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