Download Classification of Hypotheses on the Advantage of Amphimixis

Classification of Hypotheses on the
Advantage of Amphimixis
A. S. Kondrashov
A classification of hypotheses on the advantage of amphimixis over apomixis is
presented. According to "Immediate Benefit" hypotheses, amphimixis is advantageous regardless of reciprocal gene exchange, because either it directly increases
fitness of the progeny, reduces the deleterious mutation rate, or makes selection
more efficient. In contrast, "Variation and Selection" hypotheses attribute the advantage of amphimixis to the reciprocal gene exchange that alters genetic variability
and response to selection among the progeny. Most such hypotheses assume that
amphimixis Increases variability and efficiency of selection, but some claim that
amphimixis decreases response to selection. Variation and Selection hypotheses
require that some factor, either random drift or epistatic selection, makes distributions
of different alleles nonindependent, while another factor, either changes of the genotype witnesses or deleterious mutations, makes overrepresented genotypes nonoptimal. Numerous Variation and Selection hypotheses, dealing with either unstructured or spatially structured populations, are reviewed. Two of them seem most
plausible: better responsiveness of the amphimictic population to widely fluctuating
selection, and lower mutation load in the amphimictic population under synergistic
selection against deleterious mutations. In both cases the large advantage of amphimixis requires rather stringent conditions, which could be falsified by careful
experiment. Further progress in understanding the evolution of amphimixis will depend mostly on such experimental work.
From the Section of Ecology and Systematics, Corson
Hall, Cornell University, Ithaca, NY 14853. This paper
was delivered at a symposium titled "The Evolution
of Sex" sponsored by the American Genetic Association at Virginia Polytechnic Institute and State University in Blacksburg, Virginia, on July 10 and 11, 1992.
I am grateful to James F. Crow for many discussions
and constant nterest in this work; to John Maynard
Smith for a valuable clarification about environmental
deterministic models; to Mikhail 0. Ptitsyn for information about Serebrovsky's book; and to Nick Barton,
Deborah Charlesworth, John Willis, and Martha Hamblin for many useful comments on the manuscript. This
work was supported by the fellowship from the University of Chicago and by NIH grant GM 36827.
Journal of Heredity 1993;84:372-387: 0022-1503/93/$5.00
After more than a century of debate, the
major factors of the evolution of reproduction are still obscure. During the past
25 years, hypotheses have become so numerous and diverse that their classification is a necessity. The time is probably
ripe for this: no fundamentally new hypothesis has appeared in the last 5 years,
and I would be surprised-and delighted-if some important idea remains unpublished.
Here I present a classification of hypotheses on what makes amphimixis-that
is, a life cycle with alternating syngamy
and meiosis-advantageous over apomixis-or production of offspring from single
mitotically derived cells. Amphimixis is
used instead of the potentially confusing
term "sexual reproduction" because sexes
are exogamous classes of gametes. In some
cases of "sexual reproduction," any pair
of gametes can form a zygote (e.g., homothally in fungi), and there are no sexes.
Similarly, apomixis is used instead of
"asexual reproduction" because the latter
also sometimes includes vegetative repro-
duction when a progeny appears from
many cells.
The proposed classification is based on
population genetic reasoning, because I
believe that genetic processes in populations are the key factor in the evolution of
reproduction. Other approaches would
lead to very different classifications. In an
ecological classification, for example, hypotheses that invoke changing selection
caused by negative biotic interactions
would be placed together. Here, however,
they belong to several different classes because I am not concerned with why a population is under some particular mode of
selection, but only with what populational
processes this leads to.
Many features of my classification are
not new. I accept Felsenstein's (1974, 1985,
1988) understanding of the basic dichotomy between "Immediate Benefit" and
"Variation and Selection" hypotheses. The
distinction between the two factors that
can cause nonindependence of distributions of different alleles, genetic drift and
epistatic selection, was also emphasized
by Felsenstein (1985) who, however, ignored all other differences between various hypotheses. The 2 x 2 classification
of the Variation and Selection hypotheses
concerned with unstructured populations
was proposed independently by Maynard
Smith (1988a) and Kondrashov (1988a).
However, some other decisions are new,
and I hope that this classification will help
organize the variety of ideas. Only a few
early works will be cited (see Farley 1982;
Mooney 1992). Consideration of each hypothesis and of its possible significance
will be brief. I ask those who favor hypotheses that will be dismissed in one or
two sentences to realize that this reflects
the lack of space, not lack of respect for
their views.
Only the simplest problem of the competition between obligate amphimixis
(high rates of recombination and outcrossing are assumed) and obligate apomixis is considered here, although I will
sometimes use results on individual selection. The advantage of amphimixis in
such a situation is necessary to protect the
amphimictic population from apomictic
clones that appear from it in one step. Here,
group selection arguments are necessary
and sufficient (Maynard Smith 1978; see
the last sentence in the book): competing
against obligate apomicts is always a group
selection process. Still the group selection
advantage of amphimixis should be relatively short term in the sense that after a
transition to apomixis some bad consequences should appear soon, before amphimicts are outcompeted (Maynard Smith
1978, Ch. 1). This advantage must also be
large, because it must outweigh the twofold cost of amphimixis with anisogamy
and 1:1 sex allocation (see Lively and Lloyd
1990), together with its other costs (Crow
1988, 1992; Daly 1978; Hastings 1992; Lewis 1983).
In some taxa the transition from amphimixis to secondary apomixis is very difficult (Maynard Smith 1986; Tortolero and
Medina 1992), although it still may be successfully completed in the long run
(Suomalainen et al. 1987). Particularly in
mammals, both female and male gametes
are necessary to start development (see
Markert 1988), because of different patterns of DNA methylation. Thus, mammals
are probably the only group in which virgin birth is impossible without a miracle.
In such cases no short-term evolutionary
factor protecting amphimixis is necessary.
However, such protection is required in
many other groups, certainly including
some of the ancestors of mammals, where
transition to apomixis can be simple, and
in taxa where apomixis and amphimixis
coexist (see Hebert et al. 1989). Therefore,
ignoring the problem of maintaining amphimixis (Margulis and Sagan 1986) is incorrect.
Obviously, the group selection advantage of obligate amphimixis over obligate
apomixis does not guarantee that individual selection will cause gradual evolution
of amphimixis from apomixis, or that recombination or outcrossing rates in the
amphimictic population will not be gradually reduced to zero, essentially destroying amphimixis. These two problems are
more complex and will not be systematically considered here, but usually individual selection for amphimixis requires more
stringent conditions than group selection.
Therefore, a group selection advantage for
amphimixis gives necessary, but not sufficient, conditions for its existence.
Immediate Benefit Versus Variation
and Selection
If we bear in mind that in sexual propagation twice as many individuals are required
inorder to produce any number of descendants and if we further remember the important morphological differentiations
which must take place in order to render
sexual propagation possible, we are led to
the conviction that sexual propagation must
confer immense benefits upon organic life.
I believe that such beneficial results will be
found in the fact that sexual propagation
may be regarded as a source of individual
variability, furnishing material for the operation of natural selection (Weismann 1887,
p. 609).
In modern terms, this remarkable statement attributes the advantage of amphimixis to the changes of variability among
the progeny, due to reciprocal gene exchange (segregation and recombination).
Obviously, these changes can be beneficial only indirectly, through their influence on the results of selection, because
reciprocal processes do not alter the allele
frequencies and, thus, cannot "improve"
the population directly. This idea gave rise
to various hypotheses, which I call Variation and Selection. Different hypotheses
offer different reasons for why amphimixis
changes variability, and why this is beneficial. Usually, following Weismann, amphimixis is supposed to increase variability and thus enhance the response to
selection, although some hypotheses claim
that amphimixis actually reduces variability or, at least, decreases response to
selection.
Alternatively, reciprocal gene exchange,
together with the changes of variability it
may cause, can be viewed as only a neutral
or even detrimental by-product of some
other process which confers an immediate
benefit and, thus, is the real reason for the
existence of amphimixis. The first such
non-Weismannian hypothesis claimed that
amphimixis is necessary for "rejuvenation." More recently several other hypotheses of this kind were proposed. Such hypotheses are in some sense simpler than
the Weismannian hypotheses because their
key arguments do not require quantitative
analysis at the population level. Thus, I
treat them first.
Immediate Benefit Hypotheses
When talking about a benefit, we must ask
"to whom?" and "why?" As far as I know,
nobody has attributed any benefit of amphimixis to the parents who are engaged
in it, and the supposed beneficiaries are
the offspring. Three broad immediate benefits are possible: (1) increased fitness of
offspring not caused by changes in their
genotypes, (2) better offspring genotypes
because of a lower deleterious mutation
rate, and (3) better offspring genotypes
because of more effective selection (Appendix 1).
The possibility that amphimixis evolved
for the benefit of parasitic DNA (see Hickey and Rose 1988) may be relevant to its
origin, but not to its maintenance, especially in multicellular organisms. Parasites can only decrease the fitness of amphimicts as a group (Hastings 1992), and,
in contrast to E. coli, where F- cells may
be unable to refuse mating with F ones,
an apomictic dandelion will not change its
habits only because its amphimictic neighbor is sick.
