Balance between Selection and Mutation in a Spatial Stochastic Model

#### R.B. Schinazi

2001, v.7, №4, 595-602

ABSTRACT

We introduce a new interacting particle system on $Z^d$ to model the competition between selection and mutation. We have two types of particles. Type 1 and type 2 particles give birth to particles of the same type. We assume that type 1 particles have a selective advantage in that their birth rate is higher than the type 2 birth rate. Both types die at the same constant rate. Type 1 particles can mutate into type 2 particles (there are no reverse mutations). We show that depending on the birth rates and the mutation rate the three following evolutions are possible. We may have coexistence of both particles, showing balance between mutation and selection. We may have type 2 particles taking over. Finally, the whole population may die out.

Keywords: multi-type contact process,mutation,selection,interactingparticle system

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