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Transition between stochastic evolution and deterministic evolution in the presence of selection: general theory and application to virology.

TitleTransition between stochastic evolution and deterministic evolution in the presence of selection: general theory and application to virology.
Publication TypeJournal Article
Year of Publication2001
AuthorsIM Rouzine, Rodrigo, A, Coffin, JM
JournalMicrobiol Mol Biol Rev
Volume65
Issue1
Pagination151-85
Date Published2001 Mar
ISSN1092-2172
KeywordsBiological Evolution, Genes, Viral, HIV, Humans, Markov Chains, Mathematics, Models, Biological, Polymorphism, Genetic, Selection Bias, Selection, Genetic, Stochastic Processes, Viruses
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.

DOI10.1128/MMBR.65.1.151-185.2001
Alternate JournalMicrobiol. Mol. Biol. Rev.
PubMed ID11238990
PubMed Central IDPMC99023
Grant ListK25 AI001811 / AI / NIAID NIH HHS / United States
1K25AI01811 / AI / NIAID NIH HHS / United States
R35CA44385 / CA / NCI NIH HHS / United States