Habitat association models  Independent Multinomial Selections (IMS): (McCracken, Manly, & Vander Heyden, 1998) Product multinomial likelihood with multinomial logit parameterization Assumes repeat sightings of same animal are independent  Persistence Model: (Ramsey & Usner, 2003) One parameter extension of IMS model to relax independence assumption using an H-state Markov chain for H habitat types Persistence parameter = : equivalent to IMS model : greater chance of staying (“persisting”) One-step transition probabilities: 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 2. Different HSP’s by season, one persistence parameter 3. Different HSP’s and persistence parameters by season  Priors: multinomial logit parameters: Non-seasonal model: Seasonal model 1: Seasonal model 2: Radio telemetry data  Sequences of observed habitat use over time Data example  A year long radio-telemetry study of westslope cutthroat trout in 2 streams of the headwaters of the John Day River in eastern Oregon  S = 3 seasons : Winter, Spring, Summer ( )  26 trout radio tracked weekly from stream side through the 3 seasons Rail Creek F = 9 Roberts Creek F = 17 Each trout located weekly from stream side  Habitat inventory of entire creek once per season Channel unit type & structural association of pools For this analysis: H = 3 habitat classes 1.In-stream-large-wood pool 2. Other pool 3. Fast water 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 streams Investigate use vs. availability 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 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.  Model can also be used with other covariates by changing the parameterization of the multinomial logit Estimated persistence  Persistence All persistence parameters are less than 1 indicating presence of persistence and that assumption #1 of IMS model is violated FUNDING/DISCLAIMER The work reported here was developed under the STAR Research Assistance Agreement CR 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. Future Work  Incorporate multiple streams into the model This research is funded by U.S.EPA – Science To Achieve Results (STAR) Program Cooperative Agreement # CR Estimated habitat selection probabilities (HSPs) SUMMERWINTERSPRING FISH 2 FISH 1 Habitat 1Habitat 3Habitat 2missing = number of sightings of animal i in habitat h = habitat selection probability (HSP) for habitat h = number of times animal i is sighted = number of moves from habitat h* to habitat h ; = indicator for initial sighting habitat= number of stays in habitat h ; ~ diffuse normal ~ Beta(a,b ) a,b Range of westslope cutthroat trout † †‡‡ ‡ s = 1, …, S h = 1, …, H i = 1, …, F where T = reference season R = reference habitat = habitat selection probability (HSP) for habitat h in season s