The effect of deleterious alleles on adaptation in asexual populations.

We calculate the fixation probability of a beneficial allele that arises as the result of a unique mutation in an asexual population that is subject to recurrent deleterious mutation at rate U. Our analysis is an extension of previous works, which make a biologically restrictive assumption that selection against deleterious alleles is stronger than that on the beneficial allele of interest. We show that when selection against deleterious alleles is weak, beneficial alleles that confer a selective advantage that is small relative to U have greatly reduced probabilities of fixation. We discuss the consequences of this effect for the distribution of effects of alleles fixed during adaptation. We show that a selective sweep will increase the fixation probabilities of other beneficial mutations arising during some short interval afterward. We use the calculated fixation probabilities to estimate the expected rate of fitness improvement in an asexual population when beneficial alleles arise continually at some low rate proportional to U. We estimate the rate of mutation that is optimal in the sense that it maximizes this rate of fitness improvement. Again, this analysis relaxes the assumption made previously that selection against deleterious alleles is stronger than on beneficial alleles.

[1]  Mandy J. Haldane,et al.  A Mathematical Theory of Natural and Artificial Selection, Part V: Selection and Mutation , 1927, Mathematical Proceedings of the Cambridge Philosophical Society.

[2]  R. A. Fisher,et al.  The Genetical Theory of Natural Selection , 1931 .

[3]  H. Muller.  Some Genetic Aspects of Sex , 1932, The American Naturalist.

[4]  Motoo Kimura,et al.  Some Problems of Stochastic Processes in Genetics , 1957 .

[5]  T. E. Harris,et al.  The Theory of Branching Processes. , 1963 .

[6]  H. Muller.  THE RELATION OF RECOMBINATION TO MUTATIONAL ADVANCE. , 1964, Mutation research.

[7]  T MUKAI,et al.  THE GENETIC STRUCTURE OF NATURAL POPULATIONS OF DROSOPHILA MELANOGASTER. I. SPONTANEOUS MUTATION RATE OF POLYGENES CONTROLLING VIABILITY. , 1964, Genetics.

[8]  W. G. Hill,et al.  The effect of linkage on limits to artificial selection. , 1966, Genetical research.

[9]  E. Pollak.  On the survival of a gene in a subdivided population , 1966, Journal of Applied Probability.

[10]  M. Kimura,et al.  The mutational load with epistatic gene interactions in fitness. , 1966, Genetics.

[11]  Some effects of fluctuating offspring distributions on the survival of a gene , 1966 .

[12]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[13]  W J Ewens,et al.  The probability of survival of a new mutant in a fluctuating environment , 1967, Heredity.

[14]  T. Ohta,et al.  The Average Number of Generations until Fixation of a Mutant Gene in a Finite Population. , 1969, Genetics.

[15]  M. Kimura,et al.  Probability of fixation of a mutant gene in a finite population when selective advantage decreases with time. , 1970, Genetics.

[16]  A. Robertson.  The reduction of fitness from genetic drift at heterotic loci in small populations. , 1970, Genetical research.

[17]  T. Maruyama.  An invariant property of a structured population. , 1971, Genetical research.

[18]  E. Pollak.  Some effects of two types of migration on the survival of a gene. , 1972, Biometrics.

[19]  T. Ohta.  Slightly Deleterious Mutant Substitutions in Evolution , 1973, Nature.

[20]  J. Felsenstein.  The evolutionary advantage of recombination. , 1974, Genetics.

[21]  J. Haigh.  The accumulation of deleterious genes in a population--Muller's Ratchet. , 1978, Theoretical population biology.

[22]  M. Kimura,et al.  The neutral theory of molecular evolution. , 1983, Scientific American.

[23]  T. Nagylaki.  Geographical invariance in population genetics. , 1982, Journal of theoretical biology.

[24]  J. Gillespie.  A simple stochastic gene substitution model. , 1983, Theoretical population biology.

[25]  J. Gillespie.  Some Properties of Finite Populations Experiencing Strong Selection and Weak Mutation , 1983, The American Naturalist.

[26]  J. Manning,et al.  Muller's ratchet and the accumulation of favourable mutations , 1984 .

[27]  J. Gillespie.  MOLECULAR EVOLUTION OVER THE MUTATIONAL LANDSCAPE , 1984, Evolution; international journal of organic evolution.

[28]  N. Barton.  The probability of establishment of an advantageous mutant in a subdivided population. , 1987, Genetical research.

[29]  N. Barton,et al.  The frequency of shifts between alternative equilibria. , 1987, Journal of theoretical biology.

[30]  R. A. Fisher,et al.  On the dominance ratio , 1990 .

[31]  J. Drake.  A constant rate of spontaneous mutation in DNA-based microbes. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[32]  T. Ohta.  THE NEARLY NEUTRAL THEORY OF MOLECULAR EVOLUTION , 1992 .

