Transition between Stochastic Evolution and Deterministic Evolution in the Presence of Selection: General Theory and Application to Virology

Abstract

We present here a self-contained analytic review of the role of stochastic factors acting on a virus population. We develop a simple one-locus, two-allele model of a haploid population of constant size including the factors of random drift, purifying selection, and random mutation. We consider different virological experiments: accumulation and reversion of deleterious mutations, competition between mutant and wild-type viruses, gene fixation, mutation frequencies at the steady state, divergence of two populations split from one population, and genetic turnover within a single population. In the first part of the review, we present all principal results in qualitative 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 first principles for the virus population model. We show that the leading factors and observable behavior of evolution differ significantly in three broad intervals of population size, N. The “neutral limit” is reached when N is smaller than the inverse selection coefficient. When N is larger than the inverse mutation rate per base, selection dominates and evolution is “almost” deterministic. If the selection coefficient is much larger than the mutation rate, there exists a broad interval of population sizes, in which weakly 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

Dynamics of HIV-1 recombination in its natural target cells

“…Despite a mutation rate that is only of average magnitude among RNA viruses (2,29), the high rate of HIV-1 replication in vivo ensures rapid diversification (1,9). Recombination represents a complementary mechanism that has the potential to accelerate HIV-1 diversification and evolution greatly (30,31), although some models challenge this view (32,33).…”

“…Although abundant coinfection has been documented recently within the spleens of HIV-1-infected individuals, indicating an environment supportive of a high level of recombination (5), the kinetics of coinfection and recombination remain undefined. As a result, recombination has been so far excluded from most quantitative models of HIV-1 dynamics and evolution (1,(6)(7)(8)(9). Here, we examine the dynamics of HIV-1 coinfection and recombination in real time in biologically relevant cell types, T lymphocytes, and macrophages, as well as an in vivo animal model.…”

Adaptations to fluctuating selection in Drosophila

“…Evolutionary equilibrium defines the unique stationary solution p eq (x) with a vanishing substitution current, Jp eq (x) ϭ 0, i.e., there is detailed balance between forward and backward substitutions. The equilibrium distribution, given exactly for all values of by p eq (x) ϭ [x(1 Ϫ x)] Ϫ1ϩ e x ͞Z eq with a normalization factor Z eq (30), has the form (Eq. 6) with…”

Purifying Selection Masks the Mutational Flexibility of HIV-1 Reverse Transcriptase

“…4 and 5) suggests that motif B and other RT mutants are present at low frequencies in the complex mixtures of variants that comprise HIV-1 populations in vivo (44). Components of these mutant "swarms" or "quasispecies" can emerge as the dominant member of a population as a result of changing environmental demands (24,44,60). This is clearly evident in the development of resistance to antiviral therapy, where positive selection often results in the outgrowth of rare, drug-resistant variants that preexist in drug-naive patients (42,50,(61)(62)(63)(64).…”