The Evolution of Sex Dimorphism in Recombination
a CEFE-Centre National de la Recherche Scientifique, 34293 Montpellier, France#1\$'7, 百拇医药
ABSTRACT#1\$'7, 百拇医药
Sex dimorphism in recombination is widespread on both sex chromosomes and autosomes. Various hypotheses have been proposed to explain these dimorphisms. Yet no theoretical model has been explored to determine how heterochiasmy—the autosomal dimorphism—could evolve. The model presented here shows three circumstances in which heterochiasmy is likely to evolve: (i) a male-female difference in haploid epistasis, (ii) a male-female difference in cis-epistasis minus trans-epistasis in diploids, or (iii) a difference in epistasis between combinations of genes inherited maternally or paternally. These results hold even if sources of linkage disequilibria besides epistasis, such as migration or Hill-Robertson interference, are considered and shed light on previous verbal models of sex dimorphism in recombination rates. Intriguingly, these results may also explain why imprinted regions on the autosomes of humans or sheep are particularly heterochiasmate.
MEIOSIS in males and females differs in several important respects. A female produces only one large gamete (ovule) from the four meiotic products whereas a male produces four small motile gametes (spermatozoa) from the four meiotic products. Often, the timing of male and female meiosis is different: in animals, for example, male meiosis tends to be continuous whereas female meiosis generally stops twice, just after meiosis begins and just before it ends. And at least sometimes, the amount of genetic recombination during meiosis differs between males and females because of differences in crossing over number and/or position. How did these meiotic differences evolve, and how are they maintained?h|es, 百拇医药
The first aspect—the evolution of anisogamy—has received considerable theoretical treatment (see, for example, RANDERSON and HURST 2001 ); but aspects such as the evolution of dimorphism in recombination have received much less attention, especially with respect to formal models. The aim of this article is to determine the conditions under which a recombination dimorphism can evolve. I begin by reviewing the facts about recombination dimorphism and the different hypotheses that have been proposed to account for it. I then present a formal model for the evolution of recombination dimorphism on autosomes and on sex chromosomes.
A recombination dimorphism can occur on sex chromosomes (or close to a sex-determining locus) or on autosomes. In the autosomal case, recombination may be completely absent in one sex, a phenomenon known as achiasmy, or it may vary quantitatively between sexes, a phenomenon that I term "heterochiasmy."rw1|)#, 百拇医药
Recombination dimorphism on sex chromosomes:rw1|)#, 百拇医药
In species with a large sex-chromosome heteromorphism (X vs. Y or Z vs. W), the sex chromosomes in the heterogametic sex do not exchange genetic material along much of their length. This is the most conspicuous and widespread recombination dimorphism between the sexes. Two related theories have been advanced to explain selection for reduced recombination around sex-determining loci: (i) recombination is disadvantageous for sex-linked alleles with opposite effects in the two sexes (CHARLESWORTH and CHARLESWORTH 1980 ), and (ii) recombinant genotypes have an "intersex" unfit genotype because of the accumulation of linked sex factors (NEI 1969 ).
Achiasmy:+gn, http://www.100md.com
Although it has received less attention, recombination dimorphism on autosomes is also common. In the most conspicuous cases, achiasmy, one sex apparently lacks recombination completely. This is not related to the loss of meiosis that often occurs with parthenogenesis: achiasmy occurs in taxa where parthenogenesis is rare or unknown, e.g., Lepidoptera, Trichoptera, Diptera, and isolated species of molluscs, water-mites, copepods, grasshoppers, and alder-flies (BELL 1982 ). When achiasmy occurs in dioecious species, it is almost always the heterogametic sex that is achiasmate, a phenomenon known as the "Haldane-Huxley rule" [ HALDANE 1922 ; HUXLEY 1928 ; for examples, see BELL 1982 , Table 5.3; however, some species in Musca and Culex genera are possible exceptions (BULL 1983 )]. The Haldane-Huxley rule has been explained either as a pleiotropic consequence of selection against recombination between X and Y (or Z and W)—the pleiotropy hypothesis—or as the consequence of the evolution of the Y (or W) in the sex that initially had no recombination—the no-recombination hypothesis.
Both hypotheses are plausible in principle. However, both can be criticized in several ways. For example, the pleiotropy hypothesis provides no explanation for why the pleiotropic effect should be so extreme: after all, there is ample within-species genetic variation for recombination rates on autosomes. The hypothesis does not explain why achiasmate meiosis occurs in only one gender within hermaphrodites (e.g., some Liliaceae in the genus Fritillaria; NODA 1975 ). It cannot explain why achiasmy has evolved in the heterogametic sex in species with a XX/XO sex-determination system (e.g., according to WHITE 1976 this has occurred eight separate times in Mantodea), unless one supposes that each XX/XO system has passed through an XX/XY system followed by the complete degeneration of the Y. Finally, the pleiotropy hypothesis does not explain why achiasmate meiosis in the heterogametic sex is maintained once sex-chromosome heteromorphism has evolved such that the sex chromosomes would no longer be homologous and able to recombine (e.g., in the extreme case recombination on the sex chromosome cannot occur in XO individuals).
