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Role of Biased Gene Conversion in One-Locus Neutral Theory and Genome Evolution

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Role of Biased Gene Conversion in One-Locus Neutral Theory and Genome Evolution Copyright 0 1983 by the Genetics Society of America ROLE OF BIASED GENE CONVERSION IN ONE-LOCUS NEUTRAL THEORY AND GENOME EVOLUTION JAMES BRUCE WALSH’ Department of Genetics, SK-50, University of Washington, Seattle, Washington 98195 Manuscript received May 12, 1983 Revised copy accepted July 5, 1983 ABSTRACT The implications of biased gene conversion acting on selectively neutral alleles are investigated for a single diallelic locus in a finite population. Even a very slight conversion bias can significantly alter fixation probabilities. We argue that most newly arising mutants will be at a conversion disadvantage, resulting in a potentially greatly decreased substitution rate of new alleles com- pared with predictions from strict neutral theory. Thus, conversion bias poten- tial allows for conservation of particular alleles without having to invoke selec- tion. Conversely, we also show that bias can be important in the maintenance of repeated gene families without altering the substitution rate at other loci that experience the same amount of conversion bias, provided that the number of genes in the family is sufficiently large. Bias can, therefore, be important at the genomic level and yet be unimportant at the populational level. Finally, we discuss the role of biased gene conversion in speciation events, concluding that this type of molecular turnover acting independently at many individual loci is very unlikely to decrease the time required for two allopatric populations to speciate. HE evolutionary implications of molecular turnover processes within the T genome such as gene conversion, unequal crossing over and transposition have recently received much attention. The potential for these processes to give rise to “selfish” DNA (DOOLITTLEand SAPIENZA1980; ORCELand CRICK 1980) as well as the role of these forces in speciation events (DOVER1982; ROSEand DOOLITTLE1983) has been the subject of much discussion. Popula- tion genetics models of molecular turnover have examined the evolution of multigene families (OHTA 1981; NAGYLAKIand PETES 1982), the amount of selfish DNA in the genome (OHTA and KIMURA1981; OHTA 1983) and de- terministic single-locus models of gene conversion and transposition opposed by selection (HICKEY1982; LAMBand HELMI 1982). None of these models specifically addresses the consequences of molecular turnover processes for a single-locus neutral theory. Here, we examine the implications of biased gene conversion acting on a single diallelic locus in a finite population, with special attention to the effects of biased gene conversion on selectively neutral alelles. We also examine the ’ Present address: Department of Biophysics and Theoretical Biology, The University of Chicago, 920 East 58th Street, Chicago, Illinois 60637. Genetics 105: 461-468 October, 1983. 462 J. B. WALSH role of biased gene conversion in speciation events and investigate under what conditions bias in conversion can be important in the evolution of multigene families and yet be unimportant in the evolution of unique single loci which experience the same levels of biased conversion. The first section reviews molecular models of conversion bias. In the second, we use standard diffusion results to determine the fixation probabilities and substitution rates of selec- tively neutral alleles with a conversion bias. The third section examines under what conditions bias in conversion is important at the genomic level (changing the composition of multigene families) and yet unimportant at the population level (not altering the substitution dynamics of alleles at unique single loci). The fourth section deals with the speciation implications of single-locus biased conversion acting independently at many loci as a model system of speciation by molecular turnover mechanisms. MOLECULAR MODELS OF BIASED CONVERSION Gene conversion is the nonreciprocal transfer of genetic information from one variant to another and usually results in a departure from normal Men- delian segregation. Conversion is said to be biased if one variant is preferen- tially produced over another during conversion events. Existing molecular models of conversion imply that conversion bias is not at all unexpected, and data from fungal systems (LAMBand HELMI1982; NAGYLAKIand PETES 1982) support this view. Current models of gene conversion comprise two classes: single strand break models and double strand break models. Single strand break models were introduced by HOLLIDAY(1 964) with subsequent refine- ments by MESELSON and RADDING(1975). Conversion is initiated by a single strand break in one of the DNA duplexes of an interacting chromatid pair. This single strand invades the other duplex, forming a region of heteroduplex DNA through strand displacement. Conversion occurs when mismatch repair of the heteroduplex DNA results in a change of the allelic composition of the chromatid pair. Bias