ROLE OF BIASED GENE CONVERSION IN ONE-LOCUS NEUTRAL THEORY AND GENOME EVOLUTION

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. T h e potential for these processes to give rise to “selfish” DNA (DOOLITTLE and SAPIENZA 1980; ORCEL and CRICK

1980) as well as the role of these forces in speciation events (DOVER 1982; ROSE and DOOLITTLE 1983) has been the subject of much discussion. Popula- tion genetics models of molecular turnover have examined the evolution of multigene families (OHTA 1981; NAGYLAKI and PETES 1982), the amount of selfish DNA in the genome (OHTA and KIMURA 1981; OHTA 1983) and de- terministic single-locus models of gene conversion and transposition opposed

by selection (HICKEY 1982; LAMB and 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.

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. T h e 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. T h e 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). T h e 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 (LAMB and HELMI 1982; NAGYLAKI and 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 (SAVAG and HASTINGS 1981; FOCEL et 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.

463

FIXATION PROBABILITIES AND SUBSTITUTION RATES

Theoretical models of biased gene conversion acting at a single locus are formally equivalent to meiotic drive (GUTZ and LESILE 1976; LAMB and 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

=

l h ) ; 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 (GUTZ and LESILE 1976; WALSH 1982; NACYLAKI 1983a). 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 (NAGYLAKI 1983b).

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

q p ]

x (1

-

e-4fiN9/(1

-

(1)

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 (KIMURA 1964)

U [ 1 @No)]

=

1 /(2No) for 4NeI d

I

<<

1 ( 2 4 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 LAMB and 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 4Ne1 d I

>>

1, bias in conversion overcomes genetic drift and can be a significant evolutionary force. In these cases newly arising mutants at a conversion disadvantage (d

<

0) are fixed only very rarely compared with strictly neutral alleles, whereas alleles at a conversion advantage (d

>

0) have a much higher relative chance of fixation compared to strictly neutral alleles. What little information is available on ( d

I

suggests that some populations are large enough for biased conversion to be a significant evolutionary force. Fungal systems are the best characterized, with a mean value of Id

1

ranging from 3

x

to 4 x lo-* in a variety of species (LAMB and HELMI 1982). Preliminary evidence from corn (NELSON 1975) and Drosophila (HILLIKER and CHOVNICK 1981) suggests that

I

d

I

may be considerably lower in higher eu-

karyotes (I d ]

<

as an estimate of the average value of

Id

I

in eukaryotes implies that effective population sizes in excess of lo4 are required for biased gene conversion to be an important evolutionary force when acting on a single locus. If the average value of Id I in eukaryotes is considerably smaller than 1 0-4, larger effective population sizes are required and vice versa.

Intimately coupled with fixation probabilities is the per generation substitu- tion rate R of new alleles at a specific locus. Let p be the per generation mutation rate of the type allele to new alleles at the locus in question. We assume that all mutants have the same conversion parameter d relative to the type allele and further assume that, if biased gene conversion occurs between mutant alleles, it is sufficiently small relative to d to be ignored. Under these assumptions, the probability of fixation of each new mutant is the same and is

given by U [ 1 /(21Vn)]. Since 2N0p new mutants arise on average each generation, R (2Nnp)U[1/(21Vc,)] (KIMURA and OHTA 1971). R measures the rate of allelic substitutions, and given that new alleles are often created by mutational events which involves more than single nucleotide changes, it is very difficult to accurately determine R from comparative sequence data (see NEI 1975, pp. 101-102). R

=

p for strictly neutral alleles (KIMURA 1968; GUESS and EWENS 1972), so from (2) it follows that (1) if d

>>

1/(4Ne), gene conversion increases the substitution rate compared with strictly neutral alleles; (2) if d

<<

-1/(4Ne), conversion exponentially decreases the substitution rate; and (3) if

-

1 /(4N,)

<

465

those loci that experience gene conversion, these substitution rates suggest that existing selectively neutral alleles most likely have undergone several rounds of conversion. These surviving alleles will have been “selected” to be at a conversion advantage relative against a wide spectrum of competing alleles. NAGYLAKI and PETES ( 1 982), addressing the role of intrachromosomal gene conversion in the homogenization of gene families, come to a similar conclu- sion regarding existing repeats in a multigene family.

Thus, for selectively neutral alleles at loci experiencing gene conversion we expect most newly arising mutants to be at a conversion disadvantage relative to the standard allele, potentially resulting in a greatly decreased substitution rate at these loci compared with predictions from strict neutral theory. Given the equivalence between additive selection and biased conversion most newly arising mutants at these loci have the same properties as slightly deleterious alleles. OHTA (1976) reviews the role of slightly deleterious alleles in molecular evolution, demonstrating that the presence of such alleles can account for the excess of rare alleles seen in some populations over predictions from strict neutral theory. Biased gene conversion can, therefore, also account for these deviations from strict neutral theory without having to invoke selection.

EFFECTIVENESS OF BIAS AT T H E GENOMIC AND POPULATIONAL LEVELS

In the previous section we examined the consequences of biased gene con- version acting at single loci. This is “classical” gene conversion, conversion between different alleles at the same locus on homologous chromosomes (we will refer to this as interchromosomal gene conversion). More generally, con- version can occur between different loci, which has very important conse- quences for genome evolution. One scheme for such conversions is intra- chromosomal gene conversion, in which the conversion occurs between different loci on the same chromosome. OHTA (1977) and NAGYLAKI and PETES (1982)

showed that intrachromosomal conversion results in the homogenization of repeated gene families. Thus, we can view conversion as operating on two different evolutionary levels: populational and genomic. T h e populational level refers to the effects of conversion at single unique loci (i.e., not members of repeated gene families), and as was shown bias in conversion can have an important effect at the populational level. T h e genomic level refers to the organization and composition of repeated sequences within the genome. Unlike at the populational level, both biased and unbiased conversion are potentially important at the genomic level, with bias being particularly important in gene families with a large number of members (NAGYLAKI and PETES 1982).

