Vol. 12, No. 8, 2019

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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
Abstract

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.

Keywords
two-sex models, mate-finding Allee effect, bistability
Mathematical Subject Classification 2010
Primary: 92D25, 92D50
Milestones
Received: 1 February 2019
Revised: 7 July 2019
Accepted: 7 July 2019
Published: 25 October 2019

Communicated by Kenneth S. Berenhaut
Authors
Elizabeth Anderson
Department of Mathematics and Statistics
Villanova University
Villanova, PA
United States
Daniel Maxin
Department of Mathematics and Statistics
Valparaiso University
Valparaiso, IN
United States
Jared Ott
Department of Mathematics
University of Nebraska
Lincoln, NE
United States
Gwyneth Terrett
Mathematics Department
Taylor University
Upland, IN
United States