Coexistence and extinction in a data-based ratio-dependent model of an insect community

Mathematical Biosciences and Engineering

Yang Kuang¹  Kaifa Wang² 

[1] 1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ 85287, USA;2. School of Mathematics and Statistics, Southwest University, Chongqing 400715, P.R. China;

关键词: coexistence;    extinction;    competition;    stability;    predator-prey;    hopf bifurcation;   

DOI  :  10.3934/mbe.2020187

来源: DOAJ

【 摘 要 】

In theory, pure competition often leads to competitive exclusion of species. However, what we often see in nature is a large number of distinct predator or consumer species coexist in a community consisting a smaller number of prey or plant species. In an effort of dissecting how indirect competition and selective predation may have contributed to the coexistence of species in an insect community, according to the replicated cage experiments (two aphid species and a specialist parasitoid that attacks only one of the aphids) and proposed mathematical models, van Veen et. al. [5] conclude that the coexistence of the three species is due to a combination of density-mediated and trait-mediated indirect interactions. In this paper, we formulate an alternative model that observes the conventional law of mass conservation and provides a better fitting to their experimental data sets. Moreover, we present an initial attempt in studying the stabilities of the nonnegative steady states of this model.

【 授权许可】

Unknown