Time-delay effect of a stochastic genotype selection model

Abstract

The time-delay effect of a genotype selection model driven by noise is investigated. The approximate delay Fokker-Planck equation is obtained based on the small time delay method and the stochastic equivalent rule. The explicit expression of the steady state probability distribution is derived, and the effect of the time delay on the steady sate properties of the genotype selection model driven by noise is discussed. It is found that the time delay can induce the transition from monostable state to bistable state. The time delay is helpful to select one type of genes from another type of mixing genes. The theoretical predictions are found to be in basic agreement with numerical results.