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Title: A predator-prey two-sex branching process Authors:  Carmen Minuesa Abril - Autonomous University of Madrid (Spain) [presenting]
Cristina Gutierrez Perez - University of Extremadura (Spain)
Abstract: The first branching process to describe the interaction of predator and prey populations with sexual reproduction is presented. We consider a two-type branching process, where the first type corresponds to the predator population and the second one to the prey population. The interaction and survival of both groups are modelled through control functions depending on the current number of individuals of each type in the ecosystem. The resulting model is a two-type two-sex controlled branching model. Due to the variety of mating systems, we focus on the promiscuous mating, where each female mates with only one male, whenever there are males in the population, but the same male could mate with more than one female. In this context, and given their interest for the conservation of species, we provide necessary and sufficient conditions for the ultimate extinction of both species, the fixation of one of them and the coexistence of both of them.