Transition between stochastic evolution and deterministic evolution in thepresence of selection: General theory and application to virology

We present here a self-contained analytic review of the role of stochastic factors acting on a vines population. We develop a simple one-locus, two-al lele model of a haploid population of constant size including the factors o f random drift, purifying selection, and random mutation. We consider diffe rent virological experiments: accumulation and reversion of deleterious mut ations, competition between mutant and wild-type viruses, gene fixation, mu tation frequencies at the steady state, divergence of two populations split from one population, and genetic turnover within a single population. In t he first part of the review, we present all principal results in qualitativ e terms and illustrate them with examples obtained by computer simulation. In the second part we derive the results formally from a diffusion equation of the Wright-Fisher type and boundary conditions, all derived from the fi rst principles for the virus population model. We show that the leading fac tors and observable behavior of evolution differ significantly in three bro ad intervals of population size, N. The "neutral limit" is reached when N i s smaller than the inverse selection coefficient When N is larger than the inverse mutation rate per base, selection dominates and evolution is "almos t" deterministic. If the selection coefficient is much larger than the muta tion rare, there exists a broad interval of population sizes, in which weak ly diverse populations are almost neutral while highly diverse populations are controlled by selection pressure. We discuss in detail the application of our results to human immunodeficiency virus population in vivo, sampling effects, and limitations of the model.