Epistasis causes outbreeding depression in eucalypt hybrids

The genetic architecture underlying species differentiation is essential for understanding the mechanisms of speciation and post-zygotic reproductive barriers which exist between species. We undertook line-cross analysis of multiple hybrid (F₁, F₂ and backcrosses) and pure-species populations of two diploid eucalypt species from different subseries, Eucalyptus globulus and Eucalyptus nitens, to unravel the genetic architecture of their differentiation. The populations were replicated on two sites and monitored for growth and survival over a 14-year period. The hybrids exhibited severe outbreeding depression which increased with age. Of the composite additive, dominance and epistatic effects estimated, the additive × additive epistatic component was the most important in determining population divergence in both growth and survival. Significant dominance × dominance epistasis was also detected for survival at several ages. While favourable dominance and, in the case of survival, dominance × dominance epistasis could produce novel gene combinations which enhance hybrid fitness, at the population level, these effects were clearly overridden by adverse additive × additive epistasis which appears to be a major driver of overall outbreeding depression in the hybrid populations. The lack of model fit at older ages suggested that even high-order epistatic interactions may potentially have a significant contribution to outbreeding depression in survival. The estimated composite genetic parameters were generally stable across sites. Our results argue that the development of favourable epistasis is a key mechanism underlying the genetic divergence of eucalypt species, and epistasis is an important mechanism underlying the evolution of post-zygotic reproductive barriers.     

A multiplicative-epistatic model for analyzing interspecific differences in outcrossing species

Epistasis may play an important role in evolution and speciation. Under multiplicative interactions between different loci, an analytical model is proposed to estimate genetic parameters at the individual locus level that contribute to interspecific differences in outcrossing species. The multiplicative epistasis model, inferred from a number of animal and plant experiments, suggests that genotypes at a pair of loci have genotypic values equal to the product of genotypic values at the two different loci. By considering the genetic property of outcrossing species (i.e., high polymorphisms) in the multilevel family structure analysis for an intra- and interspecific factorial mating design, a method is developed to provide estimates for allele frequencies and additive and dominant effects at individual loci in each of the two parental populations, the genotypic values of newly formed heterozygotes through species combination each with one allele from a parental population and the second from the other parental population, and the numbers of genetic factors that lead to species differentiation. Use of clones offers a tremendous power to test the adequacy of the model. However, the utilization of the model with species that cannot be cloned is also discussed. An example with interspecific hybrids of two forest tree species is used to demonstrate the model.     

Using clonal replicates to explore genetic variation in a perennial plant species

Summary An experimental design is presented for estimating genetic parameters using a family structure with clonally replicated individuals. This experimental design provides a technique to quantify genetic variation in a population, with partial separation of additive, dominance and epistatic gene action. Our method is offered as an alternative to techniques for estimating epistatic gene action that require several generations and/or inbreeding. Such methods are not particularly useful for long-lived perennials with long generation cycles. An example of the analysis is given with a forest tree species, Populus deltoides Bartr., and parameter estimates are presented for traits measured over 8 years.     

Genomic prediction of hybrid crops allows disentangling dominance and epistasis

We revisited, in a genomic context, the theory of hybrid genetic evaluation models of hybrid crosses of pure lines, as the current practice is largely based on infinitesimal model assumptions. Expressions for covariances between hybrids due to additive substitution effects and dominance and epistatic deviations were analytically derived. Using dense markers in a GBLUP analysis, it is possible to split specific combining ability into dominance and across-groups epistatic deviations, and to split general combining ability (GCA) into within-line additive effects and within-line additive by additive (and higher order) epistatic deviations. We analyzed a publicly available maize data set of Dent × Flint hybrids using our new model (called GCA-model) up to additive by additive epistasis. To model higher order interactions within GCAs, we also fitted “residual genetic” line effects. Our new GCA-model was compared with another genomic model which assumes a uniquely defined effect of genes across origins. Most variation in hybrids is accounted by GCA. Variances due to dominance and epistasis have similar magnitudes. Models based on defining effects either differently or identically across heterotic groups resulted in similar predictive abilities for hybrids. The currently used model inflates the estimated additive genetic variance. This is not important for hybrid predictions but has consequences for the breeding scheme—e.g. overestimation of the genetic gain within heterotic group. Therefore, we recommend using GCA-model, which is appropriate for genomic prediction and variance component estimation in hybrid crops using genomic data, and whose results can be practically interpreted and used for breeding purposes.     