The no-recombination hypothesis provides no explanation for why sex differences in recombination should preexist the formation of Y or W. Furthermore, the assumption on which this hypothesis rests—that heterogamety will always gradually evolve in the sex with low recombination—will not always hold: if the sex-determining mechanism depends on a single locus (even if this is considered improbable; CHARLESWORTH 2002 ), it does not depend on recombination and therefore the "heterozygote" sex, which is likely to become the heterogametic sex, should be equally likely to be the sex with or without recombination.|cys, http://www.100md.com
Heterochiasmy data:|cys, http://www.100md.com
Measuring heterochiasmy is difficult. Most data that have been collected consist of chiasma counts. This method does not often take into account the position of crossing over along chromosomes, which in general varies between males and females, resulting in a strong bias (male chiasmata are often either proterminal or procentric; e.g., FLETCHER and HEWITT 1980 ). This difference of chiasma position between the sexes is also a problem in studies using map distance between few markers: depending on where the markers are along the chromosomes more recombination may appear to be in one sex or the other when in fact it is not. Molecular techniques have also revealed a large source of variation in recombination rates from chromosome to chromosome and from genotype to genotype (see KOROL et al. 1994 , p. 280, for examples). Analyzing heterochiasmy data can present further difficulties. For example, not knowing the rate of evolution of heterochiasmy can make it difficult to judge whether there is phylogenetic inertia and thus how many species or groups of species must be contrasted when attempting to test hypotheses.
TRIVERS 1988 and BURT et al. 1991 reviewed chiasma count data and found that differences between the sexes are often large. Recent map data tend to confirm their analyses, although these data have yet to be rigorously examined. Moreover, in 75% of chiasmate species (whether dioecious or hermaphrodite), recombination rate, measured using either chiasma count (BURT et al. 1991 ) or map length (my personal observations), differs by >5% between male and female meiosis. In extreme cases, recombination in female meiosis can be as much as 3 times higher [for instance, in the zebrafish Danio rerio, which has no heteromorphic sex chromosome (SINGER et al. 2002 ), and in the planarian Schmidtea polychroa, a hermaphrodite (PONGRATZ et al. 2001 )] or ~ 1.5 times lower (e.g., in the monecious species Pinus taeda; SEWELL et al. 1999 ). Nonetheless, TRIVERS 1988 argued that in dioecious species the direction of heterochiasmy tends to be biased toward less recombination in male meiosis and is not affected much by heterogamety.
Heterochiasmy theories:^\p%$}, http://www.100md.com
Several ideas have been put forward to explain the occurrence of heterochiasmy. They fall into several groups that I briefly review before turning to the model.^\p%$}, http://www.100md.com
Mechanistic explanations: A different internal environment between male and female tissue, due to physiological or molecular processes, is a potential cause of heterochiasmy. For instance, BERNSTEIN et al. 1988 argued that higher recombination rates in females could be due to higher metabolic rates in females. This hypothesis is weak since, in hermaphrodites, both male and female meiosis occurs in the same individual. However, even in hermaphrodites, male and female meiosis may not occur at the same time—and therefore may occur under different conditions. For instance, in Pinus, male and female meiosis occurs in different seasons. Differences in temperature, which have been shown to influence recombination rates, could thus explain the observed heterochiasmy with more recombination in males in this genus (see PLOMION and OMALLEY 1996 ). But without more data on the timing of meiosis in hermaphrodites, the extent to which timing may explain heterochiasmy cannot be evaluated. Another possibility is that heterochiasmy itself may be a way to control the timing of meiosis. Crossing over has been hypothesized to regulate segregation and DNA repair; chiasma number could also modulate the speed of meiosis. For example, as mentioned above, in gonochoric animals, male meiosis tends to be continuous whereas female meiosis generally stops twice; numerous chiasmata could stabilize the female meiosis when it stops (sometimes for long periods of time), whereas few chiasmata could allow males a fast gametogenesis. However, this hypothesis may not apply to most plants for which the timing of male and female meiosis does not seem to differ much.
Pleiotropic effect of sex-chromosome heteromorphism: The Haldane-Huxley rule could explain heterochiasmy as well as achiasmy (for instance HUXLEY 1928 invoked it for marked heterochiasmy). However, at the very least, this is not a general explanation: counter examples are numerous, and a pleiotropic effect of the evolution of sex-chromosome heteromorphism cannot account for heterochiasmy in hermaphrodites (see BURT et al. 1991 )o&xf.{l, 百拇医药
The neutral hypothesis: The evolution of the average recombination rate has been well studied theoretically (see, for review, BARTON and CHARLESWORTH 1998 ; OTTO and LENORMAND 2002 ) and some experiments have shown that it can evolve (e.g., KOROL and ILIADI 1994 ). On the other hand the evolution of the difference in recombination rates between males and females has neither theoretical nor empirical support. When BURT et al. 1991 failed to find support for a correlation between the magnitude of heterochiasmy and the opportunity for sex difference in selection (which, they argued, should be high in dioecious animals, intermediate in hermaphroditic plants, and low in hermaphroditic animals), they suggested that heterochiasmy might be neutral. A failure to find support for one hypothesis, however, does not mean that a trait is neutral—especially when, as in this case, the hypothesis under consideration had no clear theoretical foundation and no empirical justification.
