On Y-Linked Genes and Bisexual Branching Processes

2000 Mathematics Subject Classification: 60J80.

In this paper we survey the results concerning the extinction problem for a two-allele Y-linked gene in a two-sex monogamic population, with a preference of females for males carrying one of the two alleles of the gene. First we give the mathematical definition of the Y-linked bisexual branching process to model this situation and study some of its relevant properties. Then, we research the extinction of the population and also the survival of each genotype depending on the behaviour of the other genotype. Finally, we simulate the evolution of the population and conjecture its long term behaviour, for some critical situations.

This research was supported by the Ministerio de Educacion y Ciencia and the FEDER through the Plan Nacional de Investigaci´on Cient´ıfica, Desarrollo e Innovaci´on Tecnologica, grant MTM2006-08891.