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TRENDS in Ecology and Evolution
Vol.20 No.7 July 2005
‘Haldane’s Sieve’ in a metapopulation:
sifting through plant reproductive
polymorphisms
John R. Pannell1, Marcel E. Dorken1 and Sarah M. Eppley1,2
1
2
Department of Plant Sciences, University of Oxford, South Parks Road, Oxford, UK, OX1 3RB
Current address: Department of Biological Sciences, Victoria University of Wellington, PO Box 600, Wellington, New Zealand
An important result of population genetics is that
advantageous mutations will be fixed by selection in a
population with a greater probability if they are
dominant rather than recessive. This selective filter on
new variants entering a population, termed ‘Haldane’s
Sieve’, has hitherto been invoked to account for the
greater role of dominant than completely recessive
mutations in adaptive evolution. Here, we suggest that
a process similar to Haldane’s Sieve will act on migrants
into subpopulations of a metapopulation, and that the
repeated action of Haldane’s Sieve on alleles maintained
by frequency-dependent selection, such as those
responsible for many plant reproductive polymorphisms, is expected to bias their frequency distribution in
favour of dominant alleles. The genetic and phenotypic
signatures left by these processes might provide
additional indirect support for the contentious idea
that metapopulation dynamics have had an important
role in shaping the ecology and evolution of some plant
species.
Evolutionary models of a wide range of life-history,
mating-system and behavioural phenomena in plants
and animals are often expressed solely in terms of the
phenotypes involved without regard to the underlying
genetic mechanisms. Although such models ignore all
genetic details, they often agree with their genetically
explicit counterparts about the expected trait composition
of populations at equilibrium ([1], but see [2]). Unlike
genetic models, however, phenotypic models are generally
unable to predict the details of evolutionary trajectories.
For instance, it is well known that the trajectory
describing the expected increase in frequency of an
advantageous mutation depends on whether the new
allele is recessive or dominant. In particular, because
variants occur almost exclusively in heterozygotes when
they are rare, recessive advantageous alleles will be
effectively neutral and thus easily lost by drift until they
become common, whereas dominant or co-dominant
alleles will be immediately selected. This idea is the
basis of an old but still remarkable result of population
genetics, attributable to J.B.S. Haldane [3], that
Corresponding author: Pannell, J.R. ([email protected]).
Available online 17 May 2005
advantageous mutations will be swept to fixation when
they first arise in an outcrossing species with a probability
equal to twice the selective advantage they confer
multiplied by their dominance coefficient. The expected
fixation bias in favour of dominant over recessive
advantageous mutations has been called ‘Haldane’s
Sieve’ [4]. It exemplifies the kind of prediction that cannot
be made by evolutionary models coined solely in phenotypic terms.
Haldane’s Sieve has been invoked to account for a range
of observations from the prominence of derived dominant
alleles for the melanic forms of several insect species [5],
through dominant expression of alleles coding for derived
wing patterns in Müllerian mimics [4], to the dominance of
alleles for pesticide resistance [6]. In these and other
examples, Haldane’s Sieve provides a possible explanation
for the observed genetic basis of adaptation in terms of the
fixation of dominant versus recessive mutations. Here, we
propose that a process similar to Haldane’s Sieve should
act repeatedly on dominant versus recessive alleles
following migration into populations of geographically
subdivided species. In particular, when the allelic variation is maintained in a metapopulation by negative
frequency-dependent selection, Haldane’s Sieve will be an
on-going process that should alter the frequency distribution of alleles at the selected locus, and thus the
corresponding phenotypes, in a predictable way. A great
many species have genetically subdivided populations
that can be influenced by metapopulation dynamics, and
several processes such as mimicry and disassortative
mating are known to give rise to negative frequencydependent selection (Box 1).
