Download the evolution of dominance in sporophytic self

O R I G I NA L A RT I C L E
doi:10.1111/j.1558-5646.2009.00686.x
THE EVOLUTION OF DOMINANCE
IN SPOROPHYTIC SELF-INCOMPATIBILITY
SYSTEMS. II. MATE AVAILABILITY
AND RECOMBINATION
Daniel J. Schoen1,2 and Jeremiah W. Busch1,3
1
Department of Biology, McGill University, 1205 Avenue Docteur Penfield, Montreal Québec, H3A 1B1, Canada
2
E-mail: [email protected]
Received November 27, 2008
Accepted February 24, 2009
Sporophytic self-incompatibility (SSI) is a self-pollen recognition system that enforces outcrossing in plants. Recognition in SSI
systems is typically controlled by a complex locus (S-locus) with separate genes that determine pollen and stigma specificity.
Experimental studies show that S-alleles can be dominant, recessive, or codominant, and that the dominance level of a given
S-allele can depend upon whether pollen or stigma specificity is examined. Here and in the companion paper by Llaurens and
colleagues, the evolution of dominance in single-locus SSI is explored using numerical models and simulation. Particular attention
is directed at factors that can cause S-allele dominance to differ in pollen versus stigma. The effect of recombination between the
S-locus and modifier locus is also examined. The models predict that limitation in the number of compatible mates is required
for the evolution of S-allele dominance in the stigma but not in the pollen. Tight linkage between the S-locus and modifier
promotes the evolution of S-allele dominance hierarchies. Model results are interpreted with respect to published information
on the molecular basis of dominance in SSI systems, and reported S-allele dominance relationships in a variety of species. These
studies show that dominant S-alleles are more common in the pollen than in the stigma, a pattern that when interpreted in light
of model predictions, suggests that mate limitation may be relatively infrequent in natural populations with SSI.
KEY WORDS:
Plant mating systems, self-pollen recognition, mate limitation, frequency-dependent selection, population genetics.
Self-incompatibility (SI) is a key mechanism that prevents selffertilization in plants. In SI systems, the recognition of self pollen
is coded for by alleles segregating at the S-locus. In species with
the sporophytic mode of SI (SSI), the recognition phenotype (or
specificity) of the pollen and stigma is controlled by the diploid
genotype of the parent (de Nettancourt 2001), and thus dominance relationships among S-alleles may play an important role
in the determination of specificity. S-alleles can be codominant,
dominant, or recessive, and dominance level can depend upon
3Present
address: School of Biological Sciences, Washington State
University P.O. Box 644236, Pullman, WA 99164.
C
2099
the tissue (pollen or stigma) in which the S-allele is expressed
(Bateman 1954; Brennan et al. 2006). Among the taxa with SSI
that have been investigated, there is considerable interspecific
variation in numbers of dominant, recessive, and codominant Salleles (Hiscock and Tabah 2003).
Recent molecular level analyses of sporophytic selfincompatibility (SSI) in the Brassicaceae have revealed details
pertinent to the mechanism of S-allele dominance. For instance,
expression analyses of the Brassica rapa and Arabidopsis lyrata
pollen S-determinant gene, SCR, show that the 5 promoter sequences of recessive SCR alleles are inactivated by methylation
in the anther tapetum before initiation of transcription (Kusaba
C 2009 The Society for the Study of Evolution.
2009 The Author(s). Journal compilation Evolution 63-8: 2099–2113
D. J. S C H O E N A N D J. W. B U S C H
et al. 2002; Shiba et al. 2006). In the case of the stigma Sdeterminant gene, SRK, experiments using transgenic B. rapa
plants have shown that the SI phenotype of plants carrying the
SRK 28 transgene construct could be predicted based on a priori
knowledge of the dominance relationships among the S-locus
alleles in the experiment and the S28 transgene (Haytakeyama et al.
2001).
Apart from the question of how dominance evolves in SSI
systems, the evolution of dominance has been a topic of interest in its own right (Charlesworth 1979; Provine 1986; Orr
1991; Mayo and Bürger 1997; Otto and Bourguet 1999). Fisher
(1930) proposed that selection should favor modifier alleles that
cause heterozygous genotypes to more closely resemble wild-type
homozygotes. Wright (1929, 1934), however, pointed out that
the frequency of heterozygous genotypes is unlikely to be large
enough for selection to effectively increase the frequency of dominance modifiers. The now more widely accepted general theory
for the evolution of dominance is based on the notion of diminishing returns in the effects of wild-type copy number on enzyme
kinematics (Wright 1934; Kacser and Burns 1981). Nevertheless,
several recent investigations have shown that modifiers of dominance can invade a population when migration–selection balance
or negative frequency-dependent selection maintain a large number of alleles within populations (Otto and Bourguet 1999; Peischl
and Bürger 2008). Given that populations with SSI may harbor a
large number of S-alleles (Lawrence 2000), it seems plausible that
modifiers may play a role in the evolution of S-allele dominance.
Although there has been much theoretical work on the evolution and breakdown of SSI (e.g., Charlesworth 1988), the evolution of dominance in these systems has been little studied (although see Schierup et al. 1997; Billiard et al. 2007). The selective
forces that influence the evolution of S-allele interactions in SSI
systems likely include both ecological and genetic factors. Negative frequency-dependence of fitness has been suggested to play
a major role in determining the general evolutionary dynamics
of S-alleles (Wright 1939; Schierup et al. 1997). Under such a
selection regime, expression of only one of the two S-alleles of
the diploid genotype may be favored because it allows pollen
parents plants to fertilize larger numbers of individual S-locus
genotypes in the population. A parallel advantage to such unilateral S-allele expression may arise in the case of the seed parent, for
example when S-locus genotype diversity is limited in the population and/or pollinator activity is low, such that the availability of
compatible pollen limits seed production (Vekemans et al. 1998;
Billiard et al. 2007; Busch and Schoen 2008).
In this article we examine the evolution of dominance in SSI
systems by asking when associations between S-alleles and dominance modifier alleles are selected and lead to the evolution of
dominance hierarchies. We develop models for investigating the
joint change in frequency of S-alleles and dominance modifier
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alleles, and use them to investigate the selection of haplotypes
involving specific alleles at both the S and modified loci, with
emphasis on contrasting situations in which there is mate limitation arising because of low pollinator activity or low diversity
of S-alleles. This article complements the companion paper by
Llaurens et al. (2009), in which the main focus is the role of
genetic load on dominance evolution at the S-locus, and where
recombination between a dominance modifier and the S-locus is
not considered. The model predictions from the present work are
discussed within the context of published information pertaining
to the occurrence and number of levels of dominance of S-locus
expression in pollen and pistils in several plant species.
Methods
BASIC MODEL ASSUMPTIONS
The molecular genetic basis of S-allele dominance has been examined in detail only in the Brassicaceae, and so it is premature
to generalize about its control, although dominance hierarchies
of S-alleles have been found in other families with SSI (e.g.,
Kowyama et al. 1994; Brennan et al. 2006). It seems reasonable
to assume that position within the dominance hierarchy is determined either by the sequence of the S-allele itself, or by associated cis-regulatory factors. Given the assumption that dominance
relationships of S-alleles arise from the interactions between regulatory sequences and regulatory molecules, we have opted to
treat the problem using the tools of two-locus population genetics
theory in which a cis-regulatory factor (the modifier locus M in
our model) influences the dominance expression of the S-allele.
For example, a given S-allele, S i , would be recessive to another
allele, S j , if the cis-regulatory factor associated with S i leads to
suppression of S i (Kooter et al. 1999).
We assume a population of cosexual, diploid plants. The
stigma and pollen phenotypes of an individual bearing two different S-alleles are determined by the tissue-specific expression
of these alleles, which in turn depends upon the associated alleles
at the dominance modifier locus (Table 1). We examine the evolution of dominance modification in two basic situations—where
the modifier locus has its affect on: (1) the dominance relationships of S-alleles expressed in the pollen; or (2) the dominance
relationships of S-alleles expressed in the stigma. We restrict our
treatment to populations containing two alleles at the modifier
locus, a “wild-type” modifier allele and a “mutant” modifier that
alters the dominance rank of the associated S-allele. If the S-alleles
of an individual are each associated with the same modifier allele,
they are assumed to exhibit codominance (Table 1). Recombination between the S-locus and locus M is assumed to occur with
recombination fraction c.
