Copyright1998 by the Genetics Society of America
An Adaptive Hypothesis for the Evolution of the
Y
Chromosome
H. Allen Orr and Yuseob Kim
Department of Biology, University of Rochester, Rochester, New York 14627 Manuscript received May 28, 1998
Accepted for publication September 16, 1998
ABSTRACT
Population geneticists remain unsure of the forces driving the evolution of Y chromosomes. Here we consider the possibility that the degeneration of the Y reflects its inability to evolve adaptively. Because the overwhelming majority of favorable mutations on a nonrecombining proto-Y suffer a zero probability of fixation, the fitness of the Y must lag far behind that of the recombining X. At some point, this disparity will grow so large that selection favors an increase in the expression of (fit) X-linked alleles and a decrease in the expression of (unfit) Y-linked alleles. Our calculations suggest that this process acts far more rapidly than hitchhiking-induced erosion of the Y and at least as rapidly as the fixation of deleterious alleles on the Y by background selection. Most important, this hypothesis can explain the evolution of Y chromosomes in taxa such as Drosophila that have very large population sizes.
G
IVEN the ubiquity of Y chromosomes (Bull1983), than that estimated from molecular studies of Drosoph-it is surprising that we remain uncertain of the ila (MoriyamaandPowell1996), a group that harbors forces driving the evolution of these largely inert chro- degenerate Y chromosomes. (2) Dosage compensation mosomes. There have, of course, been many attempts suggests that the Y did not degenerate due to the accu-to explain Y evolution. Virtually all assume that the Y mulation of completely recessive alleles: there can be was, ancestrally, a normal recombining homolog that no selection for dosage compensation if individuals car-harbored functional genes, an assumption for which rying a single functional copy of a gene enjoy the same there is good evidence (e.g.,Goodfellowet al. 1983). fitness as those carrying two functional copies.Moreover, all of these explanations depend on the fact Charlesworth (1978) instead proposed that Y de-that at some point the proto-Y stopped recombining generation results from Muller’s ratchet, the
irreversi-with its proto-X homolog. ble accumulation of deleterious alleles due to stochastic
Muller(1918) offered the first theory of Y degenera- loss of mutation-free nonrecombining chromosomes. tion. He noted that, because the Y is nonrecombining, As then understood, this theory differed profoundly
Y-linked mutations remain permanently heterozygous. from Nei’s: Muller’s ratchet caused only an increase in
Recessive mutations are therefore unopposed by selec- the mean number of deleterious alleles per Y, not fixa-tion and so might slowly accumulate on the Y, ultimately tion of Y-linked mutations. Recent work, however, has rendering the chromosome nonfunctional. Unfortu- shown that this interpretation is incorrect, at least for nately, Fisher (1935) showed that Muller’s intuition haploid chromosomes like the Y. In such cases, each was mistaken: the inevitable unmasking of Y-linked mu- turn of Muller’s ratchet is associated with fixation of a tations by homologous X-linked mutations suffices to deleterious mutation (Charlesworth and Charles-keep Y-linked deleterious alleles at low frequencies. worth1997). Muller’s ratchet can then, in principle, Although more modern theories of Y evolution have cause inactivation of Y-linked genes. Unfortunately, fared somewhat better, none is wholly satisfactory.Nei however, Muller’s ratchet turns at an exceedingly slow
(1970), for instance, showed that Muller’s argument rate in large species (
Stephanet al. 1993). Using
param-can be rescued in sufficiently small populations because
eter values from Drosophila, Charlesworth (1996) deleterious Y-linked alleles can drift to fixation. But as
estimates that, in a species of population 1 million, 1030
Charlesworth(1978) pointed out, this theory, while
generations pass between each turn of the ratchet. Even formally sound, suffers two problems: (1) Because the
in fast-breeding organisms (e.g., one generation per relevant effective size is that of the species, it seems
un-week), there therefore has not been enough time since likely that the theory can apply to many taxa. Indeed,
the origin of the universe for a single turn of the ratchet Nei’s theory requires that the effective size be less than
(but seeGessler 1995). Thus, while Charlesworth
z10,000, a figure several orders of magnitude smaller
(1996) and Charlesworth and Charlesworth
(1997) conclude that Muller’s ratchet might play some role in Y evolution in taxa such as mammals, it would
Corresponding author: H. Allen Orr, Department of Biology,
Univer-not appear an effective force in large species like
Dro-sity of Rochester, Rochester, NY 14627.
