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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 2100 EVOLUTION AUGUST 2009 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). EVOLUTION AUGUST 2009 2101 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 2102 EVOLUTION AUGUST 2009 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, EVOLUTION AUGUST 2009 2103 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- 2104 EVOLUTION AUGUST 2009 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 2105 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). 2106 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 EVOLUTION AUGUST 2009 2107 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 . 2108 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 2110 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). 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Kohn 2112 EVOLUTION AUGUST 2009 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 . 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 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. EVOLUTION AUGUST 2009 2113