Increased Fitness of Progeny
Regardless of Genotypes
Amphimixis and apomixis are profoundly
different at the cellular and organismal
levels and, in principle, any feature that
distinguishes amphimixis could be claimed
to enhance the fitness of amphimictically
produced progeny. Of course, amphimicts
must be compared with "real" apomicts,
which reproduce quite efficiently, and not
with half-evolved secondary forms suffering from "sexual hang-ups" (Maynard
Smith 1986). Two options are:
1. A progeny is better off having two
parents-father and mother (Lloyd 1980,
p. 91). This a very straightforward as-
Kondrashov Advantages of Amphinis 373
sumption, because, from the point of view
of a diploid progeny, two parents instead
of one is a major distinguishing property
of amphimixis.
2. Chromosome conjugation during
meiosis allows repair of double-strand DNA
damage (see Bernstein and Bernstein 1991;
Dougherty 1955; Michod 1993), which
could provide a mechanism for "rejuvenation" (see Bell 1988; Bernstein and
Bernstein 1991, pp. 6-10; Farley 1982, pp.
203-208).
Both hypotheses can work even in a
monomorphic population and do not require population genetic analysis. However, they have serious problems. The
number of parents is irrelevant in species
without parental care. Even in monogamous species when the father cares for the
progeny, amphimixis is defenseless against
females who are behaviorally normal but
produce only daughters by apomixis.
Repair of double-strand damage may, at
best, require chromosome conjugation, but
not amphimixis: permanently diploid or
polyploid apomicts, which are numerous
among lower eukaryotes (Margulis et al.
1990), could also do this. In fact, doublestrand gaps may be efficiently repaired in
diploid mitosis without any significant increase of crossing over of outside markers
(Nassif and Engels 1993). Moreover, there
is no direct evidence that DNA repair is a
purpose of meiosis. On the contrary, the
data (Cao et al. 1990) show that doublestrand breaks are deliberately introduced
during meiosis to initiate reciprocal recombination, while in mutants incapable
of recombination these breaks do not appear. This is hardly consistent with the
view that recombination is only a by-product of the repair of such breaks. This view
also failed to provide a credible explanation for outcrossing (Maynard Smith 1988a,
p. 107; Szatmary and K6ver 1991).
"Rejuvenation" in some experiments
with ciliates may simply reflect the inability of the macronucleus to reproduce
itself indefinitely (perhaps because it divides amitotically, see Bell 1988). If so,
rejuvenation is not related to the evolutionary advantage of amphimixis any more
than aging in higher organisms, where both
apomixis and amphimixis can produce
equally "young" offspring.
Decreased Deleterious Mutation Rate
Three hypothetical mechanisms for a decrease in the deleterious mutation rate under amphimixis have been proposed:
1. Most new mutations are deletions,
which form gaps during chromosome con-
374 The Joumal of Heredity 1993:85)
jugation, and these gaps can be filled by
biased conversion (Bengtsson 1985).
2. Most new mutations are insertions,
which loop out during conjugation and can
be cut out (Ettinger 1986).
3. Most new epimutations are demethylations, which can be reverted during
conjugation by maintenance methylases
(Holliday 1988).
All three hypotheses claim that there is
some nonreciprocal genetic process associated with chromosome conjugation,
which, in contrast to harmful conventional
nonreciprocal processes (Crow 1991), is
beneficial, because the cell can distinguish
between good and bad. Of course, hypotheses 1 and 2 cannot be simultaneously correct, because each length difference
can be viewed as the result of either insertion or deletion.
In contrast to the hypothesis that considers DNA damage, these hypotheses can
account for syngamy and outcrossing
(Holliday 1988, p. 53). Suppose that a nonreciprocal process usually goes in the right
direction, but sometimes makes a mistake.
This leads to a homozygous mutation (or
epimutation) which, however, can be reverted with high probability after mating
with an unrelated individual.
All three hypotheses require high genomic deleterious mutation (or epimutation) rates, to make their reduction important, and some population genetic
analysis is necessary to evaluate its consequences. An important conclusion from
this analysis is that even rare cases when
a bad allele is mistakenly favored by the
nonreciprocal process have disproportionately severe consequences on fitness
(Bengtsson 1990). Thus, deleterious mutations or epimutations must almost always have a particular molecular nature,
which seems impossible. Furthermore, no
extant data show that the proposed mechanisms actually exist.
More Efficient Selection
In an amphimictic population there is a
component of fitness-mating successthat does not exist under apomixis. With
polygamy, more stringent selection among
males is not involved with any additional
cost. The same is true for selection among
abundant male gametes or pollen. Therefore, amphimixis can be beneficial due to
increased efficiency of selection if there is
a positive correlation between the fitnesses of progeny and of the father. This was
first noted by Geodakyan (1965, p. 106)
who concluded that "the advantages of
sexual reproduction with two different
sexes are not limited to genetic heterogeneity of the progeny."
Sexual selection can actually cause females to choose best mates or best gametes (Trivers 1976; see also Manning
1984; Manning and Jenkins 1980; Seger and
Hamilton 1988, p. 190). In case of gamete
or pollen selection (see Walsh and
Charlesworth 1992) this also requires similar selection in the haploid and diploid
phases (Crow 1991; Hastings 1991), which
may be the case if selection operates
through pollen viability. Here amphimixis
is supposed not to create variability "furnishing material for the operation of natural selection" but to improve selection
itself.
Obviously, females should choose the
best males. Recently, Koeslag and Koeslag
(1993) claimed that even preferring the
standard mates may be beneficial. This can
probably be true if variability is caused by
severely deleterious mutations with low
frequencies, so that most individuals do
not carry them, and if "standard" means
"best." If, however, we consider slightly
deleterious mutations, the population distribution of their number per genome is
roughly symmetrical, and average individuals have just average genotypes.
The "better selection" hypothesis requires serious population genetic analysis.
In particular, selection tends to reduce the
heritability of fitness, so that some process
must operate to create additive genetic
variance. This is also essential for Weismannian hypotheses. Additional work is
needed to calculate the advantage of different modes of mate choice in various
situations.
I regard the better selection hypothesis
as the only one of importance within the
Immediate Benefit category. However, it
can hardly be the leading factor in the evolution of amphimixis (D. Charlesworth and
Charlesworth 1992) and certainly has only
limited applicability, because exclusion of
some gametes from syngamy is costly in
isogamous amphimicts (probably including the primitive ones), while exclusion of
some individuals is costly in monogamous
populations.
Classification of Variation and
Selection Hypotheses
In the early age of population genetics, the
advantage of reciprocal gene exchange was
widely assumed to be self-evident and
large. The main argument was that segregation and recombination lead, in heterozygous parents, to enormous genetic
variability among the progeny, which dramatically increases the opportunity for selection (e.g., Castle 1916, 1930; East 1918;
Jennings 1913; Morgan 1913; Svedelius
1927). Most of the recent progress in the
area was stimulated by the realization that
(1) reciprocal gene exchange does not always change variability and that (2) when
it does, this is not always advantageous.
Of course, the same problems are also relevant to the opposite view (Walton 1915),
which attributes the benefit of amphimixis
to reduction of variability among the progeny.
It is now well understood that when different alleles are not associated (i.e., when
they are distributed in the population independently) reciprocal gene exchange
has no effect on the genetic structure of
the progeny at the level of the whole population (see Felsenstein 1988). If the haploid phase of the amphimictic life cycle is
considered, segregation is always useless,
while in the diploid phase it has no effect
when alleles of the same locus are unassociated (Hardy-Weinberg equilibrium).
Recombination is useless if alleles of different loci are unassociated (linkage equilibrium). Therefore, insofar as segregation
and recombination rapidly destroy associations, some factor must, to make transition to apomixis disadvantageous, constantly re-create them.
However, even if distributions of different alleles are nonindependent-that is, if
associations exist-there is no guarantee
that their destruction is advantageous. First
of all, there must be some nonneutral genetic variability, so that selection must
constantly operate in the population despite the fact that it removes maladapted
genotypes and usually decreases nonneutral variability. This problem was appreciated very early: "In a mass culture the
favorable combinations for that culture will
soon be made, ... the race will become a
pure strain, and further conjugation could
do nothing for it even if it were transferred
to a medium insulted to it" (Morgan 1913,
p. 11). Thus, some factor must permanently supply nonneutral genetic variability. But even when associations involve
nonneutral alleles, their reduction, which
means destruction of the genotypes already tested by selection, can be harmful.
When a population without spatial structure is considered, each of the questions"What creates associations?" and "What
makes their destruction beneficial?"-allows two answers, which leads to the 2 x
2 classification of the relevant Variation
and Selection hypotheses (Table 1, com-
Table . Clasificaton of Variation and Selection bypotbeases (local population)
Cause of nonindependence
Genetic drift
Epistatic selection
Causes of excess of nonoptimal genotypes:
Deleterious mutations
Changes of environment
Environmental
stochastic (ES)
Environmental
deterministic (ED)
pare with Maynard Smith 1988a, p. 115,
1989, p. 253; Kondrashov 1988a, p. 436).
Hypotheses from these four classes will
be considered next (Appendix 2), then
populations with spatial structure, where
associations within subpopulations are
important (Appendix 3), will be examined.
Two Causes of Associations Between
Alleles
Distributions of different alleles can become nonindependent due to either stochastic (genetic drift in finite populations)
or deterministic (epistatic selection in
populations of any size) factors. Both repulsion (alleles with similar phenotypic
effects are distributed more uniformly than
randomly, so that the variance is decreased) and coupling (similar alleles tend
to be together, which leads to increased
variance) associations may be created.
