweightsMNWTV<‐aggregate(x=NSdata[,c("MNWT")],by=list(NSdata$YR),FUN=mean)names(MNWTV)<‐c("Year","MW")#ReplaceMNWTforanyyearwhereitismissingwiththemeanofmeansforotheryears(78‐92:n=623)for(iin1:dim(MNWTV)[1]){if(is.na(MNWTV$MW[i])){MNWTV$MW[i]<‐mean(MNWTV$MW,na.rm=T)}}#ThenreplaceNO.CRBwithNAsforrecordswhereMNWTisoutsidethequantilesfor(iin1:dim(NSdata)[1]){if(NSdata$MNWT[i]<q2[[1]]||NSdata$MNWT[i]>q98[[1]]||is.na(NSdata$MNWT[i])){NSdata$NO.CRB[i]<‐NA}}#NextdeleteNANO.CRBrecordsNSdata<‐na.omit(NSdata)#GetridofMNWTdatacolumnNSdata<‐NSdata[,c(1:10)]#ComputecounterfordimensionsofNSdatan<‐dim(NSdata)[1]#Createvectorsfor:"Monthofyear,""Weekofyear,"and"Modifiedstatisticalarea"MOY<‐numeric(n);WOY<‐numeric(n);MSA<‐character(n)for(iin1:n){d<‐NSdata$DTLND[i];MOY[i]<‐as.numeric(format(d,format="%m"));WOY[i]<‐as.numeric(format(d,format="%W"))if(NSdata$SA[i]==616331||NSdata$SA[i]==616401||NSdata$SA[i]==626331||NSdata$SA[i]==626401||NSdata$SA[i]==626402){MSA[i]<‐"Inner"}elseif(NSdata$SA[i]==636330||NSdata$SA[i]==636401||NSdata$SA[i]==636402||NSdata$SA[i]==646301||NSdata$SA[i]==646330||NSdata$SA[i]==646401||NSdata$SA[i]==646402){MSA[i]<‐"Mid"}elseif(NSdata$SA[i]==656300||NSdata$SA[i]==656330||NSdata$SA[i]==656401||NSdata$SA[i]==656402||NSdata$SA[i]==666230||NSdata$SA[i]==666300||NSdata$SA[i]==666330||NSdata$SA[i]==666401){MSA[i]<‐"Outer"}elseif(NSdata$SA[i]==666402||NSdata$SA[i]==666431||NSdata$SA[i]==676300||NSdata$SA[i]==676330||NSdata$SA[i]==676400||NSdata$SA[i]==676430||NSdata$SA[i]==676501||NSdata$SA[i]==686330){MSA[i]<‐"OuterNorth"}}#MakenewcolumnsfactorsMOY<‐as.factor(MOY);WOY<‐as.factor(WOY);MSA<‐as.factor(MSA)#Createvectorsfor"CPUE"intermsofnumbersandpoundsCPUE.NO<‐round(NSdata$NO.CRB/NSdata$EFRT,1)CPUE.LB<‐round(NSdata$LB.CRB/NSdata$EFRT,1)


