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Journal of Heredity 2010:101(Supplement 1):S135–S141
doi:10.1093/jhered/esq019
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Finite Populations, Finite Resources, and
the Evolutionary Maintenance of
Genetic Recombination
SOL ACKERMAN, AMIR R. KERMANY,
AND
DONAL A. HICKEY
From the Department of Biology, Concordia University, 7141 Sherbrooke West, Montréal, Québec, Canada, H3G 1M8.
Address correspondence to Donal A. Hickey at the address above, or e-mail: [email protected].
Abstract
Most previous models for the evolution of sex implicitly assume infinite population sizes and limitless resources. However,
because favorable mutations are very rare and eukaryotic populations are finite, it has already been shown that multiple
favorable mutants virtually never occur by chance. Therefore, sex is required to combine different favorable mutations into
a single lineage. Second, we show that even when multiple favorable mutations do coexist, competition between genotypes
can create negative epistasis for fitness, thus favoring recombination. Competition is especially effective when selection is at
the level of viability in K-selected species living in a resource-limited environment. This means that recombination is
advantageous both for incorporating new favorable mutations into the gene pool and for accelerating their increase to
fixation. These advantages of recombination are diminished, however, as genome sizes decrease or as the amount of
competition within the species is a less important component of selection.
Key words: competition, epistasis, evolution of sex, fitness, recombination, sex
Sex is not a necessity of life; this is clearly illustrated by the
many instances of asexual reproduction that exist, especially
among microbes. Yet, most biologists believe that sexual
reproduction and the resulting genetic recombination do
provide some selective advantage and, based on the broad
patterns of distribution of sex among taxa, we can infer that the
advantage of recombination is more important for large
multicellular eukaryotes than it is for small single-celled
prokaryotes: recombination and sexual reproduction are
ubiquitous among higher eukaryotes (Hadany and Comeron
2008), whereas bacteria are primarily asexual (Narra and
Ochman 2006). But we still do not know what the nature of
this advantage is. Indeed, the evolution of sex is one of the
longest standing unsolved problems in biology (for a review,
see Agrawal 2006). It is now almost 80 years since Ronald
Fisher wrote that sexual reproduction ‘‘is a development of
some special value to the organisms which employ it’’ (Fisher
1930). Eight decades later, we are still trying to decipher what
that ‘‘special value’’ might be. As Sarah Otto remarked recently
(see Otto 2009), we are still trying to ‘‘solve the paradox of sex.’’
Biologists have invested a large amount of research
effort into this problem and several models for the
evolution of genetic recombination have been proposed.
Earlier theories proposed that the benefit of recombination
lay in the fact that it combined different beneficial mutations
into a single genotype (Muller 1932, 1964; Crow and
Kimura, 1965, 1970). Later work, however, showed that the
benefits of combining advantageous mutations are offset by
the fact that recombination also breaks up these favorable
combinations once it has been formed (Maynard Smith
1968, 1978). In other words, recombination simply randomizes genotypes, without regard to the fitness of the alleles
being recombined.
Population genetics theory predicts that genetic recombination will be an advantage in those situations where there is
a dearth of favorable combinations in the population, that is,
there is negative linkage disequilibrium between alleles at
selected loci (Maynard Smith 1978). In this case, simple
randomization of genotypes will increase the variance in
fitness among the genotypes and thus accelerates the response
to selection. Negative linkage disequilibrium could arise either
through the effects of genetic drift (Hill and Robertson 1966;
Felsenstein 1974; Keightley and Otto, 2006) or through the
action of selection itself, provided that selection acted in
a negatively epistatic fashion (Kimura and Maruyama 1966;
Kondrashov 1982, 1988; Barton 1995). The challenge for
evolutionary biologists and ecologists, however, has been to
describe conditions that are both widely distributed in nature
and that would result in negative epistasis for fitness. Spatially
complex environments, such as described by the Tangled
Bank model (Bell 1982), might be expected to favor sexual
organisms that produce genetically variable offspring, but it is
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Journal of Heredity 2010:101(Supplement 1)
temporally fluctuating environments—such as described by
the Red Queen model (Van Valen 1973; Hamilton 1980;
Hamilton et al. 1990; Peters and Lively 1999)—that provide
the conditions necessary for the buildup of negative linkage
disequilibrium between loci. Not only does selection have to
fluctuate over time, however, it has to undergo periodic
reversals. This has been most extensively studied in the case of
host–parasite coadaptation cycles. Although the Red Queen
explanation for the evolution of sex is attractive, its general
relevance to the problem of sex is still debated (Neiman and
Koskella 2009) because it depends on particular ecological
conditions, such as host–parasite coevolution. In this situation,
the adaptation of parasites to the most common host
genotypes will provide an advantage to hosts with a rare
genotype produced by recombination. This advantage, by its
very nature, is negatively frequency dependent. Consequently,
as the frequency of favored rare genotype increases, the
direction of selection will be reversed. However, it has been
shown that the periodicity of the selection reversals is quite
constrained (Otto and Nuismer 2004; Salathé et al. 2008). Thus,
although this form of selection could explain the evolution of
sex, some biologists feel that it requires a set of ecological
circumstances that seem far too narrow to explain the nearuniversality of sexual reproduction among eukaryotes.