The origin of associations due to genetic
drift was described in the context of the
evolution of amphimixis by Felsenstein
(1988, pp. 82-85). The simplest example
is that if a genotype has an expected frequency of 10 6 in a population of size 104,
then the distributions of alleles that constitute this genotype simply cannot be independent. Roughly speaking, there will
be no individuals of such genotype 99 generations out of every 100 and one such
individual in the rest. Thus, the actual frequency of the rare genotype is usually
slightly less than expected (0) but sometimes is much higher (10 4), and most of
the time the alleles that constitute it are
in repulsion, but rarely is there a much
stronger coupling association. In this case,
the repulsion association can have a disproportionately high effect (see below). In
contrast, ifthe considered genotype is frequent, a finite population spends approximately equal time with coupling and repulsion associations, and random drift is
probably not important for our purposes.
Creation of associations by epistatic selection was studied by Felsenstein (1965).
Imagine a pair of factors I and 11, such that
each individual carries two of them. These
two factors can be either alleles of the same
locus, if we consider the diploid phase, or
equally frequent alleles at two loci, when
Mutational
stochastic (MS)
Mutational
deterministic (MD)
I means, say, A or B, while II means a or
b, if individuals are haploid. When these
factors are distributed independently in
the population, the frequencies of individuals carrying none, one, and two of factor
11are p, = a2 , p, = 2a(1 - a), and P2 = (I
- a)2 , where a is the frequency of factor
II. Evidently, under any a, PoP = 0.25pl2
(if we distinguish between different orders
of factors and consider four frequencies,
Poo = Po, Po = Plo = 0.5p,, and p, = P3, this
implies d = ooP], - P0,opo = 0, where d is
the coefficient of linkage disequilibrium,
see Lewontin 1974, p. 284).
It is easy to show that, after selection,
independence persists only if w,2 = w,
where wi is the relative fitness of individuals carrying i factors II. This means that
these factors influence the fitness independently, in the sense that the fitness of
a genotype is a product of "fitnesses" of
factors which constitute it. Otherwise, if
w,2 > w0w2, selection causes excess of individuals with one factor 11, such that after
selection PPz < 0.25p,2 , while if w,2 < uw2,
such individuals are in deficit and PoP2 >
0. 25p, 2 after selection. Obviously, the first
case yields repulsion and the second gives
coupling association.
Multiplicative selection that does not
create associations is always directionalthat is, wl is between w0 and w2 (the case
of no selection, w0 = w, = w2 also belongs
here), while stabilizing selection [w >
max(uw, w2)] causes repulsion and disruptive selection [w < min(ub,w2 )] causes
coupling association. Of course, directional selection can also cause association in
either direction. If selection acts on the
total number of factors II, coupling associations facilitate selection, while repulsion associations slow it down (obviously,
with p = 1 selection is impossible, see
Felsenstein 1988, p. 77).
The situation is analogous if a genome
carries many factors and selection acts on
the total number of factors of some type
in the genome. If factors are distributed
independently, the trait x, a continuous
approximation to the number of factors,
has Gaussian distribution. Selection w(x)
does not change the variance of this distribution if w(x) = e, which corresponds
Kondrashov ·Advantages of Amphimuxis 375
to multiplicative selection w(x) = (1 + s)'
in the discrete case. Selection always decreases the population variance ("narrowing" selection), causing repulsion association, if [uw(x)'/w(x)]' < 0 for all x, and
increases the variance ("widening" selection) and causes coupling association if
[w(x)'/w(x)]' > 0 for all x(Shnol and Kondrashov, 1993).
As in the case of two factors, stabilizing
selection (e.g., of Gaussian shape) causes
repulsion and disruptive selection coupling associations. Interestingly, the realistic modes of directional selection, where
fitness tends to some positive limit when
x changes in one direction, and to zero
when it changes in the other, also usually
cause repulsion associations. f the trait is
the number of deleterious mutations and
w'(x) < 0, selection is narrowing under
synergistic epistatis-that is, when each
mutation added causes a larger change
(decrease) in relative fitness (Kimura and
Maruyama 1966). Conversely, if the trait is
the number of beneficial mutations and
u(x)' > 0, selection is narrowing under
diminishing epistasis-that is, when each
additional mutation results in a smaller
change (increase) of relative fitness (Crow
and Kimura 1965; Eshel and Feldman
1970).
Two Causes of the Advantage of
Destroying Associations
Obviously, destruction of associations is
not always beneficial. Consider an apomictic population under constant selection. At equilibrium it can either be completely genetically monomorphic or it can
consist of one heterozygous genotype (if
individuals are diploid) or of several genotypes, which can happen either if these
genotypes have exactly the same fitnesses
or, more realistically, if selection is frequency-dependent. In the first case, segregation and recombination are useless;
in the second and third, they are deleterious because of segregation and recombination load (Crow 1970), with the sole
unlikely exception of the case when frequency-dependence exactly favors the independent distribution of alleles, when the
reciprocal gene exchange is neutral.
Thus, an apomictic population under
constant selection reaches an optimal state
and, as long as nothing disturbs the match
between selection and the population distribution, segregation and recombination
are (contrary to some claims, see Wills
1981, pp. 275-276) deleterious or, at best,
neutral (Fisher 1930; see Liberman and
Feldman 1986). Selection tends to create
376 The Journal of Heredity 1993:845)
an excess of "good" genotypes, and the
destruction of associations may be advantageous only if some factor permanently
impairs the match between the genotypes
and what selection favors, which make
overrepresented "good" genotypes maladapted. Of course, this also requires the
presence of nonneutral genetic variability.
What can cause a population distribution to deviate from the optimum? In principle, several forces can do this, including
changes of selection, mutations, random
drift, and immigration. So far I have
touched on only the first two forces as
factors that can make destruction of associations advantageous in unstructured
population. Thus we come to the second
dimension for the 2 x 2 classification of
Variation and Selection hypotheses dealing with such populations (Table 1). Drift
can be important within subpopulations of
a structured population, but in unstructured populations of reasonable size it is
probably too slow. Nobody, to my knowledge, has considered the possible advantage of amphimixis in populations under
pressure from immigrants, which are either maladapted themselves or produce
maladapted hybrids. This scenario does
not seem plausible because amphimixis
can cause matings of well-adapted residents with these immigrants.
If some factor causes deviation of the
population distribution from the optimal,
two different situations are possible. First,
this deviation can lead to directional selection (e.g., in case of deleterious mutations or of beneficial mutations which can
be interpreted as the consequences of irreversibly changing selection) or stabilizing selection with the optimum deviating
from the population mean (when, for example, this optimum fluctuates). In both
cases repulsion associations are created
either by random drift or by directional or
stabilizing selection. Their destruction is
beneficial only if selection is mostly directional, when the increased variance enhances the ability of a population to respond.
Alternatively, selection may fluctuate
between narrowing (stabilizing or directional) on the one hand, and widening
(disruptive) on the other, thus creating
associations in alternating directions at different times. Destruction of such alternating associations can also be beneficial in
some situations. In this case, then, amphimixis can both increase and decrease
(by destroying coupling associations) the
variance, making selection either more or
less efficient, which allows for many dif-
ferent possibilities. Let us now consider
four classes of Variation and Selection hypotheses that can be applied to geographically unstructured populations.
Environmental Stochastic (ES)
Hypotheses
Generating associations by random drift is
a very slow process, if the population is
not extremely small. Therefore, if all the
possible genotypes are present in substantial numbers, selection (and we are
interested in highly selectable variability)
can easily overcome any effects of random
drift. Thus, all stochastic hypotheses depend on rare events. In unstructured populations such events appear most naturally if we assume an irreversibly changing
environment in which adaptation depends
on the immediate incorporation of new
beneficial mutations because the same alleles were always deleterious in the past
and, thus, are initially absent in the population.
Interactions Between Beneficial
Mutations
If selection favors previously deleterious
alleles at more than one locus simultaneously, finite amphimictic populations
can accumulate beneficial mutations faster
than apomictic, because mutations that
appear in different individuals can later be
combined in the same genotype. This is
usually called the Fisher-Muller hypothesis (Fisher 1930; Muller 1932; see Crow
and Kimura 1965), although Morgan (1913,
p. 14) expressed essentially the same idea
much earlier saying that with amphimixis
"the new character would be brought into
relation with all the other variations that
are found in the component races and increase thereby its chances of favorable
combination." Similarly, in diploid amphimictic populations a beneficial mutation can become homozygous without appearing twice (Kirkpatrick and Jenkins
1989).
In infinitely large populations, as long
as mutations occur independently, their
distributions are initially independent.
However, the expected frequencies of genotypes carrying many mutations are extremely low, and randomly generated associations make selection less efficient,
because repulsion associations are disproportionally important (called the HillRobertson effect; see Felsenstein 1988, pp.
82-86). Thus, even in very large, but finite,
populations new beneficial mutations are
mostly in repulsion association (Crow and
Kimura 1969; Felsenstein 1988, p. 79; Maynard Smith 1978, p. 15; Quammen and Nyberg 1989), so that the best genotypes are
initially absent and amphimixis can accelerate evolution. If the environment
changes rapidly-that is, if previously deleterious alleles become beneficial at several loci each generation-amphimixis can
greatly increase the ability of populations
of any reasonable size to adapt (Griffin
1983).