We first describe the process of Haldane’s Sieve in a
metapopulation in terms of overlapping evolutionary
trajectories within local populations that are prevented
from reaching equilibrium by recurrent population turnover. We then highlight the potential for studying this
phenomenon in subdivided plant populations that display
reproductive or mating polymorphisms maintained by
negative frequency-dependent selection as a result of
disassortative mating; such systems continue to offer
outstanding material for addressing a broad range of
evolutionary questions. Finally, we note that the effect of
Haldane’s Sieve in a metapopulation should depend on the
size and dynamics of the populations concerned, and that
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TRENDS in Ecology and Evolution
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375
Box 1. Negative frequency-dependent selection and plant reproductive polymorphisms
Under negative frequency-dependent selection (FDS), rare phenotypes have higher fitness than do more common ones, with the
implication that polymorphism is protected from loss through drift
and that underlying genetic variation can be maintained for long
periods of evolutionary time [39]. A particularly well understood
mechanism of negative FDS is disassortative mating, where mating
unions are more common between different mating phenotypes and
rare phenotypes enjoy high fitness through their access to a greater
number of compatible mating partners (e.g. [40,41]). We list here a
diverse range of polymorphisms maintained by negative FDS through
disassortative mating in plants. These are typically a result of the
expression of major genes with dominant-recessive relations.
† Androdioecy: the co-occurrence of hermaphrodites and males.
Although rare, androdioecy has evolved several times independently
in plants and animals [25]. Maleness is governed by a dominant allele
in several plant species (e.g. [42]) and by a recessive allele in several
interrelated species of crustaceans (e.g. [43]).
† Dioecy: the co-occurrence of males and females. Dioecy has multiple
evolutionary origins and occurs in 157 (43%) angiosperm families [44].
Its genetic basis varies, but males commonly carry a dominant allele
conferring maleness [45].
† Distyly: the co-occurrence of two classes of hermaphrodite, ‘pins’
and ‘thrums’, that differ in their stigma and anther positions. Pins have
long styles and anthers held low in the floral tube, whereas thrums
have short styles and high-placed anthers. Distyly has multiple
evolutionary origins and is known in 22 families. Short-styled plants
usually result from expression of a dominant allele [46].
† Enantiostyly: the co-occurrence of hermaphrodites with either
‘right-handed’ or ‘left-handed’ flowers, in which the style and anthers
are held to one or other side of the flower, with reciprocal placement of
floral parts in the two different morphs. Dimorphic enantiostyly is
reported in three plant families [47]. In one species, right-styled plants
are heterozygous for the dominant allele [48].
† Flexistyly: the co-occurrence of two classes of hermaphrodites that
differ in the direction of movement that styles undergo during
flowering. In one morph, styles begin in an upward position and
move downward, whereas the movement is in the opposite direction
in the other morph. Anthers are held in the same position throughout,
but shed pollen only when styles are in the ‘up’ position, promoting
disassortative mating between floral morphs. Flexistyly was discovered only recently and is known in only a single family [49].
† Flower colour polymorphism: the co-occurrence of plants with
different coloured flowers in a population. In at least one case [50], the
polymorphism appears to be maintained by negative FDS.
a distinct process of drift will oppose it when local
populations are small. This balance between the forces of
drift, migration and selection can account for observed
phenotype frequencies that deviate from those expected in
a single large population at equilibrium. We also suggest
that the effect of processes such as Haldane’s Sieve and the
interaction among drift, migration and selection might
help to establish the extent to which metapopulation
dynamic processes have been important in the evolution
and ecology of plants.
Haldane’s Sieve in a subdivided population
Analyses predicting the action of Haldane’s Sieve usually
consider the fate of new recessive versus non-recessive
variants as they arise in a population through mutation
(although see [7]). However, a similar process should occur
when advantageous alleles invade a population via
immigration. If the population is large and mating is
random, all the early descendants of immigrants that
carry an advantageous allele will be heterozygous. Those
alleles that are recessive will remain unexpressed while in
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† Gametophytic self-incompatibility (GSI): a genetic polymorphism in
which hermaphrodites are prevented both from self-fertilising their
own ovules and from crossing with hermaphrodites that share the
same diploid genotype at the self-incompatibility (SI) locus. Mating
thus occurs only between plants that do not share both incompatibility
alleles [51]. GSI is widespread among flowering plants and is common
in several large families [52].
† Gynodioecy: the co-occurrence of hermaphrodites and females.
Gynodioecy is taxonomically widespread in flowering plants, occurring in at least 35 plant families [53]. It commonly results from the
expression of genes in the mitochondrion, but simple dominantrecessive relations are typical when governed by nuclear loci.
† Heterodichogamy: the co-occurrence of two classes of hermaphrodite, a protandrous class that flowers first as male and a protogynous
class that flowers first as female. Heterodichogamy has a widespread
taxonomic distribution, occurring in 11 families of flowering plants
[54]. In two species, a dominant allele gives rise to protogynous
individuals (reviewed in [54]).