Evolutionary explanations, sexual selection: TRIVERS 1988 proposed that heterochiasmy could be due to sexual selection. He supposed that because of the higher variance of reproductive success in males, "the genes and combinations of genes being passed in males would be superior on average, compared to genes passed in females" (p. 277). He concluded that "insofar as the actual combinations in which a male's gene appear are important to their success, then he will be selected to reduce rates of recombination (compared to females) in order to preserve these beneficial combinations." Trivers argued that this explains why males recombine less—and that exceptions can be accounted for by changes in the regime of sexual selection. However, this theory is largely inspired by models of evolution of sex chromosomes (NEI 1969 ) and has received as yet no theoretical foundation for autosomes. Worse, the opposite verbal model has been made: "As two potentially important sources of linkage disequilibrium are selection and drift, one might expect that the sex experiencing the more intense selection, or otherwise having the higher variance in reproductive system, should have more recombination" (BURT et al. 1991 ).
MODEL7xv3&, http://www.100md.com
Here, I present a three-locus model to determine the selection coefficient on a recombination modifier having different effects in males and females. Alleles at this modifier locus change the recombination rate between two loci subject to both haploid and diploid selection. A Mathematica notebook (WOLFRAM 1999 ) with the full recursions can be obtained at .7xv3&, http://www.100md.com
Genetic setting:7xv3&, http://www.100md.com
Consider a sexual dioecious population with three autosomal loci {i, j, k}. Suppose that locus i is a sex-specific recombination modifier locus and that loci j and k are under viability selection. The aim is to compute the frequency change at the modifier locus over one generation to determine under which conditions a recombination dimorphism can evolve. I follow notation used in BARTON and TURELLI 1991 and BARTON 1995 for variables (see 1). Each locus l has two alleles and is modeled using a random variable Xl, which takes the value of 0 or 1 for the first and second allele, respectively. Let x(s) = {Xi(s), Xj(s), Xk(s)} and x(s)* represent a haploid set of alleles inherited from the father and the mother, respectively, in an individual of sex s (s = m, f for male or female) and let the couple (x(s), x(s)*) be a diploid genotype (which is either a male or a female). The subscript (s) denotes a sex-specific value throughout. The average frequency of the allele coded by 1 in the whole diploid population is the expectation of Xlm + Xlm* + Xlf + Xlf*. The linkage disequilibria between loci are measured by
where U, V represents the different possible sets of loci (i.e., U, V {, i, j, k, ij, ik, jk, ijk}) distributed on maternal and paternal chromosome and by convention and . In haploids, only the associations between loci on a single chromosome are needed (U or V is empty). I also assume for simplicity (and because I am not aware of any corresponding genetic mechanism) that sex-of-origin effects do not extend back more than one generation (i.e., like with imprinting, meiosis resets eventual sex-of-origin marks of the previous generation). As a consequence, in haploids CU, (s) = C, U(s) and we simply note the disequilibria CU(s).l:4}jf, 百拇医药
fig.ommittedl:4}jf, 百拇医药
Table 1. Table of notationsl:4}jf, 百拇医药
Life cycle:l:4}jf, 百拇医药
The model describes a species undergoing the following events during its life cycle: diploid selection (D), meiosis (M), haploid selection (H), and syngamy (S). The superscripts D, M, H, and S denote these different events. By construction of the life cycle, male and female populations are strictly identical just after syngamy on autosomes because both male and female individuals are made from the fusion of a male and a female gamete and because I suppose for now that sex is determined at unlinked loci (I consider linkage to a sex-determining locus at the end of the MODEL section). Therefore, I consider the start of a generation just after syngamy when male and female populations have exactly the same frequency and combinations of autosomal genes. The linkage disequilibria are measured within a generation relative to the gene frequency at this moment. Denote CU,V any value of linkage disequilibrium measured just after syngamy. Within one generation during the life cycle, the CU,V will vary around this value and these variations will be sex specific until the next syngamy event. I therefore denote CU,V, CDU,V(s), CDMU(s), CDMHU(s), CDMHSU,V the linkage disequilibria values measured along the life cycle (1), after syngamy, diploid selection, meiosis, haploid selection, and syngamy, respectively. Note that after meiosis, only the disequilibria defined on haploids are needed to describe the population. I follow these events in this order in the next sections.
fig.ommittedqlz.c, 百拇医药
Figure 1. Life cycle. Thick and thin lines represent diploid and haploid phases, respectively. Dashed and nondashed lines represent male and female life cycles, respectively. The notation for the linkage disequilibria is described in the text.qlz.c, 百拇医药
Diploid selection:qlz.c, 百拇医药
I use a sex-specific diploid fitness function that allows for dominance, cis-, and trans-epistasis terms (i.e., a combination of genes may have different fitness effects if the genes are on the same or different chromosomes) and sex-of-origin effects (i.e., a gene or combination of genes in a diploid individual is not considered to have the same fitness effect if it is contributed from the mother or the father). Selective interactions between more than two loci are ignored. Specifically, the fitness function isqlz.c, 百拇医药
where U and V represent the set of selected alleles inherited from the father and the mother, respectively (i.e., one of the following set of indices U, V = {, j, k, jk}, with the convention that ), (s) indicates the gender of the individual carrying the alleles (whether it is a male or a female), and the superscript D indicates that these parameters represent selection during the diploid phase. For instance aDj,(s) is the additive effect of the selected allele at locus j during the diploid phase (D) in an individual of sex (s) when this allele is inherited from the father. Overall, for two loci, diploid selection is described using 30 independent parameters: there is no constraint on the fitness matrix (16 selected genotypes are in each sex and hence 15 relative fitness).