in conversion results if one strand of the heteroduplex DNA preferentially serves as the template for mismatch repair. Recent exper- imental results (SAVAGand HASTINGS1981; FOCELet al. 1978) suggest that, for single strand break models, mismatch repair must use the invading strand for the template. Thus, an unequal frequency of single strand breaks and invasions between two different variants can result in conversion bias. Double strand break conversion models (SZOSTAKet al. 1983) proceed from a double strand break in one of the DNA duplexes of a chromatid pair which is subsequently enlarged into a double strand gap by exonuclease action. Gap repair occurs by a double strand transfer of information from the other duplex without the direct involvement of heteroduplex DNA formation. In this model, biased conversion results from unequal formation of double strand nicks on chromatids carrying different alleles. It is interesting to note that in the single strand break model sequences that are preferentially nicked are at a conversion advantage, whereas such sequences are at a conversion disadvantage in double strand break models. BIASED GENE CONVERSION 463 FIXATION PROBABILITIES AND SUBSTITUTION RATES Theoretical models of biased gene conversion acting at a single locus are formally equivalent to meiotic drive (GUTZand LESILE1976; LAMBand HELM 1982), because both result in departures from normal 1:l Mendelian segre- gation in heterozygotes. For a diallelic system with alleles A and a, we can define the drive strength, d = 2k- 1, where the segregation ratio of A:a is k:l - k from Aa heterozygotes. d = 0 if normal 1:l segregation occurs (e.g., k = lh); otherwise, d ranges from 1 (only A-bearing gametes are produced by heterozygotes) to -1 (only a-bearing gametes are produced). To compute d for gene conversion, let be the probability of an unequal conversion event and /3 be the conditional probability that allele a is converted to A given that an unequal conversion event occurs. Hence, (1 - y) of the segregation events produce equal numbers of A- and a-bearing gametes, whereas y/3 of the seg- regation events produce only A-bearing gametes, implying k = (1 - y)(l/z) + y/3 and d = y(28 - 1). If the gene conversion is unbiased (i.e., neither allele is favored in an unequal conversion event) /3 = '1'2 and d = 0, independent of the frequency of unequal conversion y. The most general one-locus diallelic model of biased gene conversion as- sumes that the genotypes AA:Aa:aa have fitnesses 1: 1 + h: 1 + s. Provided that d, h and s are small enough to ignore terms of second and higher order, an allele A with the above fitnesses which has a conversion bias d behaves dynam- ically like an allele with no conversion bias and fitnesses 1 + 2d:l + d + h:l + s (GUTZand LESILE 1976; WALSH 1982; NACYLAKI1983a). It immediately follows that a selectively neutral (h = s = 0) allele with a conversion bias is equivalent to an unbiased allele with additive fitness d. Unless otherwise stated, we restrict our attention to such alleles in one-locus dialleic models for the remainder of this paper. Standard results from the theory for additive selection apply to our problem using this equivalence. For an infinite, randomly mating population, an allele at a conversion disadvantage (d < 0) is lost, whereas an allele at a conversion advantage (d > 0) is fixed. The dynamics of multiallelic systems in infinite populations are considerably more complex (NAGYLAKI1983b). Focusing on finite populations with random mating, KIMURA'S (1957) clas- sical results for loci with additive fitnesses can be used to obtain fixation probabilities and substitution rates for the diallelic case with no selection. NA- GYLAKI (1 983a) investigates the more general case of multiple alleles with conversion bias, selection and mutation, obtaining the diffusion equation this processes satisfies. Equilibrium properties of such multiple allele systems can be examined by the methods employed by LI (1978), but, here, we wish to focus only on the properties of a simple diallelic locus. Given that Ne, the variance effective population size, is large and Id I is small, the probability (U[p]) that allele A is fixed given an initial frequency p is qp]x (1 - e-4fiN9/(1- (1) We are particularly interested in v[ 1/(2Na)], the probability of fixation given 464 J. B. WALSH that A began as a single copy in a population of iV, diploids. Since I d I << 1, and 1/(2N,) << 1, equation (1) gives (KIMURA1964) U[1 @No)] = 1/(2No) for 4NeI d I << 1 (24 U[1 /( 2N,)] = 2dN,/N, for 4Ned >> 1 (2b) U[1/(2N,)] = (-2d~V,/N~)e~"*~for 4N,d << -1 (2c) For a strictly neutral allele (no conversion bias or selection), U[1/(2N,)] = 1/ (2N,), implying that conversion is overcome by drift when 4N,I d I << 1. Re- marks by DOVER(1982) and LAMBand HELMI(1982) that fixation by biased gene conversion proceeds as easily in small as in large populations are, there- fore, incorrect, at least in the context of conversion acting on a single locus. However, when 4Ne1d I >> 1, bias in conversion overcomes genetic drift and can be a significant evolutionary force.
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