A branching process for predator-prey systems

C. Minuesa Abril, C. Gutiérrez Pérez

The aim of this work is to introduce a stochastic process to describe the interaction of predator and prey populations with sexual reproduction and promiscuous mating. To that end, we present a two-type two-sex controlled branching process. In our model, couples of each species produce offspring independently of the others. The interplay of predator and prey populations is modelled through a control process. Precisely, the total number of individuals of each species which survive in each generation is described by a binomial distribution with size given by this number of individuals and probability of success depending on the proportion of preys per predator. We show that under some weak conditions, this new model enables us to depict the typical fluctuating behaviour of predator-prey systems. We also present results about fixation, extinction and coexistence of both species.

Keywords: predator-prey model, two-sex branching process, oscillations, promiscuous mating, extinction, coexistence, density dependence

Scheduled

GT17 Stochastic Processes and their Applications II
June 7, 2022  3:30 PM
A26

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