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The Accumulation of Sexually Antagonistic Genes as a Selective Agent Promoting
the Evolution of Reduced Recombination between Primitive Sex Chromosomes
William R. Rice
Evolution, Vol. 41, No. 4. (Jul., 1987), pp. 911-914.
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Evolution, 41(4), 1987, pp. 91 1-914
Department of Biology, University of New Mexico, Albuquerque, NM 87131
Received August 4, 1986. Accepted February 17, 1987
The evolution ofdimorphic sex chromosomes is generally thought to proceed in two stages: first a breakdown in recombination between the primitive X and
Y chromosomes ( W a n d Z in a WZ system), followed
by the loss of function of most Y-linked genes (for
reviews, see Mittwoch [1967], Ohno [1979], and Bull
[1983]). By primitive X and Y sex chromosomes, I
mean homologous chromosomes that are differentiated only by the alleles (x or y; note that lower case
symbols refer to genes, and upper case symbols refer
to entire chromosomes) that they carry at a single sexdetermining locus.
Fisher (193 1) was the first to suggest that linkage to
a sex-determining locus facilitates the accumulation of
genes that are selectively favored in males (more generally, the heterogametic sex) but selected against in
females. This idea was extended to the case of chromosomal translocations by Charlesworth and Charlesworth (1980). Close linkage to t h e y allele causes malebenefit/female-detriment genes to be transmitted more
frequently to sons, where they are selectively favored.
If such sexually antagonistic genes were to accumulate
in linkage with a y allele, they would cross over onto
the primitive X chromosome and reduce the average
fitness of females. This crossover of male-benefit/female-detriment genes from y- to x-linkage produces
natural selection for both reduced recombination in
the heterogametic sex and also sex-specific gene expression.
Bull (1983, pp. 265-269) partially quantifiedFisher's
verbal model by considering two special cases: when
the allele with sex-specific fitness is unlinked to the
sex-determining locus, and when it is completely linked.
He concluded that linkage between a sex-determining
locus and a sexually antagonistic locus facilitates the
maintenance of polymorphisms for alleles with opposing fitness effects in the two sexes.
The work by Fisher (1931), Charlesworth and
Charlesworth (l980), and Bull (1983) demonstrates that
tight linkage between the sex locus and the sexually
antagonistic locus facilitates the initial increase and
maintenance of y-linked male-benefit genes when they
are detrimental to females. An important question that
remains is how tight linkage must be in order to promote the accumulation (to substantial frequency) of
male-benefit/female-detriment genes, especially when
the disadvantage to females is high. That is, what are
the "linkage constraints" (Charlesworth and Charlesworth, 1980) for the buildup of y-linked sexually antagonistic genes? The answer to this question is crucial,
because the feasibility of breakdown in X-Y recom-
bination via the accumulation of sexually antagonistic
genes depends critically on the "genetic opportunity"
for such genes to evolve. The looser the requisite linkage, the larger the pool of genetic variability that could
be selected in a sex-specific manner, and the more feasible the model.
Here, I address this question by solving for the equilibrium frequency of sexually antagonistic genes as a
function of their recombinational distance from the sex
locus. I conclude that very tight linkage is not required
for the accumulation of genes that are lethal or semilethal to the homogametic sex.
The Model
Consider a large population with genic sex determination. Males are assumed to be the heterogametic
sex. The male-determining gene is designated y and
assumed to be dominant and epistatic to all other sex
determining genes. Thus males have genotype xy and
females xx. The sex chromosomes are assumed to be
undifferentiated except at the sex-determining locus. A
second locus (the A locus) is initially monomorphic for
allele A,, which produces unit fitness (viability) in both
sexes. Mutation recurrently introduces a second allele
(A,) which increases male fitness by an increment S
when homozygous and h S when heterozygous (see Table 1). In females the A, allele reduces fitness by a
decrement T when homozygous and h T when heterozygous. The coefficient h indicates dominance, with
h = 0 for a fully recessive and h = 1 for a fully dominant
A, allele. The A locus is located R recombinational
units away from the sex determining locus.