Assuming that the directional selection coefficients aDj,(s), aDk,(s), aD,j(s), aD,k(s) are small, of order {xi} , a small parameter, and that all other selection coefficients—interactions between alleles—are smaller, of order {xi} 2, the different disequilibria measured between loci i, j and k change after selection on diploids as0.su, http://www.100md.com
where0.su, http://www.100md.com
(with the value of Cj, and Ck, given in the syngamy section) and0.su, http://www.100md.com
Symmetrical moments (CD,jk, CDk,j, CD,ij, CD,ijk) can be obtained by permuting all U and V indices in (3) and (4). The recursions for CDik, and CD,ik are equivalent to recursions for CDij, and CD,ij, respectively, with subscript j replaced by k throughout. Note that only the variations in the disequilibria that are useful below are given in (3) (for instance, diploid selection changes Cj,j, but this moment does not influence frequency change at the recombination modifier locus).
The assumption that selective interactions between alleles are smaller than directional selection allows the analysis of a case more general than the situation in which all selection coefficients have the same order (BARTON 1995 , see results section for details). For the sake of discussion, I also introduce in (3) an unspecified sex-specific source of linkage disequilibrium, Djk(s), between the selected loci j and k during the diploid phase, which could be created by forces other than those considered in this model, such as migration (LENORMAND and OTTO 2000 ) or drift (OTTO and BARTON 1997 ).-yamm, http://www.100md.com
Meiosis:-yamm, http://www.100md.com
Meiosis occurs after diploid selection in a sexual life cycle. Let rBU(s) equal the basal recombination rate between the set of loci U, i.e., when the 0 allele at the modifier locus is fixed in the population. Each copy of the modifier allele at locus i modifies the recombination rate between the viability loci j and k by a small amount (s) = O() in an individual of gender s. I simply denote rU(s) the average recombination between the set of loci U over the different genotypes at locus i in the population of gender s. Assuming that the loci are in the order i-j-k,
where rijk is the chance that the trilocus genotype is broken apart by recombination. Note that when locus i is involved, the recombination rate does not depend on the frequency of the modifier allele because recombination matters only when locus i is heterozygous. After meiosis the different disequilibria measured between loci i, j, and k change as follows:08([}hl, 百拇医药
The recursion for CDMij(s) (respectively CDMik(s)) is equivalent to recursion for CDMjk(s) with subscript k (respectively j) replaced by i.08([}hl, 百拇医药
Haploid selection:08([}hl, 百拇医药
Haploid fitness is defined in the same way as diploid fitness except that there are no trans-effects and no sex-of-origin effects of alleles. A superscript H indicates selection occurring during the haploid phase, with fitness equal to08([}hl, 百拇医药
Overall, for two loci, haploid selection is described using six parameters (three relative fitnesses in each sex). Assuming, as for diploid selection, that Hj(s), Hk(s) are O() and that {alpha} Hjk(s) is O({xi} 2) the different linkage disequilibria change after selection on haploids as
where again, I introduce an unspecified, sex-specific source of linkage disequilibrium, Hjk(s), between the selected loci j and k during the haploid phase.0;ydg$, http://www.100md.com
Syngamy:0;ydg$, http://www.100md.com
I assume that each new diploid individual results from the random fusion of a male and a female gamete and that its gender is independent of its autosomal genes. After syngamy the different disequilibria measured between loci i, j, and k change as0;ydg$, http://www.100md.com
where the sums are over disjoint partitions of U or V with the convention S, T, W if these partitions exist [because U and V may contain less than three (two) loci, the triple (double) partition may not be possible] and0;ydg$, http://www.100md.com
in which the notation xDH is shorthand for xD + xH.0;ydg$, http://www.100md.com
Under random mating (BARTON and TURELLI 1991 ). In this model, however, mating is not random (female gametes fuse with male gametes). Extra terms in CDMHSU,V arise because the frequencies of the selected alleles are different between male and female gametes before syngamy. These frequency differences are caused by differences in diploid and haploid selection between males and females. This extra source of linkage disequilibrium is analogous to the linkage disequilibria created by migration between populations with different gene frequencies (LENORMAND and OTTO 2000 ).
Frequency change at the modifier locus:u9p., 百拇医药
The frequency change at the modifier locus over one generation is found by linearizing the exact recursions to order {xi} 5,u9p., 百拇医药
where To simplify this expression, I use a quasi-linkage equilibrium (QLE) approximation (see NAGYLAKI 1976 ; BARTON and TURELLI 1991 ; BARTON 1995 ) to determine the value of the different disequilibria after syngamy (CU,V) or meiosis (CDMU(s)).u9p., 百拇医药
QLE assumption:u9p., 百拇医药
Assuming that recombination rates are of higher order than epistasis, the different disequilibria quickly reach "quasi-linkage" equilibrium, at which point their values, denoted with a circle superscript, can be obtained by solving to leading order in {xi} the difference equation,u9p., 百拇医药
where CDMHSU is rewritten in terms of CU using , , , and . To simplify the result, it is much simpler to partition the selection coefficients into four terms: the average effect of a gene or gene combination over sex and sex-of-origin,u9p., 百拇医药
the sex-effect averaged over sex-of-origin,(Thomas Lenormand)
ABSTRACT#1\$'7, 百拇医药
Sex dimorphism in recombination is widespread on both sex chromosomes and autosomes. Various hypotheses have been proposed to explain these dimorphisms. Yet no theoretical model has been explored to determine how heterochiasmy—the autosomal dimorphism—could evolve. The model presented here shows three circumstances in which heterochiasmy is likely to evolve: (i) a male-female difference in haploid epistasis, (ii) a male-female difference in cis-epistasis minus trans-epistasis in diploids, or (iii) a difference in epistasis between combinations of genes inherited maternally or paternally. These results hold even if sources of linkage disequilibria besides epistasis, such as migration or Hill-Robertson interference, are considered and shed light on previous verbal models of sex dimorphism in recombination rates. Intriguingly, these results may also explain why imprinted regions on the autosomes of humans or sheep are particularly heterochiasmate.