71

#CbindnewcolumnstoNSdataNSdata<‐as.data.frame(cbind(NSdata,MOY,WOY,MSA,CPUE.NO,CPUE.LB))##Savesummarizedfulldatafiletable.name<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/NSdata",Yrname,".csv",sep="")write.csv(NSdata,file=table.name,row.names=T)##‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐##Coredataselectionprocedure#FirstsummarizebyYr,ADFG#,Tcktnm,fordata=sum(LBS)NSdata2<‐aggregate(x=NSdata[,c("LB.CRB")],by=list(NSdata$YR,NSdata$VSL,NSdata$TCKTNM),FUN=sum)names(NSdata2)<‐c("YR","VSL","TCKTNM","S.LB.CRB")#Thenextractthefirst3columnsCore<‐NSdata2[,c(1:3)]#SummarizebyYear,ADFG#fordata=count(TCKTNM)(n=682)library(plyr)Core<‐ddply(.data=Core,.var=c("YR","VSL"),.fun=nrow)names(Core)<‐c("YR","VSL","NMTCKT")#FilterforTcktnm>=2,3,5,or7if(Dlchoice=="2"){Core<‐Core[Core$NMTCKT>1,]}else{if(Dlchoice=="3"){Core<‐Core[Core$NMTCKT>2,]}else{if(Dlchoice=="5"){Core<‐Core[Core$NMTCKT>4,]}else{if(Dlchoice=="7"){Core<‐Core[Core$NMTCKT>6,]}}}}Core<‐ddply(.data=Core,.var=c("VSL"),.fun=nrow)names(Core)<‐c("VSL","NMYR")#WhenNMYR=2,3,5,or7replaceCorewith">1yr"">2yr",">4yr",or">6yr"n<‐dim(Core)[1];Core7<‐character(n);Core5<‐character(n);Core3<‐character(n);Core2<‐character(n)for(iin1:n){ifelse(Core$NMYR[i]>6,Core7[i]<‐"Y",Core7[i]<‐"N")ifelse(Core$NMYR[i]>4,Core5[i]<‐"Y",Core5[i]<‐"N")ifelse(Core$NMYR[i]>2,Core3[i]<‐"Y",Core3[i]<‐"N")ifelse(Core$NMYR[i]>1,Core2[i]<‐"Y",Core2[i]<‐"N")}#CbindCorewithCore2,3,5,and7Core<‐cbind(Core,Core7,Core5,Core3,Core2)#Savesummarizedcoredefinitiontable.name<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/Coredef",Dataname,".csv",sep="")write.csv(Core,file=table.name,row.names=T)#JoinNSdatawithCorebyADFG#NSdata<‐merge(NSdata,Core,by=c("VSL"),all.x=TRUE,all.y=TRUE)#Filteraccordingtodesiredno.yearshavingspecifiedno.deliveries(78‐12:n=4807*25;);(78‐92:n=229*25),(93‐12:n=4581*25)if(Yrchoice=="2"){NSdata<‐NSdata[NSdata$Core2=="Y"&NSdata$CPUE.NO>0,]


72

}else{if(Yrchoice=="3"){NSdata<‐NSdata[NSdata$Core3=="Y"&NSdata$CPUE.NO>0,]}else{if(Yrchoice=="5"){NSdata<‐NSdata[NSdata$Core5=="Y"&NSdata$CPUE.NO>0,]}else{if(Yrchoice=="7"){NSdata<‐NSdata[NSdata$Core7=="Y"&NSdata$CPUE.NO>0,]}}}}#GetridofNAsand0CPUE(78‐12:n=4721);(78‐92:n=169),(93‐12:n=4554)NSdata<‐na.omit(NSdata)NSdata<‐NSdata[NSdata$CPUE.NO!=0,]NSdata$CPUE.NO<‐NSdata$CPUE.NO+0.1#Addnewcolumnsforlog(CPUE.LB),log(CPUE.NO)L.CPUE.NO<‐log(NSdata$CPUE.NO)L.CPUE.LB<‐log(NSdata$CPUE.LB)NSdata<‐as.data.frame(cbind(NSdata,L.CPUE.NO,L.CPUE.LB))NSdata<‐na.omit(NSdata)##RecodeOWNRandVSLtopreserveconfidentiality#Firstcreatevectorsofequallengthcontainingalphabetn<‐dim(NSdata)[1]NSdata$VSL<‐NSdata$VSL[drop=TRUE]o<‐length(levels(NSdata$VSL))VSLL<‐levels(NSdata$VSL)ALPHS<‐character(n)for(iin0:23){for(jin1:24){ALPHS[i*24+j]<‐paste(LETTERS[i+1],LETTERS[j],sep="")}}VSL.codes<‐ALPHS[1:o]#NextreplaceVSLwithtwo‐digitalphabeticcharactersrequire(car)for(iin1:o){NSdata$VSL<‐recode(NSdata$VSL,"VSLL[i]=VSL.codes[i]")}##Selectvariablesforinclusioninmodelbyconductingscatterplot,correlationandcalculatingVIFs##createafunctiontomakehistogramstoputonthediagonalpanel.hist<‐function(x,...){usr<‐par("usr");on.exit(par(usr))par(usr=c(usr[1:2],0,1.5))h<‐hist(x,plot=FALSE)breaks<‐h$breaks;nB<‐length(breaks)y<‐h$counts;y<‐y/max(y)rect(breaks[‐nB],0,breaks[‐1],y,col="black",...)}##createafunctiontomakecorrelationstoputonthediagonalpanel.cor<‐function(x,y,digits=2,prefix="",cex.cor,...){usr<‐par("usr");on.exit(par(usr))par(usr=c(0,1,0,1))r<‐abs(cor(x,y,method="spearman"))txt<‐format(c(r,0.123456789),digits=digits)[1]txt<‐paste(prefix,txt,sep="")if(missing(cex.cor))cex.cor<‐1.25/strwidth(txt)text(0.5,0.5,txt,cex=cex.cor*r)