Will the A, allele increase when rare? In a previous
paper examining a different aspect of sex-chromosome
evolution (Rice, 1986), I determined, to a conservative
approximation, that A, will increase when rare whenever R < hSl(1
hS). This result, however, tells us
little about the generation of selection for reduced recombination between the sex chromosomes, since a
trivial accumulation ofA, alleles will have virtually no
Here, I ask how tight linkage must be for an A, allele
to accumulate to substantial frequency in linkage with
the y gene. To answer this question, I first consider the
analytically tractable case of a completely dominant A,
allele (h = 1) that is beneficial to males (S > 0) and
lethal to females ( T = 1) (see fitness model in Table
1). In the model, it is assumed that the life cycle is
discrete and that the population is censused at the adult
stage. The A locus influences fitness by modifying zygote-to-adult survivorship.
TABLE1. The fitness model. In, the analytical model
h = 1 and T = 1, so that the frequencies a, c, J and g
are necessarily equal to 0. In the simulation model, h
and T are unconstrained. In both models, p = a + b
is the fraction of Ychromosomes canying the A2 allele.
y-A2/x-A 1
y-A 1 / ~ - A 2
y-A I/x-A 1
1 + S
1 hS
1 + hS
x-A llx-A 1
X-A I / ~ - A 2
1 - hT
1- T
Whenh= 1 a n d T = l,thenp=band,
FIG. 1. The equilibrium frequency (a) of Y chromosomes that carry an A, allele that is dominant and
lethal to females but increases male fitness by an increment S.
For Ap > 0,
I specifically solve for the fraction (p) of primitive
Y chromosomes that carry the A, allele (designated by
the haplotype y-A,). The equilibrium frequency ofy-A,
(Table 1) can be shown to be:
Equation (1) was used to construct Figure 1. This
figure illustrates that dominant A, alleles with a lethal
effect in females can accumulate to high frequency even
when the advantage to males (5') is quite small. The
larger the advantage to males, the looser the requisite
linkage and the higher the equilibrium frequency for a
specified value of R. To illustrate the use of Figure 1,
suppose males carrying a dominant A, allele had their
fitness increased by 5%. Ifthe recombinational distance
between the sex locus and the A locus were 2%, then
p = 0.592. This would result in about 1.2% of females
dying each generation due to recombination and
expression of A, in females.
The sensitivity of the equilibrium values predicted
from this simple genetic model to incomplete dominance and semilethality have been investigated numerically by computer simulation (see Rice [I9861 for
a description of the computer model). The simulations
demonstrate that p is approximately equal to or greater
than 1 - R/[hS(l - R)]. Figure 2 illustrates the effect
of deviations of h and T from unity. Note that when
S > T the A, allele can increase when rare without the
benefit of linkage to the y gene (see Rice, 1984). In
summary, the simulations demonstrate that A, alleles
that have low or no dominance will only accumulate
in the area immediately adjacent to the sex locus, while
dominant and semidominant A, alleles can accumulate
at much more distal locations.
The analytical and simulation models illustrate how
male-benefit (female-benefit in the case of female heterogamy) genes can accumulate to high frequency even
when they are highly detrimental to females. The requisite linkage depends on both dominance and the benefit of the allele to males. If one concludes that a fitness
advantage of 5-10% for polymorphic alleles is not uncommon in nature (e.g., see Endler, 1986 Ch. 6), then
a segment of chromosome 18 centimorgans in length
(?9 centimorgans about the sex locus) will potentially
support the accumulation of dominant male-benefit/
female-detriment genes. In the case of Drosophila melanonaster, this would encompass about 6% ofthe entire
genome. Because such a large portion of the genome
is influenced by the presence of a y gene, male-benefit/
female-detriment genes need not be common in nature
to be important in the evolution of reduced X- Y recombination. Nonetheless, one must ask whether or
not such sexually antagonistic genes can be expected
to occur in nature.
