Analytic approach to the evolutionary effects of genetic exchange

We present an approximate analytic study of our previously introduced model of evolution including the effects of genetic exchange. This model is motivated by the process of bacterial transformation. We solve for the velocity, the rate of increase of fitness, as a function of the fixed population size, $N$. We find the velocity increases with $\ln N$, eventually saturated at an $N$ which depends on the strength of the recombination process. The analytical treatment is seen to agree well with direct numerical simulations of our model equations.