Although the rates of interchromosomal and intrachromosomal conversion are likely to be very different, the amount of bias given a conversion event occurs conceivably is quite similar. Therefore, we wish to ask whether it is possible for bias in conversion to be important at the genomic level and yet be unimportant at the populational level. That is, are substitution rates at

certain loci constrained when bias is important at the genomic level?

dition for biased conversion to behave significantly different from unbiased conversion in gene family evolution provided small amounts of bias (@ close, b u t not equal, to Vz). This condition can be expressed as GI

2P

-

1

I/@

>>

1 ,

where g is the number of members of the gene family and

/3

(as defined earlier) is our measure of bias. If this condition is satisfied, those variants at a conver- sion advantage

(P

>

l/z) have a much higher relative probability of fixation compared with unbiased conversion, and the appearance of such variants can result in a change in the composition of a gene family. Those newly arising variants that are at a conversion disadvantage (/3 C Y2), however, have an

extremely low relative probability of fixation compared with unbiased conver- sion, and in these cases the effect of the bias is to conserve the existing repeats in the family. T h e rate of intrachromosomal gene conversion does not enter into the condition because NACYLAKI and PETES follow only a single chromo- somal lineage, rescaling time so that one conversion event occurs each gener- ation. Although this rescaling effects the time to fixation, it does not affect the probability of fixation, and, hence, this condition is independent of the actual rate of intrachromosomal conversion, provided that it is positive.

Combining our conditions for drift overcoming conversion at a single locus (4N,yl2/3

-

1 I

<

1) with NACYLAKI and PETES’ condition gives

G

>>

PI1

2P

-

1

I

>

4NeyP (3)

as a sufficient condition that allows for biased conversion to greatly alter fix- ation probabilities in gene families (compared with unbiased conversion) and still be ineffective at the population level (for those individual loci with the same conversion bias parameter

P).

A necessary condition for equation (3) to be satisfied is that the number of members in the gene family must be suffi- ciently large (G

>>

4Ney/3). Values for y from fungal systems (LAMB and HELMI

1982) are approximately lo-‘, so if Ne = 1000 and /3 close (but not equal) to

0.5, G

>>

20. For these parameters, if intrachromosomal conversion bias is important in gene families with fewer than 20 members, then we expect in- terchromosomal gene conversion to reduce the substitution rate of selectively neutral alleles at those other loci that have the same conversion bias

8.

Like- wise, if the number of genes in the gene family is sufficiently large, very slight amounts of bias which would be unimportant at the populational level are nevertheless quite important at the genomic level.

BIASED CONVERSION, MOLECULAR DRIVE AND SPECIATION

BIASED GENE CONVERSION 467

pendently at many single loci have on the speciation rate of isolated populations if we assume speciation by fixation of underdominant alleles? WALSH (1

982)

examined speciation rates in finite populations, assuming fixation of underdom- inant chromosome rearrangements, and addressed the consequences of meiotic drive. If d is the drive strength, and the fitnesses of genotypes AA:Aa:aa are 1:l

-

h:l,

then, provided that N d

>>

1, genes with h

<

d are likely to become fixed. If NJ 1, genes with h

>

1.3/Ne

are very unlikely to become fixed. Thus, meiotic drive increases the speciation rate by allowing fixation of genes that would not be fixed without drive (viz., those genes for which

1.3/Ne

<

h

C d). Likewise, gene conversion can potentially increase speciation rates but only in populations with fairly large effective population sizes, e.g., N,

>>

l / d .

Even in these populations, reproductive isolation accumulates very slowly be- cause only those underdominant alleles with h C d are likely to become fixed, and since d is expected to be small many fixation events are required for even a small increase in reproductive isolation. Furthermore, we would expect the occurrence of underdominant alleles with a conversion advantage to be very infrequent. Finally, as we have shown, gene conversion is not a powerful force in small populations, but there is widespread conviction that population bottlenecks are critical to species formation (CARSON

1975).

If such founding events are important in speciation, gene conversion plays little role in this type of speciation process. Therefore, it seems unlikely that gene con- version acting independently at many single loci could appreciably increase speciation rates, except in very unusual circumstances. ROSE and DOOLITTLE (1

983)

suggest on biological grounds that gene conversion acting to homoge- nize a multigene family is also unlikely to be effective in speciation events. Thus, it appears from the present state of knowledge of genome organization that gene conversion does not play an important role in changing the rate at which allopatric populations speciate.

I thank L. SANDLER, C. LAIRD, M. SLATKIN and T. OHTA for useful discussions. I especially wish to thank TOM NAGYLAKI for helpful comments and communications. This research was supported in part by a National Science Foundation predoctoral fellowship, by National Institutes of Health training grant GM07748, and in part by test agreement DE-AT06-76EV71005 of contract DE-AM06-76L02225 between the United States Department of Energy and the University of Washington. This paper is dedicated to HERSCHEL ROMAN, a pioneer in the study of gene conversion, for his outstanding commitment to graduate education.

\

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