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Microbiology and Molecular Biology Reviews, March 2001, p. 151-185, Vol. 65, No. 1
1092-2172/01/$04.00+0   DOI: 10.1128/MMBR.65.1.151-185.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.

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

I. M. Rouzine,1,* A. Rodrigo,2 and J. M. Coffin1

Department of Molecular Biology and Microbiology, Tufts University, Boston, Massachusetts 02111,1 and School of Biological Sciences, University of Auckland, Auckland, New Zealand2

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.

* Corresponding author. Mailing address: Department of Molecular Biology and Microbiology, Tufts University, Boston, MA 02111. Phone: (617) 782-3872. Fax: (617) 636-4086. E-mail: irouzine{at}emerald.tufts.edu.

Microbiology and Molecular Biology Reviews, March 2001, p. 151-185, Vol. 65, No. 1
1092-2172/01/$04.00+0   DOI: 10.1128/MMBR.65.1.151-185.2001
Copyright © 2001, American Society for Microbiology. All rights reserved.


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Copyright © 2001 by the American Society for Microbiology. All rights reserved.