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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

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
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
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 Creek F = 17
      • Rail Creek F = 9
    • Winter, Spring, Summer (2000-2001)
      • S=3
habitat association
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
Goals of habitat analysis
  • Incorporate
    • multiple seasons
    • multiple streams
    • Other covariates
  • Investigate “Use vs. Availability”
radio telemetry data

WINTER

SPRING

SUMMER

FISH 1

FISH 2

Habitat 2

Habitat 3

missing

Habitat 1

Radio telemetry data
  • Sequences of observed habitat use
independent multinomial selections model ims

= 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
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
persistence model

: 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 :
persistence likelihood

= 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
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:
multinomial logit parameterization
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

iii seasonal persistence non seasonal hsps

= 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

iv seasonal persistence seasonal hsps

~ diffuse normal

~ diffuse normal

IV. Seasonal persistence / Seasonal HSPs

Likelihood

Priors for all models

bic comparison
BIC comparison

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

conclusions
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
v multiple stream persistence

= 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

markov chain persistence
Markov chain persistence

One-step Transition Probability Matrix:

where

persistence example
Persistence example
  • h = 1 -> IMS
  • h < 1 -> greater chance of remaining in previous habitat
estimate of use vs availability
Estimate of Use vs. availability
  • Selection Probability Ratio (SPR)
  • SPR/(Area Ratio) for Use vs. Availability
stuff
stuff

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

model IV. p = 7 in basemodelROB and

model III. p = 5 in seaspersonlyROB

priors

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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