As is the case in studies of the evolution of other characters that influence reproductive success (Morgan and Schoen
E VO L U T I O N O F D O M I NA N C E AT T H E S - L O C U S
S-locus phenotypes in the presence of polymorphism at
a dominance locus1 .
Table 1.
SiMk
Si
Si
SiSj
Si
SiMl
Si
Si
Sj
SiSj
SjMk
SiSj
Sj
Sj
Sj
SjMl
Si
SiSj
Sj
Sj
Modifier allele (allele M l ) causes dominance of
associated S-allele
SiMk
SiMl
SjMk
SjMl
1
SiMk
Si
Si
SiSj
Sj
SiMl
Si
Si
Si
SiSj
SjMk
SiSj
Si
Sj
Sj
INDIVIDUAL MATINGS, AND THE EFFECT OF
MUTANT DOMINANT MODIFIER ALLELES
Modifier allele (allele M l ) causes recessiveness of
associated S-allele
SiMk
SiMl
SjMk
SjMl
S-LOCUS PHENOTYPES, COMPATIBILITY OF
SjMl
Sj
SiSj
Sj
Sj
Parental gametes listed in top row and first column of each table.
Phenotypic expression (in boldface type).
1999), the investigation of selection of S-allele dominance modifiers requires explicit consideration of transmission genetics. The
numerical methods adopted for examining changes in S-locus
genotype frequencies are built upon those of Vekemans and colleagues (Schierup et al. 1997; Vekemans et al. 1998; Billiard et al.
2007)—i.e., after specifying initial S-locus genotype frequencies,
along with the pollen and stigma specificities, we calculated genotype frequencies in the next generation, taking into account the
current state of the population, the expected frequencies of compatible matings, and the progeny genotype proportions expected
from these matings. Two distinct types of selective regimes were
explored through numerical analysis of the resulting recurrence
equations. The first is where frequency-dependent selection operates only through the male (or pollen) component of mating
(FDS m ) (e.g., Wright 1939). This situation applies when pollinators are abundant in populations and stigmas receive pollen from
all compatible pollen parents in proportion to their prevalence in
the population. In this case, seed set is not limited by mate availability. The second selective regime is where frequency-dependent
selection operates through both male and female parental components of mating (FDS m/f ), termed “fecundity selection” (FS) by
Vekemans et al. (1998). This type of selection is expected to occur
in cases in which pollinators are sufficiently rare such that female
parents receive compatible pollen from only a limited number of
pollen parents—in the most extreme case (hereafter referred to as
“strict FS”), the fecundity of individual seed parent genotypes is
directly proportional to the frequency of compatible pollen parent
genotypes in the population.
Populations are assumed to contain n unique alleles at the S-locus.
Crosses between plants sharing the same S-allele specificities are
assumed to be incompatible, whereas crosses between plants not
sharing S-allele specificities are treated as compatible. The population is initially fixed for a single (wild-type) modifier allele
at locus M. Our principal focus is to ask when two dominance
classes of S-alleles can evolve in a population that at first contains only a single dominance class. Thus, the starting population
consists of individuals with S-alleles that are all codominant. We
proceed to ask when a rare mutant modifier allele that alters the
dominance state of S-alleles can increase in frequency in the population and lead to the evolution of an S-allele dominance hierarchy
(defined here as a stable association between particular S-alleles
and dominance modifier alleles).
Generalizing from Billiard et al. (2007), we let the variables
αik.jl and φik. jl represent the dominance level of haplotype S i M k
over haplotype S j M l in the pollen and pistil, respectively, where
αik. jl = 1 − α jl.ik and φik. jl = 1 − φ jl.ik . When S i M k is completely dominant over haplotype S j M l in the pollen, αik. jl = 1
and α jl.ik = 0, whereas when S i M k and S j M l are codominant
in the pollen, αik. jl = 0.5 and α jl.ik = 0.5—i.e., these variables
can be considered equivalent to the proportions of i-specific and
j-specific gene products deposited on the pollen coat by parents
with genotype S i M k /S j M l . Following further from Billiard et al.
(2007), we let Aik. jl and P ik. jl represent vectors, each of dimension n, that respectively store the pollen and pistil S-locus
phenotypes of the genotype S i M j /S k M l . For example, in the case
of the pollen phenotype vector, Aik. jl ≡ [x 1 ,. . ., x u , . . ., x n ], x u =
0 for u ∈{i, j}, x u = αik. jl = 1 for i = j, and x u = αik. jl and
xu = α jl.ik = 1 − αik. jl for i = j. In the case of the pistil phenotype vector P ik. jl , a parallel set of relationships holds to that
described for Aik. jl , except we substitute φik. jl for αik. jl . If we
consider paternal and maternal plant genotypes S i M k /S j M l and
T
S p X r /S q M s , when the product Aik. jl . Ppr.qs
= 0 (where superscript T denotes vector transposition), the cross is compatible,
T
whereas when Aik. jl . Ppr.qs
0, the cross is incompatible; in these
instances, the compatibility indicator variable C ik. jl: pr.qs takes on
values of 1 and 0, respectively.
NUMERICAL ITERATION OF GENOTYPE FREQUENCIES
Recursion equations for genotype frequencies follow the approach
developed by Billiard et al. (2007). The proportion of the population’s seed arising from crosses between paternal genotype
S i M k /S j M l and maternal genotype S p M r /S q M s depends upon the
type of frequency-dependent selection assumed to be operating
(Schierup et al. 1997; Vekemans et al. 1998; Billiard et al. 2007)
(Appendix).
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D. J. S C H O E N A N D J. W. B U S C H
We assume that generations are discrete and that population
size is infinite. The proportion of seeds produced by genotypes
S i M k /S j M l and S p X r /S q M s acting as paternal and maternal parents
is wik. jl: pr.qs + w pr.qs:ik. jl . The proportions of seed of each of
the different genotypes produced thus depends upon: (1) initial
genotype frequencies; (2) the fitness wik. jl: pr.qs and w pr.qs:ik. jl ;
and (3) and the recombination fraction, c, for loci S and M. In
view of studies showing that recombination in the S-locus region
is low, and because upstream binding sites for transcription factors
and enhancers that could play a role in dominance expression
of S-locus products are likely to be located nearby the S-locus,
we restricted most of our analyses to a fairly narrow range of
recombination fractions (0 < c ≤ 0.01).
To investigate the evolution of dominance interactions, the
mutant modifier allele was introduced at a frequency of 10−4
into populations in which genotypes heterozygous for different
S-alleles were initially equally frequent (i.e., the expected equilibrium genotype configuration in populations with codominant
S-alleles). The mutant modifier was introduced in association with
the S 1 allele (in the S 1 S 2 genotype), and genotype frequencies in
each generation were calculated iteratively until the population
reached equilibrium. Dependency of the results on initial starting genotype frequencies was examined by starting from 1000
different random frequencies of S-locus heterozygote frequencies. Because of limited computing resources and the fact that run
times increased geometrically with increasing number of S-alleles
analyzed, this latter check was carried out only for numerical iterations in populations with n = 4 and 8 S-alleles.
THE EFFECT OF VARYING THE STRENGTH OF
FECUNDITY SELECTION
Strict FS, as studied using the numerical methods described above,
is equivalent to the case in which a single pollen parent genotype
per seed parent is drawn at random from the population in proportion to its frequency in the population, and where no seed is
produced if the S-locus genotype of the pollen parent is incompatible with that of the seed parent. Weaker FS may also occur
in nature; that is when the number of pollen parent genotypes
per seed parent is > 1 but still limited in number, as may occur
due to low levels of pollinator activity and low allele diversity.
Although the numerical approach is straightforward in the case
of strict FS, it becomes cumbersome for the analysis of weaker
FS. Thus, weaker FS was explored using stochastic simulations
of mating.
In implementing these simulations, we assumed a diploid,
hermaphroditic population of size N = 10,000 individuals. At the
start of each generation, female and male parents were selected
at random with replacement from the population, each with probability 1/N. If the mating was compatible, the zygote genotype
was formed by fusion of randomly selected gametes from both
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parents. If the mating was incompatible, a new male parent was
drawn at random. To investigate the strength of FS as a parameter
in the simulation, the number of times that an incompatible pollen
parent genotype could be drawn from the population before rejecting the seed parent (denoted “NP” below) was varied. If a
seed parent was rejected due to lack of a compatible pollen parent, we repeated the steps of drawing the seed parent, followed
by drawing pollen parents. The entire process was repeated N
times, and each simulation trial was run for 50,000 generations,
by which time allele frequencies had achieved quasi-equilibrium.
