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Occupancy times for time-dependent stage-structured models.

George Chappelle1, Alan Hastings2,3, Martin Rasmussen4

  • 1Department of Mathematics, Imperial College London, 180 Queen's Gate, London, SW7 2AZ, United Kingdom. gdc17@ic.ac.uk.

Journal of Mathematical Biology
|February 3, 2022
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Summary
This summary is machine-generated.

This study introduces time-dependent models to calculate how long populations stay in certain states, even when environments change. This helps understand long-lived species dynamics and breeding patterns affected by varying conditions.

Keywords:
Inhomogeneous markov chainMcKendrick–von foerster equationOccupancy timeSouthern fulmar

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Area of Science:

  • Ecology
  • Mathematical Biology
  • Population Dynamics

Background:

  • Occupancy time measures an individual's duration in specific population states.
  • Previous models assumed constant environmental conditions.
  • Time-varying environments necessitate dynamic models for accurate population analysis.

Purpose of the Study:

  • To develop and apply time-dependent stage-structured models for calculating occupancy times.
  • To derive formulas for occupancy time, its expectation, and higher-order moments under changing environmental conditions.
  • To analyze population dynamics in species with transitions between reproductive and non-reproductive stages.

Main Methods:

  • Utilized absorbing inhomogenous Markov chains.
  • Employed the discrete-time McKendrick-von Foerster equation.
  • Derived explicit formulas for occupancy time and its moments with time-dependent transition rates.

Main Results:

  • Provided explicit formulas for occupancy time and its moments in time-varying environments.
  • Demonstrated insights into the dynamics of long-lived populations with bidirectional stage transitions.
  • Applied the model to the Southern Fulmar, revealing dependencies of breeding attempts on temporal environmental variations.

Conclusions:

  • Time-dependent models are crucial for understanding population dynamics in fluctuating environments.
  • The derived formulas offer a robust framework for analyzing occupancy times in ecological studies.
  • This approach enhances our understanding of how environmental changes impact species, using the Southern Fulmar as a case study.