MEIOSIS in males and females differs in several important respects. A female produces only one large gamete (ovule) from the four meiotic products whereas a male produces four small motile gametes (spermatozoa) from the four meiotic products. Often, the timing of male and female meiosis is different: in animals, for example, male meiosis tends to be continuous whereas female meiosis generally stops twice, just after meiosis begins and just before it ends. And at least sometimes, the amount of genetic recombination during meiosis differs between males and females because of differences in crossing over number and/or position. How did these meiotic differences evolve, and how are they maintained?h|es, 百拇医药
The first aspect—the evolution of anisogamy—has received considerable theoretical treatment (see, for example, RANDERSON and HURST 2001 ); but aspects such as the evolution of dimorphism in recombination have received much less attention, especially with respect to formal models. The aim of this article is to determine the conditions under which a recombination dimorphism can evolve. I begin by reviewing the facts about recombination dimorphism and the different hypotheses that have been proposed to account for it. I then present a formal model for the evolution of recombination dimorphism on autosomes and on sex chromosomes.
A recombination dimorphism can occur on sex chromosomes (or close to a sex-determining locus) or on autosomes. In the autosomal case, recombination may be completely absent in one sex, a phenomenon known as achiasmy, or it may vary quantitatively between sexes, a phenomenon that I term "heterochiasmy."rw1|)#, 百拇医药
Recombination dimorphism on sex chromosomes:rw1|)#, 百拇医药
In species with a large sex-chromosome heteromorphism (X vs. Y or Z vs. W), the sex chromosomes in the heterogametic sex do not exchange genetic material along much of their length. This is the most conspicuous and widespread recombination dimorphism between the sexes. Two related theories have been advanced to explain selection for reduced recombination around sex-determining loci: (i) recombination is disadvantageous for sex-linked alleles with opposite effects in the two sexes (CHARLESWORTH and CHARLESWORTH 1980 ), and (ii) recombinant genotypes have an "intersex" unfit genotype because of the accumulation of linked sex factors (NEI 1969 ).
Achiasmy:+gn, http://www.100md.com
Although it has received less attention, recombination dimorphism on autosomes is also common. In the most conspicuous cases, achiasmy, one sex apparently lacks recombination completely. This is not related to the loss of meiosis that often occurs with parthenogenesis: achiasmy occurs in taxa where parthenogenesis is rare or unknown, e.g., Lepidoptera, Trichoptera, Diptera, and isolated species of molluscs, water-mites, copepods, grasshoppers, and alder-flies (BELL 1982 ). When achiasmy occurs in dioecious species, it is almost always the heterogametic sex that is achiasmate, a phenomenon known as the "Haldane-Huxley rule" [ HALDANE 1922 ; HUXLEY 1928 ; for examples, see BELL 1982 , Table 5.3; however, some species in Musca and Culex genera are possible exceptions (BULL 1983 )]. The Haldane-Huxley rule has been explained either as a pleiotropic consequence of selection against recombination between X and Y (or Z and W)—the pleiotropy hypothesis—or as the consequence of the evolution of the Y (or W) in the sex that initially had no recombination—the no-recombination hypothesis.
Both hypotheses are plausible in principle. However, both can be criticized in several ways. For example, the pleiotropy hypothesis provides no explanation for why the pleiotropic effect should be so extreme: after all, there is ample within-species genetic variation for recombination rates on autosomes. The hypothesis does not explain why achiasmate meiosis occurs in only one gender within hermaphrodites (e.g., some Liliaceae in the genus Fritillaria; NODA 1975 ). It cannot explain why achiasmy has evolved in the heterogametic sex in species with a XX/XO sex-determination system (e.g., according to WHITE 1976 this has occurred eight separate times in Mantodea), unless one supposes that each XX/XO system has passed through an XX/XY system followed by the complete degeneration of the Y. Finally, the pleiotropy hypothesis does not explain why achiasmate meiosis in the heterogametic sex is maintained once sex-chromosome heteromorphism has evolved such that the sex chromosomes would no longer be homologous and able to recombine (e.g., in the extreme case recombination on the sex chromosome cannot occur in XO individuals).
