Habitat selection models to account for seasonal persistence in radio telemetry data Megan C. Dailey* Alix I. Gitelman Fred L. Ramsey Steve Starcevich.

Habitat selection models to Habitat selection models to account for seasonal persistence account for seasonal persistence

in radio telemetry datain radio telemetry data

Megan C. Dailey*Megan C. Dailey*Alix I. GitelmanAlix I. GitelmanFred L. RamseyFred L. RamseySteve StarcevichSteve Starcevich

* Department of Statistics, Colorado State University* Department of Statistics, Colorado State UniversityDepartment of Statistics, Oregon State UniversityDepartment of Statistics, Oregon State University

Oregon Department of Fish and WildlifeOregon Department of Fish and Wildlife

†

‡

†

†

‡

Westslope Cutthroat TroutWestslope Cutthroat Trout Year long radio-telemetry study (Year long radio-telemetry study (Steve Starcevich)Steve Starcevich)

• 2 headwater streams of the John Day River in eastern 2 headwater streams of the John Day River in eastern OregonOregon

• 26 trout were tracked ~ weekly from stream side26 trout were tracked ~ weekly from stream side Roberts CreekRoberts Creek F = 17F = 17 Rail CreekRail Creek F = 9F = 9

• Winter, Spring, Summer (2000-2001)Winter, Spring, Summer (2000-2001) S=3S=3

Study Area

Headwaters of the John Day River

Habitat associationHabitat association Habitat inventory of entire creek once per seasonHabitat inventory of entire creek once per season

• Channel unit typeChannel unit type• Structural association of poolsStructural association of pools• Total area of each habitat typeTotal area of each habitat type

For this analysis: For this analysis: • H = 3 habitat classesH = 3 habitat classes

1.1. In-stream-large-wood pool (ILW)In-stream-large-wood pool (ILW)

2.2. Other pool (OP)Other pool (OP)

3.3. Fast water (FW)Fast water (FW)

• Habitat availability = total area of habitat in creekHabitat availability = total area of habitat in creek

Goals of habitat analysisGoals of habitat analysis IncorporateIncorporate

– multiple seasonsmultiple seasons– multiple streamsmultiple streams– Other covariatesOther covariates

Investigate “Use vs. Availability”Investigate “Use vs. Availability”

Radio telemetry dataRadio telemetry data Sequences of observed habitat useSequences of observed habitat use

SUMMERWINTER SPRING

FISH 2

FISH 1

Habitat 1 Habitat 3Habitat 2 missing

2,2,1,3,3,3,3,3,1,1,3,3,1,1,3,3,3,0winter,2 sfX

2,2,3,3,3,3,1,3,3,1,3,3,3,3,3,3,3,3winter,1 sfX

Independent Multinomial Selections Independent Multinomial Selections Model (IMS)Model (IMS)

(McCracken, Manly, & Vander Heyden, JABES 1998)(McCracken, Manly, & Vander Heyden, JABES 1998)

Product multinomial likelihood with multinomial logit parameterization

F

i

H

h ih

yh

i ynP

ih

1 1 !!)|(

πX

= number of sightings of animal i in habitat hihy

h = habitat selection probability (HSP) for habitat h

= number of times animal i is sightedin

IMS Model: 3 AssumptionsIMS Model: 3 Assumptions

1. Repeat sightings of same animal represent independent habitat selections

2. Habitat selections of different animals are independent

3. All animals have identical multinomial habitat selection probabilities

Evidence of persistenceEvidence of persistence

Persist percentagePersist percentage0

50

10

01

50

20

02

50

Roberts Creek

Winter Spring Summer

PersistsMoves

05

01

00

15

02

00

25

0

Rail Creek


PersistsMoves

84.6 %

63.0 %76.2 % 80.4 %

50.0 %63.8 %

Persistence ModelPersistence Model(Ramsey & Usner, Biometrics 2003)(Ramsey & Usner, Biometrics 2003)

One parameter extension of the IMS model to One parameter extension of the IMS model to relax assumption of independent sightingsrelax assumption of independent sightings

H-state Markov chain H-state Markov chain (H = # of habitat types)(H = # of habitat types)

Persistence parameter :Persistence parameter :

11 : equivalent to the IMS model

: greater chance of staying (“persisting”)

Persistence likelihoodPersistence likelihood One-step transition probabilities:One-step transition probabilities:

LikelihoodLikelihood

hh)habitat tomovePr(

)1(1h)habitat in stay Pr( h

F

i

H

h

vh

vh

f

h

ihhihhihP1 1

)))1((1()(),|( * πX

= number of moves from habitat h* to habitat h ;

*ihhv

ihf = indicator for initial sighting habitat= number of stays in habitat h ;ihhv

Bayesian extensions

I.I. Reformulation of the original non-seasonal Reformulation of the original non-seasonal persistence model into Bayesian framework:persistence model into Bayesian framework:

II.II. Non-seasonal persistence / Seasonal HSPs:Non-seasonal persistence / Seasonal HSPs:

III.III. Seasonal persistence / Non-seasonal HSPs:Seasonal persistence / Non-seasonal HSPs:

