  We describe a stochastic birth-and-death model of evolution of horizontally
transferred genes in microbial populations. The model is a generalization of
the stochastic model described by Berg and Kurland and includes five
parameters: the rate of mutational inactivation, selection coefficient,
immigration rate (i.e., rate of arrival of a novel sequence from outside of the
recipient population), within-population horizontal transmission rate, and
population size. The model of Berg and Kurland included four parameters,
namely, mutational inactivation, selection coefficient, population size, and
transmission rate. However, the effect of transmission was disregarded in the
interpretation of the results, and the overall conclusion was that horizontally
acquired sequences can be fixed in a population only when they confer a
substantial selective advantage onto the recipient and therefore are subject to
strong positive selection. By contrast, analysis of the present model in
different domains of parameter values shows that, as long as the rate of
within-population horizontal transmission is comparable to the mutational
inactivation rate and there is even a low rate of immigration, horizontally
acquired sequences can be fixed in the population or at least persist for a
long time even when they are neutral or slightly deleterious. The available
biological data strongly suggest that intense within-population and even
between-populations gene flows are realistic for at least some prokaryotic
species and environments. Therefore our modeling results are compatible with
the notion of a pivotal role of horizontal gene transfer in the evolution of
prokaryotes.