The fate of the mutant modifier was studied introducing it into
populations fixed for the wild-type modifier. As we were primarily
interested in the effect of varying FS on the strength of selection
of associations of S-alleles and dominance modifiers (rather than
the interaction of selection and drift), the mutant modifier allele
was introduced at a relatively high frequency (10−2 ) to counteract
frequent stochastic loss by drift (this, in effect, would make the
effective recombination rate lower than the parameter value used
in the simulation, as it reduces the time period during which the
modifier can recombine with the S-allele).
TABULATION OF DATA ON POLLEN AND STIGMA
DOMINANCE
We surveyed all published experiments in which diallel crosses
were used to characterize the nature of dominance interactions
between S-alleles in species with single-locus SSI. Where diallel crosses were conducted between plants of unknown parentage
(Devall and Thien 1992; Karron et al. 1990), nonreciprocal crossincompatibility may have been due either to pollen or stigma
dominance, and so we restricted our attention to studies that either employed crosses among full-siblings or among individuals
with previously typed S-alleles. For each set of diallels, we noted
the number of S-alleles that conclusively could be shown to be
dominant or recessive in either pollen or the stigma. In reconstructing interactions among alleles from the diallel data, we selected
the explanation that required the fewest assumptions. In some
instances, there were two equally probable scenarios, as occurs
when there is codominance between all alleles but one case of
nonreciprocal incompatibility. Because this pattern can be caused
either by a single pollen recessive or stigma recessive allele, such
diallel data were not included in our analysis.
Direct examination of the dominance hierarchy diagrams employed to summarize the interactions among S-alleles in pollen
and styles (e.g., as in fig. 3 in Kowyama et al. 1994) provided a
second method for identifying the tissue-specific nature of dominance (e.g., Kowyama et al. 1994; Mehlenbacher 1997). If an
allele was indicated as acting the same in both reproductive tissues, that allele was not considered, as our principle interest was
in tissue-specific differences in dominance, whereas when interactions among alleles were shown to occur only in the pollen or
E VO L U T I O N O F D O M I NA N C E AT T H E S - L O C U S
Results
SELECTION OF DOMINANCE MODIFIERS IN
S-ALLELES EXPRESSED IN THE POLLEN
The model results depend upon whether the dominance modifier has its effect in the pollen or stigma, and whether it causes
the S-allele it was introduced with to be recessive or dominant.
Results for selection of pollen recessiveness and dominance are
shown first, followed by the selection of stigma recessiveness and
dominance.
Summarization of the results on the evolution of dominance
hierarchies of S-alleles is aided by introducing modified linkage
disequilibrium measures that quantify the extent to which the
mutant and wild-type modifier alleles are each associated with
specific S-alleles. We do this with the measure
D S−M =
n
f (Si M2 )
i=1
−
n
f (Si ) f (M2 ),
where S i denotes the i = 1 to n different S-alleles with equilibrium
frequencies that match that of allele S 1 (the S-allele in which the
mutant modifier was introduced into the population; e.g., alleles
S 1 through S 5 in left side of Fig. 2B,D), S j denotes the j = n +1
to n remaining S-alleles. Because this measure is influenced by
allele frequency variation, for the purposes of comparing model
results it is preferable to use the modified measure
(D S−M )2
,
n−n
f (Si )
f (S j ) f (M1 ) f (M2 )
n
i=1
B
1
.8
r2S M
.8
.6
.6
S1M 2
.4
.4
S i M 1 (i=2,..,4 )
.2
S i M 1 (i=2,..,16)
S1M 1
0
0
50
1
S1M 2
.2
0
100
150
200
r2S M
C
S1M 1
0
50
100
150
D
r2S M
1
.8
200
.8
S1M 2
.6
.6
.4
.4
S i M 1 (i=2,..,4 )
.2
.2
S i M 1 (i=2,..,16)
S1M 1
0
0
50
0
100
150
r2S M
1
S1M 2
200
E
S1M 1
0
50
100
150
200
F
r2S M
1
.8
.8
.6
S1M 2
.6
.4
.4
S i M 1 (i=2,..,4 )
.2
0
50
S i M 1 (i=2,..,16)
0
S1M 1
0
S1M 2
.2
100
150
200
S1M 1
0
50
100
150
200
Generation
Figure 1.
Haplotype frequencies versus generation for (A) n = 4,
FDS m , pollen; (B) n = 16, FDS m , pollen; (C) n = 4, FDS m/f , pollen;
(D) n = 16, FDS m/f , pollen; (E) n = 4, FDS m/f , stigma; (F) n = 16,
FDS m/f , stigma. Recombination fraction, c = 0.0001.
i=1
2
=
r S−M
A
r2S M
1
Frequency (or Association Measure)
stigma, the allele was considered to be pollen or stigma dominant
or recessive, respectively. If an allele was pollen or stigma dominant or recessive to multiple S-alleles, to avoid pseudo-replication,
the allele was counted only once. For each species studied, we
noted the total number of S-alleles characterized and the prevalence of pollen or stigma recessiveness. Our analyses of diallel
patterns disagree with those of the original authors in only one
case (that of Eenink 1981)—the most parsimonious explanation
of the data in this case suggests that the S-allele in question is
recessive in pollen and not the stigma. To test the hypothesis
that pollen and stigma recessive S-alleles are equally frequent,
two-sided t-tests were conducted on the difference in the prevalence of pollen versus stigma recessiveness observed within each
species.
j=n +1
where Sj denotes the j = n + 1 to n remaining S-alleles.
This measures ranges from 0 (no association between specific
S-alleles and specific modifier alleles), to 1 (complete association
between specific S-alleles and specific modifier alleles).
Provided the recombination fraction is small (c < 0.01),
when the mutant modifier allele (M 2 ) causing recessiveness is
introduced into a population containing only the wild-type allele
(M 1 ), its frequency, along with that of the associated S-allele
(i.e., the frequency of the S 1 M 2 haplotype) rises rapidly, and the
frequencies of the remaining S i M 1 (i = 2, . . . ,n) haplotypes fall
from 1/n to ≈ [1 − f (S 1 M 2 )]/(n − 1) (Fig. 1). Associations of
2
the S 1 allele and modifier allele M 2 as measured by r S−M
reach
their maximum in conjunction with these changes. These new
equilibria are attained rapidly in < 100 generations in cases in
which S-allele diversity is low (e.g., n = 4, 8), but even with
higher S-allele diversity they are attained within a few hundred
generations (Fig. 1).
A graphical representation of the equilibrium haplotype frequencies provides a convenient method for visualizing the results,
particularly with respect to the emergence of S-allele dominance
hierarchies (Fig. 2). For brevity, we show graphs only in the case
of n = 8 S-alleles; tables are used to show results for other values of n (see below). When the modifier causes recessiveness,
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D. J. S C H O E N A N D J. W. B U S C H
Equilibrium haplotype frequencies when the mutant modifier causes pollen-expressed S-alleles to be recessive or dominant.
Results for n = 8. Each bar shows the total frequency of an S-allele (first bar is for allele S 1 , other bars for remaining S-alleles). Unshaded
portions of bars corresponds to the frequency of the haplotype bearing the wild type modifier M 1 , shaded portion of bars corresponds
Figure 2.
to the frequency of the haplotype bearing the mutant modifier M 2 . Results are shown separately for the FDS m/f (graphs A and B) and
FDS m models (graphs C and D). In graphs labeled “recessive” (graphs A and C), the modifier allele M 2 causes the associated S-allele to
be recessive. In the graphs of graphs labeled “dominant” (graphs B and D), the modifier allele M 2 causes the associated S-allele to be
dominant.
associations between S-alleles and modifier alleles are such that a
distinct dominance hierarchy of S-alleles emerges under both the
FDS m and FDS m/f models (Fig. 2A, C). In both instances allele
S 1 (the S-allele that the modifier was introduced with) evolves to
be recessive to all remaining S-alleles, and is present at a higher
frequency than the remaining dominant S-alleles, a result that
has been reported elsewhere and referred to as the “recessive
effect” (Sampson 1974). Under the FDS m/f model, equilibrium
frequencies of the S 1 M 2 haplotype are somewhat higher than under the FDS m model (Fig. 2A,C), reflecting the fact that the total
strength of frequency-dependent selection is greater under the
former model.