IV.IV. Seasonal persistence / Seasonal HSPs:Seasonal persistence / Seasonal HSPs:

),( sh

),( shs

),( hs

),( h

Multinomial logit Multinomial logit parameterizationparameterization

Habitat Selection Probability (HSP):Habitat Selection Probability (HSP):

Multinomial logit parameterization:Multinomial logit parameterization:

sh

shsh

shhTR

shsh

)Aratln(ln)logit(

TR

sh

Area

AreaArat

s = 1, …, S h = 1, …, H i = 1, …, F

T = reference seasonR = reference habitat

0 sRThR

sh

sh

Seasonal persistenceSeasonal persistence

hss)season in h habitat tomovePr(

hh

hh

),( hs

)1(1s)season in h habitat in stay Pr( hs

• Seasonal one-step transition probabilities:Seasonal one-step transition probabilities:

sseasonforparameter epersistencs

ss

ss

IIIIII.. Seasonal persistence / Non-seasonal HSPsSeasonal persistence / Non-seasonal HSPs

F

i

S

s

H

h

vhs

vhs

f

h

ishhishhishP1 1 1

)))1((1()(),|( * ηπX

h h

hh


),( hs

ishf = indicator for initial sighting habitat h in season s

= number of stays in habitat h in season sishhv= number of moves from habitat h* to habitat h in season s*ishhv

IV. Seasonal persistence / Seasonal HSPsIV. Seasonal persistence / Seasonal HSPs),( shs

F

i

S

s

H

h

vshs

vshs

f

sh

ishhishhishP1 1 1

)))1((1()(),|( * ηπX

sh sh

shsh


Priors for all modelsPriors for all models

h ~ diffuse normal

sh ~ diffuse normal

ss

ss

)1,0(Unif~

s )1,0(Unif~

ROBERTS Persistence Parameter (eta): 95% Posterior Intervals

persistence parameter

0.0 0.2 0.4 0.6 0.8 1.0

Non-seasonal persistence / Seasonal HSP model

( )

Seasonal persistence / Non-seasonal HSP model

( )WINTER

( )SPRING

( )SUMMER

Seasonal persistence / Seasonal HSP model

( )WINTER

( )SPRING

( )SUMMER

Estimated persistence parameters:Estimated persistence parameters:Roberts CreekRoberts Creek

s

ss

s

),( sh

),( shs

),( hs

RAIL Persistence Parameter (eta): 95% Posterior Intervals

persistence parameter

0.0 0.2 0.4 0.6 0.8 1.0

Non-seasonal persistence / Seasonal HSP model

( )

Seasonal persistence / Non-seasonal HSP model

( )WINTER

( )SPRING

( )SUMMER

Seasonal persistence / Seasonal HSP model

( )WINTER

( )SPRING

( )SUMMER

Estimated persistence parameters:Estimated persistence parameters:Rail CreekRail Creek

s

ss

s

),( sh

),( shs

),( hs

Estimated habitat selection probabilities:Estimated habitat selection probabilities:Roberts CreekRoberts Creek

0.0 0.2 0.4 0.6 0.8 1.0

Seasonal Persistence

HSP

In-Stream-Large-Wood

( ) WINTER

( ) SPRING

( ) SUMMER

Other Pools

( ) WINTER

( ) SPRING

( ) SUMMER

Fast Water

( ) WINTER

( ) SPRING

( ) SUMMER

),( shs

),( hs

Non-seasonal Persistence

SPR/AR

0 10 20 30 40 50


( ) WINTER

( ) SPRING

( ) SUMMER

Other Pools

( ) WINTER

( ) SPRING

( ) SUMMER

Fast Water

WINTER

SPRING

SUMMER

Seasonal Persistence

SPR/AR

0 10 20 30 40 50


( ) WINTER

( ) SPRING

( ) SUMMER

Other Pools

( ) WINTER

( ) SPRING

( ) SUMMER

Fast Water

WINTER

SPRING

SUMMER

Selection Probability Ratio/Area Ratio:Selection Probability Ratio/Area Ratio:Rail CreekRail Creek

s

ss

s

),( sh ),( shs

BIC comparisonBIC comparison

MODELMODEL PersistencePersistence HSPHSP BIC RobertsBIC Roberts BIC RailBIC Rail

II NS NS 742.6 482.2482.2

IIII NS seasonal 751.2 479.4479.4

IIIIII seasonal NS 711.6 ** 467.8 **467.8 **

IVIV seasonal seasonal 717.0 469.2469.2

),( sh ),( shs ),( hs

BIC = -2*log(likelihood) + p*log(n)

),( h

ConclusionsConclusions Relaxes assumption of independent sightingsRelaxes assumption of independent sightings

Biological meaningfulness of the persistence parameterBiological meaningfulness of the persistence parameter

Provides a single model for the estimation of seasonal Provides a single model for the estimation of seasonal persistence parameters and other estimates of interest persistence parameters and other estimates of interest (HSP, (SPR/Arat)), along with their respective uncertainty (HSP, (SPR/Arat)), along with their respective uncertainty intervalsintervals

Allows for seasonal comparisons and the incorporation of Allows for seasonal comparisons and the incorporation of multiple study areas (streams)multiple study areas (streams)

Allows for use of other covariates by changing the Allows for use of other covariates by changing the parameterization of the multinomial logitparameterization of the multinomial logit

Affiliations and fundingAffiliations and funding

FUNDING/DISCLAIMERThe work reported here was developed under the STAR Research Assistance Agreement CR-829095

awarded by the U.S. Environmental Protection Agency (EPA) to Colorado State University. This

presentation has not been formally reviewed by EPA. The views expressed here are solely those of the

authors and STARMAP, the Program they represent. EPA does not endorse any products or commercial

services mentioned in this presentation.