The no-recombination hypothesis provides no explanation for why sex differences in recombination should preexist the formation of Y or W. Furthermore, the assumption on which this hypothesis rests—that heterogamety will always gradually evolve in the sex with low recombination—will not always hold: if the sex-determining mechanism depends on a single locus (even if this is considered improbable; CHARLESWORTH 2002 ), it does not depend on recombination and therefore the "heterozygote" sex, which is likely to become the heterogametic sex, should be equally likely to be the sex with or without recombination.|cys, http://www.100md.com
Heterochiasmy data:|cys, http://www.100md.com
Measuring heterochiasmy is difficult. Most data that have been collected consist of chiasma counts. This method does not often take into account the position of crossing over along chromosomes, which in general varies between males and females, resulting in a strong bias (male chiasmata are often either proterminal or procentric; e.g., FLETCHER and HEWITT 1980 ). This difference of chiasma position between the sexes is also a problem in studies using map distance between few markers: depending on where the markers are along the chromosomes more recombination may appear to be in one sex or the other when in fact it is not. Molecular techniques have also revealed a large source of variation in recombination rates from chromosome to chromosome and from genotype to genotype (see KOROL et al. 1994 , p. 280, for examples). Analyzing heterochiasmy data can present further difficulties. For example, not knowing the rate of evolution of heterochiasmy can make it difficult to judge whether there is phylogenetic inertia and thus how many species or groups of species must be contrasted when attempting to test hypotheses.
TRIVERS 1988 and BURT et al. 1991 reviewed chiasma count data and found that differences between the sexes are often large. Recent map data tend to confirm their analyses, although these data have yet to be rigorously examined. Moreover, in 75% of chiasmate species (whether dioecious or hermaphrodite), recombination rate, measured using either chiasma count (BURT et al. 1991 ) or map length (my personal observations), differs by >5% between male and female meiosis. In extreme cases, recombination in female meiosis can be as much as 3 times higher [for instance, in the zebrafish Danio rerio, which has no heteromorphic sex chromosome (SINGER et al. 2002 ), and in the planarian Schmidtea polychroa, a hermaphrodite (PONGRATZ et al. 2001 )] or ~ 1.5 times lower (e.g., in the monecious species Pinus taeda; SEWELL et al. 1999 ). Nonetheless, TRIVERS 1988 argued that in dioecious species the direction of heterochiasmy tends to be biased toward less recombination in male meiosis and is not affected much by heterogamety.
Heterochiasmy theories:^\p%$}, http://www.100md.com
Several ideas have been put forward to explain the occurrence of heterochiasmy. They fall into several groups that I briefly review before turning to the model.^\p%$}, http://www.100md.com
Mechanistic explanations: A different internal environment between male and female tissue, due to physiological or molecular processes, is a potential cause of heterochiasmy. For instance, BERNSTEIN et al. 1988 argued that higher recombination rates in females could be due to higher metabolic rates in females. This hypothesis is weak since, in hermaphrodites, both male and female meiosis occurs in the same individual. However, even in hermaphrodites, male and female meiosis may not occur at the same time—and therefore may occur under different conditions. For instance, in Pinus, male and female meiosis occurs in different seasons. Differences in temperature, which have been shown to influence recombination rates, could thus explain the observed heterochiasmy with more recombination in males in this genus (see PLOMION and OMALLEY 1996 ). But without more data on the timing of meiosis in hermaphrodites, the extent to which timing may explain heterochiasmy cannot be evaluated. Another possibility is that heterochiasmy itself may be a way to control the timing of meiosis. Crossing over has been hypothesized to regulate segregation and DNA repair; chiasma number could also modulate the speed of meiosis. For example, as mentioned above, in gonochoric animals, male meiosis tends to be continuous whereas female meiosis generally stops twice; numerous chiasmata could stabilize the female meiosis when it stops (sometimes for long periods of time), whereas few chiasmata could allow males a fast gametogenesis. However, this hypothesis may not apply to most plants for which the timing of male and female meiosis does not seem to differ much.
Pleiotropic effect of sex-chromosome heteromorphism: The Haldane-Huxley rule could explain heterochiasmy as well as achiasmy (for instance HUXLEY 1928 invoked it for marked heterochiasmy). However, at the very least, this is not a general explanation: counter examples are numerous, and a pleiotropic effect of the evolution of sex-chromosome heteromorphism cannot account for heterochiasmy in hermaphrodites (see BURT et al. 1991 )o&xf.{l, 百拇医药
The neutral hypothesis: The evolution of the average recombination rate has been well studied theoretically (see, for review, BARTON and CHARLESWORTH 1998 ; OTTO and LENORMAND 2002 ) and some experiments have shown that it can evolve (e.g., KOROL and ILIADI 1994 ). On the other hand the evolution of the difference in recombination rates between males and females has neither theoretical nor empirical support. When BURT et al. 1991 failed to find support for a correlation between the magnitude of heterochiasmy and the opportunity for sex difference in selection (which, they argued, should be high in dioecious animals, intermediate in hermaphroditic plants, and low in hermaphroditic animals), they suggested that heterochiasmy might be neutral. A failure to find support for one hypothesis, however, does not mean that a trait is neutral—especially when, as in this case, the hypothesis under consideration had no clear theoretical foundation and no empirical justification.
