Abstract
We introduce a class of two-sex branching processes in discrete time where, in each generation, mating between females and males is randomly governed by a set of Bernoulli distributions allowing polygamous behaviour with only perfect fidelity on the part of female. Moreover, mating as well as reproduction can be influenced by the number of females and males in the population. We study here, for any population whose dynamics is modeled by such processes, conditions leading to its extinction or to a possible persistence. Moreover, the behaviours of the female and male populations are analyzed more finely in case of persistence.
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