Bayesian models for radio telemetry habitat data
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Bayesian Models for Radio Telemetry Habitat Data. †. †. ‡. Megan C. Dailey* Alix I. Gitelman Fred L. Ramsey Steve Starcevich * Department of Statistics, Colorado State University Department of Statistics, Oregon State University Oregon Department of Fish and Wildlife. †. ‡.

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Bayesian Models for Radio Telemetry Habitat Data

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Bayesian Models for Radio Telemetry Habitat Data

Megan C. Dailey*

Alix I. Gitelman

Fred L. Ramsey

Steve Starcevich

* Department of Statistics, Colorado State University

Department of Statistics, Oregon State University

Oregon Department of Fish and Wildlife


Affiliations and funding

FUNDING/DISCLAIMER

The 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 poster 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.

CR-829095


Westslope Cutthroat Trout

  • Year long radio-telemetry study (Steve Starcevich)

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

    • 26 trout were tracked ~ weekly from stream side

      • Roberts CreekF = 17

      • Rail CreekF = 9

    • Winter, Spring, Summer (2000-2001)

      • S=3


Habitat association

  • Habitat inventory of entire creek once per season

    • Channel unit type

    • Structural association of pools

    • Total area of each habitat type

  • For this analysis:

    • H = 3 habitat classes

      • In-stream-large-wood pool (ILW)

      • Other pool (OP)

      • Fast water (FW)

  • Habitat availability = total area of habitat in creek


Goals of habitat analysis

  • Incorporate

    • multiple seasons

    • multiple streams

    • Other covariates

  • Investigate “Use vs. Availability”


WINTER

SPRING

SUMMER

FISH 1

FISH 2

Habitat 2

Habitat 3

missing

Habitat 1

Radio telemetry data

  • Sequences of observed habitat use


= number of sightings of animal i in habitat h

= habitat selection probability (HSP) for habitat h

= number of times animal i is sighted

Independent Multinomial Selections Model (IMS)

(McCracken, Manly, & Vander Heyden, 1998)

  • Product multinomial likelihood with multinomial logit parameterization


IMS Model: Assumptions

  • Repeat sightings of same animal represent independent habitat selections

  • Habitat selections of different animals are independent

  • All animals have identical multinomial habitat selection probabilities


Evidence of persistence


Persists and moves


: equivalent to the IMS model

: greater chance of staying (“persisting”)

Persistence Model

(Ramsey & Usner, 2003)

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

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

  • Persistence parameter :


= number of stays in habitat h ;

= indicator for initial sighting habitat

Persistence likelihood

  • One-step transition probabilities:

  • Likelihood

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


Bayesian extensions

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

  • Non-seasonal persistence / Seasonal HSPs:

  • Seasonal persistence / Non-seasonal HSPs:

  • Seasonal persistence / Seasonal HSPs:


= habitat selection probability for habitat h in season s

= overall persistence parameter

II. Non-seasonal persistence/Seasonal HSPs

Likelihood


Multinomial logit parameterization

  • Habitat Selection Probability (HSP):

  • Multinomial logit parameterization:

s = 1, …, S

h = 1, …, H

i = 1, …, F

T = reference season

R = reference habitat


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

= number of stays in habitat h in season s

= indicator for initial sighting habitat h in season s

III.Seasonal persistence / Non-seasonal HSPs

Likelihood


~ diffuse normal

~ diffuse normal

IV. Seasonal persistence / Seasonal HSPs

Likelihood

Priors for all models


Estimated persistence parameters:Roberts Creek


Estimated persistence parameters:Rail Creek


Estimated habitat selection probabilities:Roberts Creek


Selection Probability Ratio/Area Ratio:Rail Creek


BIC comparison

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


Conclusions

  • Relaxes assumption of independent sightings

  • Biological meaningfulness of the persistence parameter

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

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

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


THANK YOU


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

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

V. Multiple stream persistence

Likelihood

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

in stream c


Evidence of persistenceRoberts Creek


Markov chain persistence

One-step Transition Probability Matrix:

where


Persistence example

  • h = 1 -> IMS

  • h < 1 -> greater chance of remaining in previous habitat


Estimate of Use vs. availability

  • Selection Probability Ratio (SPR)

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


Persistence vs. IMS


Estimated persistence parameters


stuff

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

model IV. p = 7 in basemodelROB and

model III. p = 5 in seaspersonlyROB


a,b

~ diffuse normal

~ diffuse normal

Priors

  • Multinomial logit parameters:

  • Non-seasonal persistence:

  • Seasonal persistence:

  • Hierarchical seasonal persistence:

~ Beta(a,b)


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