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Title: Self-regulating two-sex branching processes Authors:  Cristina Gutierrez Perez - University of Extremadura (Spain) [presenting]
Miguel Gonzalez Velasco - University of Extremadura (Spain)
Rodrigo Martinez Quintana - University of Extremadura (Spain)
Abstract: The standard two-sex branching process is a discrete-time process which models the evolution of a two-sex population that evolves without any restriction and in which there are females and males that form couples in order to produce females and males offspring. This process has been modified in several directions (immigration, control, varying environment, etc.) in order to obtain more applicable models, but all of them verify the dichotomy extinction-explosion usual in many branching processes. Sometimes this fact makes these models unsuitable for applications to real biological situations. We introduce a self-regulating two-sex branching process with the aim of studying the evolution of a population in which the total population size is limited by the environment. For that, we define a discrete-time two-sex branching process where at each generation only some selected couples survive to produce offspring. We introduce a random control function at mating time to make this selection. This function will depend on the number of couples initially formed in the generation and on an associated survival probability which will be related to the carrying capacity of the environment. For this model, we show the behavior of the process in long term by means of simulations and we present some results about the extinction of the population.