Some Contributions to the Class of Two-Sex Branching Processes Depending on the Number of Couples in the Population

2000 Mathematics Subject Classification: 60J80

We consider the class of two-sex branching processes with offspring and mating depending on the number of couples in the population introduced in Molina et al. (2008). In addition to its theoretical interest, this class also has clear practical implications, especially in population dynamics. We investigate its extinction probability and limiting behavior. By considering different probabilistic approaches, necessary and sufficient conditions for its almost sure extinction are determined. Assuming the nonextinction, some limiting results are derived.

This research has been supported by the Ministerio de Ciencia e Innovaci´on of Spain, the Junta de Extremadura, and the FEDER (grants MTM2009-13248 and GR10118) and by the Natural Sciences Foundation of China (grant 10971048).