  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.
