Social heterosis and the maintenance of genetic diversity

jeb_1418 2253..2265P. NONACS & K. M. KAPHEIM
Department of Ecology and Evolutionary Biology, University of California, Los Angeles, CA, USA
Introduction
tages at various levels of biological organization. Hetero-
zygous individuals are often more robust than
excessively homozygous individuals (Semel et al.,
2006). Social groups function better when genetic var-
iation produces phenotypic variation across individuals
in behaviour and morphology (Holldobler & Wilson,
1990; Robinson, 1992; Cole & Wiernasz, 1999; Mattila &
Seeley, 2007). Genetically diverse populations or species
can have higher growth rates and be less likely to go
extinct (Antonovics, 2003; Reed & Frankham, 2003;
Hanski & Saccheri, 2006; Leimu et al., 2006; Vellend,
2006). Nevertheless, the maintenance of genetic diversity
is not adequately explained by current evolutionary
theory. Natural selection inexorably reduces allelic diver-
sity when better adapted phenotypes are differentially
successful in reproduction. Episodes of selective sweeps
through populations carry optimal alleles to fixation
along with other alleles linked by proximity on chromo-
somes (Fisher, 1958; Maynard Smith & Haigh, 1974;
Kaplan et al., 1989; Falconer & Mackay, 1996; Fay & Wu,
2000). Similarly, genetic drift, especially in small popu-
lations, creates stochastic variability that leads to the loss
of alleles in populations (Amos & Harwood, 1998; Fay &
Wu, 2000). However, the surprising amount of allelic
diversity found in many species strongly suggests that
directional selection and genetic drift are often signifi-
cantly opposed (Barton & Turelli, 1989; Turelli & Barton,
2004; Roff & Fairbairn, 2007).
diversity can be maintained. Some operate through
selection at the within-genome level, such as mutation
(Turelli & Barton, 2004), heterosis or overdominance
(Dobzhansky et al., 1977; Birchler et al., 2006), gene
duplication (Lande, 1975; Li et al., 2005), epistasis
(Wright, 1931, 1932) and antagonistic pleiotropy (Barton
& Turelli, 1989; Curtsinger et al., 1994; Sih et al., 2004;
Roff & Fairbairn, 2007). Other processes act across
individuals. Most prominent is negative frequency-
dependent selection, where the average fitness of an
allele in a population declines as it increases in abun-
dance (Maynard Smith, 1982; Olendorf et al., 2006).
Multiple alleles can be maintained in the population at
Correspondence: Peter Nonacs, Department of Ecology and Evolutionary
Biology, University of California, Los Angeles, CA 90095, USA.
Tel.: +1 310 206 7332; fax: +1 310 206 3987;
e-mail: [email protected]
ª 2 0 0 7 T H E A U T H O R S . J . E V O L . B I O L . 2 0 ( 2 0 0 7 ) 2 2 5 3 – 2 2 6 5
J O U R N A L C O M P I L A T I O N ª 2 0 0 7 E U R O P E A N S O C I E T Y F O R E V O L U T I O N A R Y B I O L O G Y 2253
Keywords:
Abstract
Genetic diversity in species is often high in spite of directional selection or
strong genetic drift. One resolution to this paradox may be through fitness
benefits arising from interactions of genetically diverse individuals. Advan-
tageous phenotypes that are impossible in single individuals (e.g. being
simultaneously bold and shy) can be expressed by groups composed of
genetically different individuals. Genetic diversity, therefore, can produce
mutualistic benefits shared by all group members. We define this effect as
‘social heterosis’, and mathematically demonstrate maintenance of allelic
diversity when diverse groups or neighbourhoods are more reproductively
successful than homogenous ones. Through social heterosis, genetic diver-
sity persists without: frequency dependence within groups, migration,
balancing selection, genetic linkages, overdominance, antagonistic pleio-
tropy or nonrandom allele assortment. Social heterosis may also offer an
alternative evolutionary pathway to cooperation that does not require
clustering of related individuals, nepotistic favouritism towards kin, or overt
reciprocity.
doi:10.1111/j.1420-9101.2007.01418.x
have equal mean fitness. Populational epistasis can also
maintain diversity within and among populations by the
creation of multiple adaptive peaks through the fitness
effects of interacting traits (Brodie, 1992, 2000; Phillips
et al., 2000).
different selective pressures can keep alleles from becom-
ing fixed in any population (Sih et al., 2004; Hedrick,
2005). Varying environmental conditions can also main-
tain genetic variation by favouring different alleles at
different times (Turelli & Barton, 2004; Roff & Fairbairn,
2007).