73

}#Openaplotwindowwin.graph(width=14,height=14)#Createthescatterplotwith(NSdata,pairs(NSdata[,c(21,2,1,5,11,12,13)],upper.panel=panel.smooth,lower.panel=panel.cor,diag.panel=panel.hist,cex.labels=1.25,font.labels=2))#Savethefigureplotname<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/Scatter.plot",Dataname,".wmf",sep="")#TellRwheretosavegraphsavePlot(plotname,type="wmf")##‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐##Initialenvironmentsettingoptions(contrasts=c("contr.treatment","contr.poly"))options(object.size=100000000)#Savesummarizedcoredatafile(78‐12:n=4601)NSdata<‐NSdata[NSdata$L.CPUE.NO>0,]table.name<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/NScoredata",Dataname,".csv",sep="")write.csv(NSdata,file=table.name,row.names=T)##ReadsummarizedNortonSoundRKCfishticketdata.csvfiledatacore<‐NSdata##ProduceAICtableoffishticketdata#Produceglms‐‐notethatPFisexcludedforyearspriorto1993YR.glm<‐glm(datacore$L.CPUE.NO~factor(YR),data=datacore)MOY.glm<‐glm(datacore$L.CPUE.NO~factor(MOY),data=datacore)WOY.glm<‐glm(datacore$L.CPUE.NO~factor(WOY),data=datacore)PF.glm<‐glm(datacore$L.CPUE.NO~factor(PF),data=datacore)MSA.glm<‐glm(datacore$L.CPUE.NO~factor(MSA),data=datacore)VSL.glm<‐glm(datacore$L.CPUE.NO~factor(VSL),data=datacore)##WriteAICsfromglmstodataframemod.aic<‐c(YR.glm$aic,MOY.glm$aic,WOY.glm$aic,PF.glm$aic,MSA.glm$aic,VSL.glm$aic)names(mod.aic)<‐c("YR","MOY","WOY","PF","MSA","VSL")#Savedataintableformmod.aic<‐as.data.frame(mod.aic)table.name<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/AIC.table",Dataname,".csv",sep="")write.csv(mod.aic,file=table.name,row.names=T)##UseShapiro‐WilkstesttoseeiflogCPUE.NOisnormallydistributedshapiro.test(datacore$L.CPUE.NO)##Readfunction"stepCPUE"intoenvironment