E-mail: [email protected] sophila.
Our problem therefore is simple: given that Y chromo- deleterious alleles by background selection. Our results suggest that the ruby-in-the-rubbish process is a potent somes are as common in Drosophila as in mammals, we
require a theory of Y evolution that holds in small and force for Y evolution. Most importantly, this force can drive Y evolution in species of arbitrarily large size. In-large taxa.
Rice proposed such a theory in 1987. Under his hy- deed, it is more effective in larger taxa. pothesis, the Y degenerates as a side effect of the
substi-tution of favorable mutations. Because most Y
chromo-THE MODEL somes at mutation-selection balance carry one or more
deleterious alleles, favorable mutations often arise on Adaptive evolution on theX vs. Y:We consider adapta-mutation-bearing Y ’s. When favorable mutations sweep tion in a diploid population of size N. We assume that to fixation, they may drag deleterious alleles at other evolution is due to the substitution of favorable new
Y-linked loci to fixation, gradually eroding Y function mutations that arise at a per-chromosome rate of Uf.
(Rice1987). Unfortunately, this process is also excruci- These alleles have a distribution, f(sf), of favorable het-atingly slow. The reason is that the vast majority of favor- erozygous effects, with the mean mutation enjoying able mutations that go to fixation arise on mutation- an advantage of sf. On a recombining autosome, the free chromosomes and so cause no hitchhiking (Man- average favorable mutation enjoys a probability of fixa-ningandThompson1984;Peck1994). tion ofz2sf(with reasonably weak selection), and the
Charlesworth(1996) has recently proposed yet an- rate of adaptive substitution is therefore kA≈(2NUf) other hypothesis for the degeneration of the Y. He ar- (2sf)54NUfsf.
gues that background selection—the reduction in effec- On an equivalent-sized proto-X chromosome, the tive population size caused by deleterious mutations on adaptive substitution rate is
nonrecombining chromosomes—allows slightly
delete-kX≈(3⁄2NUf)(2sf)53NUfsf. (1) rious alleles to drift to fixation. In a recent review,
Charlesworth(1996) concludes that background se- Because the Y is not yet degenerate, we assume that lection represents the most plausible explanation of X-linked alleles are selected only for their heterozygous,
Y degeneration, at least in large taxa where Muller’s not hemizygous, effects. Equation 1 thus differs from
ratchet is ineffective. While it seems clear that back- previous formulae for adaptive substitution rates on the ground selection must act in regions of no recombina- X (e.g.,Charlesworthet al. 1987).
tion, and thus that background selection must contrib- On a nonrecombining proto-Y, probabilities of fixa-ute to the degeneration of the Y, this theory suffers the tion are reduced because favorable mutations must of-same problem as the above: it is slow, especially in large ten fall onto chromosomes bearing deleterious
muta-species (Charlesworth1996). tions. We can write
Here we consider a hypothesis for Y evolution that,
kY≈(1⁄2NUf)(2seff)5NUfseff, (2) we believe, escapes many of the problems besetting the
above theories. Following Rice(1996), we argue that where 2s
effis the average probability of fixation enjoyed the degeneration of the Y may be a consequence of its by favorable mutations appearing on the proto-Y. inability to evolve adaptively. Because, as noted above, To find s
eff, first consider the case in which all dele-the overwhelming majority of favorable mutations ap- terious mutations have the same effect, s
d. At muta-pear on Y chromosomes bearing one or more delete- tion-selection balance, the number of deleterious alleles rious mutations (Manning andThompson1984), vir- per chromosome is Poisson distributed: P
k5e2Ud/sd
tually all Y-linked favorable mutations suffer a zero (U
d/sd)k/k!, where Udis the per-Y-chromosome deleteri-probability of fixation, a situationPeck(1994) deemed ous mutation rate (Kimura and Maruyama 1966). If the “ruby-in-the-rubbish” problem (see also Fisher s
fkis the mean net selection coefficient enjoyed by favor-1930, p. 122). Nonrecombining chromosomes thus suf- able mutations arising on chromosomes carrying k dele-fer an extremely slow rate of adaptive evolution com- terious alleles, then the average favorable mutation ex-pared to recombining ones. Because the fitness of the periences an initial advantage of about
Y must lag far behind that of the X, there will be selection
≈P0sf 01 P1sf 1 1P2sf 21. . . over time to increase the expression of fit X-linked
al-leles and to decrease the expression of unfit Y-linked
≈
o
∞k50
Pk
#
∞
ksd
(sf2ksd) f(sf) dsf, (3) alleles.