Detecting epistatic genetic variance with a clonally replicated design: models for lowvs high-order nonallelic interaction

A quantitative genetic model, that uses known family structure with clonal replicates to separate genetic variance into its additive, dominance and epistatic components, is available in the current literature. Making use of offspring testing, this model is based on the theory that components of variance from the linear model of an experimental design may be expressed in terms of expected covariances among relatives. However, if interactions between a pair of quantitative trait loci (QTLs) explain a large proportion of the total epistasis, it will seriously overestimate the additive and dominance variances but underestimate the epistatic variance. In the present paper, a new model is developed to manipulate this problem by combining parental and offspring material into the same test. Under the condition described above, the new model can provide an accurate estimate for additive x additive variances. Also, its accuracy in estimating dominance and total epistatic variances is much greater than the accuracy of the previous model. However, if there is obvious evidence showing the major contribution of high-order interactions, especially among 4QTLs, to the total epistasis, the previous model is more appropriate to partition the genetic variance for a quantitative trait. The re-analysis of an example from a factorial mating design in poplar shows large differences in estimating variance components between the new and previous models when two different assumptions (lowvs high-order epistatic interactions) are used. The new model will be an alternative to estimating the mode of quantitative inheritance for species, especially for longlived, predominantly outcrossing forest trees, that can be clonally replicated.     

EPISTASIS AS A SOURCE OF INCREASED ADDITIVE GENETIC VARIANCE AT POPULATION BOTTLENECKS

The role of epistasis in evolution and speciation has remained controversial. We use a new parameterization of physiological epistasis to examine the effects of epistasis on levels of additive genetic variance during a population bottleneck. We found that all forms of epistasis increase average additive genetic variance in finite populations derived from initial populations with intermediate allele frequencies. Average additive variance continues to increase over many generations, especially at larger population sizes (N = 32 to 64). Additive-by-additive epistasis is the most potent source of additive genetic variance in this situation, whereas dominance-by-dominance epistasis contributes smaller amounts of additive genetic variance. With additive-by-dominance epistasis, additive genetic variance decreases at a relatively high rate immediately after a population bottleneck, rebounding to higher levels after several generations. Empirical examples of epistasis for murine adult body weight based on measured genotypes are provided illustrating the varying effects of epistasis on additive genetic variance during population bottlenecks.     

Recombinant hybrids retain heterozygosity at many loci: new insights into the genomics of reproductive isolation in Populus

The maintenance of species barriers in the face of gene flow is often thought to result from strong selection against intermediate genotypes, thereby preserving genetic differentiation. Most speciation genomic studies thus aim to identify exceptionally divergent loci between populations, but divergence will be affected by many processes other than reproductive isolation (RI) and speciation. Through genomic studies of recombinant hybrids sampled in the wild, genetic variation associated with RI can be observed in situ, because selection against incompatible genotypes will leave detectable patterns of variation in the hybrid genomes. To better understand the mechanisms directly involved in RI, we investigated three natural ‘replicate’ hybrid zones between two divergent Populus species via locus‐specific patterns of ancestry across recombinant hybrid genomes. As expected, genomic patterns in hybrids and their parental species were consistent with the presence of underdominant selection at several genomic regions. Surprisingly, many loci displayed greatly increased between‐species heterozygosity in recombinant hybrids despite striking genetic differentiation between the parental genomes, the opposite of what would be expected with selection against intermediate genotypes. Only a limited, reproducible set of genotypic combinations was present in hybrid genomes across localities. In the absence of clearly delimited ‘hybrid habitats’, our results suggest that complex epistatic interactions within genomes play an important role in advanced stages of RI between these ecologically divergent forest trees. This calls for more genomic studies that test for unusual patterns of genomic ancestry in hybridizing species.     

