Stabilizing effect of cannibalism in a two stages population model

Jonathan Rault 1 Eric Benoît 2 Jean-Luc Gouzé 1, *
* Corresponding author
1 BIOCORE - Biological control of artificial ecosystems
LOV - Laboratoire d'océanographie de Villefranche, CRISAM - Inria Sophia Antipolis - Méditerranée , INRA - Institut National de la Recherche Agronomique
Abstract : In this paper we build a prey-predator model with discrete weight structure for the predator. This model will conserve the number of individuals and the biomass and both growth and reproduction of the predator will depend on the food ingested. Moreover the model allows cannibalism which means that the predator can eat the prey but also other predators. We will focus on a simple version with two weight classes or stage (larvae and adults) and present some general mathematical results. In the last part, we will assume that the dynamics of the prey is fast compared to the predator's one to go further in the results and eventually conclude that under some conditions, cannibalism can stabilize the system: more precisely, an unstable equilibrium without cannibalism will become almost globally stable with some cannibalism. Some numerical simulations are done to illustrate this result.
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Jonathan Rault, Eric Benoît, Jean-Luc Gouzé. Stabilizing effect of cannibalism in a two stages population model. Acta Biotheoretica, Springer Verlag, 2013, 61, pp.119-139. ⟨10.1007/s10441-013-9172-x⟩. ⟨hal-00848443⟩

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