When the mutant modifier allele causes dominance rather
than recessiveness of the associated S-allele, dominance hierarchies again emerge, and the equilibrium frequencies of individual
recessive S-allele haplotypes are greater than those of dominant
S-allele haplotypes (Fig. 2B,D). In contrast to the case in which
the modifier causes recessiveness (where the equilibrium associ-
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ation is restricted to the S-allele that it was introduced with; S 1 ),
when the mutant modifier allele causes dominance, associations
between it and more than one S-allele develop (Fig. 2B,D). Thus,
at equilibrium, there are several dominant S-alleles and several recessive ones. The chief exceptions to the patterns described above
occur when recombination fraction is relatively large (c ≥ 0.01).
It can be seen that strong associations between particular
2
) develop such that clear
S-alleles and modifier alleles (large r S−M
dominance hierarchies of S-alleles emerge whenever the recombination fraction is less than 0.01 (Table 2). It is notable that as the
number of S-alleles in the population, n, increases, the strength
of the equilibrium associations between the loci is weaker; this is
due to reduced strength of frequency-dependent selection.
SELECTION OF DOMINANCE MODIFIERS IN
S-ALLELES EXPRESSED IN THE STIGMA
In contrast to the evolution of pollen-expressed S-alleles, the evolution of stigma-expressed S-allele dominance and recessiveness
E VO L U T I O N O F D O M I NA N C E AT T H E S - L O C U S
Table 2.
Equilibrium haplotype frequencies when the mutant modifier allele (M 2 ) influences the dominance rank of pollen-expressed
S-alleles.
Haplotype frequency1
Selection
model
Modifier
effect
FDS m/f
Recessive in pollen
S-allele
number (n)
4
8
12
FDS m/f
Dominant in pollen
4
8
12
FDS m
Recessive in pollen
4
8
12
FDS m
Dominant in pollen
4
8
12
1
Recombination
fraction (c)
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
S i M 1(i=
1, . . . ,n )
SiM2
S j M 1 (j =
n +1, . . . ,n)
SjM2
Association
2
(r S−M
)2
0.000 (0)
0.000 (0)
0.009 (1)
0.000 (0)
0.000 (0)
0.010 (1)
0.000 (0)
0.000 (0)
0.026 (1)
0.000 (0)
0.000 (0)
0.006 (2)
0.000 (0)
0.000 (0)
0.012 (6)
0.000 (0)
0.000 (0)
0.043 (12)
0.000 (0)
0.000 (0)
0.010 (1)
0.000 (0)
0.000 (0)
0.020 (1)
0.000 (0)
0.000 (0)
0.041 (12)
0.000 (0)
0.000 (0)
0.008 (3)
0.000 (0)
0.000 (0)
0.050 (2)
0.000 (0)
0.000 (0)
0.043 (12)
0.536 (1)
0.536 (1)
0.520 (1)
0.394 (1)
0.394 (1)
0.355 (1)
0.327 (1)
0.287 (1)
0.067 (1)
0.179 (2)
0.179 (2)
0.174 (2)
0.097 (5)
0.091 (6)
0.086 (6)
0.066 (8)
0.064 (9)
0.040 (12)
0.482 (1)
0.482 (1)
0.460 (1)
0.348 (1)
0.348 (1)
0.129 (1)
0.287 (1)
0.287 (1)
0.043 (12)
0.205 (2)
0.205 (2)
0.169 (3)
0.106 (5)
0.114 (4)
0.073 (2)
0.075 (7)
0.074 (7)
0.040 (12)
0.155 (3)
0.154 (3)
0.153 (3)
0.087 (7)
0.087 (7)
0.086 (7)
0.061 (11)
0.061 (11)
0.041 (11)
0.321 (2)
0.321 (2)
0.306 (2)
0.172 (3)
0.225 (2)
0.194 (2)
0.118 (4)
0.140 (3)
0.000 (0)
0.173 (3)
0.173 (3)
0.169 (3)
0.093 (7)
0.093 (7)
0.055 (7)
0.065 (11)
0.065 (11)
0.000 (0)
0.295 (2)
0.295 (2)
0.460 (1)
0.157 (3)
0.135 (4)
0.070 (6)
0.095 (5)
0.095 (5)
0.000 (0)
0.000 (0)
0.000 (0)
0.004 (3)
0.000 (0)
0.000 (0)
0.005 (7)
0.000 (0)
0.000 (0)
0.041 (11)
0.000 (0)
0.000 (0)
0.014 (2)
0.000 (0)
0.000 (0)
0.017 (2)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.008 (3)
0.000 (0)
0.000 (0)
0.067 (7)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.001 (1)
0.000 (0)
0.000 (0)
0.056 (6)
0.000 (0)
0.000 (0)
0.000 (0)
1.000
0.999
0.912
1.000
0.998
0.813
1.000
0.998
0.017
1.000
0.998
0.835
1.000
0.997
0.661
1.000
0.994
–3
1.000
0.999
0.866
1.000
0.999
0.087
1.000
0.995
–3
1.000
0.999
0.866
1.000
0.988
0.016
1.000
0.977
–3
Number in parentheses refers to the total number of haplotypes with the frequency in the table cell. This number equals n in the case of S i M 1 and S i M 2
haplotypes, and n − n in the case of S j M 1 and S j M 2 haplotypes. See Figure 2 for graphical representation of the model results when n = 8.
2 2
r S−M calculated
2
3
D S−M = 0, r S−M
as described in the text.
not defined.
depends on the mode of selection. When there is fecundity selection (the FDS m/f model), the dynamics of modifier allele parallel
those seen in the case in which the modifier influences pollen
expression (Fig. 3A, B; Table 3). Without fecundity selection
(the FDS m model), however, significant associations between the
S-alleles and modifier alleles do not arise and consequently there
is no evolution of an S-allele dominance hierarchy (Fig. 3C,D;
Table 3). In these latter cases, either the M 2 allele frequency
rises to fixation (when M 2 induces recessiveness) or alternatively, M 2 is lost (when M 2 induces dominance). Thus, the evolution of dominance hierarchies in stigma-expressed S-alleles
requires FS.
EVOLUTION AUGUST 2009
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D. J. S C H O E N A N D J. W. B U S C H
Figure 3.
Equilibrium haplotype frequencies when the mutant modifier causes stigma-expressed S-alleles to be recessive or dominant.
See caption of Figure 2 for remaining details.
For the selection of the mutant dominance modifier in both
pollen and stigma, the qualitative patterns of numerical results
summarized above are not influenced by the starting configuration
of S-locus haplotype frequencies (see Tables S1 and S2).
REDUCED FECUNDITY SELECTION AND THE
EVOLUTION OF DOMINANCE HIERARCHIES IN
STIGMA-EXPRESSED S-ALLELES
The results of numerically iterating the genotype frequencies show
that FS is required for the evolution of dominance hierarchies in
the case of stigma-expressed S-alleles (see above). Simulation
results show that as the strength of FS is reduced by increasing
the number of pollen parents (NP) in simulations, the emergence
of the S-allele dominance hierarchy becomes limited to cases
in which frequency-dependent selection is strongest (where n is
small) (Fig. 4). For FS that is close to strict FS (NP near 1),
generally dominance hierarchies are selected except in the case
of large n (where frequency-dependent selection favoring rare
specificities is relatively weaker). For weaker FS (e.g., NP >>1),
dominance hierarchies may not evolve even with small n (Fig 4C–
E). A qualitatively similar result is obtained in the case in which
the modifier induces dominance (instead of recessiveness) of
S-alleles (results not shown).
