AbstractSex determination in mammals is strongly linked to sex chromosomes. In most cases, females possess two copies of X chromosome while males have one X and one Y chromosome. It is assumed that these chromosomes originated from a pair of homologous autosomes, which diverged when recombination between them was suppressed. However, it is still debated why the sex chromosomes stopped recombining and how this process spread out over most part of the chromosomes. To study this problem, we developed a simulation model, in which the recombination rate between the sex chromosomes can freely evolve. We found that the suppression of recombination between the X and Y is spontaneous and proceeds very quickly during the evolution of population, which leads to the degeneration of the Y in males. Interestingly, the degeneration happens only when mating pairs are unfaithful. This evolutionary strategy purifies the X chromosome from defective alleles and leads to the larger number of females than males in the population. In consequence, the reproductive potential of the whole population increases. Our results imply that both the suppression of recombination and the degeneration of Y chromosome may be associated with reproductive strategy and favoured in polygamous populations with faithless mating partners.