Tracking the progression of speciation: variable patterns of introgression across the genome provide insights on the species delimitation between progenitor–derivative spruces (Picea mariana × P. rubens)

The genic species concept implies that while most of the genome can be exchanged somewhat freely between species through introgression, some genomic regions remain impermeable to interspecific gene flow. Hence, interspecific differences can be maintained despite ongoing gene exchange within contact zones. This study assessed the heterogeneous patterns of introgression at gene loci across the hybrid zone of an incipient progenitor–derivative species pair, Picea mariana (black spruce) and Picea rubens (red spruce). The spruce taxa likely diverged in geographic isolation during the Pleistocene and came into secondary contact during late Holocene. A total of 300 SNPs distributed across the 12 linkage groups (LG) of black spruce were genotyped for 385 individual trees from 33 populations distributed across the allopatric zone of each species and within the zone of sympatry. An integrative framework combining three population genomic approaches was used to scan the genomes, revealing heterogeneous patterns of introgression. A total of 23 SNPs scattered over 10 LG were considered impermeable to introgression and putatively under diverging selection. These loci revealed the existence of impermeable genomic regions forming the species boundary and are thus indicative of ongoing speciation between these two genetic lineages. Another 238 SNPs reflected selectively neutral diffusion across the porous species barrier. Finally, 39 highly permeable SNPs suggested ancestral polymorphism along with balancing selection. The heterogeneous patterns of introgression across the genome indicated that the speciation process between black spruce and red spruce is young and incomplete, albeit some interspecific differences are maintained, allowing ongoing species divergence even in sympatry. The approach developed in this study can be used to track the progression of ongoing speciation processes.     

QTL analysis of potato tuber dormancy

The potential loss of chemical sprout inhibitors because of public concern over the use of pesticides underscores the desirability of breeding for long dormancy of potato (Solanum tuberosum L.) tubers. Quantitative trait locus (QTL) analyses were performed in reciprocal backcrosses between S. tuberosum and S. berthaultii toward defining the complexity of dormancy. S. berthaultii is a wild Bolivian species characterized by a short-day requirement for tuberization, long tuber dormancy, and resistance to several insect pests. RFLP alleles segregating from the recurrent parents as well as from the interspecific hybrid were monitored in two segregating progenies. We detected QTLs on nine chromosomes that affected tuber dormancy, either alone or through epistatic interactions. Alleles from the wild parent promoted dormancy, with the largest effect at a QTL on chromosome 2. Long dormancy appeared to be recessive in the backcross to S. berthaultii (BCB). In BCB the additive effects of dormancy QTLs accounted for 48% of the measured phenotypic variance, and adding epistatic effects to the model explained only 4% more. In contrast, additive effects explained only 16% of the variance in the backcross to S. tuberosum (BCT), and an additional 24% was explained by the inclusion of epistatic effects. In BCB variation at all QTLs detected was associated with RFLP alleles segregating from the hybrid parent; in BCT all QTLs except for two found through epistasis were detected through RFLP alleles segregating from the recurrent parent. At least three dormancy QTLs mapped to markers previously found to be associated with tuberization in these crosses.Paper number 55 of the Department of Fruit and Vegetable Science, Cornell University     

Effects of genetic background and environment on QTLs and epistasis for rice (Oryza sativa L.) panicle number