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EVOLUTION AUGUST 2009
EFFECT OF VARIATION IN THE RECOMBINATION
FRACTION
As suggested by the results described above, the evolution of
dominance hierarchies in SSI system requires close linkage of the
S-locus and dominance modifier locus. This requirement becomes
more stringent as n is increased, and the strength of frequencydependent selection at the S-locus is reduced. This can be seen
more clearly by examining the relationship between r2S−M , n, and
c across a range of values (Fig. 5). For low values of n and
c, distinct S-allele dominance hierarchies (large r2S−M ) are seen,
whereas when n and c are increased, dominance hierarchies do not
emerge (r2S−M is small). There is a clear threshold of combinations
of n and c beyond which r2S−M drops to near 0.
PATTERNS OF POLLEN AND STIGMA DOMINANCE OF
S-ALLELES FROM PUBLISHED STUDIES
SSI is found in seven plant families (Asteraceae, Betulaceae,
Brassicaceae, Caryophyllaceae, Convulvaceae, Polemoniaceae,
and Sterculiaceae) (Table 4). In both Caryophyllaceaeous species
studied (Lundqvist 1990, 1994), no dominance interactions
have been observed, which suggests a molecular basis of selfincompatibility that may constrain the evolution of dominance.
E VO L U T I O N O F D O M I NA N C E AT T H E S - L O C U S
Table 3.
Equilibrium haplotype frequencies when the mutant modifier allele (M 2 ) influences the dominance rank of stigma-expressed
S-alleles.
Haplotype frequency1
Selection Modifier
model
effect
S-allele
Recombination
number (n) fraction (c)
S i M 1(i=
1, . . . ,n )
FDS m/f
4
Recessive in stigma
8
12
FDS m/f
Dominant in stigma 4
8
12
FDS m
Recessive in stigma
4
8
12
FDS m
Dominant in stigma 4
8
12
1
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
10−6
10−4
10−2
0.000 (0)
0.000 (0)
0.009 (1)
0.000 (0)
0.000 (0)
0.010 (1)
0.000 (0)
0.000 (0)
0.026 (1)
0.000 (0)
0.000 (0)
0.006 (2)
0.000 (0)
0.000 (0)
0.014 (5)
0.000 (0)
0.000 (0)
0.043 (12)
0.000 (0)
0.000 (0)
0.003 (4)
0.001 (0)
0.001 (8)
0.002 (8)
0.000 (0)
0.001 (12)
0.002 (12)
0.250 (4)
0.250 (4)
0.250 (4)
0.125 (8)
0.125 (8)
0.125 (8)
0.083 (12)
0.083 (12)
0.083 (12)
SiM2
S j M 1 (j =
SjM2
n +1, . . . ,n)
0.536 (1)
0.536 (1)
0.520 (1)
0.394 (1)
0.393 (1)
0.355 (1)
0.327 (1)
0.327 (1)
0.067 (1)
0.179 (2)
0.179 (2)
0.174 (2)
0.097 (5)
0.091 (6)
0.088 (5)
0.066 (8)
0.066 (8)
0.040 (12)
0.250 (4)
0.250 (4)
0.247 (4)
0.125 (8)
0.124 (8)
0.123 (8)
0.083 (1)
0.082 (12)
0.081 (12)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.155 (3)
0.154 (3)
0.153 (3)
0.087 (7)
0.087 (7)
0.086 (7)
0.061 (11)
0.061 (11)
0.041 (11)
0.321 (2)
0.321 (2)
0.306 (2)
0.172 (3)
0.225 (2)
0.146 (3)
0.118 (4)
0.117 (4)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.004 (3)
0.000 (0)
0.000 (0)
0.005 (7)
0.000 (0)
0.000 (0)
0.041 (11)
0.000 (0)
0.000 (0)
0.014 (2)
0.000 (0)
0.000 (0)
0.017 (3)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
0.000 (0)
Association
2
(r S−M
)2
1.000
0.999
0.912
1.000
0.998
0.813
1.000
0.998
0.017
1.000
0.998
0.835
1.000
0.997
0.573
1.000
0.992
–3
–3
–3
–3
–3
–3
–3
–3
–3
–3
–3
–3
–3
–3
–3
–3
–3
–3
–3
Number in parentheses refers to the total number of haplotypes with the frequency in the table cell. This number equals n in the case of S i M 1 and S i M 2
haplotypes, and n − n in the case of S j M 1 and S j M 2 haplotypes. See Figure 2 for graphical representation of the model results when n = 8.
2 2
r S−M calculated
2
3
D S−M = 0, r S−M
as described in the text.
not defined.
Diallel analyses of SSI have been concentrated primarily on
plants in the Asteraceae and Brassicaceae. Table 4 shows data
collected from all of the known species with single-locus SSI
in which the interactions among alleles have been clearly determined. In the Asteraceae, 13 of 38 studied S-alleles show pollen
dominance, whereas stigma dominance has been shown for only
a single allele in Senecio squalidus (the remaining alleles are
codominant). In the Brassicaceae, pollen and stigma dominance
has been observed for 58 and 29 S-alleles respectively, from a total
of 196 alleles investigated. In Hazelnut (Corylus avellana), there
are eight levels to the dominance hierarchy in pollen, whereas all
alleles are codominant in the stigma. As a result, 23 of 25 known
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D. J. S C H O E N A N D J. W. B U S C H
.6
A
NP=1
.5
.4
.3
.2
.1
0
0
4
8 12 16 20 24 28 32 36
.6
NP=3
.5
B
Joint influence of number if S-alleles (n) and recombination fraction (c) on the emergence of an S-allele dominance
Figure 5.
.4
.3
hierarchy. Results shown for the FDS m model case when the M 2
allele causes pollen recessiveness of associated S-allele.
.2
.1
0
0
4
8 12 16 20 24 28 32 36
.6
C
Frequency
.5
NP=5
.4
.3
.2
.1
S-alleles exhibit pollen dominance. Pollen dominance is
more prevalent than stigma dominance in Ipomoea trifida
(Convulvaceae) and in Cola nitida (Sterculiaceae), whereas the
reverse is true in Linanthus parviflorus (Polemoniaceae). Summarizing the results statistically (in families in which there are
sufficient examples), we see that pollen- as opposed to stigmadominance is significantly more common within species of the
Asteraceae (t df=7 = 8.29, P < 0.001) and in the Brassicaceae
(t df=11 = 2.42, P < 0.05).
0
0
4
8 12 16 20 24 28 32 36
Discussion
.6
.5
NP=7
D
.4
.3
.2
.1
0
0
4
8 12 16 20 24 28 32 36
.6
E
NP=9
.5
.4
.3
.2
.1
0
0
4
8 12 16 20 24 28 32 36
Number of S alleles
Figure 4.
Equilibrium frequency of the S 1 M 2 haplotype under
variable FS when the M 2 allele causes the S 1 specificity to be
recessive in the stigma. Squares show the simulation results. Circle
show expected equilibrium frequencies of S-alleles when there is
no dominance hierarchy. FS decreases from A to E. Recombination
fraction, c = 10−3 .
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EVOLUTION AUGUST 2009
The results of the models show that dominance hierarchies of
S-alleles may evolve quickly in plants possessing SSI. This occurs due to frequency-dependent selection favoring modifiers that
act to permit expression of only a single specificity in heterozygous individuals, thereby allowing compatibility with a larger
number of S-locus genotypes in the population. The model results
suggest that while dominance modifiers can invade populations
when there is recombination between the modifier and S-locus,
tight linkage of the S-locus and modifier locus is required for
the evolution of stable associations between specific S-alleles and
specific dominance modifier alleles; that is an S-allele hierarchy
in which certain S-alleles are consistently dominant or recessive
with respect to other S-alleles in the population. It is well documented that the S-locus is a zone of restricted recombination
(Kamau et al. 2007). The models suggest that it may be worthwhile to look in this region for sequences associated with certain
S-alleles (e.g., enhancers or promoters) involved in either the
down- or upregulation of linked S-allele products.
Evidence suggests that the evolution of dominance relationships among S-alleles may have been constrained in some
taxa others, but not in others. For example, in the pollen
of self-incompatible Brassica species, the so-called “class II”
S-haplotypes are typically recessive to the “class I” haplotypes
E VO L U T I O N O F D O M I NA N C E AT T H E S - L O C U S
Estimates of the number of S-alleles exhibiting tissue-specific dominance as compiled from published studies of in dialleles in
species with SSI.1
Table 4.