[33]  Nicholas H. Barton,et al.  The probability of fixation of a favoured allele in a subdivided population , 1993 .

[34]  J. Peck.  A ruby in the rubbish: beneficial mutations, deleterious mutations and the evolution of sex. , 1994, Genetics.

[35]  N. Barton.  The reduction in fixation probability caused by substitutions at linked loci , 1994 .

[36]  B. Charlesworth.  The effect of background selection against deleterious mutations on weakly selected, linked variants. , 1994, Genetical research.

[37]  O. Berg.  Periodic selection and hitchhiking in a bacterial population. , 1995, Journal of theoretical biology.

[38]  D. Gessler,et al.  The constraints of finite size in asexual populations and the rate of the ratchet. , 1995, Genetical research.

[39]  A. Caballero,et al.  Response to selection from new mutation and effective size of partially inbred populations. I. Theoretical results , 1995 .

[40]  N. Barton.  Linkage and the limits to natural selection. , 1995, Genetics.

[41]  B. Charlesworth,et al.  The evolution of chromosomal sex determination and dosage compensation , 1996, Current Biology.

[42]  P. Keightley.  Nature of deleterious mutation load in Drosophila. , 1996, Genetics.

[43]  D. Hartl,et al.  Compensatory nearly neutral mutations: selection without adaptation. , 1996, Journal of theoretical biology.

[44]  Gillespie,et al.  Development of Neutral and Nearly Neutral Theories , 1996, Theoretical population biology.

[45]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[46]  Michael Lynch,et al.  Estimate of the genomic mutation rate deleterious to overall fitness in E. coll , 1996, Nature.

[47]  M. Whitlock,et al.  The probability of fixation in populations of changing size. , 1997, Genetics.

[48]  Allan Pinkus,et al.  Fourier Series and Integral Transforms: Fourier Series , 1997 .

[49]  TOWARDS A THEORY OF EVOLUTIONARY ADAPTATION , 1998 .

[50]  H. A. Orr,et al.  THE POPULATION GENETICS OF ADAPTATION: THE DISTRIBUTION OF FACTORS FIXED DURING ADAPTIVE EVOLUTION , 1998, Evolution; international journal of organic evolution.

[51]  H. A. Orr,et al.  An adaptive hypothesis for the evolution of the Y chromosome. , 1998, Genetics.

[52]  J. Drake,et al.  Rates of spontaneous mutation. , 1998, Genetics.

[53]  K. Dawson.  The dynamics of infinitesimally rare alleles, applied to the evolution of mutation rates and the expression of deleterious mutations. , 1999, Theoretical population biology.

[54]  S. Elena,et al.  Clonal interference and the evolution of RNA viruses. , 1999, Science.

[55]  Gilean McVean,et al.  The effect of background selection at a single locus on weakly selected, partially linked variants , 1999 .

[56]  M. Lynch,et al.  PERSPECTIVE: SPONTANEOUS DELETERIOUS MUTATION , 1999, Evolution; international journal of organic evolution.

[57]  H. A. Orr,et al.  The evolutionary genetics of adaptation: a simulation study. , 1999, Genetical research.

[58]  P. Keightley,et al.  Perspectives Anecdotal , Historical and Critical Commentaries on Genetics , 1999 .

[59]  T. Johnson.  The approach to mutation–selection balance in an infinite asexual population, and the evolution of mutation rates , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[60]  A. D. Peters,et al.  High frequency of cryptic deleterious mutations in Caenorhabditis elegans. , 1999, Science.

[61]  D. Cutler,et al.  Understanding the overdispersed molecular clock. , 2000, Genetics.

[62]  T. Johnson,et al.  The evolution of mutation rates: separating causes from consequences , 2000, BioEssays : news and reviews in molecular, cellular and developmental biology.

[63]  H. A. Orr,et al.  ADAPTATION AND THE COST OF COMPLEXITY , 2000, Evolution; international journal of organic evolution.

[64]  H. A. Orr,et al.  The rate of adaptation in asexuals. , 2000, Genetics.

[65]  L. Chao,et al.  Evolvability of an RNA virus is determined by its mutational neighbourhood , 2000, Nature.

[66]  Art Poon,et al.  COMPENSATING FOR OUR LOAD OF MUTATIONS: FREEZING THE MELTDOWN OF SMALL POPULATIONS , 2000, Evolution; international journal of organic evolution.

[67]  B. Charlesworth,et al.  The degeneration of asexual haploid populations and the speed of Muller's ratchet. , 2000, Genetics.

[68]  M Imhof,et al.  Fitness effects of advantageous mutations in evolving Escherichia coli populations. , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[69]  W. Rice,et al.  Sexual Recombination and the Power of Natural Selection , 2001, Science.

[70]  P. Gerrish.  The rhythm of microbial adaptation , 2001, Nature.

[71]  R. Lenski,et al.  The fate of competing beneficial mutations in an asexual population , 2004, Genetica.