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source("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Rcode/stepCPUE.R")##‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐##FindthebestmodelfromfitoflogCPUE.NObyglmandstepwiseglmusingthefunction"stepCPUE"glm.object<‐glm(L.CPUE.NO~factor(YR),data=datacore)obsdatout<‐stepCPUE(glm.object,scope=list(upper=~factor(YR)+factor(VSL)+factor(WOY)+factor(MSA)+factor(PF),lower=~factor(YR),direction="forward",trace=9,r2.change=0.01))#Testforsecond‐orderinteractionsobsdatout<‐stepCPUE(glm.object,scope=list(upper=~(factor(YR)+factor(VSL)+factor(MSA)+factor(WOY))^2,lower=~factor(YR),direction="forward",trace=9,r2.change=0.01))##Resultsfromfitoflog(NO.CRB)tothebestmodelbest.glm<‐glm(L.CPUE.NO~factor(YR)+factor(VSL)+factor(WOY)+factor(MSA)+factor(PF),data=datacore)##‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐‐#Testforcollinearityrequire(car)fit<‐lm(best.glm$formula,data=datacore)vfit<‐vif(fit)detach(package:car)#Writeviftabletoafiletable.name<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/VIF.table",Dataname,".csv",sep="")write.csv(vfit,file=table.name,row.names=T)detach(package:car)###Starthereforglm##Readfunction"getCPUE"intoenvironmentsource("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Rcode/getCPUE.R")##Getrelativeindices(withthebaseyear=1)sumglm<‐summary(best.glm)##Getcanonicalindices(CL)#std.cpue.glm<‐getCPUE(best.glm,2:14,c(1977:1987,1989,1990,1992))##1977‐1992std.cpue.glm<‐getCPUE(best.glm,2:19,c(1993:1998,2000:2012))##1993‐2012#Getbase‐yearglmintermsofNo.(withthebaseyear=1)(BY)base.glm<‐glm(L.CPUE.NO~factor(YR),y=TRUE,data=datacore)sumglm1<‐summary(base.glm)##GetarithmeticCPUEindexintermsofNO(A)RCPUE<‐as.data.frame(tapply(datacore$CPUE.NO,datacore$YR,mean))RCPUE<‐na.omit(RCPUE)names(RCPUE)<‐c("CPUE")GMRCPUE<‐exp(sapply(log(RCPUE),mean))RCPUEdash<‐RCPUE$CPUE/GMRCPUE##Getbase‐yearrelativeindices(withbaseyear=1)#base.cpue.glm<‐getCPUE(base.glm,2:14,c(1977:1987,1989,1990,1992))##1977‐1992base.cpue.glm<‐getCPUE(base.glm,2:19,c(1993:1998,2000:2012))##1993‐2012


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##Makedataframefromall3CPUEindicesNS.Std.CPUE<‐as.data.frame(cbind(base.cpue.glm$Year,base.cpue.glm$Index,base.cpue.glm$SE,std.cpue.glm$Index,std.cpue.glm$SE,RCPUEdash))names(NS.Std.CPUE)<‐list("YR","BY.CPUE","BY.SE","ST.CPUE","ST.SE","A.CPUE")table.name<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/NS.Std.CPUE",Dataname,".csv",sep="")write.csv(NS.Std.CPUE,file=table.name,row.names=T)##PlotCPUE#Openagraphicswindowwin.graph(width=14,height=14)#Setgraphicsparameterspar(mfrow=c(1,1),cex=.75,ps=12)library(gplots)#forplotCIattach(NS.Std.CPUE)if(Yrname=="77‐92"){plotCI(x=NS.Std.CPUE$YR,y=NS.Std.CPUE$ST.CPUE,uiw=NS.Std.CPUE$ST.SE,liw=NS.Std.CPUE$ST.SE,col="black",barcol="black",pch=21,pt.bg="white",cex=2,cex.axis=1.25,cex.lab=1.5,lty=1,type="o",gap=0,sfrac=0.005,xlim=c(1976,1994),xaxs="r",xaxp=c(1976,1994,9),xlab="Year",ylim=c(0,5),yaxs="r",yaxp=c(0,5,5),ylab="RelativeCPUEindex",main="NortonSoundRedKingCrabStandardizedCPUE",las=1,font.lab=1)plotCI(x=NS.Std.CPUE$YR,y=NS.Std.CPUE$BY.CPUE,uiw=NS.Std.CPUE$BY.SE,liw=NS.Std.CPUE$BY.SE,col="black",barcol="black",pch=22,pt.bg="white",cex=2,lty=1,type="o",gap=0,sfrac=0.005,add=TRUE)plotCI(x=NS.Std.CPUE$YR,y=NS.Std.CPUE$A.CPUE,uiw=NA,col="black",barcol="black",pch=23,pt.bg="white",cex=2,lty=0,type="o",gap=0,sfrac=0.005,add=TRUE)legend(x=1990,y=3.5,box.lty=0,legend=c("ST.CPUE","BY.CPUE","A.CPUE"),pch=c(21,22,23),pt.bg=c("white","white","white"),pt.cex=c(1.8,1.8,1.8),lty=c(1,1,1))}else{if(Yrname=="93‐12"){plotCI(x=NS.Std.CPUE$YR,y=NS.Std.CPUE$ST.CPUE,uiw=NS.Std.CPUE$ST.SE,liw=NS.Std.CPUE$ST.SE,col="black",barcol="black",pch=21,pt.bg="white",cex=2,cex.axis=1.25,cex.lab=1.5,lty=1,type="o",gap=0,sfrac=0.005,xlim=c(1992,2014),xaxs="r",xaxp=c(1992,2014,11),xlab="Year",ylim=c(0,3),yaxs="r",yaxp=c(0,3,3),ylab="RelativeCPUEindex",main="NortonSoundRedKingCrabStandardizedCPUE",las=1,font.lab=1)plotCI(x=NS.Std.CPUE$YR,y=NS.Std.CPUE$BY.CPUE,uiw=NS.Std.CPUE$BY.SE,liw=NS.Std.CPUE$BY.SE,col="black",barcol="black",pch=22,pt.bg="white",cex=2,lty=1,type="o",gap=0,sfrac=0.005,add=TRUE)plotCI(x=NS.Std.CPUE$YR,y=NS.Std.CPUE$A.CPUE,uiw=NA,col="black",barcol="black",pch=23,pt.bg="white",cex=2,lty=0,type="o",gap=0,sfrac=0.005,add=TRUE)legend(x=2010,y=2.3,box.lty=0,legend=c("ST.CPUE","BY.CPUE","A.CPUE"),pch=c(21,22,23),pt.bg=c("white","white","white"),pt.cex=c(1.8,1.8,1.8),lty=c(1,1,1))}}plotname<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/CPUE.plot",Dataname,".wmf",sep="")savePlot(plotname,type="wmf")detach(NS.Std.CPUE)detach(package:gplots)


