Examining the influence of prey dynamics on predator–prey interactions

ABSTRACT

We develop variations of a discrete-time predator–prey model to examine how intrinsic properties of the prey population may impact overall system dynamics. We focus on two properties of the prey species, namely developmental stage structure and undercompensatory (contest competition) versus overcompensatory (scramble competition) density dependence. Through analysis of these models, we examine how these different prey features affect system stability. Our results show that when prey growth is overcompensatory, the predator may have a stabilizing effect on the system dynamics with increasing predator density reversing the period doubling route to chaos observed with Ricker-type nonlinearities. Moreover, we find that stage structure in the prey does not have a destabilizing effect on the system dynamics unless the prey projection matrix is imprimitive or close to imprimitive, as may occur for semelparous species. In this case, a sufficiently large predator density may stabilize cycles that are otherwise unstable.

KEYWORDS:

• Discrete-time predator–prey models
• stability
• persistence
• stage-structure
• overcompensatory and undercompensatory density dependence

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 92-10
• 92D25

Disclosure statement

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

Additional information

Funding

The research of A. S. Ackleh is supported in part by funds from the R.P. Authement Eminent Scholar and Endowed Chair in Computational Mathematics. The research of A. Veprauskas is supported in part by the Louisiana Board of Regents Office of Sponsored Programs RCS Fund, LEQSF(2020-23)-RD-A-28.