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Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 Project May 31, 2007
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Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

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Page 1: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Population Connectivity and Management of an Emerging

Commercial Fishery

Crow White ESM 242 Project May 31, 2007

Page 2: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Adult (15 cm)

Recruits

Kellet’s whelk

Kelletia kelletii

Page 3: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Focus of developing fishery

Sold to US domestic Asian market (mostly in LA)

Mean price = $1.43/kg = ~$0.15/whelk

Ase

ltin

e-N

eils

on

et

al.

200

6

Page 4: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Caught as by-catch by commercial trap fishermen

Page 5: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Research questions:

What is the optimal harvest path that maximizes net present value of the Kellet’s whelk fishery?

Short-term.

Long-term.

How do they differ?

Page 6: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

SBA

NCI

Focus on Santa Barbara area

Two patches:

SBA: Santa Barbara mainland

NCI: Northern Channel Islands

Patches differ with respect to:

Habitat area, stock size & density

Intra- and inter-patch dispersal dynamics

Protection in reserves

Santa Barbara

Page 7: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

)(...

)...)()()...(

...)((

,,

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1

tAttA

TmKAg

ABTt

AATttt

HAmH

eeCB

CAAA

jAjTtA

j

j

EQUATION OF MOTION (patch A):

Adult stock [mt] Growth rate “Connectivity” = probability of dispersal

Harvest [mt] Annual natural mortality rate

Density dependent recruitment K = kelp [km2]

Juvenile mortality

t = time in years

Tj = time until reproductively mature = age of legal size for fishery

Page 8: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

CONSTRAINTS:

tt NH 0Harvest in a patch must be equal or greater than zero, as well as equal or less than the current stock in that patch

*, 2.0 BBH tBt

In Northern Channel Islands patch harvest may not reduce stock below 20% of its virgin size

Page 9: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

12 reserves constituting ~20% of the NCI coastline

Page 10: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

)(...

)...)()()...(

...)((

,,

)1(/

1

tAttA

TmKAg

ABTt

AATttt

HAmH

eeCB

CAAA

jAjTtA

j

j

EQUATION OF MOTION (patch A):

Adult stock [mt] Growth rate “Connectivity” = probability of dispersal

Harvest [mt] Annual natural mortality rate

Density dependent recruitment K = kelp [km2]

Juvenile mortality

t = time in years

Tj = time until reproductively mature = age of legal size for fishery

Page 11: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

SBA

NCI

Thanks Mike!

Page 12: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.
Page 13: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.
Page 14: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

SBA NCI

0.00

0.20

0.40

0.60

0.80D

en

sit

y +

/- S

E [

#/m

^2

]

(N = 4) (N = 4)

Pattern supported by lobster/Kellet’s whelk fisherman (John Wilson, per. comm. 16 May 2007)

Page 15: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.
Page 16: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Protected in reserves

Page 17: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

)(...

)...)()()...(

...)((

,,

)1(/

1

tAttA

TmKAg

ABTt

AATttt

HAmH

eeCB

CAAA

jAjTtA

j

j

EQUATION OF MOTION (patch A):

Adult stock [mt] Growth rate “Connectivity” = probability of dispersal

Harvest [mt] Annual natural mortality rate

Density dependent recruitment K = kelp [km2]

Juvenile mortality

t = time in years

Tj = time until reproductively mature = age of legal size for fishery

Page 18: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Mean size (n = 1000+)

m = 1/mean age = 0.068

Tj = ~6 years

Annual natural mortality rate:

Time until mature:

Mature:

(Growth data from D. Zacherl 2006 unpub. Res.)

Page 19: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

)(...

)...)()()...(

...)((

,,

)1(/

1

tAttA

TmKAg

ABTt

AATttt

HAmH

eeCB

CAAA

jAjTtA

j

j

EQUATION OF MOTION (patch A):

Adult stock [mt] Growth rate “Connectivity” = probability of dispersal

Harvest [mt] Annual natural mortality rate

Density dependent recruitment K = kelp [km2]

Juvenile mortality

t = time in years

Tj = time until reproductively mature = age of legal size for fishery

Page 20: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Kellet’s whelk, Kelletia kelletii

1000+ larvae per egg capsule

Page 21: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

mLog

K

Ng

1*

Density dependence coefficient

Given each patch is a closed system and Tj = 1:

N* = virgin carrying capacity.

Page 22: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

)(...