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##Getmodelfitdiagnosticsforglm#Lookatmodelsummarymod.sum<‐summary(best.glm)table.name<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/Model_summary",Dataname,".csv",sep="")write.csv(mod.sum$coefficients,file=table.name,row.names=T)#Lookatdesignmatrixdes.mat<‐model.matrix(best.glm)table.name<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/Design_matrix",Dataname,".csv",sep="")write.csv(des.mat,file=table.name,row.names=T)##Extractvariousinfluencemeasuresforglmrequire(car)y.hat<‐best.glm$fitted.valuese<‐best.glm$residuals#Computestandardizedresidualsr<‐rstandard(best.glm)#Extractleveragesh<‐hatvalues(best.glm)#Extractstudentizeddeletedresidualsstud<‐rstudent(best.glm)#GetCooksdistancec.d<‐cooks.distance(best.glm)#GetDFfitsd.f<‐dffits(best.glm)#Getmodelnandkn<‐length(best.glm$effects)k<‐length(best.glm$xlevels)##Plotmodelfitdiagnosticsandresidualsglmwin.graph(width=14,height=14)#Setgraphicsparameterspar(mfrow=c(4,2),cex=.75,ps=12,mai=c(.6,.6,.3,.3))#win.graph(width=14,height=14)#Setgraphicsparameters#par(mfrow=c(3,2),cex=.75,ps=12,mai=c(.6,.6,.3,.3))#Pearsonresidualsvs.explanatoryvariablesinmodelresidualPlots(best.glm,terms=~.,layout=NA)#QQplotofresidualsqqnorm(r,main="")abline(a=0,b=1,lty=1)#Nameandsaveplotplotname<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/Resid_Fit.plot",Dataname,".wmf",sep="")#TellRwheretosavegraphsavePlot(plotname,type="wmf")##PlotPearsonresidualsforvariablesnotinmodelglm#Openagraphicswindow