Megan’s research is also partially supported by the PRIMES National Science Foundation Grant DGE-

0221595003.

CR-829095

THANK YOUTHANK YOUs

sh

sh

sh

sh

sh

shs

s

s

s

s

s s

s

s

ss s

V.V. Multiple stream persistence Multiple stream persistence

C

c

F

i

S

s

H

h

vcshcs

vcshcs

f

csh

icshhicshhicshP1 1 1 1

)))1((1()(),|( * ηπX


icshf = indicator for initial sighting in habitat h in season s in stream c

= number of stays in habitat h in season s in stream cicshhv

= number of moves from habitat h* to habitat h in season s in stream c

*icshhv

),( cshcs

Markov chain persistenceMarkov chain persistence

One-step Transition Probability Matrix:One-step Transition Probability Matrix:

1 2 K 1 K

1 2 K 1 K

1 2

K 1 K

1 2 K 1 K

1 1

1 1

=

1 1

1 1

)1(

1,

1min0

hh where

Persistence examplePersistence example

= 1 1 2 3

1 0.2 0.3 0.5

2 0.2 0.3 0.5

3 0.2 0.3 0.5

= 0.5 1 2 3

1 0.60 0.15 .25

2 0.10 0.65 .25

3 0.10 0.15 0.75

= 1 -> IMS= 1 -> IMS < 1 -> greater chance of remaining in previous habitat< 1 -> greater chance of remaining in previous habitat

Estimate of Use vs. availabilityEstimate of Use vs. availability Selection Probability Ratio (SPR)Selection Probability Ratio (SPR)

SPR/(Area Ratio) for Use vs. AvailabilitySPR/(Area Ratio) for Use vs. Availability

shhTR

sh SPR

Arat)ln()ln(ln

Arat

SPR

)exp( shhArat

SPR

)exp(Arat shhTR

shSPR

Arat

SPRArat

SPR

Arat

SPR

Persistence vs. IMSPersistence vs. IMS

Persistence vs. IMS: SPR/AreaRatio Wald's 95% CIs

SPR/AR

0 5 10 15 20

( ) Winter RIFFLE-PERS( ) Winter RIFFLE-IMS

( ) Winter GLIDE-PERS( )

Winter GLIDE-IMS( ) Winter SCOUR-PERS

( )Winter SCOUR-IMS

() Spring RIFFLE-PERS() Spring RIFFLE-IMS

( ) Spring GLIDE-PERS( ) Spring GLIDE-IMS

( ) Spring SCOUR-PERS( ) Spring GLIDE-IMS

Estimated persistence parametersEstimated persistence parameters

0.0 0.2 0.4 0.6 0.8 1.0

ROBERTS Persistence Parameter (eta): 95% Posterior Intervals

Eta

Hierarchical seasonal model

( )WINTER

( )SPRING

( )SUMMER

( )OVERALL Persistence

Non-seasonal persistence, seasonal HSPs model

( ) persistence parameter

stuffstuff

BIC = -2*mean(llik[1001:10000]) - p*log(17)

model IV. p = 7 in basemodelROB and

model III. p = 5 in seaspersonlyROB

PriorsPriors

Multinomial logit parameters:Multinomial logit parameters:

Non-seasonal persistence:Non-seasonal persistence:

Seasonal persistence:Seasonal persistence:

Hierarchical seasonal persistence:Hierarchical seasonal persistence:

h ~ diffuse normal

sh ~ diffuse normal

s )1,0(Unif~

)1,0(Unif~

s ~ Beta(a,b) a,b ),0(Unif~

),0( Is

0.0 0.2 0.4 0.6 0.8 1.0

Non-seasonal Persistence

HSP


( ) WINTER

( ) SPRING

( ) SUMMER

Other Pools

( ) WINTER

( ) SPRING

( ) SUMMER

Fast Water

( ) WINTER

( ) SPRING

( ) SUMMER

Evidence of persistenceEvidence of persistenceRoberts CreekRoberts Creek

05

01

00

15

02

00

Number of persists and moves per season


PersistsMoves


0.0

0.2

0.4

0.6

0.8

1.0

Percent persists of total sightings

Habitat selection models to account for seasonal persistence in radio telemetry data Megan C. Dailey* Alix I. Gitelman Fred L. Ramsey Steve Starcevich.

Documents

habitat h slide

reference habitat slide

habitat classesh

total area of habitat

independent habitat

habitat typetotal area

habitat selection models

goals of habitat analysis