A two-sex matrix population model to represent harem structure

Anthony  Tongen; María  Zubillaga; Jorge E.  Rabinovich; Anthony  Tongen; María  Zubillaga; Jorge E.  Rabinovich

doi:10.3934/mbe.2016031

Mathematical Biosciences and Engineering

2016, Volume 13, Issue 5: 1077-1092. doi: 10.3934/mbe.2016031

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A two-sex matrix population model to represent harem structure

1.
Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA 22807
2.
Centro de Estudios Parasitológicos y de Vectores (CEPAVE, CONICET-CCT-La Plata, UNLP), Universidad Nacional de La Plata, La Plata, Prov. de Buenos Aires

Received: 01 December 2014 Accepted: 29 June 2018 Published: 01 July 2016
MSC : Primary: 92D25, 92D50; Secondary: 15A42.

Population dynamic models often include males in the calculation of population change, but even in those cases males have rarely been introduced to represent polygyny (harem social structure), where it is particularly important to include males in the reproductive performance of the population. In this article we develop an adaptable matrix population modeling framework for species that have a harem-like social structure under an assumption that the transitions from newborn to juvenile and juvenile to adult both take one time step. We are able to calculate not only the growth rates and stable stage distributions, but also the mathematical expressions for harem size for this model. We then provide applications of this model to two mammal species with slightly different harem behavior.
- two-sex models,
- sex ratio.,
- harem structure,
- Stage-structured models
Citation: Anthony Tongen, María Zubillaga, Jorge E. Rabinovich. A two-sex matrix population model to represent harem structure[J]. Mathematical Biosciences and Engineering, 2016, 13(5): 1077-1092. doi: 10.3934/mbe.2016031

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Abstract

Population dynamic models often include males in the calculation of population change, but even in those cases males have rarely been introduced to represent polygyny (harem social structure), where it is particularly important to include males in the reproductive performance of the population. In this article we develop an adaptable matrix population modeling framework for species that have a harem-like social structure under an assumption that the transitions from newborn to juvenile and juvenile to adult both take one time step. We are able to calculate not only the growth rates and stable stage distributions, but also the mathematical expressions for harem size for this model. We then provide applications of this model to two mammal species with slightly different harem behavior.

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