Sexually Antagonistic Alleles In Nature The empirical studies pertaining to genes with sexspecific fitness effects have been reviewed by Bull (1983
Ch. 18). He concludes that, in the case of bright-coloration genes in poeciliid fishes, there is empirical support for the kind of sex-specific fitness presumed in the
above model. Interestingly, as predicted by the model,
17 out of the 18 naturally occurring coloration genes
in the guppy (Poecilia reticulata; 2n = 46) are linked
within ten centimorgans of the sex-determining locus,
and all of these are dominant (Wingle, 1927). However,
other well documented examples of genes with sexspecific fitness effects are uncommon in the literature
(Bull, 1983).
Previously (Rice, 1984), I suggested that there "should
be" natural circumstances that favor different phenotypic optima in the two sexes and that this will make
the occurrence of sexually antagonistic genes inevitable. As an example, consider energy allocation in a
hypothetical annual plant that has recently evolved
dioecy. Suppose a particular gene increased flower production by substantially draining the energy reserves
needed for later growth. Such a gene may be selectively
favored in males, since growth and survival subsequent
to flowering are of no consequence, but this gene would
virtually eliminate female reproductive success, since
females must provision their fertilized embryos after
Is there empirical evidence for large sex-specific differences in the fitness effects of specific genes? In a
survey of the hundreds of known mutants of D. melanogaster, Lindsley and Grell(1968) showed that genes
with major fitness differences between the sexes are
common. Most of these mutants produce the same, or
similar, gross phenotype in both sexes (e.g., eye color,
wing shape, bristle shape, etc.) but produce sterility or
near sterility in only one of the sexes.
As an example of how genes highly detrimental to
the homogametic sex might be selectively favored in
the heterogametic sex, suppose environmental change
produced selection for reduced body size in a population of D. melanogaster. One of the many mutants
known to produce smaller body size is the gene ty(tiny).
Viability of ty ty genotypes is high in both sexes, but
females are sterile while males are fertile. If a gene such
as ty were present in an ancestral population of Drosophila that had genic sex determination, and if it were
located within hSl(1 - hS) centimorgans of a y gene,
it would be expected to increase in frequency and thereby depress the viability of females (the homogametic
sex in Drosophila) due to crossover between primitive
Xand Ychromosomes. Note that, in this case, selection
for small body size is presumed to occur in both sexes.
The sexual antagonism results from sex-specific pleiotropy and not from different optima in the two sexes.
Is the ty gene atypical? To answer this question, I
surveyed all of the recorded D. melanogaster mutants
known to produce small body size (i.e., those listed in
Lindsley and Grell [I968 pp. 433-47 11). I found a total
of 66 genes that reduced body size. Of these, 22 (33%)
produced sterility (or lethality-semilethality) in one but
not both sexes. One might reasonably argue that many
of these genes pleiotropically produce other detrimental effects (and thus drastically reduce fitness) and do
not represent a sample of the genes that might reasonably be expected to be acted upon by natural selection.
To partially eliminate this problem, I removed from
the tally of 66 small-body genes all of those that were
reported to reduce viability and/or fertility or that produced major deformities in the sex not rendered sterile.
Of the 20 remaining small-body genes, eight (40%)
produced sex-specific sterility (or lethality-semilethality). This survey supports the idea that genes with major fitness difference between the sexes may be more
common than is generally presumed. It also demonstrates that selection for different phenotypes in the
two sexes is not required to promote the accumulation
of A, alleles. When selection is similar in both sexes,
all that is required is sex-specific pleiotropy.
I do not suggest, however, that 33-40% of all mutations producing a major effect on a quantitative trait
also pleiotropically produce sterility in one or the other
sex. I use this example only to point out that the developmental pathways for males and females are very
different and that this provides the potential for sexspecific pleiotropy, which may render many genes beneficial to one sex while detrimental to the other.