Although this idea was previously sketched by Rice
(1996), he did not present calculations on the efficiency where we assume multiplicative fitness effects among deleterious mutations [and that 12(12sd)k≈ksd] and of adaptation-driven degeneration of the Y. Here we
calculate substitution rates for favorable mutations on ignore those cases where a mutation’s favorable effect is less than the chromosome’s net deleterious effects, the proto-Y vs. proto-X and, more importantly, contrast
the efficiency of the ruby-in-the-rubbish process for Y because such chromosomes cannot contribute to distant future generations.
When sf! sd, adaptive evolution is constrained by the fitness between the X and Y. The important question is quantitative: Is this effect smaller or larger or on par with size of the zero class, P0, and Equation 3 reduces to
these other forces? Here we compare these processes.
seff≈e2Ud/sdsf. (4) First consider hitchhiking. Because hitchhiking’s ef-fect is proportional to the rate of adaptive substitution
Peck(1994) andBarton(1995, p. 830) have previously
on the Y (≈NUfseff), and to the average number, k, of shown that, as expected, twice Equation 4 gives the
deleterious mutations that get dragged to fixation with correct probability of fixation for favorable mutations
each substitution (including those cases in which none arising on nonrecombining chromosomes [see
espe-is dragged along), the fitness of the Y relative to X ciallyPeck(1994), Table 1, which includes the results
declines at a rate of of computer simulations]. The intuitive reason is that,
when sf! sd, favorable mutations arising on
mutation-free chromosomes enjoy a “normal” probability of fixa- d ln wW/Y
dt ≈NUfseffksH. (7)
tion of 2sf, while those arising on deleterious
mutation-bearing chromosomes suffer a zero probability of fixa- This rough calculation considers only those loci at which tion; the net probability of fixation is therefore 2sf, deleterious mutations get fixed; i.e., we generously ig-weighted by the frequency of mutation-free
chromo-nore the fact that favorable substitutions improve the
somes (exp(2Ud/sd)). fitness of some loci and of the Y chromosome as a whole.
The biologically important point is that the rate of
In Equation 7 k will be close to adaptive substitution on the X relative to the Y is
k≈
o
∞
k50k Pk
#
∞
ksH
(sf2ksH)f(sf)dsf
o
∞k50 Pk
#
∞
ksH
(sf2ksH)f(sf)dsf
, (8)
kX
kY 53sf
seff
≈3eUd/sd. (5)
For plausible parameter values, this ratio is very large.
i.e., the number of deleterious mutations per
chromo-If, for instance, Ud50.1, sd50.02 (Peck1994;Charles- some class (k50, 1, . . . ) weighted by the mean fitness
worth1996), and sf50.001, we get kX/kY5445. With
advantage of such a chromosome (conditional on a net weak selection, this ratio has the convenient property
advantage).
of being nearly independent of sf(Equation 5), a poorly Substituting Charlesworth’s parameter values into known quantity.
Equations 7 and 8 and allowing favorable effects to be So far we have only allowed for a distribution of
favor-exponential with sf5 0.001, we find that the ruby-in-able effects. If we also allow for a distribution of
delete-the-rubbish process causes a 109-fold faster divergence rious effects, Equations 4 and 5 remain reasonably
ac-in X vs. Y fitness than hitchhikac-ing. (It is worth notac-ing curate if we replace sd with the harmonic mean sH of
that this comparison is independent of the rate of muta-deleterious effects among newly arising mutations [see
tion to favorable alleles as both processes depend
appendixandCharlesworth(1996)]. [This
approxi-equally on Uf.) Although this numerology should not mation is good as long as there are not too many
muta-be taken too literally, the effect of hitchhiking is clearly tions of very small effect (Charlesworth 1996). We
small relative to the ruby-in-the-rubbish. The reason is have confirmed the accuracy of this approximation in
simple: when sf, sH, k must be quite small because al-computer simulations (results not shown).]Crowand
most all favorable substitutions involve Y chromosomes
Simmons’s (1983) review of the Drosophila data
sug-that are free of deleterious mutations; i.e., adaptive evo-gests that sH50.02 (see also Charlesworth 1996).
lution is almost entirely constrained to the k5 0 class Thus, with Ud50.1, we still obtain kX/kY≈445, and the
(Peck1994). Thus, as Charlesworth(1996, p. 155)
Y chromosome lags far behind the rapidly evolving X.