† Sporophytic self-incompatibility (SSI): SSI is similar to GSI in that it
prevents self-fertilization and outcrossing with individuals with the
same diploid genotype at the SI locus. However, it differs in that it
can also prevent mating between individuals that share just one of
the two alleles at the SI locus. If the SI alleles contained by a
mating pair of individuals have co-dominant expression, mating is
possible only if all four alleles are unique [51]. However, unlike
GSI, gene expression of SI alleles can be dominant or recessive.
SSI has evolved on several occasions in flowering plants and is
common in several large families [52].
† Stigma-height dimorphism: the co-occurrence of two classes of
hermaphrodites, one with long styles and one with short styles.
The dimorphism is analogous to distyly, except that all individuals
share a similar anther position. Stigma-height dimorphism has
evolved independently in several angiosperm families [47]. The
inheritance of style length is analogous to that found in distyly,
with a dominant allele for short styles, and long-styled plants
modified into plants with mid-styles by a dominant allele at a
second locus [55].
† Tristyly: the co-occurrence of short-styled, mid-styled and longstyled hermaphrodites, with the reciprocal placement of two levels of
anthers at the position not occupied by the stigma (cf. distyly, which
has only two morphs). Tristyly is reported from six families. The
inheritance of short styles under tristyly is typically the same as that
under distyly, with a dominant allele at a second locus modifying longstyled plants to those with mid-length styles [46].
the heterozygous state, rendering them prone to early loss
as a result of drift. By contrast, dominant alleles will be
expressed in all progeny and will thus be better protected
against random loss by positive selection. As a consequence, dominant alleles should diffuse more readily
through a subdivided metapopulation than should recessive alleles. This effect of Haldane’s Sieve was termed
‘dominance drive’ by Mallet [8], who modelled the
maintenance of dominant versus recessive wing-colour
variants in a hybrid zone between Müllerian butterfly
mimics. Mallet [8] found that ‘[e]ven if the two phenotypes
are equally fit ‘dominance drive’ tends to increase the area
in which the dominant allele is present.’
We expect a particularly interesting scenario to arise
when a polymorphism is maintained by negative frequency-dependent selection in a subdivided population or
metapopulation. In this case, Haldane’s Sieve will be an
ongoing process that acts indefinitely on standing genetic
variation during its repeated introduction into subpopulations through migrations (Figure 1). The outcome of this
process is likely to be complicated because the advantage
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0.8
Recessive allele
Allele frequency
0.6
1 2
3
0.4
Dominant allele
0.2
0.0
Time
TRENDS in Ecology & Evolution
Figure 1. The action of Haldane’s Sieve on migrant alleles in a large population. The
curves show expected frequency trajectories of dominant versus recessive alleles
under negative frequency-dependent selection following their migration into a
population. Alleles migrate into the population at time point 1. The rate of increase
in frequency is slower for a recessive allele than for a dominant one. Therefore, it
takes longer for a recessive allele to get close to its equilibrium frequency (time
point 3) than it does for a dominant one (time point 2). Shading corresponds to an
elevated risk of allele loss because of drift in small populations: while the frequency
of the migrant allele remains low, it runs a high risk of stochastic loss through drift
(dark shading). Although Haldane’s Sieve favours dominant migrant alleles
because they more quickly rise to higher frequency in the population, they are
maintained at a lower frequency and are more likely to be lost through drift in small
populations than are recessive alleles (light shading). This is because frequencydependent selection acts on phenotypes rather than on the alleles themselves.
There will therefore be more recessive alleles segregating in a population at
equilibrium than dominant ones because all recessive alleles in heterozygotes are
not expressed as well as because individuals with phenotypes with recessive
expression carry two recessive alleles whereas those with phenotypes with
dominant expression might carry only one. In small populations, Haldane’s Sieve
will also be less effective because inbreeding increases the frequency of
homozygotes.
conferred upon dominant alleles by Haldane’s Sieve will
be opposed by the tendency of recessive alleles to be
maintained at higher frequencies in a population at
equilibrium and thus to be better protected from loss by
drift than dominant alleles. We suggest that this interaction between selection, drift, migration and gene
expression can be illuminated by its potential effect on
the maintenance of plant reproductive polymorphisms in a
metapopulation. Although the prevalence of metapopulation dynamics in plants is still hotly debated (Box 2),
variation in the frequency of mating-system phenotypes of
several plant species suggests that metapopulation processes might have been important in their past.