genetic diversity. It is not our intention to rate their
importance, except to emphasize that no single mecha-
nism explains the considerable amount of the genetic
diversity observed in nature. Our goal is to introduce the
concept of ‘social heterosis’ as an additional mechanism
for the maintenance of genetic diversity. Social heterosis
maintains genetic diversity through a mutualistically
advantageous expression of multiple alleles at a single
locus across interacting individuals (i.e. the simultaneous
expression of as many as 2n alleles for a single trait,
where n is the group or neighbourhood size). Fitness
benefits of genetic diversity accrue at the individual and
group levels. Individuals in genetically heterogeneous
groups are predicted to have higher reproductive rates
than those in homogeneous groups. Diverse groups
would experience more beneficial collective properties
than would arise within homogenous groups. These
benefits can surface as synergisms of genetic diversity,
per se, and not specific to particular allele combinations.
Mechanisms for individual-level fitness benefits
Social heterosis can arise in several ways when genetic
differences produce behavioural or morphological differ-
ences. More diverse groups may exploit a wider range of
resources in ways that produce character displacement
and reduce intragroup competition. Relevant examples
include brook charr (Salvelinus fontinalis) having a
genetically based, trophic polymorphism, where individ-
uals specialize in feeding in the littoral or pelagic zones
(Bourke et al., 1997; Sacotte & Magnan, 2006), and
colour polymorphisms in birds being more likely to be
found in species with wider niche breadths (Galeotti &
Rubolini, 2004). If differences in behaviour or colour-
ation reduce niche overlap due to specialized feeding
strategies, the neighbourhood and individual-level fit-
ness benefits gained from reduced competition could
maintain trait variation through social heterosis. A
review of individual specialization across a broad range
of taxa found 93 species with intrapopulation individual
specialization on resources, with at least 16 known to
have a genetic basis (Bolnick et al., 2003).
Mechanisms for group-level fitness benefits
Social heterosis may be particularly important when the
optimal phenotype cannot be expressed by any single
individual. No one individual can be simultaneously tall
and short, bold and shy or fast and slow. Yet within each
set of dichotomous traits, each character state may have
its own unique advantages. Thus, a group of individuals
that display a range of capabilities can create a common
skill pool that far surpasses the abilities of any one
individual (Giraldeau, 1984). Another significant advan-
tage of genetic diversity within a group is increased
parasite and disease resistance (Schmid-Hempel & Cro-
zier, 1999). If we think of interacting individuals as
superorganisms (Oster & Wilson, 1978; Wilson & Sober,
1989), then their relative immune function would result
from the collective properties of each individual’s para-
site resistance capabilities.
pools and enhanced parasite resistance, are benefits that
are more likely to accrue in genetically diverse popula-
tions. We propose that social heterosis can maintain this
diversity in the face of directional selection and genetic
drift. To validate this concept, we present a model
demonstrating the conditions under which social hetero-
sis can operate.
Methods
The basic premise of social heterosis is that alleles (A and
B) have higher fitness in the presence of individuals
carrying different alleles than with individuals having
like alleles (i.e. WA(B) > WA(A) and WB(A) > WB(B)). In our
examples, the relative fitness of allele A never exceeds
that of allele B, either when comparing across pure
groups or within mixed groups. Thus, WB(B) ‡ WA(A) and
WB(A) ‡ WA(B). Under these conditions, we examine two
questions: (1) when can A possibly invade a population
fixed for B; and (2) how effectively can social heterosis
maintain genetic diversity in the face of directional
selection and genetic drift? Our model assumes haploid
reproduction, such that alleles A and B produce individ-
uals and offspring with phenotypes A and B respectively.
Overdominance within individuals is not possible. Our
model also addresses the simplest case where reproduc-
tive success of groups is determined by the number of
alleles present and not by their frequency or identity. We
do not consider opportunities for coadaptation between
alleles, which has been modelled in other studies (see
Wolf & Brodie, 1998). There is no selective benefit for
any particular pair of alleles to co-occur in the same
group. We examine social heterosis only at a single locus
in our model, but evolutionarily it is possible that the
process could be acting at multiple loci simultaneously.
In a population fixed for allele B, allele A can
potentially invade whenever its average fitness is greater
( WA > WB). If social heterosis benefits B more than A
2254 P. NONACS AND K. M. KAPHEIM
ª 2 0 0 7 T H E A U T H O R S . J . E V O L . B I O L . 2 0 ( 2 0 0 7 ) 2 2 5 3 – 2 2 6 5
J O U R N A L C O M P I L A T I O N ª 2 0 0 7 E U R O P E A N S O C I E T Y F O R E V O L U T I O N A R Y B I O L O G Y
(WB(A) > WA(B)), then A can only invade in populations
that are subdivided into groups with varying allele
frequencies to form structured demes (Wilson, 1980).
