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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. †. ‡.

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Bayesian Models for Radio Telemetry Habitat Data

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  1. 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 † ‡

  2. 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 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. CR-829095

  3. 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

  4. 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

  5. Goals of habitat analysis • Incorporate • multiple seasons • multiple streams • Other covariates • Investigate “Use vs. Availability”

  6. WINTER SPRING SUMMER FISH 1 FISH 2 Habitat 2 Habitat 3 missing Habitat 1 Radio telemetry data • Sequences of observed habitat use

  7. = 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

  8. 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

  9. Evidence of persistence

  10. Persists and moves

  11. : 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 :

  12. = 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 ;

  13. 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:

  14. = habitat selection probability for habitat h in season s = overall persistence parameter II. Non-seasonal persistence/Seasonal HSPs Likelihood

  15. 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

  16. = 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

  17. ~ diffuse normal ~ diffuse normal IV. Seasonal persistence / Seasonal HSPs Likelihood Priors for all models

  18. Estimated persistence parameters:

  19. Estimated habitat selection probabilities:Roberts Creek

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

  21. 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

  22. THANK YOU

  23. = 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

  24. Evidence of persistenceRoberts Creek

  25. Markov chain persistence One-step Transition Probability Matrix: where

  26. Persistence example • h = 1 -> IMS • h < 1 -> greater chance of remaining in previous habitat

  27. Estimate of Use vs. availability • Selection Probability Ratio (SPR) • SPR/(Area Ratio) for Use vs. Availability

  28. Persistence vs. IMS

  29. Estimated persistence parameters

  30. stuff BIC = -2*mean(llik[1001:10000]) - p*log(17) model IV. p = 7 in basemodelROB and model III. p = 5 in seaspersonlyROB

  31. 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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