Our approach has been to concentrate on the effects of
competitive interactions between genotypes within a population. Whereas there is a large theoretical literature describing
the interactions between different species in an ecosystem,
relatively little attention has been paid to competitive
interactions between genotypes within a population. Instead,
genotypes are usually assigned fixed fitness values that do not
depend either on the availability of resources or on the
frequencies of other genotypes in the population. Yet, as
noted by Lewontin (1955), ‘‘it would be strange if what
applied to different species did not apply to some extent to
different genotypes within the same species.’’ Thus we have
asked how selection would play out if the genes affected
fitness indirectly through the production of fixed phenotypes
with different competitive abilities. In this scenario, the
phenotype is uniquely determined by the genotype, but the
resulting fitness depends not only on the phenotype itself but
also on the phenotypes of the competing genotypes. This
scenario should apply to any species where the ‘‘struggle for
existence’’ not only involves a struggle with the external
environment but also some degree of competitive struggle
with other genotypes within the same species. Most previous
models of intraspecific competition between genotypes have
focused primarily on their potential for maintaining genetic
polymorphism (Trotter and Spencer 2007) or for promoting
speciation (Bürger et al. 2006). A couple of other studies,
however, have looked explicitly at the relationship between
intraspecific competition and recombination (e.g., Peck and
Waxman 2000; Bagnoli and Guardiani 2005).
Finite Populations
Population genetics models tend to fall into 2 categories:
deterministic models that imply infinite population size and
S136
stochastic models that emphasize the effects of gamete
sampling in small populations. But many natural populations
are neither very small nor infinitely large; they exist in a gray
area where we are not sure whether their evolution is
dominated by deterministic or stochastic forces. For many
years, the field of population genetics was engulfed in
a controversy between those who believed that stochastic
sampling effects were insignificant and those who believed
that, to the contrary, the random sampling of gametes in
finite populations was a major force behind the change in
allelic frequencies. The deadlock has been broken by the
accumulation of a large amount of comparative DNA
sequence data. From those data it is clear that stochastic
sampling is a major force in DNA sequence divergence. This
means that the population size, N, is generally smaller than
the reciprocal of the mutation rate, l. Roughly speaking, we
can conclude that real population sizes, although they may be
large, are generally significantly less than one billion
individuals. This finding is important for discussions of the
evolution of genetic recombination, especially when we
consider the expected numbers of double mutations in
natural populations. For example, Maynard Smith (1968,
1978) pointed out that double mutants could be produced by
mutation alone provided that the population size were large
enough, making the generation of doubly favorable mutants
by recombination unnecessary. But for this to happen in
practice, the population size would have to be of the order of
1016, and for triple mutants we would need population sizes
of 1024. These numbers are based on the estimate of 105
favorable mutations per genome per generation, as reported
by Perfeito et al. (2007), which translates into a per-gene rate
of 108, assuming that there are at least 1000 genes per
haploid genome. The projected population numbers are
clearly unrealistic for the majority of eukaryotic species,
especially multicellular eukaryotes. Although it is often
impossible to measure population sizes directly, and
impossible to measure historical effective population sizes,
we can obtain indirect measures because the effective size N
of a population is related to the genetic diversity that is
maintained in the population (Kimura and Crow 1964). Such
analyses of polymorphism data yield an estimated effective
population size of approximately 10 000 for the modern
human lineage (e.g., Takahata 1993; Yu et al. 2001) and less
than 100 000 for other primate lineages (Burgess and Yang
2008). Given that the mutation rate for favorable alleles is
orders of magnitude less than the reciprocal of the
population size, new favorable mutants in a given gene are
essentially unique and are, for all practical purposes
nonrecurring. It should be noted that this problem is less
acute for prokaryotes and single-celled eukaryotes that can
have very large population sizes and that have rapid doubling
times (20 min in Escherichia coli vs. 20 years in humans).