Interactions Between Beneficial and
Deleterious Mutations
Usually, the name Fisher is mentioned only
in connection with interactions between
beneficial mutations. Actually, Fisher
(1930, p. 122) considered, in the same sentence, two related but different phenomena:
If ... the mutation rates, both of beneficial
and of deleterious mutations, are high
enough to maintain any considerable genetic diversity, it will only be the best
adapted genotypes which can become the
ancestors of further generations and the
beneficial mutations which occur will have
only the minutest chance of not appearing
in types of organisms so inferior to some
of their competitors, that their offspring will
certainly be supplanted by those of the latter.
Thus, under apomixis a beneficial mutation must, to confer maximal advantage,
appear in a genome which not only carries
all the beneficial mutations available but
also is deleterious mutation-free. Otherwise, either the beneficial mutation is
eliminated or its spread leads to fixation
of one or more deleterious alleles. Obviously, there is no such restriction in an
amphimictic population (Manning and
Jenkins 1980; Manning and Thompson
1984).
As before, here amphimixis is advantageous because it destroys repulsion associations created by the appearance of
rare beneficial mutations. However, the
current mechanism does not require that
more than one beneficial mutation is on
its way to fixation at any time, because
deleterious mutations are always present.
Therefore, randomly generated associations can interfere even with slow evolution.
Interactions Between Beneficial
Mutations and Polymorphisms
If selection maintains a polymorphism in
an apomictic population, the genotype with
the highest frequency will accumulate
beneficial mutations faster than others.
This may destroy the polymorphism
(Manning 1983), whereas if selection
strongly protects it, a beneficial allele must
independently take over each genotype
(Manning 1982c) to take over the whole
population. This is not the case with amphimixis, which can thus have some advantage.
Fluctuating Selection In Finite
Populations
Seger and Hamilton (1988, p. 190) suggested that biotic interactions can drive
some genotypes to very low frequencies
even when the environment does not
change irreversibly. Then such genotypes
can go extinct by chance, and amphimixis
can be beneficial by recreating them after
they become favorable again. I am not
aware of other attempts to attribute importance to the rare events which are necessary for ES hypotheses under fluctuating, instead of irreversible, selection.
Possible Importance of ES Hypotheses
Stochastic hypotheses apply only to finite
populations. However, this can hardly be
a serious limitation of ES hypotheses if the
population waits for beneficial mutations
at several loci or when slightly deleterious
mutations are considered, because in both
cases the expected frequency of a genotype in which a new beneficial allele can
cause maximal advantage can be extremely low. Thus, populations of any possible
size still may behave as finite.
However, ES hypotheses do not easily
lead to a short-term advantage of amphimixis (Wiener et al. 1992). Inability of an
apomictic population to incorporate new
beneficial mutations becomes important
only after a new mutation is incorporated
into an amphimictic population. Thus, the
characteristic time after which transition
to apomixis becomes deleterious is no less
than the average interval between successive fixations of beneficial alleles under
amphimixis. Actually, this time can be
much longer, if the absence of many new
beneficial alleles in an apomictic population is alone sufficient to counterbalance
its twofold advantage.
Thus, ES hypotheses can lead to shortterm advantage of amphimixis, and, therefore, to its protection from apomictic
clones, only in populations that undergo
fast, irreversible changes. Most data indicate that in nature irreversible changes
are, in fact, very slow. Besides, even very
low rates of recombination and outcrossing can destroy the randomly generated
associations, so that stochastic hypotheses (both environmental and mutational)
can hardly explain the evolution within
amphimictic populations. Therefore, deterministic hypotheses are generally more
promising. However, genetic drift can be
important in the long run, limiting the life
span of obligately apomictic populations
and determining their taxonomic distribution. Probably the slower rate of accumulation of beneficial mutations in the
presence of deleterious mutations is the
most important among the ES hypotheses.
Environmental Deterministic (ED)
Hypotheses
Irreversibly changing selection can also
lead to an advantage of amphimixis when
genetic drift can be ignored. Even if initially beneficial mutations are distributed
independently, repulsion associations will
be created by selection that favors them
if they interact with diminishing epistasis.
Because epistatic selection can create associations very quickly; the deterministic
advantage of amphimixis may be large and
short term; and, in contrast to stochastic
hypotheses, no rare events are necessary
here. Thus, amphimixis may be advantageous when the alleles that are beneficial
under a "new" environment were already
beneficial in the past and, consequently,
always have significant frequencies. This
means that selection can be fluctuating instead of irreversible.
Therefore, the deterministic advantage
of amphimixis can appear due to the reorganization of preexisting variability,
without immediate incorporation of rare
and new mutations, if the necessary allele
combinations are underrepresented. However, maintaining substantial variability
under fluctuating selection is not automatic and requires some specific conditions. If selection fluctuates widely, amphimixis can be advantageous by
enhancing the population's response. An
opposite phenomenon is also possible:
amphimixis can decrease the reaction of
the population to some regimes of fluctuating selection, and this can also be beneficial.
Irreversible Environment
Suppose that selection is either directional
or stabilizing with a moving optimum. In
both cases, the population lags behind the
optimum. Such selection naturally leads to
repulsion associations between the alleles
that influence the trait in the same direction and to reduced variance of their number per genome. Restoration of the variance by amphimixis is beneficial because
Kondrashov Advantages of Amphimxis 377
it enhances the population response to selection (Eshel and Feldman 1970; Felsenstein 1965; Fraser 1957; Mather 1943; Maynard Smith 1978, p. 14). Like the
corresponding ES hypothesis, this requires that more than one allele be simultaneously on their way to fixation.
Asignificant advantage of amphimixis is
possible in this situation (B. Charlesworth
1993, in press; Crow 1992), but this requires strong and effectively directional
selection, which causes substantial lag load
(Maynard Smith 1978, p. 21). Under
Gaussian selection, the optimum must
move each generation by at least about 3%
of the standard deviation of the population
distribution of the trait to cause a higher
mean fitness of the amphimictic population. If it moves faster, the advantage of
amphimixis can be very large (B. Charlesworth 1993, in press). Obviously, in the
long run, the population mean must evolve
irreversibly at the same rate.
Fluctuating Environment: Better
Responsiveness
Assume that selection-for example, the
optimum of stabilizing selection-fluctuates within some range and that the amplitude of fluctuations is large while their
typical period is not very short. Then there
is a big advantage of, and time for, adaptation, and the best strategy is to follow
these fluctuations with as small a lag as
possible. Thus, like under irreversible selection, amphimixis can be advantageous
by destroying repulsion associations,
which are constantly created by selection,
but irreversible changes in the population
can be avoided.
Quantitatively, the effect of amphimixis
on fitness depends on the balance between directional selection (when destruction of repulsion associations and increased variance are beneficial) and
stabilizing selection (when an increase of
variance is disadvantageous) (Bergman
and Feldman 1990; B. Charlesworth 1993,
in press; Korol and Preigel 1989; Korol et
al. 1990; Mather 1943; Maynard Smith 1980,
1988b; Slatkin and Lande 1976; Treisman
1976). Thus, the larger the amplitude of
changes in the fitness optimum, the more
advantageous is the amphimixis (B.
Charlesworth 1993, in press).
Under the simplest "all-or-nothing" selection (fitness is 1 if the trait deviates no
more than d from the optimum; otherwise
fitness is zero) amphimixis is advantageous ifthere is no "middle" genotype with
positive (i.e., 1) fitness under any possible
selection regime. Otherwise an apomictic
378 The Joural of Heredty 1993:84(5)
population consisting of individuals with
this genotype will win (Treisman 1976).
This condition requires that the amplitude
of fluctuations of the optimum is more than
2d.Then, after one "environmental cycle,"
every clone and thus the whole apomictic
population will die.
The variance of quantitative traits is
probably always smaller than the width of
the selection function that acts on them.
About 32% of a population with a Gaussian
distribution deviates from the mean by
more than I SD. Thus, d must be at least
about 1 SD of the trait to prevent too high
a genetic load, even when the population
mean coincides with the fitness optimum.
Experimental data (Turelli 1984) suggest
that the trait variance usually is about one
order of magnitude smaller than the width
of the selection curve. Therefore, absence
of the "middle" genotypes requires fluctuations of the fitness optimum with the
range of at least I SD of a trait, and probably much larger. Consideration of Gaussian selection, where apomixis is selected
against if every genotype sometimes has
very low fitness, leads to a similar conclusion (B. Charlesworth, 1993, in press). Directional selection with fluctuating direction also acts similarly.
The situation probably remains essentially the same if selection acts on many
traits simultaneously, because selection
still cannot be too stringent in terms of
individual traits without causing too high
a load. If, for example, the population mean
and the fitness optimum coincide, individuals who deviate from the mean by less
than I SD in every trait must have high
fitnesses. Thus, the projection of the fitness optimum on each axis must fluctuate,
to ensure the advantage of amphimixis, in
the range of at least I SD of the trait. Still,
with many traits, amphimixis can be maintained more easily because fluctuation of
the fitness optimum even within some limited volume may lead to effectively irreversible selection (Kondrashov AS, unpublished).
Similar phenomena are possible even
with one locus if selection acts during the
diploid phase (Weinshall 1986). Here,
however, there is probably "not enough
room" to make better responsiveness advantageous with only two alleles. In this
case, if the fitness of the heterozygote is
more than the geometric mean of fitnesses
of homozygotes (a condition for repulsion
association), an apomictic population
consisting of heterozygous individuals
wins. However, amphimixis can be advantageous with three alleles if allele A, (ei-
ther homo- or heterozygous) is necessary
to survive during the first generation, allele A2 is necessary during the second, and
allele A3 is necessary during the third. In
this case the apomictic population is extinct after three generations because no
genotype contains all three alleles and thus
no clone can survive all three seasons,
whereas an amphimictic population persists indefinitely because all genotypes are
present in each generation (Eshel and
Weinshall 1987; Weinshall 1986; Weinshall
and Eshel 1987). Obviously, here the advantage of amphimixis is caused exclusively by segregation.
