HIERARCHICAL BAYESIAN MODELS for SEASONAL RADIO TELEMETRY HABITAT DATA †‡ ‡ Megan C. Dailey*, Alix I. Gitelman , and Fred L. Ramsey *STARMAP, Department of Statistics, Colorado State University † STARMAP, ‡Department of Statistics, Oregon State University Radio telemetry data Abstract Radio telemetry data used for habitat selection studies typically consists of repeated measures of habitat types for each individual. Existing models for estimating habitat selection probabilities have incorporated covariates in an independent multinomial selections (IMS) model (McCracken et al., 1998) and an extension of the IMS to include a persistence parameter (Ramsey and Usner, 2003). These models assume that all parameters are fixed through time. However, this may not be a realistic assumption in radio telemetry studies that run through multiple seasons. We extend the IMS and persistence models using a hierarchical Bayesian approach that allows for the selection probabilities, the persistence parameter, or both, to change with season. These extensions are particularly important when movement patterns are expected to be different between seasons, or when availability of a habitat changes throughout the study period due to weather or migration. The models are motivated by radio telemetry data for westslope cutthroat trout. Bayesian extensions 1. Reformulation of the original non-seasonal persistence model Sequences of observed habitat use over time 2. Different HSP’s by season, one persistence parameter WINTER SPRING SUMMER ROBERTS Persistence Parameter (eta): 95% Posterior Intervals F S A year long radio-telemetry study of westslope cutthroat trout in 2 streams of the headwaters of the John Day River i 1 s 1 h 1 S = 3 seasons : Winter, Spring, Summer (2000-2001) 26 trout radio tracked weekly from stream side through the 3 seasons F=9 FISH 2 Each trout located weekly from stream side • Channel unit type & structural association of pools • For this analysis: H = 3 habitat classes Habitat 1 Habitat 2 Habitat 3 3. Fast water Range of westslope cutthroat trout Habitat availability measured by total area of the habitat for each season Data collected by Steve Starcevich, Oregon DFW Goals of habitat association analysis: Ability to incorporate covariates, seasons, and multiple X f 1,s winter 3,3,3,3,3,3,3,3,1,3,3,1,3,3,3,3,2,2 • sh = habitat selection probability (HSP) Investigate use vs. availability X f 2, s winter 0,3,3,3,1,1,3,3,1,1,3,3,3,3,3,1,2,2 H P( X | π, η) Habitat association models f ish sh i 1 s 1 h 1 Independent Multinomial Selections (IMS): ( s sh ) Priors: (McCracken, Manly, & Vander Heyden , 1998) U.S.EPA – Science To Achieve Results (STAR) Program Cooperative # CR - 829095 Agreement ( ) vishh* (1 ( s (1 sh ))) vishh F ~ Unif (0,1) ni = number of times animal i • Seasonal model 1: s ~ Unif (0,1) •Assumes repeat sightings of same animal are independent • Seasonal model 2: s ) OVERALL Persistence Non-seasonal persistence, seasonal HSPs model ( 0.2 ) persistence parameter 0.4 0.6 0.8 1.0 Eta •All persistence parameters are less than 1 indicating presence of persistence and that assumption #1 of IMS model is violated Conclusions Bayesian formulation results in a single model to use for the estimation of seasonal persistence parameters and HSPs along with their associated 95% intervals. Allows comparisons of seasons and gives a glimpse into seasonal differences in movement related to specific habitats. a,b ~ Unif (0, ) ~ Beta(a,b) ) ( Persistence sh~ diffuse normal • Non-seasonal model: ( T = reference season R = reference habitat h ~ diffuse normal • multinomial logit parameters: H h yih yih = number of sightings of animal i in habitat h P( X | π) ni ! h = habitat selection probability i 1 h 1 yih ! (HSP) for habitat h ) SUMMER 0.0 S ( SPRING Area sh Arat Area TR 3. Different HSP’s and persistence parameters by season Model can also be used with other covariates by changing the parameterization of the multinomial logit Persistence Model: (Ramsey & Usner, 2003) •Persistence parameter = 1 1 0 min , h (1 h ) Estimated habitat selection probabilities (HSPs) ( ) P( X | π, ) h ( h ) vihh* ) SPRING ) SUMMER Other Pools ( ) ( f ih WINTER ( ( • pr (stay in habitat h) (1 ) h • pr (move to habitat h) H Incorporate multiple streams into the model In-Stream-Large-Wood •One-step transition probabilities: F Future Work ROBERTS Habitat Selection Probability 95% Posterior Intervals • 1 : equivalent to IMS model • 1 : greater chance of staying (“persisting”) i 1 h 1 This research is funded by Hierarchical seasonal model for habitat h in season s s = 1, …, S h = 1, …, H i = 1, …, F h streams vihh WINTER R Th sR 0 assumption using an H-state Markov chain for H habitat types 2. Other pool (1 ( (1 sh ))) missing • One parameter extension of IMS model to relax independence 1. In-stream-large-wood pool • ( sh ) vihh* logit( sh ) ln( Arat ) h sh is sighted Habitat inventory of entire creek once per season • sh where Roberts Creek F = 17 • f ih • Product multinomial likelihood with multinomial logit parameterization in eastern Oregon Rail Creek H P( X | π, ) FISH 1 F Data example Estimated persistence (1 ( (1 h ))) WINTER FUNDING/DISCLAIMER SPRING ( vihh ) SUMMER The work reported here was developed under the STAR Research Assistance Agreement CR829095 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 poster. Fast Water ( ) ( vihh* = number of moves from habitat h* to habitat h ; vihh = number of stays in habitat h ; f ih= indicator for initial sighting habitat ) ) ( 0.0 0.2 WINTER ) 0.4 SPRING SUMMER 0.6 HSP 0.8 1.0