Consequently, without recombination most of the favorable
mutants that occur in finite populations—even very large
finite populations—will eventually be lost. For instance,
Barrick and Lenski (2009) showed that, in asexual
populations, some beneficial mutations can be lost through
competition with other beneficial mutations.
Ackerman et al. Maintenance of Genetic Recombination
Finite Resources
In the previous section, we have tried to demonstrate why the
larger genomes, smaller population sizes, and slower
replication rates that characterize multicellular eukaryotes, as
compared with many single-celled prokaryotes, might favor
the maintenance of genetic recombination. A correlated
difference between large multicellular eukaryotes and small
single-celled prokaryotes is the greater importance of
competition among large eukaryotes. In ecological terms,
prokaryotes tend to be r-selected, whereas multicellular
eukaryotes are more K-selected—although this is not
a universal rule of course. Although it is difficult to measure
competition in absolute terms, a number of predictions have
been made regarding the response of natural selection to
increasing levels of intraspecific competition. For instance,
Adler and Levins (1994) predicted that viability selection
would become more important than fecundity selection as
the level of intraspecific competition increased, and a number
of subsequent studies (e.g., Mappes et al. 2008) have provided
empirical evidence in support of this prediction. Here, we
explore how the competitive component of selection also
favors the maintenance of genetic recombination.
Natural selection favors genotypes that are better
adapted to the environment; this includes both the physical
and biotic environments. In the case of the biotic
component of the environment, most researchers have
focused on interactions between species in an ecosystem
and relatively little attention has been paid to the
interactions between individuals within a species. Indeed,
it is this competitive interaction between individuals that
Darwin (1859) saw as the essence of his ‘‘struggle for
existence.’’ He wrote: ‘‘Two canine animals in a time of
dearth, may be truly said to struggle with each other which
shall get food and live. But a plant on the edge of a desert
is said to struggle for life against the drought, though more
properly it should be said to be dependent on the moisture.
A plant which annually produces a thousand seeds, of
which on an average only one comes to maturity, may be
more truly said to struggle with the plants of the same and
other kinds which already clothe the ground.’’ In other
words, Darwin saw natural selection as a zero-sum game
where the number of surviving offspring is no greater than
the number of parental individuals and where competition
between conspecific individuals plays a crucial role. This is
in contrast to many population genetics models that assign
fixed fitnesses to genotypes which then implicitly engage
in replication races during which less fit types are diluted
out by fitter types rather than being culled from the
population.
In our model, which mirrors Darwin’s scenario where
only one offspring on average comes to maturity, the
genotype specifies a fixed phenotype and this phenotype
determines competitive ability. Fitness depends on the
outcome of pairwise competition between individuals. This
means that fitness depends not only on the phenotype of
the individual itself but also on the phenotype of its
competitor, and the latter depends in turn on the frequency
of competitor genotypes. This is summarized in Table 1.
Moreover, as selection proceeds, the frequency of the
competitors changes; specifically, the frequency of the better
competitors increases making competition more stringent.
Meanwhile, since the population size does not increase,
there is always an average of one surviving offspring per
parent, yielding a constant average fitness, with a value of 1,
for the population.
Based on the competitive interactions shown in Table 1,
the expected fitnesses of the individual genotypes were
calculated as follows:
WAB 5½PAB þ ðPAB ÞðPAb Þ þ ðPAB ÞðPaB Þ þ ðPAB ÞðPab Þ=PAB
WAb 5 ½PAb ðPAb ÞðPAB Þ þ ðPAb ÞðPab Þ=PAb
WaB 5 ½PaB ðPaB ÞðPAB Þ þ ðPaB ÞðPab Þ=PaB
Wab 5 ½Pab ðPab ÞðPAB Þ ðPab ÞðPAb Þ ðPab ÞðPaB Þ=Pab
where (PAB) represents the frequency of the AB genotype,
etc. among the competing offspring. (These equations are
also shown in legend of Figure 1b).