A double-haploid (DH) population and a recombinant inbred (RI) line population, derived from a cross between a tropical japonica variety, Azucena, as male parent and two indica varieties, IR64 and IR1552, as female parents respectively, were used in both field and pot experiments for detecting QTLs and epistasis for rice panicle number in different genetic backgrounds and different environments. Panicle number (PN) was measured at maturity. A molecular map with 192 RFLP markers for the DH population and a molecular map with 104 AFLP markers and 103 RFLP markers for the RI population were constructed, in which 70 RFLP markers were the same. Six QTLs were identified in the DH population, including two detected from field experiments and four from pot experiments. The two QTLs, mapped on chromosomes 1 and 12, were identical in both field and pot experiments. In the RI population, nine QTLs were detected, five QTLs from field conditions and four from the pot experiments. Three of these QTLs were identical in both experimental conditions. Only one QTL, linked to CDO344 on chromosome 12, was detected across the populations and experiments. Different epistasitic interaction loci on PN were found under different populations and in different experimental conditions. One locus, flanked by RG323 and RZ801 on chromosome 1, had an additive effect in the DH population, but epistatic effects in the RI population. These results indicate that the effect of genetic background on QTLs is greater than that of environments, and epistasis is more sensitive to genetic background and environments than main-effect QTLs. QTL and epistatic loci could be interchangeable depending on the genetic backgrounds and probably on the environments where they are identified. Received: 26 May 2000 / Accepted: 19 October 2000     

PATTERNS OF MATING IN WILD SUNFLOWER HYBRID ZONES

Theory predicts that homoploid hybrid speciation will be facilitated by selfing, yet most well-documented hybrid species are outcrossers. One possible explanation for this puzzle is that conditions in hybrid populations may favor selfing, even in otherwise outcrossing species. For example, in self-incompatible plants, mixtures of self and interspecific pollen often induce selfing. Here, we examine patterns of mating in three hybrid zones and four “pure” populations of Helianthus annuus and H. petiolaris, wild, self-incompatible sunflower species that are thought to have parented three homoploid hybrid species. Fourteen to 16 maternal families from each pure population and 44–46 maternal families from each hybrid zone were analyzed for seven polymorphic isozyme loci. Maximum-likelihood (ML) methods were used to estimate multilocus outcrossing rates (T_m) and hybridization frequencies for each maternal family, each phenotypic group within each hybrid zone (annuus-like, hybrid, and petiolaris-like), and each population. As predicted for self-incompatible species, all four parental populations have outcrossing rate ML estimates of 1.0. Within the hybrid zones, outcrossing rates were lowest in the H. annuus–like fraction of the population (0.73, 0.72, and 0.74 in the three hybrid zones, respectively), largely intermediate in the H. petiolaris–like group (0.94, 0.90, and 0.94), and highest in the hybrid group (0.97, 0.93, and 0.97). Although outcrossing rates are lower in hybrid zones than in pure populations, it is unlikely that the observed decrease facilitates hybrid speciation because outcrossing rates in the critical hybrid fraction of the population do not differ significantly from 1.0. Dividing the outcrossed pollen pool into intraspecific and interspecific components revealed that maternal plants are largely fertilized by conspecific pollen, confirming an important role for pollen competition as a reproductive barrier. Highly sterile hybrid plants do not appear to discriminate between parental species pollen, but hybrids with higher fertility tend to be fertilized by pollen from the parental group they resemble genetically. Thus, gametic selection leads to substantial assortative mating in these hybrid zones.     

Signatures of hybridization and speciation in genomic patterns of ancestry*

Genomes sampled from hybrid zones between nascent species provide important clues into the speciation process. With advances in genome sequencing and single nucleotide polymorphism (SNP) genotyping, it is now feasible to measure variation in gene flow with high genomic resolution. This progress motivates the development of conceptual and analytical frameworks for hybrid zones that complement well‐established cline approaches. We extend the perspective that genomic distributions of ancestry are sensitive indicators of hybridization history. We use simulations to examine the behavior of the number of ancestry junctions—a simple summary of genomic patterns—in hybrid zones under increasingly realistic scenarios. Neutral simulations revealed that ancestry junction number is shaped by population structure, migration rate, and population size. Modeling multiple genetic architectures of hybrid dysfunction, with an emphasis on epistatic hybrid incompatibilities, showed that selection reduces junction number near loci that confer reproductive barriers. The magnitude of this signature was affected by the form of selection, dominance, and genomic location (autosome vs. sex chromosome) of incompatible loci. Our results suggest that researchers can identify loci involved in reproductive isolation by scanning hybrid genomes for local reductions in junction number. We outline necessary directions for future theory and method development to realize this goal.     

