In other words, with a probability ϵ ϵ G ( ξ ξ n ( N , i ) ) the particle ξ ξ n ( N , i ) evolves to a new state ξ ξ n + 1 ( N , i ) = y randomly chosen with the probability distribution M ( ξ ξ n ( N , i ) , y ) ; otherwise, ξ ξ n ( N , i ) jumps to a new location ξ ξ n ( N , j ) randomly chosen with a probability proportional to G ( ξ ξ n ( N , j ) ) and evolves to a new state ξ ξ n + 1 ( N , i ) = y randomly chosen with the probability distribution M ( ξ ξ n ( N , j ) , y ) . If G ( x ) = 1 is the unit function and ϵ ϵ = 1 , the interaction between the particle vanishes and the particle model reduces to a sequence of independent copies of the Markov chain X n . When ϵ ϵ = 0 the mean field particle model described above reduces to a simple mutation-selection genetic algorithm with fitness function G and mutation transition M. These nonlinear Markov chain models and their mean field particle interpretation can be extended to time non homogeneous models on general measurable state spaces (including transition states, path spaces and random excursion spaces) and continuous time models.