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Fitting Markovian binary trees using global and individual demographic data.

Sophie Hautphenne1, Melanie Massaro2, Katharine Turner3

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Summary
This summary is machine-generated.

This study introduces Markovian binary trees (MBTs) using a transient Markovian arrival process (TMAP) for demographic modeling. The developed methods enhance existing models and offer insights for conservation management.

Keywords:
Branching processMarkov processMaximum likelihoodNon-linear regressionPetroica traversi

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Area of Science:

  • Population dynamics
  • Stochastic processes
  • Mathematical biology

Background:

  • Continuous-time branching processes are crucial for modeling populations.
  • Markovian binary trees (MBTs) offer a framework for such models.
  • Transient Markovian arrival processes (TMAPs) can model individual lifetimes and reproduction.

Purpose of the Study:

  • To develop parameter estimation methods for TMAPs within MBTs.
  • To refine existing MBT models for human demography.
  • To provide tools for conservation management of species like the Chatham Island black robin.

Main Methods:

  • Utilizing age-specific reproduction and mortality rates for parameter estimation.
  • Employing age-specific individual demographic data for parameter estimation.
  • Applying weighted non-linear regression or maximum likelihood approaches based on data availability.
  • Investigating criteria for determining the optimal number of states in TMAPs.

Main Results:

  • Successful estimation of TMAP parameters within the MBT framework.
  • Improved accuracy of MBT models for human demographic data.
  • Demonstrated applicability to conservation biology, specifically for the Chatham Island black robin.

Conclusions:

  • The developed methods provide robust parameter estimation for TMAP-based MBTs.
  • Enhanced demographic models can better inform conservation strategies.
  • This approach offers valuable insights for managing threatened populations.