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win.graph(width=14,height=14)#Setgraphicsparameterspar(mfrow=c(2,2),cex=.75,ps=12,mai=c(.6,.6,.3,.3))#Plots#nextgraphplot(e~datacore$MOY,xlab="MonthofYear",sub="(b)",ylab="Residuals",ylim=c(‐5,5),yaxp=c(‐5,5,10))abline(h=c(‐2,0,2),lty=c(2,1,2))#nextgraph#plot(e~datacore$PF,xlab="PermitFishery",sub="(b)",#ylab="Residuals",ylim=c(‐5,5),yaxp=c(‐5,5,10))#abline(h=c(‐2,0,2),lty=c(2,1,2))plotname<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/NIMResidual.plot",Dataname,".wmf",sep="")savePlot(plotname,type="wmf")#Plotinteractionsglm#Openagraphicswindowwin.graph(width=14,height=14)#Setgraphicsparameterspar(mfrow=c(2,2),cex=.75,ps=12,mai=c(.6,.6,.3,.3))interaction.plot(NSdata$YR,NSdata$VSL,NSdata$L.CPUE.NO,fun=mean,type=c("l"),legend=TRUE,xlab="Year",ylab="ln(CPUE,no)",col=palette(rainbow(6)))interaction.plot(NSdata$YR,NSdata$MSA,NSdata$L.CPUE.NO,fun=mean,type=c("l"),legend=TRUE,xlab="Year",ylab="ln(CPUE,no)",col=palette(rainbow(6)))interaction.plot(NSdata$YR,NSdata$PF,NSdata$L.CPUE.NO,fun=mean,type=c("l"),legend=TRUE,xlab="Year",ylab="ln(CPUE,no)",col=palette(rainbow(6)))interaction.plot(NSdata$YR,NSdata$WOY,NSdata$L.CPUE.NO,fun=mean,type=c("l"),legend=TRUE,xlab="Year",ylab="ln(CPUE,no)",col=palette(rainbow(6)))#Nameplotandsavegraphplotname<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/Interaction.plot",Dataname,".wmf",sep="")savePlot(plotname,type="wmf")##Testfornonlinearitythroughcomponentplusresidualplotsglm#Openagraphicswindowwin.graph(width=14,height=14)#Setgraphicsparameterspar(mfrow=c(3,2),cex=.75,ps=12,mai=c(.6,.6,.3,.3))crPlots(best.glm,layout=c(3,2))#TellRwheretosavegraphplotname<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/CPR.plot",Dataname,".wmf",sep="")savePlot(plotname,type="wmf")#Influenceplotsglm#Openagraphicswindowwin.graph(width=14,height=14)#Setgraphicsparameterspar(mfrow=c(2,2),cex=.75,ps=12,mai=c(.6,.6,.3,.3))#Plothat‐valuesplot(y.hat,h,xlab="Fittedvalues",ylab="Hat‐values",ylim=c(0,1),yaxp=c(0,1,5),xlim=c(‐5,5),xaxp=c(‐5,5,10))abline(h=c(‐2*mean(h),0,2*mean(h)),lty=c(2,1,2))


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#Identifyextremepointsidentify(y.hat,h)#Plot|DFfits|plot(y.hat,abs(d.f),xlab="Fittedvalues",ylab="|DFFits|",xlim=c(‐5,5),xaxp=c(‐5,5,10),ylim=c(0,1.5),yaxp=c(0,1.5,3))df.limit<‐2*sqrt((k+1)/(n))abline(h=c(0,df.limit),lty=c(1,2))#Identifyextremepointsidentify(y.hat,abs(d.f))#PlotCooksdistancesplot(y.hat,c.d,xlab="Fittedvalues",ylab="Cooksdistance",xlim=c(‐5,5),xaxp=c(‐5,5,10),ylim=c(0,.1),yaxp=c(0,.1,5))abline(h=qf(.5,5,36),lty=2)#Identifyextremepointsidentify(y.hat,c.d)#Influenceplotmod.influence<‐influencePlot(best.glm,id.n=5)plotname<‐paste("C:/Users/ghbishop/Documents/Analyses/NortonSndGLM/Analysis/Influence.plot",Dataname,".wmf",sep="")savePlot(plotname,type="wmf")detach(package:car)