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 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 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

3. Westslope Cutthroat Trout  Year long radio-telemetry study ( Steve Starcevich) 2 headwater streams of the John Day River in eastern Oregon2 headwater streams of the John Day River in eastern Oregon 26 trout were tracked ~ weekly from stream side26 trout were tracked ~ weekly from stream side  Roberts CreekF = 17  Rail CreekF = 9 Winter, Spring, Summer (2000-2001)Winter, Spring, Summer (2000-2001)  S=3

4. Habitat association  Habitat 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: H = 3 habitat classesH = 3 habitat classes 1.In-stream-large-wood pool (ILW) 2.Other pool (OP) 3.Fast water (FW) Habitat availability = total area of habitat in creekHabitat availability = total area of habitat in creek

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

6. Radio telemetry data  Sequences of observed habitat use SUMMERWINTERSPRING FISH 2 FISH 1 Habitat 1 Habitat 3Habitat 2missing

7. Independent Multinomial Selections Model (IMS) (McCracken, Manly, & Vander Heyden, 1998)   Product multinomial likelihood with multinomial logit parameterization = number of sightings of animal i in habitat h = habitat selection probability (HSP) for habitat h = number of times animal i is sighted

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. 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 : : equivalent to the IMS model : greater chance of staying (“persisting”)

12. Persistence likelihood  One-step transition probabilities:  Likelihood = number of moves from habitat h* to habitat h ; = indicator for initial sighting habitat= number of stays in habitat h ;

13. Bayesian extensions I.Reformulation of the original non-seasonal persistence model into Bayesian framework: II.Non-seasonal persistence / Seasonal HSPs: III.Seasonal persistence / Non-seasonal HSPs: IV.Seasonal persistence / Seasonal HSPs:

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

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. III. Seasonal persistence / Non-seasonal HSPs Likelihood = indicator for initial sighting habitat h in season s = number of stays in habitat h in season s = number of moves from habitat h* to habitat h in season s

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

18. Estimated persistence parameters: Roberts Creek

19. Estimated persistence parameters: Rail Creek

20. Estimated habitat selection probabilities: Roberts Creek

21. Selection Probability Ratio/Area Ratio: Rail Creek

22. BIC comparison MODELPersistenceHSP BIC Roberts BIC Rail INS 742.6482.2 IINSseasonal751.2479.4 IIIseasonalNS 711.6 ** 467.8 ** 467.8 ** IVseasonal 717.0469.2 BIC = -2*log(likelihood) + p*log(n)

23. 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

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25. V. Multiple stream persistence Likelihood = indicator for initial sighting in habitat h in season s in stream c = number of stays in habitat h in season s in stream c = number of moves from habitat h* to habitat h in season s in stream c

26. Evidence of persistence Roberts Creek

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

28. Persistence example  = 1 123 10.20.30.5 20.20.30.5 30.20.30.5  = 0.5 123 10.600.15.25 20.100.65.25 30.100.150.75   = 1 -> IMS   greater chance of remaining in previous habitat

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

30. Persistence vs. IMS

31. Estimated persistence parameters

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

33. Priors  Multinomial logit parameters:  Non-seasonal persistence:  Seasonal persistence:  Hierarchical seasonal persistence: ~ diffuse normal ~ Beta(a,b ) a,b