Allele A will always decrease within all mixed groups.
The fitness of a rare, mutant allele A would exceed the
mean fitness of allele B, when:
WAðBÞ > ½ðN 1Þn WBðBÞ þ ðn 1ÞWBðAÞ=ðNn 1Þ;
where n is the size of the group or neighbourhood that
experiences the benefit of social heterosis and N is the
number of such groupings in a panmictic population. As
Nfi¥, the minimum benefit required through social
heterosis for A to invade declines such that WA(B)fiWB(B).
By contrast, the social heterosis benefit to A must
increase as group size (n) increases. Thus, with the
minimum number of possible groups (N ¼ 2), as nfi¥,
WA(B)fi(WB(B)+WB(A))/2. This latter invasion criterion is
based on the assumption that having one A individual
allows all B individuals to gain equally through social
heterosis. This is plausible in small groups, but as group
size gets larger the positive effect of A on B might be
diluted across all Bs. This would create within-group
frequency dependence where gains through social het-
erosis would depend both on the number of different
alleles present and their proportional representation.
Although within-group frequency dependence is biologi-
cally realistic, we ignore it in our analysis to demonstrate
that social heterosis is possible in the absence of any such
benefits. This is a conservative assumption relative to
exploring social heterosis effects. Adding within-group
frequency dependence would make invasion by A more
likely.
subdivided population whenever WA(B) > (WB(B)+WB(A))/
2 and despite B having higher fitness than A in mixed
groups (WB(A) > WA(B)), in homogeneous groups (WB(B)
> WA(B)) and alone (WB > WA). In a stochastic world,
however, alleles can be lost through genetic drift and
other nonselective processes even if they have higher
relative fitness (Orr, 2000). Thus, to understand the effect
of social heterosis on selection for genetic diversity, we
need to understand how it can prevent allele loss
through drift.
To do so, we constructed a simple haploid model to
track allelic diversity in a population. A population is
defined as consisting of N groups, each composed of n
individuals. In the first generation, multiple alleles (i ¼ 2–10) are present in equal frequency. If all members of a
group are of the same allele type (or individuals are
alone), the given fitness of alleles is W1 ¼ 1 and for all
other alleles Wi ¼ fs, with fs £ 1. This defines allele 1 as
always having the highest relative fitness. Social heter-
osis is expressed when an allele’s fitness is higher in the
presence of other alleles. Thus for allele 1, W1(a) ¼ 1+y(az)1), where y is a constant for the proportional
increment in fitness as allele diversity in the group
increases (y ¼ 0.05–0.5). A linear effect (z ¼ 1) from the
number of alleles (a) present in the group means that
each increase in genetic diversity adds the same propor-
tional benefit. Thus, the benefits of diversity behave
similarly to additive genetic variance. If z < 1, then
genetic diversity has diminishing fitness returns. If z > 1,
then genetic diversity has increasing fitness returns,
which mimics nonadditive genetic variance. The fitnesses
of all other alleles in genetically diverse groups are
relative to the ‘best’ allele, such that Wi(a) ¼ fdW1(a), with
fd £ 1. Therefore, without social heterosis, directional
selection drives the population towards fixation of allele
1, whenever fs or fd < 1.
In this model, pure genetic drift in the absence of
selection occurs when fs ¼ fd ¼ 1 and y ¼ 0. These
stochastic processes are also present in populations under
selection (Orr, 2000). Therefore, we quantify the effects
of social heterosis relative to the rate at which a given
population is expected to lose genetic diversity through
drift. The dynamics of social heterosis are determined by
varying: group size (n), population size (N), number of
alleles initially present in the population (i), the relative
fitness of alleles (fs and fd), and the magnitude of benefit
from social heterosis (y and z).
Starting populations were simulated across 1000 gen-
erations, with 1000–10 000 replicates of each set of
starting conditions. In each generation of our model, the
population was filled by randomly drawing alleles from a
distribution reflecting the proportional representation of
each allele after reproduction in the previous generation.
Thus, groups were created through random assortment,
which negates any effect of kin structure in this model
(Pepper, 2000) and creates a population where the
average relatedness between group members is zero.
Individuals within groups were allowed to ‘reproduce’
relative to their expected fitness as defined by the values
of fs, fd, a, y and z. All the offspring were combined in a
common pool and the next generation’s population was
again randomly drawn from this pool of surviving alleles.