Family
Species
Asteraceae
Ageratum houstonianum
Calotis cuneifolia
Carthamus flavescens
Cichorium intybus
Cosmos bipinnatus
Crepis foetida
Parthenium argentatum
Senecio squalidus
Brassicaceae
Arabidopsis lyrata
Brassica campestris
B. campestris
B. oleracea var. acephala
B. oleracea var. gemmifera
B. oleracea var. italica
Iberis amara
Leavenworthia alabamica
L. crassa
Lesquerella densipila
Raphanus raphanistrum
Sinapis arvensis
Betulaceae
Corylus avellana
Caryophyllaceae Cerastium arvense
Stellaria holostea
Convulvaceae
Ipomoea trifida
Polemoniaceae
Linanthus parviflorus
Sterculiaceae
Cola nitida
Mean
1
Number of Number Number
S-alleles
pollen
stigma
studied
recessive recessive
4
4
6
8
7
4
4
7
8
18
16
28
19
20
6
18
10
9
9
35
25
6
10
28
44
3
13.7
0
3
2
2
2
2
2
2
1
6
4
7
3
2
2
2
2
5
3
22
23
0
0
13
0
1
4.2
0
0
0
0
0
0
0
1
0
5
1
8
2
4
2
0
0
0
2
5
0
0
0
3
3
0
1.4
Percent
References
pollen–stigma
recessive
0.0
75.0
33.3
25.0
28.6
50.0
50.0
14.3
12.5
5.6
18.8
−3.6
5.3
−10.0
0.0
11.1
10.0
55.6
11.1
48.6
92.0
0.0
0.0
35.7
−6.8
33.3
22.9
Stephens et al. 19823
Davidson and Stace 19863
Imrie and Knowles 19713
Eenink 19812,3
Crowe 19542
Hughes and Babcock 19503
Gerstel 19502,3
Brennan et al. 20062
Prigoda et al. 20053
Nou et al. 19933
Nou et al. 19933
Thompson and Taylor 19662
Ockendon 19743
Ockendon 19803
Bateman 19543
Busch et al. 20083
Lloyd 19673
Sampson 1958
Sampson 19673
Stevens and Kay 19892
Mehlenbacher 19972
Lundqvist 19903
Lundqvist 19943
Kowyama et al. 19942
Goodwillie 19973
Jacob 19802
Alleles were not included if they were recessive in both pollen and stigma. Alleles that exhibited pollen or pistil dominance to one other S-allele were
counted once to avoid pseudoreplication.
2
Based on published diagrams of S-allele interactions in pollen and stigma.
3
Based on diallel analysis of S-allele interaction.
(Haytakeyama et al. 1998; Shiba et al. 2002; Kakizaki et al.
2003). These two haplotype classes are highly divergent and appear to have split from one another as much as 40 million years
ago (Mya) (Uyenoyama 1995), suggesting that while position
within the dominance hierarchy could be an evolved property
of individual S-locus haplotypes, such evolution may occur only
rarely. Among the more recently diverged class II haplotypes of
Brassica, there are haplotypes that fall into several dominance
classes (Shiba et al. 2002), although again these have diverged
as much as 7 Mya (Uyenoyama 1995, 2000). Likewise, reconstructions of genealogical relationships among SRK sequences
in A. lyrata show that alleles with recent common ancestors often share the same position in the S-allele dominance hierarchy
(Prigoda et al. 2005), again suggesting relatively slow evolution
of dominance relationships. On the other hand, there are a number
of S-haplotypes that are shared between A. lyrata and its closely
related sister species, A. halleri, that do not exhibit the same dominance relative ranking (Llaurens et al. 2008), suggesting more
recent evolution of dominance relationships. In the Compositae,
studies of the plant S. squalidus in Great Britain suggest evolution of dominance relationships of S-alleles because it was introduced from Spain about 300 years ago. In particular, alleles
that showed a pollen dominant-recessive relationship in one population were codominant in another population (Brennan et al.
2006).
A major prediction of the models is that the evolution of
dominance hierarchies in SSI systems should occur most readily
for S-alleles expressed in the pollen, where selective conditions
are less-stringent compared with the case of stigma expression. As
shown above, the evolution of S-allele dominance hierarchies for
EVOLUTION AUGUST 2009
2109
D. J. S C H O E N A N D J. W. B U S C H
alleles expressed in the stigma requires pronounced FS. Support
for the prediction comes from the literature survey results that
show that dominant and recessive S-alleles are more often found
in pollen. Thus one interpretation of these findings is that FS may
not be a predominant feature of natural populations with SSI. Indeed, while some empirical studies examining mate availability
and seed production over several seasons have shown evidence
for compatible mate limitation (DeMauro 1993; Wagenius et al.
2007; Glemin et al. 2008), other studies have failed to find strong
evidence of mate limitation (Agren 1996; Schierup et al. 2006;
Holderegger et al. 2008; Llaurens et al. 2008). Mate-limitation
may not be a persistent force, even though pollinator limitation
of seed set is a common feature of natural populations of SSI
plants (Burd 1994; Knight et al. 2005). Whether FS does prove
to be uncommon in general in species with SSI is not only of
relevance to the evolution and breakdown of outcrossing, but is
important for understanding the genealogy of S-alleles, as simulations have shown that both allelic turnover and coalescence times
are influenced by FS (Schierup et al. 1998).
The models described above are simple in the sense that they
do not consider all factors that may influence the evolution of
dominance hierarchies in SSI system. For example, in developing
these models we have not focused on how finite population and
variation in S-locus mutation rate may influence the evolution of
dominance hierarchies. Schierup et al. (1997) and Billiard et al.
(2007) have shown that when there is a mixture of dominant and
codominant pollen-recessive alleles in a population, dominant alleles are expected to persist for longer periods than recessive ones.
Yet another factor that may influence the evolution of dominance
hierarchies is inbreeding depression arising from S-linked mutational load (Uyenoyama 1997; Stone 2004; Beschgaard et al.
2004) or from unlinked load. Llaurens et al. (2009) show that
inbreeding depression can exert important effects on the evolution of dominance of S-alleles, generally favoring the evolution
of S-allele dominance hierarchies.
We note that selection of dominance modifiers has also been
found to be effective in other genetic systems in which balancing
selection favors polymorphism (Otto and Bourguet 1999; Peischl
and Bürger 2008). Otto and Bourguet (1999) used a two-locus
model to study the evolution of dominance in the presence of
a balanced polymorphism, where balance is maintained by either overdominant selection or migration between patches. They
found that the strength of selection favoring a dominance modifier
was roughly proportional to the product of the probability that the
modifier occurs in individuals heterozygous at the site in question
and the fitness increase due to the modifier. In SI systems lacking
dominance interactions, all S-locus genotypes are expected to be
heterozygous, and so the modifier should be strongly selected.
Interestingly, the fitness benefit enjoyed by the modifier is contingent upon the pool of compatible pollen that is available to
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EVOLUTION AUGUST 2009
maternal plants, which itself is highly dependent upon the ecology and demographic history of populations (Busch and Schoen
2008).
The evolution of supergenes, or tightly linked blocks of loci
that act in unison to produce a discrete phenotype, seems to be
a common feature of systems experiencing balancing selection.
Pertinent examples include the tightly linked genes controlling
color and wing patterning in Batesian mimics (Clarke and rd
1960), clusters of plant resistance genes (Bergelson et al. 2001),
linked genes causing homomorphic self-incompatibility (FobisLoisy et al. 2004), and the linked complex of genes causing
heteromorphic incompatibility (McCubbin 2008). Given the advantages of rarity at each of these supergenes, one might also
expect regulatory elements modifying dominance patterns to also
be widespread in these regions.
ACKNOWLEDGEMENTS
We thank Deborah Charlesworth for discussing this topic with us, and
Simon Joly for comments on the manuscript. This research was supported
by an NSERC Discovery grant to DJS and a Tomlinson Post-Doctoral
Fellowship to JWB.
LITERATURE CITED
Agren, J. 1996. Population size, pollinator limitation, and seed set in the
self-incompatible herb Lythrum salicaria. Ecology 77:1779–1790.
Bateman, A. J. 1954. Self-incompatibility systems in angiosperms II. Iberis
amara. Heredity 8:305–332.
Bechsgaard, J., T. Bataillon, and M. H. Schierup. 2004. Uneven segregation of
sporophytic self-incompatibility alleles in Arabidopsis lyrata. J. Evol.
Biol. 17:554–561.