concluded, hitchhiking is “almost certainly less impor-In fact, it is easy to calculate just how much the Y lags
tant than was originally envisaged.” behind. If wX/Ygives the ratio of X to Y fitness and fitness
Now consider the fixation of deleterious alleles by is multiplicative across loci, the rate at which this fitness
background selection. By reducing the effective size of difference grows is
nonrecombining chromosomes, background selection against strongly deleterious alleles can allow very slightly
d ln wX/Y
dt 53NUfs
2
f 2NUfseffsf
deleterious mutations to drift to fixation. Such alleles must have extremely small deleterious effects or
fixa-≈3NUfs2f, (6) tion is essentially impossible. Thus, asCharlesworth
(1994, 1996) emphasized, these alleles form a distinct where the approximation assumes that adaptation on
class from the more strongly deleterious ones actually the Y is negligibly slow.
causing background selection. (Charlesworth suggests
Comparison with hitchhiking and background
selec-that the former’s effects are at least two orders of
magni-tion:The ruby-in-the-rubbish process—and hitchhiking
tude smaller than the latter’s.) To emphasize this dis-and the fixation of deleterious alleles by background
and Us for the per-chromosome rate of mutation to, of mutations per Y. Subsequent selection was thus in-voked to explain the heightened expression of the X slightly deleterious alleles.
Fixation of deleterious alleles by background selec- chromosome and the “shutting off” of the Y chromo-some (Charlesworth1978).
tion causes the fitness of the Y relative to the X to decline
at a rate of roughly Similarly, the current leading theory of Y evolution—
fixation of deleterious alleles by background selec-tion—also likely requires subsequent direct selection
d ln wX/Y
dt ≈
P0NUss2s exp(P0Nss)21
. (9)
to explain Y-inactivation. As Charlesworth (1996) emphasizes, background selection can only cause fixa-This result is essentially equivalent to Equation 3 in
tion of mutations of very slightly deleterious effect.
Charlesworth(1996), except that we express time in
Y-inactivation, therefore could evolve in two ways. First,
units of generations and assume an even sex ratio (N5
multiple mutations might get fixed in each Y-linked 2Nm). From Equations 6 and 9, the ruby-in-the-rubbish
gene, ultimately inactivating it. This gene-by-gene evo-therefore will cause faster divergence in X vs. Y fitness
lution of inactivation, and of dosage compensation, than background selection when
would be exceedingly slow. If on average 3 very slightly deleterious substitutions were required to inactivate a 3Ufs2f .
P0s2sUs exp(P0Nss)21
. (10)
functional gene, 3000–6000 background-selection-induced deleterious substitutions would be required to Substituting Charlesworth’s favored parameter values, produce a modern, inactive Drosophila melanogaster Y the ruby-in-the-rubbish effect exceeds that due to fixa- (where we assume that each of Bridges’s bands corre-tion of deleterious alleles when s2
f Uf/Us. 10211. Thus, sponds to one to two loci). Alternatively, fixation of if sf5 0.001 and favorable mutations are 1000-fold rarer deleterious alleles by background selection might cause than those to very slightly deleterious alleles, the ruby- the evolution of X dosage compensation and of Y-inac-in-the-rubbish process is two orders of magnitude faster tivation on a chromosome “block by block” basis; the than fixation by background selection. This could well fixation of slightly deleterious alleles then “creates a be an underestimate for two reasons. First, Charles- selection pressure for increasing the activity of X-linked worth’s (1996) parameter values were explicitly chosen loci at the expense of the homologous Y-linked loci, to find the maximum rate of decline in Y fitness due leading eventually to the evolution of inactive Y-linked to fixation of deleterious alleles. In particular, fixation loci” (Charlesworth1996, p. 155). This is the same of deleterious alleles must occur at far lower rates in two-step scenario invoked by the present theory. populations that are larger than those assumed by The intuition that rapid adaptive evolution of the X Charlesworth. Second, because the number of muta- cannot explain the degeneration of the Y is perhaps tions that can occur at any locus is limited [i.e.,Gilles- best dispelled by the following exercise. Imagine that pie’s (1991) granularity argument], few mutations may the X and the Y accumulate favorable substitutions at fall into the required very slightly deleterious class at the same rapid rate. Now imagine that, after a long
any locus. period of time, all those Y-linked genes at which
favor-able substitutions occurred suddenly revert to their an-cestral alleles. These now-unfit revertants obviously be-DISCUSSION
have as deleterious mutations, and we would expect all the evolutionary consequences of an accumulation of The present hypothesis may seem counterintuitive
for two reasons. First, because the ruby-in-the-rubbish such deleterious alleles to follow, e.g., selection for
Y-inactivation. But clearly these Y-linked alleles are just
process does not cause fixation of nonfunctional alleles
on the Y, it may seem to fail to explain that feature of as deleterious whether they just mutated or were there all along.
the Y that most needs explaining—its genetic inertness.
