A two-sex matrix population model to represent harem structure
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 t...
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| Format: | Article |
| Language: | English |
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AIMS Press
2016-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016031 |
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| author | Anthony Tongen María Zubillaga Jorge E. Rabinovich |
| author_facet | Anthony Tongen María Zubillaga Jorge E. Rabinovich |
| author_sort | Anthony Tongen |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-4e5b1cb8562e4d39b3ef5468c816d5e8 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-4e5b1cb8562e4d39b3ef5468c816d5e82025-01-24T02:36:57ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-06-011351077109210.3934/mbe.2016031A two-sex matrix population model to represent harem structureAnthony Tongen0María Zubillaga1Jorge E. Rabinovich2Department of Mathematics and Statistics, James Madison University, Harrisonburg, VA 22807Centro de Estudios Parasitológicos y de Vectores (CEPAVE, CONICET-CCT-La Plata, UNLP), Universidad Nacional de La Plata, La Plata, Prov. de Buenos AiresCentro de Estudios Parasitológicos y de Vectores (CEPAVE, CONICET-CCT-La Plata, UNLP), Universidad Nacional de La Plata, La Plata, Prov. de Buenos AiresPopulation 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.https://www.aimspress.com/article/doi/10.3934/mbe.2016031two-sex modelssex ratio.harem structurestage-structured models |
| spellingShingle | Anthony Tongen María Zubillaga Jorge E. Rabinovich A two-sex matrix population model to represent harem structure Mathematical Biosciences and Engineering two-sex models sex ratio. harem structure stage-structured models |
| title | A two-sex matrix population model to represent harem structure |
| title_full | A two-sex matrix population model to represent harem structure |
| title_fullStr | A two-sex matrix population model to represent harem structure |
| title_full_unstemmed | A two-sex matrix population model to represent harem structure |
| title_short | A two-sex matrix population model to represent harem structure |
| title_sort | two sex matrix population model to represent harem structure |
| topic | two-sex models sex ratio. harem structure stage-structured models |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016031 |
| work_keys_str_mv | AT anthonytongen atwosexmatrixpopulationmodeltorepresentharemstructure AT mariazubillaga atwosexmatrixpopulationmodeltorepresentharemstructure AT jorgeerabinovich atwosexmatrixpopulationmodeltorepresentharemstructure AT anthonytongen twosexmatrixpopulationmodeltorepresentharemstructure AT mariazubillaga twosexmatrixpopulationmodeltorepresentharemstructure AT jorgeerabinovich twosexmatrixpopulationmodeltorepresentharemstructure |