Fluctuating selection itself does not
maintain variability, and the population
eventually becomes monomorphic, even
if it causes a drastic decrease of the mean
fitness (Lande 1977; Lewontin 1964; Maynard Smith 1979). Thus, ED hypotheses
depend on the protection of variability by
some factor, e.g., mutations or frequencydependent selection (as above).
So far we have considered here only directional and stabilizing selection, which
usually create only repulsion associations.
However, amphimixis can also enhance
response to selection, which leads to associations in alternating directions. All existing models of this kind were created in
terms of individual loci.
Suppose that selection acts during haplophase in a population with two loci and
two alleles at each locus. Suppose that, for
some reason, selection is cyclical and favors, successively, AB, aB, ab, and Ab genotypes. Then, just before selection starts
to favor AB again, this genotype can be
underrepresented because selection has
not favored it for a long time (of course,
the corresponding epistasis is required).
Now amphimixis is advantageous because
it increases the population response to selection (Bell and Maynard Smith 1987).
Probably, several other models in which
negative biotic interactions are considered lead to the advantage of amphimixis
due to such a mechanism (Glesener 1979;
Hamilton 1980; Nee 1989).
Fluctuating Environment:
Nonresponsiveness
If selection fluctuates very frequently, the
best strategy for the population may be to
adopt the genetic composition corresponding to some average selection and
to minimize the response to its fluctuations. Remarkably, amphimixis may lead
to this, which can give it an advantage
(Thompson 1976; Walton 1915). In such
situations "without sexual crossing, there
would be endless changes ... , & hence
there could be no improvement' (Darwin
1838 in Barrett et al. 1987, p. 410).
Consider the extreme case of a population with one locus and two alleles A,
and A2. Suppose (Hamilton WD, personal
communication) that in odd generations
heterozygotes are inviable, while in even
generations both homozygotes are inviable. Then an apomictic population will go
extinct after two generations, while an amphimictic population, which starts every
generation in the same Hardy-Weinberg
distribution, persists indefinitely with a
load of 0.5. An analogous model can, of
course, be formulated in terms of a polygenic trait with alternating disruptive and
stabilizing selection.
In the case of one diallelic locus, amphimixis can be advantageous even if the
fitnesses of the three genotypes fluctuate
independently, because this also leads to
alterations between narrowing and widening selection, although a large advantage requires unrealistically strong selection. This situation was studied by
Roughgarden (1991), in an article with the
modest title "The Evolution of Sex," who
concluded that the advantage of amphimixis is caused by "nonresponsiveness of
an amphimictic population to changing
conditions." If, however, fluctuations are
rare, amphimixis becomes disadvantageous (Roughgarden 1991, figure 4).
The first model of this kind was proposed by Sturtevant and Mather (1938)
and is also based on alternating stabilizing
and disruptive selection. However, instead
of one locus and diploid selection it considered two diallelic loci under selection
acting in haploid phase which favors genotypes AB and ab in odd generations and
genotypes Ab and aB in even ones. If we
characterize the genotype by the number
of alleles denoted by a capital letter, this
is exactly the same alternation of stabilizing and disruptive selection as described
above. Here amphimixis cannot maintain
the frequency of 25% for all genotypes,
because interlocus associations are destroyed only asymptotically. Still, it can
reduce the amplitude of their fluctuations,
which, as before, is advantageous if selection fluctuates frequently (B. Charlesworth
1976; Sasaki and Iwasa 1987), because every genotype is produced until it becomes
favored.
In both these models, amphimixis is
beneficial under alternation of pure stabilizing and disruptive selection due to
segregation (one locus) or recombination
(two loci), while allele frequencies remain
invariant. But in some other cases of fluctuating selection, which causes alternation
in the direction of associations, allele frequencies probably change too widely, and
amphimixis was reported to be beneficial
due to nonresponsiveness because it
"stores temporarily bad alleles" (Hamilton et al. 1990).
Remarkably, the models of Bell and
Maynard Smith (1987) and of Sturtevant
and Mather (1938) consider the same genetic variability, and in both cases the direction of associations alternates. Nevertheless, selection is very different, the
period of changes is much longer, and the
allele frequencies are variable in the first
model. Consequently, in these models amphimixis is advantageous for opposite reasons: better responsiveness in the first
case, and nonresponsiveness in the second.
Possible Importance of ED Hypotheses
The problem with hypotheses assuming
irreversible selection, namely the lack or
rarity of such changes in nature, is relevant to both ES and ED hypotheses. However, according to the ED mechanism, amphimixis can also enjoy a considerable
advantage of similar nature under widely
fluctuating selection. Even in this case, the
advantage always requires wide changeseither in the mean values of polygenic traits
or in allele frequencies at individual loci.
The time over which apomixis goes extinct
cannot be shorter than the characteristic
period of such changes. So far, no data
suggest that such changes are actually
widespread in nature.
A serious problem with many ED models is maintaining variability. If selection
with a fluctuating optimum in polygenic
traits is assumed, variability can be maintained by conditionally beneficial mutations (see Kondrashov and Turelli 1992).
Another option is frequency-dependent
selection, which naturally appears under
negative biotic interactions in which being
common can be disadvantageous (Hamilton 1993; Hutson and Law 1981; Jaenike
1978; Levin 1975). However, conditions for
maintaining variability and for the advantage of amphimixis can be contradictory
(Moore and Hines 1981).
Of course, amphimixis is always disadvantageous when beneficial mutations interact synergistically or when selection favors combinations of individually
deleterious mutations. In terms of quantitative genetics, amphimixis reduces the
efficiency of selection that can act only on
the additive component of the genetic
variance, compared with the total variance
under apomixis. Amphimixis cannot be
advantageous if this effect is large (Crow
and Kimura 1965; Eshel and Feldman
1970).
Many authors emphasize negative biotic
interactions as the possible cause of selection to maintain amphimixis. Some of
them consider the effects of drift or of spatial structure, but most such models are
clearly of the ED type, because coevolution between predator and prey or host
and parasite leads to fluctuating selection.
Unfortunately, in many articles of this kind,
the mode of selection that acts on a population in which amphimixis is maintained
is not reported. It seems, however, that
most, if not all, such models lead to associations in alternating directions. More
explicit description of selection resulting
from ecological processes would be very
helpful and can lead to different conclusions (May and Anderson 1983). It would
be interesting to see if negative biotic interactions could lead to the advantage of
amphimixis if the species interact through
polygenic traits, instead of individual loci,
and if associations are always of the repulsion type.
As far as narrowing (directional or stabilizing) selection is considered, associations are always repulsion, although selection may, at different moments, favor
different directions of associations (B.
Charlesworth 1993, in press; Maynard
Smith 1988b). In this case, the advantage
of amphimixis can be caused only by better responsiveness. In contrast, if in some
dimension selection is sometimes widening (disruptive), it can actually create associations in alternating directions, instead of just favoring them. The advantage
of amphimixis can appear both because of
better responsiveness, when optimal genotypes are underrepresented but all the
necessary alleles are present (Bell and
Maynard Smith 1987), and because of nonresponsiveness, when amphimixis prevents the population from losing either genotypes (B. Charlesworth 1976; Sturtevant
and Mather 1938) or alleles (Hamilton et
al. 1990) that are temporarily deleterious.
It does not seem plausible that amphimixis can always reduce variance among
progeny. This could happen only if selection is permanently widening, but in such
a case apomixis would be favored. The
claim of Walton (1915) was partially based
on confusion, because selfing was considered instead of apomixis (see Castle 1916).
However, all "nonresponsiveness" hypotheses assume that amphimixis reduces
Kondrashov *Advantages of Amphimixis 379
the variance sometimes. Such hypotheses
are very diverse and, although frequent
alternation of stabilizing and disruptive
selection does not seem realistic, may be
rather attractive theoretically. Alternating
selection at one locus with two alleles allows elimination of apomixis in two generations. Thus, if God wanted to maintain
amphimixis, it could have been done very
easily.
Mutational Stochastic (MS)
Hypothesis
Muller's Ratchet
Muller (1964) noted that in an apomictic
population random loss of the mutationfree genotype is irreversible, ignoring
backward mutations (Muller's ratchet),
whereas amphimixis easily recreates such
a genotype. This can give amphimixis a
considerable advantage because only
complete loss of a normal allele at a locus
is irreversible in an amphimictic population. This advantage is even stronger if
accumulation of mutations leads to a decrease of the population size, which in turn
facilitates their further accumulation (mutational meltdown, see Lynch et al. 1993).
Quantitatively, the rate with which Muller's ratchet clicks depends on the expected absolute number of mutation-free
(or, more generally, the best available) individuals in a population, N.,,,. With N,,
below or about 10, such individuals will
be lost very soon; if Nt,, = 25, the ratchet
operates slowly; and if N,,, = 100 or more,
it practically does not work (Haigh 1978).
Therefore, the importance of the ratchet
under a given effective population size, N,,
depends critically on the expected frequency of best genotypes, NP,.