Figure 1 illustrates how competitive selection compares
to more traditional population genetics models. We have
used an example of a haploid model with 2 biallelic loci. In
the case of models with fixed genotypic fitnesses (Panel A),
we see that the mean fitness of the population increases as
the frequency of the fitter genotypes increases. In the
competitive selection model, however (Panel B), where the
average population fitness remains fixed with a value of one,
the realized fitnesses of the individual genotypes change in
a negative frequency-dependent fashion. Given that the
individual fitnesses change in a frequency-dependent
manner in the competitive selection model, we asked if
the value of realized epistasis—which is calculated based on
those fitnesses—also changed in a frequency-dependent
manner. The answer to that question is answered in Panel C
of Figure 1. From the Figure, we see that epistatic values are
also frequency dependent in this model and, more
important, they are negative. This shows that competitive
selection between individuals within a population can
generate negative linkage disequilibrium between the
selected alleles, which would in turn favors genetic
Table 1
Outcome of competition between pairs of individuals
Genotype
Genotype of competitor
AB
Ab
aB
ab
AB
0
Ab
þ
0
0
aB
þ
0
0
ab
þ
þ
þ
0
For each of the 4 genotypes listed in the rows on the left, their success in
competition depends both on their own phenotype and on the phenotype of
the competing individual, listed in the columns at the top. Competitive
success is indicated by a plus sign; failure by a minus sign; and a draw between
equal competitors (50% chance of success or failure) is indicated by a zero.
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Journal of Heredity 2010:101(Supplement 1)
wAB
w
1 .5
wAb
wab
1.0
Fitness (w)
2.0
A
0.6
0.8
1.0
w
Wbar 5ðWAB ÞðPAB ÞþðWAb ÞðPAb ÞþðWaB ÞðPaB ÞþðWab ÞðPab Þ
0.5
wab
wAb
0.1
0.2
Fitness (w)
0.4
Allele Frequency (PA)
wAB
1.0
B
0.2
2.0
0.0
0.2
0.4
0.6
Allele Frequency (PA)
0.8
1.0
0.0
0.0
−1.0
WaB 5 ½PaB ðPaB ÞðPAB Þ þ ðPaB ÞðPab Þ=PaB
Wab 5½Pab ðPab ÞðPAB Þ ðPab ÞðPAb Þ ðPab ÞðPaB Þ=Pab
−2.0
−1.5
Epistasis (ε)
WAb 5 ½PAb ðPAb ÞðPAB Þ þ ðPAb ÞðPab Þ=PAb
0.0
0.2
0.4
0.6
0.8
1.0
Allele Frequency (PA)
Figure 1. Comparison between selection models with
constant genotypic fitness (Panel A) and constant population
fitness (Panel B).
Panel (A) The correlation between fitness and allele frequency
when genotypes have constant fitness values.
The average fitness of the population is calculated as:
S138
Where WAB represents the fitness of the AB genotype and PAB
represents its frequency, etc.
Note that in this case, the average fitness of the population,
Wbar, increases as the frequency of the favored allele increases.
The line for WaB is not shown because it is identical to that
shown for WAb.
Panel (B) The correlation between fitness and allele frequency
when the total number of surviving offspring is constrained to
equal the total number of parents.
The expected fitnesses of the individual genotypes were
calculated as a function of their own frequency and that of
other genotypes in the population of competing offspring, as
follows:
WAB 5 ½PAB þðPAB ÞðPAb ÞþðPAB ÞðPaB ÞþðPAB ÞðPab Þ=PAB
−0.5
C
recombination between the loci. We can illustrate this with
a simple numerical example. If we assume that the
frequencies of the favored alleles at each of the 2 loci are
initially equal to 0.1, and that the genotypes are in linkage
equilibrium, then the formulas in Figure 1b give values of
1.99, 1.80, 1.80, and 0.81 for the realized fitnesses of
genotypes AB, Ab, aB, and ab, respectively. If we express
these values as relative fitness, they become 1, 0.9, 0.9, and
0.41. Now if we use these relative fitnesses, in turn, to
calculate the value of epistasis using the formula in Figure 1c,
we get E 5 0.4, that is, negative epistasis.
The calculations above provide us with the expected
outcome of this type of competitive selection. In order to
verify these expectations, we explored the effects of
competitive selection by performing individual-based computer simulations. These simulations are not dependent on
the formulas but on simple rules of competition. Nevertheless, the results of the simulations matched the expectations
based on the equations.
where (PAB) represents the frequency of the AB genotype, etc.
among the competing offspring. See text for an explanation of
the formulas.
Panel (C) The correlation between epistasis and allele frequency,
based on the realized fitness values shown in Figure 1b.
