Fitting Markovian binary trees using global and individual demographic data

Sophie Hautphenne; Melanie Massaro; Katharine Turner

doi:10.1016/j.tpb.2019.04.007

Fitting Markovian binary trees using global and individual demographic data

Sophie Hautphenne^*, Melanie Massaro, Katharine Turner

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We consider a class of continuous-time branching processes called Markovian binary trees (MBTs), in which the individuals lifetime and reproduction epochs are modelled using a transient Markovian arrival process (TMAP). We develop methods for estimating the parameters of the TMAP by using either age-specific averages of reproduction and mortality rates, or age-specific individual demographic data. Depending on the degree of detail of the available information, we follow a weighted non-linear regression or a maximum likelihood approach. We discuss several criteria to determine the optimal number of states in the underlying TMAP. Our results improve the fit of an existing MBT model for human demography, and provide insights for the future conservation management of the threatened Chatham Island black robin population.

Original language	English
Pages (from-to)	39-50
Number of pages	12
Journal	Theoretical Population Biology
Volume	128
DOIs	https://doi.org/10.1016/j.tpb.2019.04.007
Publication status	Published - Aug 2019

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10.1016/j.tpb.2019.04.007

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title = "Fitting Markovian binary trees using global and individual demographic data",

abstract = "We consider a class of continuous-time branching processes called Markovian binary trees (MBTs), in which the individuals lifetime and reproduction epochs are modelled using a transient Markovian arrival process (TMAP). We develop methods for estimating the parameters of the TMAP by using either age-specific averages of reproduction and mortality rates, or age-specific individual demographic data. Depending on the degree of detail of the available information, we follow a weighted non-linear regression or a maximum likelihood approach. We discuss several criteria to determine the optimal number of states in the underlying TMAP. Our results improve the fit of an existing MBT model for human demography, and provide insights for the future conservation management of the threatened Chatham Island black robin population.",

keywords = "Branching process, Markov process, Maximum likelihood, Non-linear regression, Petroica traversi",

author = "Sophie Hautphenne and Melanie Massaro and Katharine Turner",

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier Inc.",

year = "2019",

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doi = "10.1016/j.tpb.2019.04.007",

language = "English",

volume = "128",

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T1 - Fitting Markovian binary trees using global and individual demographic data

AU - Hautphenne, Sophie

AU - Massaro, Melanie

AU - Turner, Katharine

PY - 2019/8

Y1 - 2019/8

N2 - We consider a class of continuous-time branching processes called Markovian binary trees (MBTs), in which the individuals lifetime and reproduction epochs are modelled using a transient Markovian arrival process (TMAP). We develop methods for estimating the parameters of the TMAP by using either age-specific averages of reproduction and mortality rates, or age-specific individual demographic data. Depending on the degree of detail of the available information, we follow a weighted non-linear regression or a maximum likelihood approach. We discuss several criteria to determine the optimal number of states in the underlying TMAP. Our results improve the fit of an existing MBT model for human demography, and provide insights for the future conservation management of the threatened Chatham Island black robin population.

AB - We consider a class of continuous-time branching processes called Markovian binary trees (MBTs), in which the individuals lifetime and reproduction epochs are modelled using a transient Markovian arrival process (TMAP). We develop methods for estimating the parameters of the TMAP by using either age-specific averages of reproduction and mortality rates, or age-specific individual demographic data. Depending on the degree of detail of the available information, we follow a weighted non-linear regression or a maximum likelihood approach. We discuss several criteria to determine the optimal number of states in the underlying TMAP. Our results improve the fit of an existing MBT model for human demography, and provide insights for the future conservation management of the threatened Chatham Island black robin population.

KW - Branching process

KW - Markov process

KW - Maximum likelihood

KW - Non-linear regression

KW - Petroica traversi

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DO - 10.1016/j.tpb.2019.04.007

M3 - Article

SN - 0040-5809

VL - 128

SP - 39

EP - 50

JO - Theoretical Population Biology

JF - Theoretical Population Biology

ER -

Fitting Markovian binary trees using global and individual demographic data

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