If selection maintains polymorphism in
an apomictic population, the genotype with
the lower equilibrium frequency will accumulate deleterious mutations more rapidly, which may cause the loss of the polymorphism (Manning 1982a,b) and provide
some advantage for amphimixis.
Possible Importance of MS Hypothesis
Muller's ratchet has been studied mostly
with multiplicative selection. Then p,, =
e- u/, where U is the genomic deleterious
mutation rate and s is a selection coefficient against a mutant allele. This led to
the conclusion that with U = I the ratchet
is an important factor with s = 0.01 - 0.1
in populations of any reasonable size (paradoxically, very deleterious mutations are
of less danger in this case; see Lynch et
al. 1993; Pamilo et al. 1987).
380 The Joumal of Heredity 1993:84(5)
However, this conclusion is sensitive to
the form of selection. With strict truncation selection, where individuals with k or
less mutations have a fitness of 1 and all
others die, all individuals in an equilibrium apomictic population have exactly k
mutations. Therefore, p,, = 1, and the
ratchet cannot operate. Truncation selection represents the extreme case of synergistic epistasis, but pA,, grows, while the
mutations are accumulated, even under
moderate degrees of epistasis, which slows
down the ratchet and may even effectively
stop it (D. Charlesworth et al. 1993, in press;
Kondrashov AS, unpublished).
Two other problems with Muller's ratchet are inherent to all stochastic hypotheses that depend on rare events. First, Muller's ratchet cannot provide a short-term
advantage. The characteristic time after
which apomicts become maladapted because of the ratchet is probably at least on
the order of 100 generations, as long as
the population size is not extremely small
(Lynch et al., 1993). If mutations are significantly deleterious, the expected frequency of the best class is high, so that
the ratchet operate slowly; with slightly
deleterious mutations, on the other hand,
many clicks of the ratchet are necessary
before apomixis becomes maladapted.
Second, even very low rates of recombination or outcrossing are sufficient to stop
the ratchet. Thus, Muller's ratchet is incapable of influencing the processes ir
amphimictic populations and explaining
the evolution of its features (D. Charlesworth et al. 1992, 1993, in press). However,
it probably can be an important factor in
long-term evolution of obligate apomicts.
Mutational Deterministic (MD)
Hypothesis
Muller's Hatchet
Although synergistic epistasis slows down
the ratchet, it can make amphimixis advantageous for a purely deterministic reason. Such epistasis makes selection against
deleterious mutations more efficient in the
sense that the same U can be counterbalanced with a much smaller mutation load,
L (Crow 1970). This is true only if the population has a high variance of the number
of mutations per individual. Synergistic
epistasis reduces this variance, undermining its own efficiency. Therefore, under
apomixis, L = 1 - e u regardless of the
form of selection (Kimura and Maruyama
1966).
By contrast, amphimixis destroys repulsion associations between deleterious
alleles and restores the variance. This allows the efficiency of epistatic selection to
persist in equilibrium, leading to much
lower load (Crow 1970; Kimura and Maruyama 1966). With Uon the order of 1 or
more, the resulting advantage of amphimixis may be enough to compensate for
the twofold advantage of apomixis (Kondrashov 1982). This is the mutational deterministic (MD) hypothesis for the evolution of amphimixis.
For example, consider again the case of
truncation selection. In an equilibrium
apomictic population, all the individuals
have exactly k mutations, and a progeny
survives only if it does not receive new,
deleterious mutations. If mutations occur
independently, this happens with probability e ' , so that L = I - e ' , which is
very close to I under large U.
The same selection has very different
consequences with amphimixis where, under free recombination, the associations
between loci are reduced twofold each
generation. Thus, an equilibrium variance
of the per-genome number of mutations
before selection, a2, is at least M/2, where
M k and is the mean number of mutations per genome. When a fraction, L, of
the population is removed by selection,
the absolute value of the selection differential, D, the difference between the mean
numbers of mutations after and before selection, can be arbitrarily large, provided
that a is large enough. At equilibrium U =
- D and the load is small if a > U, which
requires M > 2 ! (see Kondrashov 1988a).
Thus, if mutations are only slightly deleterious, so that k is large, synergistic epistasis can allow the population to survive
under any U This effect is caused by both
recombination and, if selection acts in the
diploid phase, segregation, which alone
can lead to significant decrease of the load
under moderate U (B. Charlesworth 1990;
Dickson and Manning 1984; Manning and
Dickson 1986).
Muller (1950, p. 151) was probably the
first to realize that synergistic epistasis can
decrease the mutation load, and Kimura
and Maruyama (1966) and Crow (1970)
showed that this happens only with amphimixis. However, they did not draw any
evolutionary implications because at that
time U was assumed to be too low for
changes of the mutation load to be important (in their Table 1, Kimura and Maruyama considered only two possible values of U,0.10 and 0.14). This view changed
during the 1970s (Crow 1979; Crow and
Kimura 1979; Mukai et al. 1972) after which
the MD hypothesis was proposed (Crow
1983; Crow and Simmons 1983, p. 7; Kondrashov 1982). Actually, the same idea was
applied earlier to the evolution of recombination in an amphimictic population
(Feldman et al. 1980). However, the MD
hypothesis has sometimes been completely ignored, even quite recently (e.g., Felsenstein 1988).
Possible Importance of MD Hypothesis
Deleterious mutations are ubiquitous, and
formally the MD hypothesis is simple and
certainly correct (B. Charlesworth 1990).
Its applicability depends only on the magnitude of the genomic deleterious mutation rate and the mode of selection against
mutations in nature.
Amphimixis in Spatially Structured
Populations
So far we have considered unstructured
populations. Spatial structure has a profound impact on population processes, and
maintenance of amphimixis is no exception. Still, the two basic requirements for
any Variation and Selection hypothesiscreation of associations and the advantage
of destroying them-remain valid.
In a spatially structured population, each
subpopulation may be considered as a
sample from the whole population. If subpopulations are finite, then sampling leads
to genetic drift and associations are created within each subpopulation. If, however, the size of subpopulations is too large
to make drift important, associations can
be generated only by epistatic selection.
Thus, as before, both stochastic and deterministic hypotheses are possible here.
Felsenstein (1985) correctly noted that
sampling from a structured population is
essentially the same process as that from
random drift in an unstructured population, when the whole next generation is a
sample of the progeny created in the previous generation. However, in contrast to
an unstructured population, here many
samples with different associations coexist in each generation. Therefore, following Maynard Smith (1978, p. 123), consider the hypotheses involving spatial
structure separately.
Actually, the samples assumed here are
usually just breeding pairs, and the stochastic hypotheses considered here emphasize, in accord with the views of East
(1918) and Svedelius (1927), the variability among relatives. In this case, in contrast with stochastic hypotheses concerned with unstructured populations,
amphimixis can have a rather short-term
advantage. This is caused by the fact that
here the sample size is so small (two parents) that associations are generated instantly, although Felsenstein (1985) attributed this, I believe erroneously, to
stronger selection. Obviously, only in a
structured population, which consists of
many "samples," can such a small sample
size be assumed without the immediate
loss of genetic variability.
Variability of Relatives: Difference
Between Parents and Offspring
Amphimixis causes differences between
genotypes of both parents and each offspring. Rice (1983a,b) suggested that this
may preclude the spread of diseases that
may be transmitted during reproduction.
This is one more hypothesis based on negative interspecific interactions.
Variability of Relatives: Chances to
Include the Optimal Genotype
Variability among competing sibs generated by amphimixis can be beneficial for
two reasons (Young 1981). First, it increases the probability that at least one of them
has a genotype necessary for survival under some particular conditions (Williams
1975; Williams and Mitton 1973). Obviously, it requires changing selection in a
patch where the family lives, because otherwise apomicts who have the same genotypes as parents have the advantage.
Substantial advantage of amphimixis requires actually very strong selection (Barton and Post 1986; Bulmer 1980; Taylor
1979). The advantage probably disappears
when the number of winners per patch
grows.
Variability of Relatives: Benefits of
Diversity Itself
Alternatively, the diversity itself can be
beneficial if it reduces the intensity of competition (Bell 1982; Maynard Smith 1978;
Price and Waser 1982). This can provide
a substantial advantage for amphimixis.
The same mechanisms can be applied to
other close relatives if they compete with
each other.
This idea is unique among all Variation
and Selection hypotheses. Here drift is responsible not only for creation of associations, but also for deviation of the subpopulation composition from the optimum
prescribed by frequency-dependent selection. With any reasonable size of the unstructured population this can hardly happen, so that only environmental and
mutational hypotheses were proposed for
such populations. The possibility of "stochastic stochastic" mechanism is one more
reason why structured populations should
be considered separately.
Deterministically Generated
Associations
In principle, amphimixis can be beneficial
in a spatially structured population in
which the size of each subpopulation is
large. This idea was first proposed by
Aleksandr Serebrovsky (1973) in a book
written in 1939 but only published 25 years
after his death. Serebrovsky noted that if
different subpopulations accumulate beneficial alleles at different loci, amphimixis
with intersubpopulational mating can be
beneficial because of "summation of evolutionary achievements" (p. 101). Similarly, Maynard Smith (1978) considered the
situation when a patch in which an AB
genotype is optimal is colonized by immigrants from two patches with Ab and aB
genotypes. Such models were studyed by
Slatkin (1975) and D. Charlesworth and
Charlesworth (1979).