)...)()()...(

...)((

,,

)1(/

1

tAttA

TmKAg

ABTt

AATttt

HAmH

eeCB

CAAA

jAjTtA

j

j

EQUATION OF MOTION (patch A):

Adult stock [mt] Growth rate “Connectivity” = probability of dispersal

Harvest [mt] Annual natural mortality rate

Density dependent recruitment K = kelp [km2]

Juvenile mortality

t = time in years

Tj = time until reproductively mature = age of legal size for fishery

Page 23: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Csource-destination:

CSBA-SBA = 0.15

CSBA-NCI = 0.34

CNCI-NCI = 0.35

CNCI-SBA = 0.27

Gastropod larva K. kelletia settler

(OIPL 2007) (Koch 2006)

SBA

NCI

Thanks James!

Page 24: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Of the total number of settlers arriving at a patch:

Santa Barbara Area Northern Channel Islands

SBA NCI

Closed system:

Page 25: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Economics:

Revenue based on demand curve:

revenue(t) = choke price – (Harvest[t])(slope)

Cost based on stock effect:

cost(t) = θ / stock density

π(t) = (revenue[t] – cost[t])(1 – r)^-t

r = discount rate = 0.05

Page 26: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Choke price = max(Price [1979-2005])

All whelks in system

Profit calculated at end of each year’s harvest

Page 27: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

mr = mc = θ / density, when

density = 0.1*min(SBA* or NCI*)

Page 28: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

mr, given supply = 1 mt

Marginal profit calculated during harvest

Page 29: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Optimization procedure

Short-term: 40 years of harvest

Let un-harvested system equilibrate

Search for optimal harvest path: employ constrained nonlinear optimization function (derivative-based algorithm) in program Matlab.

Goal: find optimal H that maximizes NPV = ∑ π(t)

Long-term: Steady state (t → ∞)

Iterative exploration of all combinations of constant escapement (A – H ≈ 0 – 100%) in each patch.

run until system equilibrates

Goal: identify escapement combination that maximizes π at t = final.

Page 30: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Short-term (40-year) optimal harvest path

Page 31: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.
Page 32: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Harvest path is variable and different in the two patches

Page 33: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

HigherLower

Page 34: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Initial spike in harvest

Page 35: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Harvest limited by NCI reserve constraint

Page 36: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Harvest until mr = mc

Page 37: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Harvest path is semi-cyclic: due to delayed development?

Page 38: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

NPV = ∑ π(t) = $1,279,900

~$32,000/year

Page 39: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.
Page 40: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

10,000 simulations:NPV

H*H* - (v/2)(H*) H* + (v/2)(H*)

H(t) = H* + U[-v/2, +v/2](H*)

Page 41: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

10,000 simulations:

90% NPVH*H* - (v/2)(H*) H* + (v/2)(H*)

NPV

H(t) = H* + U[-v/2, +v/2](H*)

Page 42: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Long-term optimal harvest

Page 43: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Harvest everything

Page 44: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Harvest everything

$68,067/year

Page 45: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Harvest everything

$68,067/year

40-year horizon and r = 0.05: ~$31,000/year

Page 46: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Harvest everything

$68,067/year

40-year horizon and r = 0.05: ~$31,000/year

Page 47: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Harvest everything

$68,067/year

40-year horizon and r = 0.05: ~$31,000/year

Page 48: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Harvest everything

90%

Page 49: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

90%

Harvest everything

Plenty

Room for uncertainty:

Little

Page 50: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

90%

NCI reserve constraint

Harvest everything

NCI used as a source, regardless of regulation!

Page 51: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Future research:

1.Improve accuracy in parameter estimates (e.g., λ, population density) and re-run analysis.

1.Relevance of NCI reserve constraint?

2.Incorporate known variability (e.g., connectivity across years) and uncertainty (e.g., in λ and form of density dependence function) into analysis.

3.Apply model to a variety of systems characterized by different levels of connectivity.

Page 52: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Currents

Oceanographic boundaries

(Gaylord & Gaines 2000)

Page 53: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Central CA

Southern CA

US

Mexico

Borders dividing fishery management jurisdictions

Is cooperation in cross-border management part of the optimal solution?

Page 54: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Thank you!

Page 55: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Thank you!

Page 56: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

10,000 simulations:

90% net present value

H*H* - U[1-v,1+v](H*)

H* + U[1-v,1+v](H*)

Page 57: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Southern hemisphere cetaceans (Hilborn et al. 2003)

Page 58: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

“Rapid worldwide depletion of predatory fish” (Myers &

Worm 2003)

Page 59: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Mean size (n = 1000+)

m = 1/mean age = 0.068

Annual natural mortality rate:

Page 60: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Excellent for lawn art (match gnomes beautifully!)

Page 61: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.

Thank you!

Page 62: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.
Page 63: Population Connectivity and Management of an Emerging Commercial Fishery Crow White ESM 242 ProjectMay 31, 2007.