Adaptive delayed reproduction in a 2-dimensional discrete-time competition model

Abstract

This paper studies a 2-dimensional discrete-time competition model of Ricker type with reproductive delay. The model is examined under the assumption that species 1 and 2 have the same properties except that a fraction η of species 1 individuals delays the initiation of reproduction. This assumption ensures that species 1 is dominated by species 2 in the sense that species 2 is increasing whenever species 1 is increasing. It is shown that, even under this assumption, delayed reproduction can be adaptive, i.e. species 1 can invade the monoculture system of species 2 while species 2 cannot invade the monoculture system of species 1, if the population is fluctuating. The result is obtained by analytically examining the species invasibility at boundary 2-cycles, whose coordinates can be estimated by assuming $\eta \approx 0$.

Keywords:

• 2-cycle
• Ricker map
• invasibility
• semelparity
• iteroparity

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by JSPS KAKENHI [grant number 20K03735], Japan.