The value of epistasis was calculated as follows:
E 5 WAB Wab WAb WaB
Note that the fitness values that go into the calculation of
epistasis are themselves changing in a frequency-dependent
manner as shown in Figure 1b.
0. 8
0.6
0 .4
Frequency of Sexuals
0.2
0.8
0.6
0.4
0
2
4
6
Generation
8
0.0
0. 2
sexual
asexual
0.0
Frequency of AB Genotype (PAB)
1.0
1.0
Ackerman et al. Maintenance of Genetic Recombination
0
Figure 2. Individual-based simulations of pairwise
competitive selection. The figure shows the change in the
frequency of the doubly favored genotype, AB, in 5 replicate
asexual populations (shown in black) and 5 replicate sexual
populations (shown in grey). The population size for each
replicate was 10 000 individuals and because each individual
produced an average of 2 offspring, there were 20 000
competing offspring in each replicate every generation.
In the simulations individuals competed in pairs and the
expected outcome of the pairwise competitive interactions
was dependent on the phenotypes of the 2 competitors, as
shown in Table 1. We assume a 2-locus, diallelic, haploid
population of competing individuals with genotypes ab, Ab,
aB, and AB. Generations are discrete and nonoverlapping, and
the population has the carrying capacity K. At the beginning of
each generation, each individual produces Poisson (2) number
of offspring. The population is then reduced down to a size of
K through simultaneous pairwise competitions. Therefore,
when the population has reached carrying capacity, we expect
the population to produce 2K offspring, K of which are
subsequently eliminated through competition. When competing, the individual with the greatest number of uppercase
alleles wins the competition (AB . Ab 5 aB . ab). We
performed simulations with various population sizes and with
different initial genotype frequencies. The results were
consistent over a wide range of parameter values.
In the example shown in Figure 2, simulations were
initiated with populations of 10 000 haploid individuals with
2 biallelic loci and where the frequencies of the favored
alleles, A and B were initially low (0.1). Each favored allele
increased the phenotypic value of the individual by 0.1,
changing that value from 1 to 1.1. We assumed no epistatic
interaction between loci. In other words, the phenotypic
value of the AB genotype was assumed to be multiplicative
and had a value of 1.21. Despite the lack of epistasis at the
phenotypic level, however, epistatic effects at the fitness level
were caused by the competitive selection itself. As pointed
out by Milkman (1973), in a competitive selection situation,
the phenotype represents the fitness potential rather than the
5
10
15
Generation
10
Figure 3. Increase in the frequency of sexual individuals in
mixed populations. These simulations were similar to those
shown in Figure 2, but rather than simulating either entirely
sexual or entirely asexual populations, here we initiated the
simulation with a mixture of types: 10% sexuals and 90%
asexuals. The Figure shows that the frequency of the sexuals
increased during the course of the simulation. The results for 5
replicate simulations are shown. The population size for each
replicate was 10 000 individuals which produced 20 000
competing offspring each generation.
fitness itself. The resulting realized fitness of each genotype is
the result of an interaction between the fitness potential
and the frequency of other competing genotypes in the
population. It is the nonlinear mapping of fitness potential
onto realized fitness that produces negative epistasis. This
is why it is possible to have nonepistatic effects at the
phenotypic level, but epistasis at the realized fitness level.
Genetic recombination (random assortment of alleles at
the 2 loci) was included in 10 replicate simulations; the other
10 replicates lacked recombination. As we can see from
Figure 2, those simulations that included a round of
recombination resulted in a more rapid fixation of the
doubly favored genotype, AB. The advantage of recombination is that it reduces the negative linkage disequilibrium
that builds up in response to the negatively epistatic
competitive selection (see Figure 1c).
The fact that fixation of the doubly mutant genotype, AB,
occurs faster in the recombining population suggests that sexual
strains would be at an advantage in a mixed population. We
tested this prediction directly by simulating mixtures of sexual
and asexual individuals within a single population. As shown in
Figure 3, the frequency of the sexual type does indeed increase
during the course of competitive selection. Our next step will be
to test populations where all the individuals are sexual but
where there is allelic variation for recombination rate.
Discussion
Our model shows that recombination can be advantageous
provided that resources are limited. This assumption of
limited resources results in a finite maximum population size
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Journal of Heredity 2010:101(Supplement 1)
and it implies a significant degree of competition between
individuals, especially once the population reaches its carrying
capacity. Competition results in frequency-dependent realized fitnesses, and the epistatic values calculated from these
fitnesses are themselves both frequency dependent and
negative. This means that the competitive selection process
itself creates negative linkage disequilibrium between selected
alleles. The advantage of recombination is that it breaks down
this negative linkage disequilibrium.
