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The Evolution of the Y Chromosome with X-Y Recombination

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The Evolution of the Y Chromosome with X-Y Recombination Copyright 8 1988 by the Genetics Society of America The Evolution of the Y Chromosome With X-Y Recombination Andrew G. Clark Department of Biology, Pennsylvania State University, University Park, Pennsylvania 16802 Manuscript received October 18, 1987 Revised copy accepted March 11, 1988 ABSTRACT A theoretical population genetic model is developed toexplore the consequences of X-Y recombination in the evolution of sex chromosome polymorphism. The model incorporates one sex-determining locus and one locus subject to natural selection. Both loci have two alleles, and the rate of classical meiotic recombination between the loci is r. The alleles at the sex-determining locus specify whether the chromosome is X or Y, and the alleles at the selected locus are arbitrarily labeled A and a. Natural selection is modeled as a process of differential viabilities. The system can be expressed in terms of three recurrence equations, one for the frequency of A on the X-bearing gametes produced by females, one for each of the frequency of A on the X- and Y-bearing gametes produced by males. Several special cases are examined, including X chromosome dominance and symmetric selection. Unusual equilibria are found with the two sexes having very different allele frequencies at the selected locus. A significant finding is that the allowance of recombination results in a much greater opportunity for polymorphism of the Y chromosome. Tighter linkage results in a greater likelihood for equilibria with a large difference between the sex chromosomes in allele frequency. key factor in the evolution of dimorphic sex autosomes, and found that a necessary condition for A chromosomes is the suppression ofrecombi- invasion is that different allele frequencies in the two nation between the proto-X and Y chromosomes. The sexes be maintained by sex-specificselection. This classical theory of sexchromosome evolution was first condition is analogous to the requirement of linkage articulated by MULLER(1914) with credit given to A. disequilibrium for invasionof recombination sup- H. STURTEVANT.The proto-Y chromosome, which is pressing alleles (FELDMAN1972). The special case of present only in males ina single dose, can accumulate viability differences due tosex chromosomes with deleterious recessive mutations because it isalways opposite effects in the two sexes (antagonistic selec- protected from homozygosity by the X chromosome. tion) has also been shown to promote the evolution Assuming a lack of X-Y exchange, deleterious alleles of reduced recombination (RICE1984, 1987). would accumulate on the Y through the operationof Another requirement of sex chromosomes is that MULLER’S ratchet (CHARLESWORTH1978), allowing theymust pair for accurate disjunction during deleterious alleles to become fixed by a process of meiosis. KOLLERand DARLINGTON(1934) presented random genetic drift. Recombination suppression photographs and drawings of X-Y chiasmata in male and concomitant evolution of dosage compensation rat meioses, and theysuggested that, despite the were necessary to avoidexchanging the dysfunctional failure to find homologous genes on the X and Y genes fromthe Y ontothe X, where they could chromosome, these chiasmatawere necessary for become expressed in a homozygous state. normal disjunction, and probably represented clas- Models for the evolution of sex chromosome re- sical crossing over. Several recent papers report that combination suppression have been provided by NEI not only do the sex chromosomes of mammals have (1969) and CHARLESWORTHand CHARLESWORTH an obligate crossing over in each meiosis, but that (1980), both ofwhich showed that recombination homologous genes exist between the X and a portion suppression can occur with sex-specific selection.NEI of the short armof the Y chromosome referred to as (1969) considered a three locus model, with a sex- pseudoautosomal (BURGOYNE1986; DARLINGet al. determining gene, a gene affecting fertility and a 1986; GOODFELLOW et al. 1986; SIMMLERet al. 1985). recombination modifier. Alleles that decrease recom- A number of studies have focused on exchange bination between the sex-determining locus and the between the X and the Y chromosome of Drosophila selectedlocus could invade whether the modifier melanogaster. Exchanges are found in the rDNA re- locus was sex-linked or autosomal. CHARLESWORTH peats of the sex chromosomes with a frequency of and CHARLESWORTH(1980) examined conditions for about lop4,but these are clearly not classical meiotic increase of fusions between sex chromosomes and recombination (WILLIAMSONand PARKER1976, GILL- Genetics 119 711-720 (July, 1988). 