This methodology replicates a design by Wade (1976,
1977) used in his classic experiments with Tribolium to
measure group-level selection for increased reproductive
productivity.
Results
Social heterosis can maintain allelic diversity under a
wide range of conditions. We start with a base case in
which allele 1 has the highest fitness in all groups (fs ¼ fd ¼ 0.95, with i ¼ 3 alleles), population and group sizes
are small (N ¼ 30 groups, with n ¼ 4 for each group),
and the benefits of heterosis are modest (y ¼ 0.1; z ¼ 1).
With these conditions, allelic diversity declines similarly
to genetic drift (Fig. 1a–c). Social heterosis strongly
counters genetic drift when either the benefits of social
heterosis increase in magnitude (Fig. 1a), additional
allelic diversity has a nonlinear positive increase
(Table 1) or the relative fitness of nonoptimal alleles in
Social heterosis 2255
ª 2 0 0 7 T H E A U T H O R S . J . E V O L . B I O L . 2 0 ( 2 0 0 7 ) 2 2 5 3 – 2 2 6 5
J O U R N A L C O M P I L A T I O N ª 2 0 0 7 E U R O P E A N S O C I E T Y F O R E V O L U T I O N A R Y B I O L O G Y
heterogeneous groups (fd) increases (Fig. 1b). Genetic
drift becomes weaker as population size (N) increases.
Thus, higher levels of allelic diversity are maintained as
social heterosis more effectively counteracts drift
(Fig. 1c). The strength of social heterosis is moderately
affected by changes in the relative fitness of alleles when
alone or in homogeneous groups (fs) and by changes in
the number of alleles (i) initially present (Table 1). If we
assume all alleles have equal fitness within genetically
diverse groups, then even small benefits from social
heterosis can counteract genetic drift and maintain high
allelic diversity (Fig. 1d).
The effect of group size on social heterosis is more
complex (Fig. 2). Allelic diversity (when starting with
i ¼ 6) is best maintained with group sizes of three to six
individuals, and the group size in which social heterosis is
most powerful increases as the benefits become larger or
positively nonlinear. These results follow from the
constraints that small groups cannot attain high allelic
diversity with only a few group members (maximum
a < i). By contrast, larger groups will tend to have low
across-group variance in allelic diversity when they are
formed randomly across each generation. This increases
the relative effects of within-group selection, because the
effects of social heterosis will be similar across groups.
Discussion
population genetic diversity is maintained in the face of
many well-documented processes that reduce it (Barton
& Turelli, 1989; Turelli & Barton, 2004). Allele loss can
result from selection that directly increases individual
survival, allele survival (meiotic drive), the reproductive
success of genetic kin or sexual selection that increases
mating success. Also, demographic processes (e.g. popu-
lation bottlenecks and genetic drift) can decrease genetic
diversity (Amos & Harwood, 1998; Fay & Wu, 2000). Yet,
a surprising number of traits retain high allelic diversity
(Barton & Turelli, 1989; Roff & Fairbairn, 2007).
M ea
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
1.0
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
3.0
0 200 400 600 800 1000 0 200 400 600 800 1000
0 200 400 600 800 1000 0 200 400 600 800 1000
Generations Generations
Generations Generations
M ea
(a) (b)
(c) (d)
Fig. 1 Social heterosis vs. genetic drift and the loss of allelic diversity over time. In all panels, genetic drift of neutral alleles (with y ¼ 0 and
fs ¼ fd ¼ 1) is given by the heavy lines, whereas social heterosis is shown by the thin lines (with fs ¼ fd ¼ 0.95, y ¼ 0.1, z ¼ 1, n ¼ 4, N ¼ 30,
and three alleles at equal frequency in generation 0 in all panels, unless otherwise noted). In A, the benefit of genetic diversity (y) is varied from
0.1 to 0.5 per added allele in groups. In B, the proportional fitness of suboptimal alleles within groups relative to best allele (fd) is varied from
0.5 to 1. In C, the number of groups (N) is varied from 30 to 240. In D, the population starts with 10 alleles at equal frequency and with fd ¼ 1,
and y is varied from 0.1 to 0.5.
2256 P. NONACS AND K. M. KAPHEIM
ª 2 0 0 7 T H E A U T H O R S . J . E V O L . B I O L . 2 0 ( 2 0 0 7 ) 2 2 5 3 – 2 2 6 5
J O U R N A L C O M P I L A T I O N ª 2 0 0 7 E U R O P E A N S…