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Semi-Markov Arnason-Schwarz models.

Ruth King1, Roland Langrock2

  • 1School of Mathematics, University of Edinburgh, James Clerk Maxwell Building, The King's Buildings, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK.

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|November 20, 2015
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Summary
This summary is machine-generated.

This study introduces a flexible semi-Markov Arnason-Schwarz model for capture-recapture data, improving biological inference on animal states and dwell times.

Keywords:
Capture-recapture-recoveryDwell-time distributionHidden Markov modelMulti-state model

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Area of Science:

  • Ecology
  • Wildlife Biology
  • Statistical Modeling

Background:

  • Traditional Arnason-Schwarz models use low-order Markov chains for multi-state capture-recapture data.
  • Low-order Markov models impose restrictive assumptions on state dwell times, potentially misrepresenting biological processes.
  • Higher-order or time-dependent models increase complexity and parameter count significantly.

Purpose of the Study:

  • To extend the Arnason-Schwarz model using a semi-Markov process for more flexible state dwell-time distributions.
  • To develop a computationally tractable hidden Markov model representation of the semi-Markov Arnason-Schwarz model.
  • To enable more accurate biological inference regarding animal state durations and transitions.

Main Methods:

  • Incorporation of general dwell-time distributions (e.g., shifted Poisson, negative binomial) into the Arnason-Schwarz framework.
  • Application of a state expansion technique to convert the semi-Markov model into a hidden Markov model.
  • Model selection using standard information criteria.

Main Results:

  • The semi-Markov Arnason-Schwarz model offers greater flexibility in state process modeling with minimal parameter increase.
  • The hidden Markov model formulation ensures computational tractability.
  • The approach allows for detailed inference on state-specific durations.

Conclusions:

  • The semi-Markov Arnason-Schwarz model provides a more biologically realistic and flexible approach to analyzing multi-state capture-recapture data.
  • This method enhances the ability to infer underlying biological processes, such as time spent in different states.
  • The model's feasibility is confirmed through simulation and application to house finch conjunctivitis data.