712 A. G. Clark INGS et al. 1987). Male D. melanogaster are generally TABLE 1 regarded as lackingrecombination, and at thecellular Mating table for one sex-determining locus and another linked level this is seen by a failure to form a synaptonemal locus complex. Since male Drosophila have no synaptone- mal complex formation, it is important to ask how Gametes chromosome pairing is accomplished and how normal XA x4 YA Y" disjunction occurs in Drosophila males. Experiments involving the construction of X deficiencies and Females X-autosome translocations have shown that the func- XAXA 1 0 0 0 xAxa 1 1 0 0 tion of normal disjunction resides in the heterochro- X"X" 0 1 0 0 matic regions of the X (MCKEE 1987, MCKEE and Males LINDSLEY1987), andthat aberrant disjunction co- xAYA 1 0 1 0 occurs with meiotic drive and male sterility in these XAY" 1(1 - r) 4r b t(l - r) structural mutants. The mechanism by which males xayA 4r f(l - r) f(l - 7) 17 X"Y" 0 1 0 1 come to lack recombination between the sex chro- mosome may be of great importance in the evolution There is one selectedlocus with alleles A and a thatcan recombine between the sex determining locus of the X and Y of the Y chromosome. In the case of Drosophila, the chromosomes. The table presents the parental genotypes and breakdown in recombination may have been quite respective gamete frequencies. sudden, while in mammals, there remains a gradient in degree ofsex linkage of Y-linked sequences x,, the frequency of XA in sperm, andy, the frequency (ROUYERet al. 1986). of YA in sperm. The recursions are: In this paper a series of models that allow recom- %v2[(1 - Xf)Xrn + xf(1 - X,)] + UIXfXrn bination between a sex-determining locus and a se- xj = lected locus are considered. In the case of mammals, UP(( 1 - Xf)Xrn + xf(l - x,)) these models address the differentpopulation genetic + VlXfX, + vs(1 - Xf)(l - x,) properties of the region of the Y chromosome that exchanges with the X, and the region that remains x, , = v4Xf)' + Tv6( 1 - Xf)y (1 - r)VsXf(l - y) Y-specific. The models are relevant to the caseof v4xfy + vs(1 - xf)y Drosophila in addressing rates of recombination as + v5Xf( 1 - y) + v7(1 - Xf)( 1 - y) lowas The general conclusionof the models v4xfy + (1 - r)v6(l - xf)y + rvsxf(1 - y) is that recombination makes a large difference in the y' = v4xfy + V6(l - xf)y likelihood of polymorphism on the Y chromosome. + v5Xf(l - y) W(1 - Xf)(l - y)' In particular, to the extent that sequence variation is maintained by natural selection, the pseudoautosomal (1) region of the mammalian Y chromosome is predicted The general scheme for analysis of the model is to to be more polymorphic than the Y-specific region. solve for critical points of the recursion (equilibria), and to test their stabilitycharacteristics by a local linear analysis. Trivial equilibria include the fixation MODEL FORMULATION of the A allele, resulting in ff = 1, f, = 1 and j = Let there be one dialleliclocus that determines 1, indicated compactly by (1, 1, l), and fixation of whether a chromosome is considered X or Y, with XX the a allele (9, = 0, 9, = 0 and j = 0). With nonzero individuals being female, XY being male, and YY recombination, the critical points 2, = 1, f, = 1, j being lethal. Another locus having alleles A and a is = 0 and 2f = 0, 2, = 0, j = 1 can never be stable, linked to the sex determining locus, and is subject to because recombination will assure that both the X natural selection. The three female genotypes XAXA, and Y chromosome have both A and a alleles. Analyses XAXa and X"X" have viabilities v1, vz and vg, respec- of the stability of the fixations (0, 0, 0) and (1, 1, 1) tively, andthe four male genotypes, XAYA, XAYa, are particularly important, because simultaneous in- X"YA and X"Y" haveviabilities v4, v5, v6 and v7. stability of both fixations may indicate protection of Recombination occurs inmales between the sex- a polymorphism. determining locus and the selected locus with fre- The general model is not solved completely, so a quency r. Segregation is assumed to be Mendelian, set offour special cases involvingpatterns of selection and these rules lead to the mating table presented in parameters is examined. The first assumes domi- Table 1. This table indicates the frequencies of the nance of the X chromosome in viability, and domi- various gametes produced by each genotype, and the nance of XA infemales. The resulting pattern of resulting offspring genotype frequencies from each viabilities can be written as v1 = v~,714 = v5, 2% = mating type, As in CLARK(1987), the recursion can v7. The viabilities may also be a function of homo- be written in terms of xf,the frequency of XA in ova, zygosity or heterozygosity of the A locus, yielding a Chromosome Evolution Sex Chromosome 713 symmetric pattern. If sexes are equivalent in viabif- solved explicitly. At (0, 0, 0) the roots are h = 0 and, ties, this gives the completely symmetric model: VI = v3 = v4 = 717, v2 = v5 = v6. If viabilities depend on sex as well, then a four-parameter symmetric pattern arises: u1 = v3, v4 = v7, v5 = v6. The fourth case is an analysis of the stability of thegeneral selection pattern under the condition that the rate of recombination is Y2.
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