It is important to understand, however, that the present Second, it may seem that the ruby-in-the-rubbish pro-cess, depending as it does on adaptive evolution, would theory posits a two-step process: (1) the fitness of the
proto-Y lags behind that of the proto-X and (2) at be too slow to account for Y evolution. There are several points to bear in mind. First, because selection to inacti-some point, this disparity grows so large that it pays to
increase the expression of X-linked genes at the expense vate the Y reflects the fact that Y chromosome fitness lags too far behind the X, the relevant substitution rates of Y-linked genes in males (this will be true as long as
the favorable mutations substituted on the X are not are those for the entire Y vs. the entire X (at least if inactivation and dosage compensation evolve block by completely dominant). This requirement of subsequent
direct selection for Y-inactivation leaves the present hy- block). Second, it is important to note that a popular alternative explanation of Y evolution—Rice’s hitchhik-pothesis in the same situation as Charlesworth’s
(1978) original Muller’s ratchet theory. As then under- ing model—also depends on adaptive evolution. Indeed, as emphasized above, the ruby-in-the-rubbish process stood, Muller’s ratchet did not involve fixation of
depends on that great majority of favorable mutations fixation of deleterious mutations declines almost lin-early with N (Equation 9). But while the rate of adaptive that are fixed on the X but not on the Y, while the latter
evolution on the Y is more or less constrained by the is limited to those rare favorable mutations that are
size of the zero class, the rate of adaptive evolution on fixed on the Y (Equations 6 and 7). Last, the leading
the X is not. Consequently, the rate at which X and Y theory of Y evolution—background selection—also
de-fitness diverge grows even faster as N increases (Equa-pends on a slow process, the fixation of deleterious
tion 6). mutations. Although perhaps occurring at an
apprecia-The biologically important point is obvious: the ruby-ble rate in small species, fixation of deleterious alleles
in-the-rubbish process can cause the evolution of Y chro-remains very difficult in large species. But even if
delete-mosomes in species of arbitrarily large size. rious substitutions on the Y do occur at an appreciable
pace—for example, even faster than adaptive substitu- We thank Brian Charlesworth, Andy Clark, Corbin Jones, Daven Presgraves, Wolfgang Stephan, and two anonymous reviewers for very
tion on the X—the total fitness effects of these Y-linked
helpful comments. This work was supported by the National Institutes
substitutions may be small relative to adaptive ones on
of Health grant GM-51932 and by the David and Lucile Packard
the X. Background selection, after all, is constrained to
Foundation.
fixing alleles of very slight (deleterious) effect, while adaptive evolution on the X might fix alleles of quite large (favorable) effect. (Technically, d ln wX/Y/dt 5
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APPENDIX: THE ROLE OF THE at mutation-selection balance. But at equilibrium, qˆ ≈
HARMONIC MEAN, sH u/s
d, where the approximation assumes that sd @ u. Substituting in A1 and simplifying, we get
When there is a distribution of deleterious effects among new mutations, it is easy to show that the mean
E[sˆd]5
1
#
1 0(1/sd)f(sd)dsd
, (A2)
fitness effect at mutation-selection balance approxi-mately equals the harmonic mean of deleterious effects
among new mutants. Let f(sd) be the probability density which is the harmonic mean of sd, as noted by Charles-of deleterious heterozygous effects among newly arising worth(1996).
mutations. At mutation-selection equilibrium, the fit- This role of the harmonic mean, which is influenced ness effect of the average deleterious mutation is more by smaller than larger values, is readily explained intuitively. Mutations of large deleterious effect are driven to low mutation-selection frequencies, while
mu-E[sˆd]5
#
10sdqˆ f(sd)dsd
#
1 0qˆ f(sd)dsd
, (A1) tations of smaller effect rise to higher equilibrium
fre-quencies. The mean fitness effect of deleterious muta-tions at equilibrium therefore must be closer to that for mild than strong deleterious new mutations.