Localized Breakdown in Recombination
A last question that must be addressed is whether
or not there is genetic variability for reduced recom-
FIG. 2. The equilibrium frequency (a) of Y chromosomes that carry an A, allele (see Fig. 1). In this
case S = 0.1, and the values of h and T a r e varied to
illustrate the effects of incomplete dominance ( h < 1,
solid curves) and semilethality in females (T < 1, dashed
bination between the primitive sex chromosomes. Empirical work concerning the alteration of recombination rate has been reviewed by Bell (1982 pp. 409411), Charlesworth and Charlesworth (1985), and
Brooks and Marks (1986). These surveys show that the
results of many experiments support the idea that a
reduction in recombination can be brought about by
Most notable is the experimental work by Chinnici
(1971), who showed that there is genetic variability in
laboratory stocks of D. melanogaster for site-specific
reduction in recombination. Chinnici selected for reduced recombination between two X-linked genetic
markers (sc and cv separated by 15.4 centimorgans).
He used flanking markers to demonstrate that the response to selection was site-specific, i.e., recombination was halved between the target markers as a consequence of artifical selection, but unchanged in the
adjacent regions. Chromosomal rearrangement was
shown not to contribute to the reduction in recombination. This work supports the contention that selection for reduced recombination in a segment of a chromosome (e.g., the area proximate to the sex locus) can
lead to a site-specific reduction in recombination. Work
on wild populations of D. melanogaster by Charlesworth and Charlesworth (1985) and Brooks and Marks
(1986) shows that genetic variability for site-specific
alteration of recombination is common in natural populations.
If selection for reduced recombination immediately
adjacent to the sex locus were successful, this would
reduce the recombination rate between the sex locus
and more distal genes. This reduction in recombination
rate would promote the accumulation of sexually antagonistic alleles at more distal regions of the primitive
sex chromosome. Such accumulation would then generate selection for reduced recombination in the inter-
vening segments of the chromosome, and a genetic
chain reaction would be initiated, which should continue until the X and Y sex chromosomes fail to recombine over their entire lengths or until there is a
sequence of sufficient recombinational length that fails
to provide genetic variation for sexually antagonistic
The model presented here supports the hypothesis,
originally articulated by Bull (1983 Ch. 18), that the
accumulation of genes with opposing fitness effects in
the two sexes may be responsible for the breakdown
in recombination between primitive sex chromosomes.
The major finding from the model is that the requisite
linkeage between a sexually antagonistic locus and the
sex-determining locus can be surprisingly loose for the
accumulation of genes that are highly detrimental to
the homogametic sex. It is also suggested that sexspecific pleiotropy may be an important genetic mechanism that is responsible for the opposing fitness effects
of sexually antagonistic genes.
I thank K. Ono, L. Brooks, and J. Bull for many
helpful comments on an earlier draft of this manuscript. This work was supported in part by grant BSR
8407440 from the National Science Foundation.
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FISHER,R. A. 1931. The evolution of dominance.
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D. L., AND E. H. GRELL. 1968. Genetic
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RICE,W. R. 1984. Sex chromosomes and the evolution of sexual dimorphism. Evolution 38:735742.
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Corresponding Editor: M. K. Uyenoyama
Evolutron, 41(4). 1987, pp. 914-917
Department of Zoology, University of Alberta, Edmonton, AB T6G 2E9, Canada, and Friday Harbor Laboratories, Friday Harbor, WA 98250 Received November 12, 1986. Accepted February 17, 1987
Egg size occupies a central position in the study of
the ecology and evolution of marine invertebrate life
histories. Egg dimensions are easily measured and frequently reported, and they show striking correlations
with other life-history characters. Thorson (1936, 1946,
1950) compiled information from several marine phyla
showing that egg size was correlated with fecundity,
I To whom correspondence should be addressed:
Department of Zoology, University of Alberta, Edmonton, AB, T6G 2E9, Canada.
larval type (feeding or nonfeeding), larval habitat
(plankton or benthos), and the duration of the larval
period. Recent reviews have provided further support
for these trends (see Hadfield, 1975; Hendler, 1975;
Rice, 1975; Chia, 1976; Hermans, 1979; Reaka, 1979;
Sastry, 1979; Hadfield and Switzer-Dunlap, 1984; Emlet et al., 1987).
Several quantitative models describing the effects of
natural selection on egg size, given some reasonable
assumptions about the reproductive and developmental correlates of differing parental investment per
offspring, have been published (Vance, 1973a, 1973b;