Bergelson, J., M. Kreitman, E. A. Stahl, and D. C. Tian. 2001. Evolutionary
dynamics of plant R-genes. Science 292:2281–2285.
Billiard, S., V. Castric, and X. Vekemans. 2007. A general model to explore
complex dominance patterns in plant sporophytic self-incompatibility
systems. Genetics 175:1351–1369.
Brennan, A. C., S. A. Harris, and S. J. Hiscock. 2006. The population genetics
of sporophytic self-incompatibility in Senecio squalidus L. (Asteraceae):
the number, frequency, and dominance interactions of S alleles across
its British range. Evolution 60:213–224.
Bourguet, D. 1999. The evolution of dominance. Heredity 83:1–4.
Burd, M. 1994. Bateman’s principle and plant reproduction—the role of pollen
limitation of fruit and seed set. Bot. Rev. 60:83–139.
Busch, J. W., and D. J. Schoen. 2008. The evolution of self-incompatibility
when mates are limiting. Trends Plant Sci. 13:128–136.
Busch, J. W., J. Sharma, and D. J. Schoen. 2008. Molecular characterization
of Lal2, an SRK-like gene linked to the S-locus in the wild mustard
Leavenworthia alabamica. Genetics 178:2055–2067.
Charlesworth, B. 1979. Evidence against Fisher’s theory of dominance. Nature
278:848–849.
Charlesworth, D. 1988. Evolution of homomorphic self-incompatibility.
Heredity 60:445–453.
Clarke, C. A., and P. M. Sheppard. 1960. Supergenes and mimicry. Heredity
14:175–185.
Crowe, L. K.,1954. Incompatibility in Cosmos bipinnatus. Heredity 8:1–11.
Davidson, J. K., and H. M. Stace. 1986. Genetics of self-incompatibility in
Calotis cuneifolia. J. Hered. 77:471–472.
E VO L U T I O N O F D O M I NA N C E AT T H E S - L O C U S
de Nettancourt, D. 2001. Incompatibility and incongruity in wild and cultivated plants. Springer-Verlag, Berlin.
DeMauro, M. M. 1993. Relationship of breeding system to rarity in the
lakeside daisy (Hymenoxys-acaulis var. glabra). Conserv. Biol. 7:542–
550.
Devall, M. S., and L. B. Thien. 1992. Self-incompatibility in Ipomoea pescaprae (Convulvaceae). Am. Midl. Nat. 128:22–29.
Eenink, A. H.,1981. Compatibility and incompatibility in witloof-chicory
(Cichorium intybus L.). 2. The incompatibility system. Euphytica 30:77–
85.
Fisher, R. A. 1928. The possible modification of the response of the wild type
to recurrent mutation. Am. Nat. 62:115–126.
———. 1930. The genetical theory of natural selection. Clarenton Press,
Oxford.
Fobis-Loisy, I., C. Miege, and T. Goude. 2004. Molecular evolution of
the S-locus controlling mating in the Brassicaceae. Plant Biol. 6:109–
118.
Goodwillie, C. 1997. The genetic control of self-incompatibility in Linanthus
parviflorus (Polemoniaceae). Heredity 79:424–432.
Gerstel, D. U. 1950. Self-incompatibility studies in Guayule II. Inheritance.
Genetics 35:482–506.
Glemin, S., C. Petit, S. Maurice, and A. Mignot. 2008. Consequences of low
mate availability in the rare self-incompatible species Brassica insularis.
Conserv. Biol. 22:216–221.
Hatakeyama, K., M. Watanabe, T. Takasaki, K. Ojima, and K. Hinata. 1998.
Dominance relationships between S-alleles in self-incompatible Brassica campestris L. Heredity 80:241–247.
Hatakeyama, K., T. Takasaki, G. Suzuki, T. Nishio, M. Watanabe, A. Isogai,
and K. Hinata. 2001. The S receptor kinase gene determines dominance
relationships in stigma expression of self-incompatibility in Brassica.
Plant Jour 26:69–76.
Hiscock, S. J., and D. A. Tabah. 2003. The different mechanisms of sporophytic self-incompatibility. Phil. Trans. R. Soc. Lond. B 358:1037–1045.
Holderegger, R., R. Haner, D. Csencsics, S. Angelone, and S.E. Hoebee. 2008.
S-allele diversity suggests no mate limitation in small populations of a
self-incompatible plant. Evolution 62:2922–2928.
Hughes, M. B., and E. B. Babcock. 1950. Self-incompatibility in Crepis foetida
(L.) subsp. rhoeadifolia (Bieb.) Schinz et Keller. Genetics 35:570–588.
Imrie, B. C., and P. F. Knowles. 1971. Genetic studies of self-incompatibility
in Carthamus flavescens Spreng. Crop Sci. 11:6–9.
Jacob, V. J.,1980. Pollination, fruit setting and incompatibility in Cola nitida.
Incomp. Newsl. 12:50–56.
Kacser, H., and J. A. Burns. 1981. The molecular basis of dominance and
recessivity. Genetics 143:621–625.
Kakizaki, T., Y. Takada, A. Ito, G. Suzuki, H. Shiba, S. Takayama, A. Isogai,
and M. Watanabe. 2003. Linear dominance relationship among four
class-II S haplotypes in pollen is determined by the expression of SP11
in Brassica self-incompatibility. Plant Physiol. 44:70–75.
Kamau, E., B. Charlesworth, and D. Charlesworth. 2007. Linkage disequilibrium and recombination rate estimates in the self-incompatibility region
of Arabidopsis lyrata. Genetics 176:2357–2369.
Karron, J. D., D. L. Marshall, and D. M. Oliveras. 1990. Numbers of sporophytic self-incompatibility alleles in populations of wild radish. Theor.
Appl. Genet. 79:457–460.
Knight, T. M., J. A. Steets, J. C. Vamosi, S. J. Mazer, M. Burd, D. R. Campbell,
M. Dudash, M. O. Johnston, R. J. Mitchell, T.-L. Ashman. 2005. Pollen
limitation of plant reproduction: pattern and process. Ann. Rev. Ecol.
Evol. Syst. 36:467–497.
Kooter, J. M., M. A. Matzke, and P. Meyer. 1999. Listening to the silent
genes: transgene silencing research identifies new mechanisms of gene
regulation and pathogen control. Trends Plant. Sci. 4:340–347.
Kowyama, Y., H. Takahasi, K. Muraoka, T. Tani, K. Hara, and I. Shiotani.
1994. Number, frequency and dominance relationships of S-alleles in
diploid Ipomoea trifida. Heredity 73:275–283.
Kusaba, M., C-W. Tung, M. E. Nasrallah, and J. B. Nasrallah. 2002.
Monoallelic expression and dominance interactions in anthers of selfincompatible Arabidopsis lyrata. Plant Physiol. 128:17–20.
Lawrence, M. J. 2000. Population genetics of homomorphic selfincompatibility polymorphisms in flowering plants. Ann. Bot. 85(Suppl.
A):221–226.
Lewis, D. 1947. Competition and dominance of incompatibility alleles in
diploid pollen. Heredity 1:85–108.
Llaurens, V., S. Billiard, J. B. Leducq, V. Castric, E. K. Klein, and X.
Vekemans. 2008. Does frequency-dependent selection with complex
dominance interactions accurately predict allele frequencies at the
self-incompatibility locus in Arabidopsis halleri? Evolution 62:2558–
2569.
Llaurens, V., S. Billiard, V. Castric, and X. Vekemans. 2009. Evolution of
dominance in sporophytic self-incompatibility systems. I. Genetic load
and coevolution of levels of dominance in pollen and pistils. Evolution.
In press.
Lloyd, D. G. 1967. The genetics of self-incompatibility in Leavenworthia
crassa Rollins (Cruciferae). Genetica 38:227–242.
Lundqvist, A. 1990. One-locus sporophytic S-gene system with traces
of gametophytic pollen control in Cerastium arvense ssp. strictum
(Caryophyllaceae). Hereditas 113:203–215.
———. 1994. “Slow” and “quick” S-alleles without dominance interaction
in the sporophytic one-locus self-incompatibility system of Stellaria
holostea (Caryophyllaceae). Hereditas 120:191–202.
Mayo, O., and R. Bürger. 1997. The evolution of dominance: a theory whose
time has passed? Biol. Rev. Camb. Phil. Soc. 72:97–110.