GENOME‐WIDE INVESTIGATION OF REPRODUCTIVE ISOLATION IN EXPERIMENTAL LINEAGES AND NATURAL SPECIES OF NEUROSPORA: IDENTIFYING CANDIDATE REGIONS BY MICROARRAY‐BASED GENOTYPING AND MAPPING

Inherent incompatibilities between genetic components from genomes of different species may cause intrinsic reproductive isolation. In evolution experiments designed to instigate speciation in laboratory populations of the filamentous fungus Neurospora, we previously discovered a pair of incompatibility loci (dfe and dma) that interact negatively to cause severe defects in sexual reproduction. Here we show that the dfe‐dma incompatibility also is a significant cause of genetic isolation between two naturally occurring species of Neurospora (N. crassa and N. intermedia). The strong incompatibility interaction has a simple genetic basis (two biallelic loci) and antagonistic epistasis occurs between heterospecific alleles only, consistent with the Dobzhansky–Muller model of genic incompatibility. We developed microarray‐based, restriction‐site associated DNA (RAD) markers that identified ～1500 polymorphisms between the genomes of the two species, and constructed the first interspecific physical map of Neurospora. With this new mapping resource, the approximate genomic locations of the incompatibility loci were determined using three different approaches: genome scanning, bulk‐segregant analyses, and introgression. These population, quantitative, and classical genetics methods concordantly identified two candidate regions, narrowing the search for each incompatibility locus to only ～2% of the nuclear genome. This study demonstrates how advances in high‐throughput, genome‐wide genotyping can be applied to mapping reproductive isolation genes and speciation research.     

Epistasis and the temporal change in the additive variance-covariance matrix induced by drift

The effect of population bottlenecks on the components of the genetic covariance generated by two neutral independent epistatic loci has been studied theoretically (additive, covA; dominance, covD; additive-by-additive, covAA; additive-by-dominance, covAD; and dominance-by-dominance, covDD). The additive-by-additive model and a more general model covering all possible types of marginal gene action at the single-locus level (additive/dominance epistatic model) were considered. The covariance components in an infinitely large panmictic population (ancestral components) were compared with their expected values at equilibrium over replicates randomly derived from the base population, after t consecutive bottlenecks of equal size N (derived components). Formulae were obtained in terms of the allele frequencies and effects at each locus, the corresponding epistatic effects and the inbreeding coefficient Ft. These expressions show that the contribution of nonadditive loci to the derived additive covariance (covAt) does not linearly decrease with inbreeding, as in the pure additive case, and may initially increase or even change sign in specific situations. Numerical examples were also analyzed, restricted for simplicity to the case of all covariance components being positive. For additive-by-additive epistasis, the condition covAt > covA only holds for high frequencies of the allele decreasing the metric traits at each locus (negative allele) if epistasis is weak, or for intermediate allele frequencies if it is strong. For the additive/dominance epistatic model, however, covAt > covA applies for low frequencies of the negative alleles at one or both loci and mild epistasis, but this result can be progressively extended to intermediate frequencies as epistasis becomes stronger. Without epistasis the same qualitative results were found, indicating that marginal dominance induced by epistasis can be considered as the primary cause of an increase of the additive covariance after bottlenecks. For all models, the magnitude of the ratio covAt/covA was inversely related to N and t.     