Possible Importance of Hypotheses
Based on Spatial Structure
Obviously, these hypotheses are of limited
applicability because many populations are
essentially panmictic. The only exception
is the first hypothesis, because the contact
between parents and offspring always exists. I do not think, however, that the conditions when this hypothesis works are
common. In fact, amphimixis, where reproductively transmitted parasites are not
confined to separate lineages and one individual can infect many, facilitates the
spread of diseases (Hickey and Rose 1988).
AIDS would not spread in an apomictic
population, despite the absence of genetic
differences between parents and offspring.
The advantage of amphimixis due to diversity between sibs or other relatives involved in competition is more plausible.
However, the first mechanism requires that
sibs are competing in the same place but
under conditions different from those under which their parents were selected
(Maynard Smith, 1988a, p. 121). This can
be the case only if selection in each patch
changes frequently, which makes it unrealistic. The second mechanism is more
plausible. Here selection can be constant
both in time and space, and uniformly favors diversity within each patch. I doubt
that this can be a major factor in the evolution of amphimixis, but biologically the
situation is quite realistic.
Hypotheses that depend on determin-
Kondrashov ·Advantages of Amphimbs 381
istically generated associations in structured populations imply that the alleles
necessary for adaptation in some particular place must frequently be supplied by
immigration. Obviously this requires some
degree of uniformity of conditions
throughout the whole range of the population, because otherwise adaptations of
the subpopulations to unique local features would make immigrants unsuccessful. In this case, however, it is not clear
why a large subpopulation cannot acquire
the necessary beneficial alleles without
immigration. One possibility is independent fluctuations of the environment in different places. Thus the best source of alleles that become beneficial in some place
can be the adjacent populations, where
they may already be frequent. Quantitative
analysis shows, however, that spatial heterogeneity of selection, both invariant and
fluctuating, is not effective in maintaining
amphimixis when the subpopulations are
large (Case and Bender 1981; D. Charlesworth and Charlesworth 1979).
The hypotheses involved with spatially
structured populations which have so far
been proposed consider either selection
or drift as the factor that makes destruction of associations beneficial. Of course,
one may also attribute this to deleterious
mutations if, for example, only mutationfree individuals can survive in the progeny
from each mating. Such hypotheses, however, will be subject to the same limitations.
Why, After All, Does Amphimixis
Exist?
Three general conclusions can be made
from this review and classification of hypotheses. First, obligate amphimixis can
be beneficial over obligate apomixis under
a variety of different circumstances. Particularly, hypotheses which assume that
associations between alleles are generated by selection, instead of drift, have
gained much strength in the last 10 years.
Thus, Felsenstein's (1974) conclusionthat only those who consider effects of
finite population size find amphimixis advantageous-is no longer valid. Naive beliefs that an advantage for amphimixis can
come from its ability to increase variability
and, thus, facilitate adaptive changes, to
help eliminate deleterious mutations, or
to reduce competition between relatives
all have turned out to be true under some
conditions. All models reviewed above are
formally correct and, although more work
382 The Joumrnal of Heredity 1993:84(5)
is needed to refine some of them, their
basic features are well understood.
Second, all plausible hypotheses can
provide the substantial short-term advantage for amphimixis only under rather
stringent conditions (rapid irreversible
evolution, wide fluctuations of fitness optimum, high genomic deleterious mutation
rate, etc.), although some Variation and
Selection hypotheses (ES and MS) can
easily provide the large, long-term advantage. Therefore, it seems that the very existence of amphimixis carries some important information about natural
populations. Of course, all Immediate Benefit hypotheses could lead to a short-term
advantage of amphimixis because transition to apomixis is punished immediately.
However, currently there are no data on
any large, immediate benefits of amphimixis.
Third, we are astonishingly ignorant of
what actually happens in nature. We have
enough, even more than enough, possible
solutions that require totally different
characterization of the basic features of
populations, but we do not have facts to
decide which solutions are actually relevant. However, I agree with Felsenstein
(1988) that the current state of "the paradox of sex" issue does not represent an
isolated crisis in evolutionary biology. Instead, it reflects the chronic lack of knowledge about natural populations. This is
caused both by an inherent difficulty in
measuring populational parameters (Lewontin 1974) and by the view, still popular
among experimentalists, that making hypotheses is a mental exercise, not an invitation to do clearly defined experiments.
Of course, amphimixis may be beneficial
for more than one reason. One can imagine that in rapidly evolving flowering plants
amphimixis combines beneficial mutations; in a small population of Latimeria it
stops Muller's ratchet; in snails it prevents
sibs from competing too hard; in Drosophila melanogasterit reduces mutational load
under synergistic epistasis; in mammals
there is simply no way back to apomixis;
while in other cases amphimixis is maintained by fluctuating selection (caused
mostly by parasites). Even in the same
population amphimixis can repair doublestrand DNA damages, reverse mutations,
improve selection, and prevent populations from responding to selection too fast
all at the same time. Such a "pluralistic"
view attracts growing support, perhaps because by accepting any single hypothesis
you make more enemies than friends.
Currently, this cannot be ruled out.
However, I find it rather unlikely. Genetically amphimixis is a remarkably uniform
phenomenon (although it may have appeared independently several times, Ivanov 1970; Margulis et al. 1990), which may
well have only one cause. The hypotheses
that can explain the origin, maintenance,
and evolution of features of amphimixis
from the same point of view are, of course,
especially attractive (this, however, does
not guarantee that they are correct). Moreover, the pluralistic view impedes designing and making critical experiments aimed
at falsifying various hypotheses and,
therefore, should be accepted only if more
than one hypothesis is directly supported
by data.
What Can Be Said About Different
Hypotheses Now?
1do not believe that there is any inherited
immediate benefit of amphimixis important enough to account for its existence,
although the improvement of selection may
play some role. Of course, direct evidence
can change this view. Therefore, only Variation and Selection hypotheses are discussed here.
In unstructured populations stochastic
hypotheses are less plausible because they
cannot provide the short-term advantage.
Hypotheses that involve rare beneficial
mutations are probably irrelevant under
normal conditions of slow evolution, while
they, together with Muller's ratchet, may
play some role in limiting the time of existence of obligately apomictic populations (Bell 1988; Chao 1990; Chao et al.
1992). The ED hypotheses that attribute
the advantage of amphimixis to destruction of associations in alternating directions, either due to better responsiveness
(Bell and Maynard Smith 1987; Nee 1989)
or to nonresponsiveness (B. Charlesworth
1976; Hamilton et al. 1990; Roughgarden
1991), do not look plausible because they
require frequent alternation of stabilizing
and disruptive selection, and this has not
been observed in nature. Finally, all hypotheses that require spatial structure, except the one that considers parent-offspring transmission of pathogenes, can be
relevant only to forms with very limited
dispersal.
Therefore, two hypotheses seem to be
the most plausible: ED (with better responsiveness of an amphimictic population because of destruction of repulsion
associations created by either irreversibly
changing or widely fluctuating selection)
and MD. They have some features in comon: both require, as well as other Variation
and Selection hypotheses, substantial nonneutral additive genetic variance;
both assume that selection is (at least most
of the time) directional; and both claim
that amphimixis is beneficial because it
enhances the population's response to selection (B. Charlesworth 1989). Quantitative analysis shows that, according to both
hypotheses, an amphimictic population
protected against invasion by apomictic
clones can have low load (lag-load in the
first case, and mutational load in the second).
Other features of ED and MD hypotheses are, however, profoundly different.
Most important, they depend on totally
different modes of genetic variability. The
ED hypotheses requires conditionally
beneficial variability, where alleles and genotypes that are currently maladapted can
become beneficial in the future. Thus, selection is assumed to permanently create
new adaptations (see Lewontin 1974). In
contrast, the MD hypothesis depends on
unconditionally deleterious variability,
which can never be utilized for adaptation,
and on stabilizing selection sensu Schmalhausen (1949). As Williams (1966, p. 54)
put this: "I regard it as unfortunate that
the theory of natural selection was first
developed as an explanation for evolutionary change. It is much more important
as an explanation for the maintenance of
adaptation."
The data on quantitative variability do
not allow one to decide which mutationsconditionally beneficial or unconditionally deleterious-are more important
(Kondrashov and Turelli 1992). In some
sense the MD hypothesis is simpler because the same factor causes the deviation
of population mean from the optimum and
maintains variability, while with fluctuating selection the maintenance of variability requires mutation, frequency-dependence, or something else.
There are no data to prove that widely
changing selection, required by ED hypotheses, is uncommon in nature. However, the traits often remain practically invariant during very long time intervals (B.
Charlesworth 1993, in press). Recently,
Meselson and Welch (unpublished)
showed that in two species of bdelloid rotifers different alleles of the same loci are
extremely divergent, which seems to confirm the absence of amphimixis in this
group during millions of years. If so, this
is in conflict with any hypothesis that
claims that amphimixis is a means to accelerate irreversible evolution, because
bdelloid rotifers became a diverse and
successful group without it. There are even
fewer data to test the hypothesis that the
fitness optimum fluctuates widely, although it is usually assumed to coincide
with the population mean (Turelli 1984),
which is inconsistent with large and rapid
fluctuations.
In contrast, the scarce data on deleterious mutation rates show that Uis at least
about 1, which is consistent with the MD
hypothesis (B. Charlesworth et al. 1990;
Houle et al. 1992; Mukai et al. 1972), although more experiments are needed. Evidence of synergistic epistasis is very
scanty (Malmberg 1977; Mukai 1969).
In addition to the group selection advantage of amphimixis, the MD hypothesis
may also account for gradual evolution of
the features of amphimictic populations,
including recombination rates (B.