Haldane’s Sieve and plant reproductive polymorphisms
Plants are famously diverse in their reproductive strategies [9]. Not only do they display a broad range of floral
forms across species, but they also present numerous
examples of floral or reproductive polymorphisms maintained within single populations by negative frequencydependent selection (Box 1). The functional significance of
these polymorphisms has attracted the attention of many
evolutionary biologists, including Darwin [10], Haldane
[11], Wright [12] and Fisher [13]. One of the attractive
features of plant reproductive polymorphisms for evolutionary study is the relative ease with which models
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Vol.20 No.7 July 2005
predicting the proportions of the different mating types in
a population can be tested. This is because the models are
simple, in that they deal with the predictable tendency of
phenotypes to mate disassortatively (i.e. like phenotypes
avoid mating), and because the frequencies of the different
mating types can usually be estimated easily in natural
populations by counting phenotypes.
Plant reproductive polymorphisms continue to be
widely adopted as models for the study of various aspects
of evolutionary biology, including the evolution of sexual
systems [14], plant-pollinator interactions [15], plantherbivore interactions [16], sex allocation [17], speciation
[18], sexual dimorphism and sexual selection [19], the
maintenance of genetic diversity [20], vestigialization
[21], and the evolution of sex and recombination [22].
They can also provide fertile material in which to look for
signatures of population structure and possible metapopulation dynamics. This is perhaps best exemplified by the
interaction between maternally inherited male-sterility
genes and nuclear genes that restore male fertility in
gynodioecious species, where females co-exist with hermaphrodites (reviewed in [23]). Here, the high variation in
sex ratio between populations is most probably a result of
colonization by genotypes with mismatched sterility and
restorer genes, giving rise to high female frequencies, and
the subsequent migration and local spread of complementary fertility restorer alleles that allow hermaphrodite
frequencies to increase (e.g. [24]).
Metapopulation processes should also affect the distribution of mating phenotypes determined by alleles at
nuclear loci with simple dominant-recessive expression
patterns, and this can be understood in terms of the
recurrent action of Haldane’s Sieve. In androdioecious
species, for example, where males co-occur with hermaphrodites [25], males are maintained at frequencies lower
than 0.5 by frequency-dependent selection if hermaphrodites sire any progeny through their male function [26]. In
a metapopulation, the repeated episodes of colonization
will tend to select against males and favour hermaphrodites that are capable of founding new populations
by self-fertilization, thereby reducing the frequency of
males still further [27,28]. If alleles determining
unisexuality are rare in the metapopulation, colonization of a new habitat by one or more hermaphrodites
will usually give rise to a purely hermaphroditic
population. In the absence of males, these populations
will be relatively female-biased in their sex allocation,
and rare males would enjoy a fitness advantage
through the large numbers of their potential mating
partners. Dominant male-determining (female-sterility)
alleles, therefore, should easily invade hermaphroditic
populations because they will immediately experience
the positive effects of negative frequency-dependent
selection on the sex allocation. By contrast, hermaphroditic populations will be relatively protected against
the local spread of recessive male-determining alleles
as a result of Haldane’s Sieve. Thus, dominant sterility
alleles should be more likely to persist in a metapopulation when they are at low frequency than would
those that are recessive [28].
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Box 2. Do plant metapopulations exist?
A metapopulation is a regional group of populations that is maintained
in a balance between local population extinctions and re-colonizations
[56]. The concept has been extremely influential in the study of animal
populations, but its utility for understanding the abundance and
distribution of plants has been disputed and is still unresolved [57–61].
From a practical point of view, several peculiarities of plant life history
and growth form make it difficult to estimate extinction and colonization
rates, or even to identify habitat patches. From a conceptual perspective,
the issue of plant metapopulations concerns whether the regional
patterns of occupancy and abundance of a plant species can be
adequately explained by extrapolating up from the local processes of
birth and death, or whether distinctly regional processes such as
migration, colonization and local extinction need to be invoked to
account for what we observe [58,62].
respond to gradients in environmental variables such that habitat
quality is better characterized as a multidimensional vector on a
continuum rather than as a binary ‘good’–‘bad’ variable [61]. This also
means that the distinction between new colonizations and recolonizations is blurred.