Evolutionary explanations, sexual selection: TRIVERS 1988 proposed that heterochiasmy could be due to sexual selection. He supposed that because of the higher variance of reproductive success in males, "the genes and combinations of genes being passed in males would be superior on average, compared to genes passed in females" (p. 277). He concluded that "insofar as the actual combinations in which a male's gene appear are important to their success, then he will be selected to reduce rates of recombination (compared to females) in order to preserve these beneficial combinations." Trivers argued that this explains why males recombine less—and that exceptions can be accounted for by changes in the regime of sexual selection. However, this theory is largely inspired by models of evolution of sex chromosomes (NEI 1969 ) and has received as yet no theoretical foundation for autosomes. Worse, the opposite verbal model has been made: "As two potentially important sources of linkage disequilibrium are selection and drift, one might expect that the sex experiencing the more intense selection, or otherwise having the higher variance in reproductive system, should have more recombination" (BURT et al. 1991 ).
MODEL7xv3&, http://www.100md.com
Here, I present a three-locus model to determine the selection coefficient on a recombination modifier having different effects in males and females. Alleles at this modifier locus change the recombination rate between two loci subject to both haploid and diploid selection. A Mathematica notebook (WOLFRAM 1999 ) with the full recursions can be obtained at .7xv3&, http://www.100md.com
Genetic setting:7xv3&, http://www.100md.com
Consider a sexual dioecious population with three autosomal loci {i, j, k}. Suppose that locus i is a sex-specific recombination modifier locus and that loci j and k are under viability selection. The aim is to compute the frequency change at the modifier locus over one generation to determine under which conditions a recombination dimorphism can evolve. I follow notation used in BARTON and TURELLI 1991 and BARTON 1995 for variables (see 1). Each locus l has two alleles and is modeled using a random variable Xl, which takes the value of 0 or 1 for the first and second allele, respectively. Let x(s) = {Xi(s), Xj(s), Xk(s)} and x(s)* represent a haploid set of alleles inherited from the father and the mother, respectively, in an individual of sex s (s = m, f for male or female) and let the couple (x(s), x(s)*) be a diploid genotype (which is either a male or a female). The subscript (s) denotes a sex-specific value throughout. The average frequency of the allele coded by 1 in the whole diploid population is the expectation of Xlm + Xlm* + Xlf + Xlf*. The linkage disequilibria between loci are measured by
where U, V represents the different possible sets of loci (i.e., U, V {, i, j, k, ij, ik, jk, ijk}) distributed on maternal and paternal chromosome and by convention and . In haploids, only the associations between loci on a single chromosome are needed (U or V is empty). I also assume for simplicity (and because I am not aware of any corresponding genetic mechanism) that sex-of-origin effects do not extend back more than one generation (i.e., like with imprinting, meiosis resets eventual sex-of-origin marks of the previous generation). As a consequence, in haploids CU, (s) = C, U(s) and we simply note the disequilibria CU(s).l:4}jf, 百拇医药
fig.ommittedl:4}jf, 百拇医药
Table 1. Table of notationsl:4}jf, 百拇医药
Life cycle:l:4}jf, 百拇医药
The model describes a species undergoing the following events during its life cycle: diploid selection (D), meiosis (M), haploid selection (H), and syngamy (S). The superscripts D, M, H, and S denote these different events. By construction of the life cycle, male and female populations are strictly identical just after syngamy on autosomes because both male and female individuals are made from the fusion of a male and a female gamete and because I suppose for now that sex is determined at unlinked loci (I consider linkage to a sex-determining locus at the end of the MODEL section). Therefore, I consider the start of a generation just after syngamy when male and female populations have exactly the same frequency and combinations of autosomal genes. The linkage disequilibria are measured within a generation relative to the gene frequency at this moment. Denote CU,V any value of linkage disequilibrium measured just after syngamy. Within one generation during the life cycle, the CU,V will vary around this value and these variations will be sex specific until the next syngamy event. I therefore denote CU,V, CDU,V(s), CDMU(s), CDMHU(s), CDMHSU,V the linkage disequilibria values measured along the life cycle (1), after syngamy, diploid selection, meiosis, haploid selection, and syngamy, respectively. Note that after meiosis, only the disequilibria defined on haploids are needed to describe the population. I follow these events in this order in the next sections.
fig.ommittedqlz.c, 百拇医药
Figure 1. Life cycle. Thick and thin lines represent diploid and haploid phases, respectively. Dashed and nondashed lines represent male and female life cycles, respectively. The notation for the linkage disequilibria is described in the text.qlz.c, 百拇医药
Diploid selection:qlz.c, 百拇医药
I use a sex-specific diploid fitness function that allows for dominance, cis-, and trans-epistasis terms (i.e., a combination of genes may have different fitness effects if the genes are on the same or different chromosomes) and sex-of-origin effects (i.e., a gene or combination of genes in a diploid individual is not considered to have the same fitness effect if it is contributed from the mother or the father). Selective interactions between more than two loci are ignored. Specifically, the fitness function isqlz.c, 百拇医药
where U and V represent the set of selected alleles inherited from the father and the mother, respectively (i.e., one of the following set of indices U, V = {, j, k, jk}, with the convention that ), (s) indicates the gender of the individual carrying the alleles (whether it is a male or a female), and the superscript D indicates that these parameters represent selection during the diploid phase. For instance aDj,(s) is the additive effect of the selected allele at locus j during the diploid phase (D) in an individual of sex (s) when this allele is inherited from the father. Overall, for two loci, diploid selection is described using 30 independent parameters: there is no constraint on the fitness matrix (16 selected genotypes are in each sex and hence 15 relative fitness).
