Mathematical modeling of evolution of horizontally transferred genes
  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. 
Artem S. Novozhilov, Georgy P. Karev, and Eugene V. Koonin