These practical difficulties will be difficult to resolve until models
that deal with the peculiarities of plants more explicitly can be applied
to data. Thus, Bullock et al. [57] recently concluded that it was still ‘too
early to determine whether true plant metapopulations exist.’ Nonetheless, a few species, such as aquatic herbs, that do not present major
difficulties associated with seed banks and habitat identification
provide relatively uncontroversial examples of plant metapopulations
(reviewed in [58]).
Conceptual issues
Practical issues
Many plants have a dormant seed bank The utility of metapopulation
theory depends largely on the extent to which rates of extinction and
colonization can be estimated. In species with a seed bank, estimating
these values can be difficult because habitat occupancy becomes
difficult to assess. For example, it is not useful to consider the
disappearance of the cohort of adult plants from a site as an extinction
event if the species persists in a seed bank. Neither is it useful from a
metapopulation perspective to consider the re-establishment of adults
from a dormant seed bank as a form of temporal rather than spatial
colonization because ‘colonization’ from a seed bank involves local
processes only and does not require consideration of the regional
process of dispersal [62]. The incorporation of seed-bank dynamics
into metapopulation theory is not straightforward and will require the
consideration of time lags in the extinction process [63]; more work is
needed in this arena.
Habitat identification, and the distinction between colonization and
re-colonization The application of classical metapopulation theory to
empirical data also presupposes an ability to distinguish categorically
between suitable and unsuitable habitats [56]. In a great many plant
species, habitat characterization is difficult because plants tend to
Reproductive polymorphisms and the effect of drift in
small populations
We expect that Haldane’s Sieve will discriminate between
dominant and recessive alleles in the way we have
described as long as local populations grow rapidly to a
large size following colonization, but not when population
sizes remain small. There are essentially two reasons for
this. First, homozygosity will be increased by inbreeding
in small populations, so that advantageous recessive
alleles are immediately selected and Haldane’s Sieve is
therefore compromised [29]. Second, alleles maintained by
frequency-dependent selection (see Box 1) are always
vulnerable to stochastic loss from small populations
(Figure 1), but dominant alleles will be lost more often
in this case than recessive ones because their equilibrium
frequencies will be lower [30,31]. The effect of Haldane’s
Sieve will therefore not only be relaxed in metapopulations with small subpopulations, but it might also be
reversed (Figure 1).
The biased loss of dominant alleles through the process
of drift has been invoked to explain the observed variation
in the frequency of floral morphs in the tristylous annual
plant Eichhornia paniculata, in which mating occurs
between three morphs with different style lengths and
anther positions [32]. In large tristylous populations of
E. paniculata, disassortative mating between the three
stylar morphs gives rise to negative frequency-dependent
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The conceptual issue of how often metapopulation dynamics need to
be invoked to explain observations made at a regional level is unclear.
Ultimately, the answer will depend on the nature of the data. From the
point of view of genetic data, there is an increasing body of evidence
from plant populations for the importance of the regional process of
colonization (reviewed in [60]). Here, the practical problems of
identifying habitat patches are less of an issue; what matters are the
populations themselves as well as the interactions among genetic
processes, such as drift during colonization bottlenecks, directional or
frequency-dependent selection, and the homogenizing force of
migration among populations [60]. Such interactions can yield
different patterns in genetic data from those acting solely at a local
level. Indeed, regional surveys of a range of plant genetic markers and
discretely inherited phenotypic traits (e.g. the plant reproductive
systems reviewed here) indicate that the colonizations and extinctions
expected in metapopulations are likely to be occurring in plants
(reviewed in [60]). That such processes can leave a genetic signature
even in species for which ecological or demographic observations are
readily explained by predominantly local processes suggests that a
distinction between ‘genetic metapopulations’ and ‘ecological metapopulations’ might be useful [64].
selection that maintains each at equal frequencies of 1/3
[33]. However, the genetic mode of inheritance for tristyly
implies that the dominant allele, which causes expression
of a short-styled phenotype, is maintained at a frequency
of 1/6 compared with the higher frequency of 5/6 at which
its recessive homologue is maintained [32]. In a metapopulation made up of small subpopulations, the frequency
of the short-styled morph should thus be lower than its
equilibrium expectation because of its stochastic loss from
some populations [32]. This hypothesis could explain the
lower frequency of the short-styled morph of E. paniculata
in areas where populations are small [32] as well as the
more frequent loss of the short-styled morph from small
populations of tristylous Lythrum salicaria [34].
