Transitions in a genotype selection model driven by coloured noises

This paper investigates a genotype selection model subjected to both a multiplicative coloured noise and an additive coloured noise with different correlation time \tau_1 and \tau_2 by means of the numerical technique. By directly simulating the Langevin Equation, the following results are obtained. (1) The multiplicative coloured noise dominates, however, the effect of the additive coloured noise is not neglected in the practical gene selection process. The selection rate \mu decides that the selection is propitious to gene A haploid or gene B haploid. (2) The additive coloured noise intensity \alpha and the correlation time \tau_2 play opposite roles. It is noted that \alpha and \tau_2 can not separate the single peak, while \alpha can make the peak disappear and \tau_2 can make the peak be sharp. (3) The multiplicative coloured noise intensity D and the correlation time \tau_1 can induce phase transition, at the same time they play opposite roles and the reentrance phenomenon appears. In this case, it is easy to select one type haploid from the group with increasing D and decreasing \tau_1.