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A logistic
two-sex model with mate-finding Allee effect
Elizabeth Anderson, Daniel Maxin, Jared Ott and Gwyneth Terrett
Vol. 12 (2019), No. 8, 1343–1355
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Abstract |
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We analyze a logistic two-sex model with mate-finding Allee effects assuming distinct sex-related parameters. We compute the threshold of the Allee-effect strength that separates population extinction from persistence and prove that a bistability regimen appears whereby the total population either goes extinct or stabilizes at a positive level depending on the initial demographic conditions. We show that this effect is the only possible outcome as far as the population limiting behavior is concerned. In addition, we compute the optimal female-sex probability at birth that maximizes this threshold. |
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Keywords
two-sex models, mate-finding Allee effect, bistability
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Mathematical Subject Classification 2010
Primary: 92D25, 92D50
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Milestones
Received: 1 February 2019
Revised: 7 July 2019
Accepted: 7 July 2019
Published: 25 October 2019
Communicated by Kenneth S. Berenhaut
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Authors |
| Elizabeth Anderson | |
| Department of Mathematics and
Statistics Villanova University Villanova, PA United States |
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| Daniel Maxin | |
| Department of Mathematics and
Statistics Valparaiso University Valparaiso, IN United States |
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| Jared Ott | |
| Department of Mathematics University of Nebraska Lincoln, NE United States |
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| Gwyneth Terrett | |
| Mathematics Department Taylor University Upland, IN United States |
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