Charlesworth 1990; Feldman et al. 1980;
Kondrashov 1984a), outcrossing (B. Charlesworth et al. 1991; D. Charlesworth et al.
1990, 1992, 1993, in press; Kondrashov
1985; Michod and Gayley 1992; Uyenoyama and Waller 1991a,b), facultative apomixis (Kondrashov 1984b, 1985), mate
choice (Kondrashov 1988b; Rice 1988), and
the relative length of the haploid and diploid phases (Kondrashov and Crow 1991;
Otto and Goldstein 1992; Perrot et al. 1991).
Probably, it may also explain the gradual
origin of amphimixis (Bengtsson 1992). In
contrast, the ED hypotheses were so far
applied only to the evolution of recombination (Bergman and Feldman 1990; B.
Charlesworth, 1993, in press; Korol and
Preigel 1989; Korol et al. 1990). It seems
that both hypotheses predict significant
selection for free recombination in the amphimictic population under similar conditions, which are usually more restrictive
than those required for the group selection advantage of amphimixis. Particularly, the genetic load (either mutational or
lag) should be at least about 0.2-0.4.
with U >> 1, it can be considered proven.
What Data Do We Need?
Let us start with the data we no longer
need. These include much indirect evidence, usually from correlations of the
mode of reproduction with some vaguely
defined features of the environment. Higher incidence of apomixis in simple, novel,
or disturbed habitats (Bell 1982; Glesener
and Tilman 1978) among endosymbionts
(Law and Lewis 1983) and overall distribution of modes of reproduction among
taxa and ecosystems (Bell 1982; Halvorson and Monroy 1985; Jackson et al. 1985;
Shields 1982) are very interesting and have
In the last case even measurements of
epistasis are unnecessary, because long
existence of a population under such U is
impossible unless it is present.
Remarkably, Uis an organismal, and not
a population-level, parameter, so that it
can be measured relatively easily. Still, the
problem is that slightly deleterious mutations cannot be individually detected
without using molecular methods. It is
generally accepted, however, that the total
per-genome mutation rate in mammals is
more than 100 (see Kondrashov 1988a),
and the only problem is what proportion
of these mutations are deleterious. Molecular methods can be decisive in solving
stimulated much thought, but they clearly
cannot lead to rejection of any hypothesis.
Similarly, the correlation between high incidence of amphimixis with high infestation by parasites (Lively 1992) can be
viewed as evidence that amphimixis either
protects the population from parasites
(and, therefore, is replaced by apomixis if
they are absent) or facilitates their spread,
or is favored by the same factor that causes high infestation.
Instead of such correlations, we need
data that explicitly test different hypotheses in various natural populations. For
Immediate Benefit hypotheses, this means
that a postulated immediate benefit of amphimixis should be demonstrated directly.
For Variation and Selection hypotheses,
three levels of proof are possible. The first
and the best one is to observe postulated
changes in the genetic composition of the
progeny, together with their effect on the
population fitness. The second one is to
show the existence of conditions that make
these postulated changes beneficial. The
third and final one is to compare the fitnesses of amphimictically and apomictically produced progeny. This last approach is the least direct, and its results
may simply suggest that amphimixis has
some short-term advantage in a particular
situation (Harshman and Futuyma 1985;
Kelley et al. 1988). However, if the fitness
is measured under carefully described
conditions, more information can be obtained (Kelley 1989a,b).
Clearly, hypotheses leading to predictions that are easier to falsify are especially attractive, and from this point of view
my favorite MD hypothesis is the uncontested winner. Its validity depends on a
single parameter, the genomic deleterious
mutation rate U. If U
1 in some popu-
lation, MD hypothesis cannot be applied
to it; with Uclose to 1, it is plausible; and
Kondrashov Advantages of Arnphimixs 383
this problem (Kondrashov and Crow
1993).
The importance of Muller's ratchet also
mostly depends on a single parameter: the
absolute number of individuals in apomictic populations with a minimal number
of mutations. This is more difficult to measure than U. Besides, it is not clear what
should be measured in an amphimictic
population to determine whether Muller's
ratchet protects it from invasion of apomictic clones. This problem is worth investigating.
ED hypotheses that postulate destruction of repulsion associations require wide
changes of selection. These changes must
also be rather (but not too) fast and frequent, to provide a short-term advantage
to amphimixis and to prevent the adaptation of apomicts due to new mutations.
Unfortunately, selection is very difficult to
measure. However, changes of selection
must lead to large and relatively rapid
changes in mean values of the traits involved, on the order of the standard deviation and probably much more, which
will be easiest to detect. Instead of studying the same population over the long term,
one can simultaneously investigate different populations. Profound differences, both
phenotypic and genetic, among such populations would be strong evidence of fluctuating selection, provided that they cannot be attributed to permanent differences
between conditions in different places. Of
course, stability or spatial uniformity of
some traits, which is what is routinely observed, can simply mean that these particular traits are not related to the advantage of amphimixis. Thus, systematic
studies of the changes of natural populations in time and space are needed.
ED hypotheses assuming association in
alternating directions (either of better responsiveness or of nonresponsiveness
type) are even more difficult to reject, because they predict smaller or no fluctuations of allele frequencies, requiring only
large and frequent fluctuations of fitnesses. This requires direct measurement of
selection and of the factors that cause its
changes. Negative biotic interactions have
repeatedly been proposed as such factors.
It seems, however, that all the models of
this type considered so far assume alternation of stabilizing and disruptive selection and "gene-to-gene" relationships between the ability of parasites to attack and
of hosts to defend themselves. This might
not apply in higher animals that have general-purpose immune systems capable of
384 The Joumal of Heredity 1993:84(5)
acting against unpredictable threats (Bremermann 1987, p. 147).
ES hypotheses critically depend on how
frequently new, beneficial mutations go to
fixation. In chemostat populations this can
happen remarkably frequently (Paquin and
Adams 1983), but there are no data from
natural populations. For hypotheses involved with spatial structure, current data
do not show a large advantage of more
diverse sibships (Bell 1991; Kelley 1989b).
In contrast, there is some evidence that
the difference between parents and offspring may be advantageous (Kelley 1989a,
in preparation), but more data are necessary.
Formulation of falsifiable predictions
should shift the emphasis to decisive experiments. I believe that further progress
in our understanding of the evolution of
reproduction will depend on the results of
such experiments much more than on theoretical work: "It is only by the further
accumulation of facts in various groups of
plants and animals that we may at length
be in position to determine what if any
unifying principle there may be in this
wide-spread phenomenon of sexuality"
(Blakeslee 1907, p. 372).
Appendix 1. Immediate Benefit
Hypotheses
Amphimixis is supposed to be directly
beneficial because:
1. It increases fitness of the progeny:
a. Because a diploid progeny has two
parents instead of one (Lloyd 1980)
b. Because double-strand DNA damages can be repaired during chromosome conjugation in meiosis
(Dougherty 1955; see Bernstein and
Bernstein 1991)
2. It reduces the deleterious mutation rate:
a. Because most deleterious mutations
are deletions, which can be recognized as gaps when chromosomes
conjugate, and can be filled by biased gene conversion (Bengtsson
1985)
b. Because most deleterious mutations
are insertions, which can be recognized as loops when chromosomes
conjugate, and can be cut (Ettinger
1986)
c. Because most deleterious epimutations are demethylations, which can
be recognized and reverted when
chromosomes conjugate (Holliday
1988)
3. It increases efficiency of selection:
Because selection among males or
male gametes may be costless (Geodakyan 1965; Trivers 1976)
Appendix 2. Variation and
Selection Hypotheses (Local
Population)
Amphimixis is supposed to be beneficial
because there is:
1. In ES hypotheses:
a. More rapid accumulation of beneficial mutations at many loci simultaneously (Fisher 1930; Morgan 1913;
Muller 1932)
b. More rapid accumulation of beneficial mutations in the presence of deleterious mutations (Fisher 1930;
Manning and Jenkins 1980)
c. More rapid accumulation of beneficial mutations when polymorphisms
are maintained in other loci (Manning 1982c, 1983)
2. In ED hypotheses:
a. An increased rate of evolution under
an irreversibly changing environment (Eshel and Feldman 1970, case
b; Mather 1943)
b. An increased rate with which a population follows the widely fluctuating
environment (Mather 1943; Maynard Smith 1980; Treisman 1976)
c. A decreased rate with which a population follows frequently fluctuating
environment (B. Charlesworth 1976;
Sturtevant and Mather 1938)
3. In the MS hypothesis:
A reversion of random losses of deleterious mutation-free genotypes
(Muller 1964)
4. In the MD hypothesis:
An increased efficiency of selection
against synergistically interacting
deleterious mutations (Crow 1983;
Crow and Simmons 1983; Kondrashov 1982)
Appendix 3. Variation and
Selection Hypotheses (Spatially
Structured Population)
Amphimixis is supposed to be beneficial
because:
1. In case of stochastically generated
associations:
a. It prevents transmission of pathogens from parents to offspring because of
their genetic dissimilarity (Rice 1983a,b)
b. It increases the chances that a group
of relatives contains an optimal genotype
(Williams and Mitton 1973)
c. It decreases competition between
relatives (Maynard Smith 1978; Svedelius
1927; Young 1981).
2. In case of deterministically generated association:
It combines different beneficial alleles
that were established in different subpopulations (Serebrovsky 1973; Slatkin 1975).
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