Habitat selection models to account for seasonal persistence in radio telemetry data

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Habitat selection models to account for seasonal
persistence in radio telemetry 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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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)
• S3

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Study Area Headwaters of the John Day River
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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

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Goals of habitat analysis

• Incorporate
• multiple seasons
• multiple streams
• Other covariates
• Investigate Use vs. Availability

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Radio telemetry data

• Sequences of observed habitat use

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Independent Multinomial Selections Model (IMS)

• (McCracken, Manly, Vander Heyden, JABES 1998)
• Product multinomial likelihood with multinomial
  logit parameterization

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IMS Model 3 Assumptions

• 1. Repeat sightings of same animal represent
  independent habitat selections
• 2. Habitat selections of different animals
  are independent
• 3. All animals have identical multinomial
  habitat selection probabilities

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Evidence of persistence
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Persist percentage
84.6
63.0
76.2
80.4
63.8
50.0
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Persistence Model

• (Ramsey Usner, Biometrics 2003)
• One parameter extension of the IMS model to relax
  assumption of independent sightings
• H-state Markov chain (H of habitat types)
• Persistence parameter

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Persistence likelihood

• One-step transition probabilities
• Likelihood

number of moves from habitat h to habitat h
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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

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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
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Seasonal persistence

• Seasonal one-step transition probabilities

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III. Seasonal persistence / Non-seasonal HSPs
Likelihood
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IV. Seasonal persistence / Seasonal HSPs
Likelihood Priors for all models
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Estimated persistence parametersRoberts Creek
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Estimated persistence parametersRail Creek
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Estimated habitat selection probabilitiesRoberts
Creek
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Selection Probability Ratio/Area RatioRail Creek
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BIC comparison
MODEL Persistence HSP BIC Roberts BIC Rail
I NS NS 742.6 482.2
II NS seasonal 751.2 479.4
III seasonal NS 711.6 467.8
IV seasonal seasonal 717.0 469.2
BIC -2log(likelihood) plog(n)
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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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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. Megans research is also
partially supported by the PRIMES National
Science Foundation Grant DGE-0221595003.
CR-829095
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THANK YOU
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V. Multiple stream persistence
Likelihood
number of moves from habitat h to habitat h in
season s in stream c
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Markov chain persistence

• One-step Transition Probability Matrix

where
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Persistence example

• h 1 -gt IMS
• h lt 1 -gt greater chance of remaining in
  previous habitat

? 1 1 2 3
1 0.2 0.3 0.5
2 0.2 0.3 0.5
3 0.2 0.3 0.5

? 0.5 1 2 3
1 0.60 0.15 .25
2 0.10 0.65 .25
3 0.10 0.15 0.75
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Estimate of Use vs. availability

• Selection Probability Ratio (SPR)
• SPR/(Area Ratio) for Use vs. Availability

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Persistence vs. IMS
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Estimated persistence parameters
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stuff

• BIC -2mean(llik100110000) - plog(17)
• model IV. p 7 in basemodelROB and
  
• model III. p 5 in seaspersonlyROB
  

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Priors

• Multinomial logit parameters
• Non-seasonal persistence
• Seasonal persistence
• Hierarchical seasonal persistence

Beta(a,b)
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Evidence of persistenceRoberts Creek