A number of previous studies have pointed out that sex
may be advantageous in small populations (Felsenstein 1974;
Christiansen et al. 1998; Otto and Barton 2001; Barton and
Otto 2005) or in geographically subdivided large populations
(Martin et al. 2006; Agrawal 2009). Our particular focus on
population size relates particularly to the occurrence of new
favorable mutations in multilocus genotypes. We argue that
since actual population sizes are generally less than the
reciprocal of the mutation rate per gene, and consequently
orders of magnitude less than the favorable mutation rate,
new favorable mutations are effectively unique events.
Consequently, without recombination, the majority of these
mutations will be lost from the population. This would not
be the case if the population size was extremely large and the
new favored mutant type had the capability of expanding to
very large numbers of descendants in a short period of time.
Such conditions may be met in bacterial populations but not
in most multicellular animal populations. The problem for
multicellular eukaryotes is compounded by the fact that they
have genomes that are typically an order of magnitude
greater in size than bacterial genomes. This combination of
larger genomes, smaller population sizes, and slower
replication rates represent special challenges for adaptive
evolution in multicellular animals. Genetic recombination
mitigates this problem to some extent.
The interaction between sex and competition was studied
previously by Case and Taper (1986). In their model, which
included both viability and fertility selection at the species
level, the advantage of sex lay in the potentially broader niche
of the sexual species, given an environmental gradient.
Doncaster et al. (2000) also studied the evolution of sex in an
ecological context and they concluded that intraspecific
competition could lead to the coexistence of sexual and
asexual species. Their model focused primarily on predator–
prey systems. A single-species model was studied by Peck and
Waxman (2000) focusing on the effects of scramble
competition, with recurrent deleterious mutations affecting
fertility only. Their model showed that recombination could
be advantageous if individuals competed in small groups. Our
model focuses on contest competition affecting viability (for
a review of single-species competition models, see Brännstrom
and Sumpter 2005). Our model does not require grouping of
competitors; it simply assumes that total resources are
finite—as is the total population size—resulting in the fact
that for every winner there is a loser. In other words, in our
model competition is a zero-sum game. The recent model
proposed by Bagnoli and Guardiani (2005) is closer to what we
present here in that it is a discrete, individual-based model,
although there are also significant differences. For instance,
S140
their model is based on the framework of quantitative genetics,
which means that they do not track the frequency of specific
genotypes nor do they calculate values of epistasis. In addition,
they consider an environmental gradient where competition is
most intense between phenotypes adapted to the same point on
that gradient. The fact that several previous studies, along with
the current work, show an advantage for recombination in
a competitive selection context, using a variety of different
competition models, gives us some confidence that a wide
range of competitive interactions may have this property. One
attraction of our model is that, because of its simplicity, it makes
the relationship between competition and negative epistasis
more transparent.
Some other proposals for an advantage for sexual
reproduction are implicitly based on some form of competition
between conspecifics. These include theories of sib competition
(Bulmer 1980) and clonal interference (Kim and Orr 2005).
A recent study (Cooper 2007) provided direct experimental
evidence that recombination can reduce clonal interference
between selected favorable alleles in bacterial populations.
Conclusion
Many previous studies of the evolution of sex have implicitly
assumed infinite populations that have access to limitless
resources. Although such models may provide a good
approximation for describing the evolutionary dynamics of
experimental populations of bacteria growing in a chemostat,
they are not realistic for many species, such as most
vertebrates, where population sizes are limited and there is
significant competition for limited resources. For such
species, there could be a significant component of selection
based on competitive ability with conspecifics. Considering
competition also helps us to put the ‘‘cost of males’’ into
perspective: in a competitive situation, producing 2 losers
does not outweigh the benefits of producing one winner.
In summary, sex is not a necessity of life but, given
limited population sizes and/or limited resources, it might
give a competitive edge to those genotypes that recombine
their genomes.
Funding
Discovery Grant from Natural Sciences and Engineering
Research Council Canada (RGPIN 8516-2008) to D.A.H.;
Canada Foundation for Innovation; Canada Research Chairs
program.
Acknowledgments
This research was supported by a Graduate Scholarship (S.A.).
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Received October 8, 2009; Revised January 15, 2010;
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Corresponding Editor: Maurine Neiman
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