McCubbin, A. 2008. Heteromorphic self-incompatibility in Primula: twentyfirst century tools promise to unravel a classic nineteenth century model
system. Pp. 289–308 in V. Franklin-Tong, ed. Self-incompatibility in
flowering plants: evolution, diversity and mechanisms. Springer-Verlag,
Berlin.
Mehlenbacher, S. A. 1997. Revised dominance hierarchy for S-alleles in
Corylus avellana L. Theor. Appl. Genet. 94:360–366.
Morgan, M. T., and D. J. Schoen. 1999. The role of theory in an emerging
new plant reproductive biology. Trends Ecol. Evol. 12:231–234.
Nou, I. S., M. Watanabe, A. Isogai, and K. Hinata. 1993. Comparison of Salleles and S-glycoproteins between two wild populations of Brassica
campestris in Turkey and Japan. Sex. Plant Reprod. 6:79–86.
Ockendon, D. J. 1974. Distribution of self-incompatibility alleles and breeding structure of open-pollinated cultivars of Brussels sprouts. Heredity
33:159–171.
———. 1980. Distribution of S-alleles and breeding structure of Cape Broccoli (Brassica oleraceae var. ‘italica’). Theor. Appl. Genet. 58:11–15.
Orr, H. A. 1991. A test of Fisher’s theory of dominance. Proc. Natl. Acad.
Sci., USA 88:11414–11415.
Otto, S. P., and D. Bourguet. 1999. Balanced polymorphisms and the evolution
of dominance. Am. Nat. 153:561–574.
Pandey, K. K. 1956. Incompatibility in autotetraploid Trifolium pretense.
Genetics 41: 353–366.
Peischl, S., and R. Bürger. 2008. Evolution of dominance under frequencydependent intraspecific competition. J. Theor. Biol. 251:210–226.
Prigoda, N. L., A. Nassuth, and B. K. Mable. 2005. Phenotypic and genotypic
expression of self-incompatibility haplotypes in Arabidopsis lyrata suggests unique origin of alleles in different dominance classes. Mol. Biol.
Evol. 22:1609–1620.
Provine, W. B. 1986. Sewall Wright and evolutionary biology. Univ. of
Chicago Press, IL.
EVOLUTION AUGUST 2009
2111
D. J. S C H O E N A N D J. W. B U S C H
Sampson, D. R. 1958. The genetics of self-incompatibility in Lesquerella
densipila and in the F 1 hybrid L. densipila X L. lescurii. Can. J. Bot.
36:39–56.
———. 1967. Frequency and distribution of self-incompatibility alleles in
Raphanus raphanistrum. Genetics 56:241–251.
Schierup, M. H., X. Mens, and F. B. Christiansen. 1997. Evolutionary dynamics of sporophytic self-incompatibility alleles in plants. Genetics
147:835–846.
———. 1998. Allelic genealogies in sporophytic self-incompatibility alleles
in plants. Genetics 150:1187–1998.
Schierup, M. H., J. S. Bechsgaard, L. H. Nielsen, and F. B. Christiansen.
2006. Selection at work in self-incompatible Arabidopsis lyrata: mating
patterns in a natural population. Genetics 172:477–484.
Schopfer, C. R., M. E. Nasrallah, and J. B. Nasrallah. 1999. The male determinant of self-incompatibility in Brassica. Science 286:1697–1700.
Shiba, H., M. Iwano, T. Entani, K. Ishimoto, F.-S. Che, Y. Satta, A. Ito, Y.
Takada, M. Watanabe, A. Isogai, and S. Takayama. 2002. The dominance
of alleles controlling self-incompatibility in Brassica pollen is regulated
at the RNA level. Plant Cell 14:491–504.
Shiba, H., T. Kakizaki, M. Iwano, Y. Tarutani, M. Watanabe, A. Isogai, and S.
Takayama. 2006. Dominance relationships between self-incompatibility
alleles controlled by DNA methylation. Nature Genet. 38:L297–299.
Stephens, L. C., P. D. Ascher, and R. E. Widmer. 1982. Genetics of selfincompatibility in diploid Ageratum houstonianum Mill. Theor. Appl.
Genet. 63: 387–394.
Stevens, J. P., and Q. O. N. Kay. 1989. The number, dominance relationships
and frequencies of self-incompatibility alleles in a natural population of
Sinapis arvensis L. in South Wales. Heredity 62:199–205.
Stone, J. L. 2004. Sheltered load associated with S-alleles in Solanum carolinense. Heredity 92:335–342.
Thompson, K. F., and J. P. Taylor. 1966. Non-linear dominance relationships
between S-alleles. Heredity 21:345–362.
Uyenoyma, M. K. 1995. A generalized least-square estimate for the origin of
sporophytic self-incompatibility. Genetics 139:975–992.
———. 2000. A prospectus for new developments in the evolutionary theory
of self-incompatibility. Ann. Bot. 85(suppl. A):247–252.
Vekemans X., M. H. Schierup, and F. B. Christiansen. 1998. Mate availability
and fecundity selection in multi-allelic self-incompatibility systems in
plants. Evolution 52:19–29.
Wagenius, S., E. Lonsdorf, and C. Neuhauser. 2007. Patch aging and the
S-allee effect: breeding system effects on the demographic response of
plants to habitat fragmentation. Am. Nat. 169:383–397.
Wright, S. 1929. The evolution of dominance. Am. Nat. 63:556–561.
———. 1934. Physiological and evolutionary theories of dominance. Am.
Nat. 68:25–53.
———. 1939. The distribution of self-sterility alleles in populations. Genetics
24:538–552.
Associate Editor: J. Kohn
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APPENDIX
NUMERICAL CALCULATION OF HAPLOTYPE
FREQUENCIES
Under the FDS m model, it is assumed that plants receive pollen
amounts that are adequate to render seed set per plant equivalent
for all genotypes. Thus, the population frequency of compatible pollen parents for a maternal parent of genotype S p M r /S q M s
equals nu,v mx,y C pr.qs:ux.vy: f ux.vy , where the number of alleles assumed to be segregating at the modifier locus is m = 2,
and where f ux.vy is the frequency of the genotype S u M x /S v M y
in the population. Ovules of plants with this genotype are fertilized with pollen from plants of genotype S i M k /S j M l with
probability
Cik. jl: pr.qs f ik. jl
,
m
n C pr.qs:ux.vy f ux.vy
u,v x,y
and so crosses between paternal genotype S i M k /S j M l and maternal
genotype S p M r /S q M s contribute a proportion of seed to the next
generation equal to
wik. jl: pr.qs =
Cik. jl: pr.qs f ik. jl f pr.qs
.
m
n C pr.qs:ux.vy f ux.vy
u,v x,y
In the case of the FDS m/f model, the pistils of a plant
with genotype S p M r /S q M s receive compatible pollen with proba bility equal to i,n j m
k,l C pr.qs:ik. jl f ik. jl . Fertilization of ovules
of a plant with genotype S p M r /S q M s occurs with probability
C pr.qs:ik. jl f ik. jl f pr.qs ; and so when individuals with compatible
pollen are rare, certain genotypes may produce less seed per plant
than others. Crosses between maternal genotype S p M r /S q M s and
paternal genotype S i M k /S j M l contributes a proportion of seed to
the next generation equal to
wik. jl: pr.qs =
C pr.qs:ik. jl f ik. jl f pr.qs
n
m
e, f,u,v g,h,x,y
(Ceg. f h:ux.vy + Cux.vy:eg. f h ) f eg. f h f ux.vy
.
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Supporting Information
The following supporting information is available for this article:
Table S1. Observed equilibrium haplotype frequencies when the mutant modifier allele (M 2 ) influences the dominance rank of
pollen-expressed S-alleles.
Table S2. Observed equilibrium haplotype frequencies when the mutant modifier allele (M 2 ) influences the dominance rank of
pollen-expressed S-alleles.
Supporting Information may be found in the online version of this article.
(This link will take you to the article abstract).
Please note: Wiley-Blackwell are not responsible for the content or functionality of any supporting information supplied by the
authors. Any queries (other than missing material) should be directed to the corresponding author for the article.
Additional results and discussion can be found in a document at http://www.repository.naturalis.nl/record/289893.
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