As in tristylous species, disassortative mating is also
responsible for the maintenance of the striking levels of
polymorphism commonly found in plant species at loci
governing molecular self-incompatibility systems
(e.g. [35]). Under sporophytic self-incompatibility (SSI),
S alleles are expected to be equally frequent in a
population when they are expressed co-dominantly [36].
However, self-incompatibility reactions in many species
are complicated by the fact that some S alleles show
dominant expression over others, in either the pollen and/
or the carpel [35,37]. Again, dominant alleles are more
likely to be lost from small populations by drift than those
with recessive expression [31,38]. This prediction that
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TRENDS in Ecology and Evolution
dominant alleles should be less frequent across the
metapopulation has found some empirical support in a
study of the frequencies of sporophytic self-incompatibility
alleles in Arabidopsis lyrata [37].
Conclusion: a balance between Haldane’s Sieve and drift
in small populations
The interaction between frequency-dependent selection,
genetic drift and gene expression is complex. However, we
suggest that some of the complexity arising from genetic
interactions in subdivided populations can be characterized by considering it in the context of two opposing forces.
On the one hand, Haldane’s Sieve should favour dominant
over recessive alleles when they migrate into large
populations. On the other hand, genetic drift within
small populations should cause the local loss of dominant
alleles more often than recessive ones. The latter effect
has often been invoked to account for the biased loss of
dominant alleles maintained by frequency-dependent
selection, with or without the added complexities of
population subdivision. However, it has been less widely
appreciated that this effect can be reversed by the
repeated action of Haldane’s Sieve acting on alleles
migrating into large subpopulations of a metapopulation.
The balance between these two opposing forces is
evident in the results of computer simulations of allelic
diversity maintained at an SSI locus in subdivided
populations [30]. These simulations show that dominant
alleles can be either more or less frequent than recessive
alleles depending on the level of migration between
subpopulations ([30] and Figure 2). SSI and the other
plant reproductive polymorphisms are idiosyncratic in
both the details of disassortative mating and the precise
mode of inheritance of alleles under frequency-dependent
0.30
Frequency of allele
0.25
0.20
0.15
0.10
0.05
0.00
Panmixis
co-dominance
Panmixis
dominance
Subdivision
dominance
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Figure 2. The expected frequency spectrum for six S alleles maintained in a
population with sporophytic self-incompatibility under contrasting scenarios of
population subdivision and gene expression. The first distribution assumes
panmixis and co-dominant gene expression in both pollen and carpel. The second
distribution assumes panmixis and dominant gene expression in carpel but not
pollen. The third distribution assumes the same pattern of gene expression as the
middle distribution, but also that the population is strongly subdivided with low
gene flow (NmZ0.01). In the middle and right-hand distributions, bars are ranked
for S alleles in increasing order of dominance. Under panmixis, recessive alleles are
maintained at a higher frequency than dominant or co-dominant ones (second
distribution), whereas this frequency hierarchy is altered substantially in a
subdivided population (third distribution). Data from [30].
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Vol.20 No.7 July 2005
selection. However, they illustrate a potentially widespread
phenomenon that deserves further modelling, particularly
for the situation where population sizes fluctuate in time or
are prone to local extinctions and re-colonizations. Plant
reproductive polymorphisms also present a diverse range of
independent systems within which to consider the old idea of
Haldane’s Sieve in a new context.
Finally, although it is widely accepted that metapopulation dynamics can be important in regulating the
abundance and distribution of animals, the extent to
which such processes occur in plants is still unclear. It
might therefore be profitable to explore the principle of
using reproductive-trait distributions as genetic signatures of such processes, as has been done with patterns of
neutral genetic diversity. In this context, further modelling will be needed to predict the outcome of specific
genetic and phenotypic interactions under different
metapopulation scenarios in terms of observable patterns
of variation among subpopulations. Equally important is
the need for more data describing these patterns.
Acknowledgements
We thank S.C.H. Barrett, M. Whitlock and an anonymous reviewer for
useful input, and we acknowledge grants from the NSF (USA) to S.M.E.
(grant INT 0202645), the NSERC (Canada) to M.E.D., and the NERC
(UK) to J.R.P. and M.E.D.
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