Effects and biological consequences of the predator-mediated apparent competition I: ODE models
Yuan Lou, Weirun Tao, Zhi-An Wang
TL;DR
This work analyzes predator-mediated apparent competition in a two-prey, one-predator system under Holling type I and II functional responses. By combining global stability proofs via Lyapunov functions with detailed case studies and numerical simulations, the authors derive invasion criteria for the invasive prey and determine how predator mortality and prey capture rates shape the fate of the native prey. The Holling type I regime yields a complete global classification of dynamics, while the Holling type II regime exhibits rich behaviors including multistability and possible limit cycles, with outcomes strongly depending on parameter regimes and initial conditions. The findings provide theoretical guidance on how predator pressure and prey traits govern invasions and coexistence, with implications for ecological management strategies that leverage predator-mediated interactions. The work highlights key open questions about spatial structure, direct interspecific competition, and mixed functional responses that warrant future investigation.
Abstract
This paper is devoted to investigating the effects and biological consequences of the predator-mediated apparent competition based on a two prey species (one is native and the other is invasive) and one predator model with Holling type I and II functional response functions. Through the analytical results and case studies alongside numerical simulations, we find that the initial mass of the invasive prey species, capture rates of prey species, and the predator's mortality rate are all important factors determining the success/failure of invasions and the species coexistence/extinction. The global dynamics can be completely classified for the Holling type I functional response function, but can only be partially determined for the Holling type II functional response function. For the Holling type I response function, we find that whether the invasive prey species can successfully invade to promote the predator-mediated apparent competition is entirely determined by the capture rates of prey species. If the Holling type II response function is applied, then the dynamics are more complicated. First, if two prey species have the same ecological characteristics, then the initial mass of the invasive prey species is the key factor determining the success/failure of the invasion and hence the effect of the predator-mediated apparent competition. Whereas if two prey species have different ecological characteristics, say different capture rates, then the success of the invasion no longer depends on the initial mass of the invasive prey species, but on the capture rates. In all cases, if the invasion succeeds, then the predator-mediated apparent competition's effectiveness essentially depends on the predator's mortality rate.