Assuming that the directional selection coefficients aDj,(s), aDk,(s), aD,j(s), aD,k(s) are small, of order {xi} , a small parameter, and that all other selection coefficients—interactions between alleles—are smaller, of order {xi} 2, the different disequilibria measured between loci i, j and k change after selection on diploids as0.su, http://www.100md.com
where0.su, http://www.100md.com
(with the value of Cj, and Ck, given in the syngamy section) and0.su, http://www.100md.com
Symmetrical moments (CD,jk, CDk,j, CD,ij, CD,ijk) can be obtained by permuting all U and V indices in (3) and (4). The recursions for CDik, and CD,ik are equivalent to recursions for CDij, and CD,ij, respectively, with subscript j replaced by k throughout. Note that only the variations in the disequilibria that are useful below are given in (3) (for instance, diploid selection changes Cj,j, but this moment does not influence frequency change at the recombination modifier locus).
The assumption that selective interactions between alleles are smaller than directional selection allows the analysis of a case more general than the situation in which all selection coefficients have the same order (BARTON 1995 , see results section for details). For the sake of discussion, I also introduce in (3) an unspecified sex-specific source of linkage disequilibrium, Djk(s), between the selected loci j and k during the diploid phase, which could be created by forces other than those considered in this model, such as migration (LENORMAND and OTTO 2000 ) or drift (OTTO and BARTON 1997 ).-yamm, http://www.100md.com
Meiosis:-yamm, http://www.100md.com
Meiosis occurs after diploid selection in a sexual life cycle. Let rBU(s) equal the basal recombination rate between the set of loci U, i.e., when the 0 allele at the modifier locus is fixed in the population. Each copy of the modifier allele at locus i modifies the recombination rate between the viability loci j and k by a small amount (s) = O() in an individual of gender s. I simply denote rU(s) the average recombination between the set of loci U over the different genotypes at locus i in the population of gender s. Assuming that the loci are in the order i-j-k,
where rijk is the chance that the trilocus genotype is broken apart by recombination. Note that when locus i is involved, the recombination rate does not depend on the frequency of the modifier allele because recombination matters only when locus i is heterozygous. After meiosis the different disequilibria measured between loci i, j, and k change as follows:08([}hl, 百拇医药
The recursion for CDMij(s) (respectively CDMik(s)) is equivalent to recursion for CDMjk(s) with subscript k (respectively j) replaced by i.08([}hl, 百拇医药
Haploid selection:08([}hl, 百拇医药
Haploid fitness is defined in the same way as diploid fitness except that there are no trans-effects and no sex-of-origin effects of alleles. A superscript H indicates selection occurring during the haploid phase, with fitness equal to08([}hl, 百拇医药
Overall, for two loci, haploid selection is described using six parameters (three relative fitnesses in each sex). Assuming, as for diploid selection, that Hj(s), Hk(s) are O() and that {alpha} Hjk(s) is O({xi} 2) the different linkage disequilibria change after selection on haploids as
where again, I introduce an unspecified, sex-specific source of linkage disequilibrium, Hjk(s), between the selected loci j and k during the haploid phase.0;ydg$, http://www.100md.com
Syngamy:0;ydg$, http://www.100md.com
I assume that each new diploid individual results from the random fusion of a male and a female gamete and that its gender is independent of its autosomal genes. After syngamy the different disequilibria measured between loci i, j, and k change as0;ydg$, http://www.100md.com
where the sums are over disjoint partitions of U or V with the convention S, T, W if these partitions exist [because U and V may contain less than three (two) loci, the triple (double) partition may not be possible] and0;ydg$, http://www.100md.com
in which the notation xDH is shorthand for xD + xH.0;ydg$, http://www.100md.com
Under random mating (BARTON and TURELLI 1991 ). In this model, however, mating is not random (female gametes fuse with male gametes). Extra terms in CDMHSU,V arise because the frequencies of the selected alleles are different between male and female gametes before syngamy. These frequency differences are caused by differences in diploid and haploid selection between males and females. This extra source of linkage disequilibrium is analogous to the linkage disequilibria created by migration between populations with different gene frequencies (LENORMAND and OTTO 2000 ).
Frequency change at the modifier locus:u9p., 百拇医药
The frequency change at the modifier locus over one generation is found by linearizing the exact recursions to order {xi} 5,u9p., 百拇医药
where To simplify this expression, I use a quasi-linkage equilibrium (QLE) approximation (see NAGYLAKI 1976 ; BARTON and TURELLI 1991 ; BARTON 1995 ) to determine the value of the different disequilibria after syngamy (CU,V) or meiosis (CDMU(s)).u9p., 百拇医药
QLE assumption:u9p., 百拇医药
Assuming that recombination rates are of higher order than epistasis, the different disequilibria quickly reach "quasi-linkage" equilibrium, at which point their values, denoted with a circle superscript, can be obtained by solving to leading order in {xi} the difference equation,u9p., 百拇医药
where CDMHSU is rewritten in terms of CU using , , , and . To simplify the result, it is much simpler to partition the selection coefficients into four terms: the average effect of a gene or gene combination over sex and sex-of-origin,u9p., 百拇医药
the sex-effect averaged over sex-of-origin,(Thomas Lenormand)