American Institute of Mathematical Sciences

Advanced
2010, 7(3): 603-622. doi: 10.3934/mbe.2010.7.603

Mechanisms for stable coexistence in an insect community

Meng Fan 1, , Bingbing Zhang 2, and  Michael Yi Li 3,

1. 

School of Mathematics and Statistics, Northeast Normal University, 5268 Renmin Street, Changchun, Jilin, 130024, China
2. 

School of Mathematics and Statistics, Northeast Normal University, Changchun, Jilin, 130024, China
3. 

Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, Alberta T6G 2G1, Canada

Received  May 2009 Revised  March 2010 Published  June 2010

In this paper, we formulate a three-species ecological community model consisting of two aphid species ( Acyrthosiphon pisum and Megoura viciae) and a specialist parasitoid ( Aphidius ervi) that attacks only one of the aphids ( A pisum). The model incorporates both density-mediated and trait-mediated host-parasitoid interactions. Our analysis shows that the model possesses much richer and more realistic dynamics than earlier models. Our theoretical results reveal a new mechanism for stable coexistence in a three-species community in which any two species alone do not co-exist. More specifically, it is known that, when a predator is introduced into a community of two competing species, if the predator only predates on the strong competitor, it can allow the weak competitor to survive, but may drive the strong competitor to extinction through over-exploitation. We show that if the weak competitor interferes the predation on the strong competitor through trait-mediated indirect effects, then all three species can stably co-exist.
Keywords: density-mediated indirect effect, biological invasion., Stable coexistence, trait-mediated indirect effect, insect community.
Mathematics Subject Classification: Primary: 92D40, 92D25; Secondary: 34D2.
Citation: Meng Fan, Bingbing Zhang, Michael Yi Li. Mechanisms for stable coexistence in an insect community. Mathematical Biosciences & Engineering, 2010, 7 (3) : 603-622. doi: 10.3934/mbe.2010.7.603
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