A logistic two-sex model with mate-finding Allee effect

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.