Genomic architecture of habitat‐related divergence and signature of directional selection in the body shapes of Gnathopogon fishes

Evolution of ecomorphologically relevant traits such as body shapes is important to colonize and persist in a novel environment. Habitat‐related adaptive divergence of these traits is therefore common among animals. We studied the genomic architecture of habitat‐related divergence in the body shape of Gnathopogon fishes, a novel example of lake–stream ecomorphological divergence, and tested for the action of directional selection on body shape differentiation. Compared to stream‐dwelling Gnathopogon elongatus, the sister species Gnathopogon caerulescens, exclusively inhabiting a large ancient lake, had an elongated body, increased proportion of the caudal region and small head, which would be advantageous in the limnetic environment. Using an F₂ interspecific cross between the two Gnathopogon species (195 individuals), quantitative trait locus (QTL) analysis with geometric morphometric quantification of body shape and restriction‐site associated DNA sequencing‐derived markers (1622 loci) identified 26 significant QTLs associated with the interspecific differences of body shape‐related traits. These QTLs had small to moderate effects, supporting polygenic inheritance of the body shape‐related traits. Each QTL was mostly located on different genomic regions, while colocalized QTLs were detected for some ecomorphologically relevant traits that are proxy of body and caudal peduncle depths, suggesting different degree of modularity among traits. The directions of the body shape QTLs were mostly consistent with the interspecific difference, and QTL sign test suggested a genetic signature of directional selection in the body shape divergence. Thus, we successfully elucidated the genomic architecture underlying the adaptive changes of the quantitative and complex morphological trait in a novel system.     

Epistasis and the evolutionary dynamics of measured genotypic values during simulated serial bottlenecks

The evolutionary effects of epistasis have been primarily explored analytically and most empirical studies have utilized yeast, viral and bacterial populations. Empirical analyses in multi‐cellular organisms are rare because of experimental constraints. Here, we report the results of a genome‐wide scan for two‐way epistasis in 16 traits related to body size and composition in F₂ mice from the LG/J by SM/J intercross. We analyze two‐locus genotypic values at quantitative trait loci (QTL), which provides an especially detailed view of epistatic architectures, to evaluate their predicted evolutionary consequences via Monte Carlo simulations. Epistatic profiles vary, but all traits show complicated genetic architectures which are largely hidden in single locus QTL scans. On average, detected epistatic effects are comparable in size to marginal effects. Simulations demonstrate an expected preservation, and often inflation, of heritable variance across several generations of small effective population size for many identified epistatic pairs over a range of starting allele frequencies.     

Finding Hybrid Incompatibilities Using Genome Sequences from Hybrid Populations

Natural hybrid zones offer a powerful framework for understanding the genetic basis of speciation in progress because ongoing hybridization continually creates unfavorable gene combinations. Evidence indicates that postzygotic reproductive isolation is often caused by epistatic interactions between mutations in different genes that evolved independently of one another (hybrid incompatibilities). We examined the potential to detect epistatic selection against incompatibilities from genome sequence data using the site frequency spectrum (SFS) of polymorphisms by conducting individual-based simulations in SLiM. We found that the genome-wide SFS in hybrid populations assumes a diagnostic shape, with the continual input of fixed differences between source populations via migration inducing a mass at intermediate allele frequency. Epistatic selection locally distorts the SFS as non-incompatibility alleles rise in frequency in a manner analogous to a selective sweep. Building on these results, we present a statistical method to identify genomic regions containing incompatibility loci that locates departures in the local SFS compared with the genome-wide SFS. Cross-validation studies demonstrate that our method detects recessive and codominant incompatibilities across a range of scenarios varying in the strength of epistatic selection, migration rate, and hybrid zone age. Our approach takes advantage of whole genome sequence data, does not require knowledge of demographic history, and can be applied to any pair of nascent species that forms a hybrid zone.     

The effect of epistasis between linked genes on quantitative trait locus analysis

The effect of epistasis between linked genes on quantitative trait locus (QTL) analysis was studied as a function of their contribution to the phenotypic variance and their genetic distance by simulation of F2 (at least 200 individuals) and recombinant inbred line (RIL) populations. Data sets were replicated 100 times. For F2 populations, the presence of epistasis improves the detection of QTLs having effects in opposite directions. Epistasis between linked QTLs (26.5 cM) was poorly detected even when its contribution was relatively high compared to the main effects, and was null for heritabilities lower than 0.10. The detection of false-positive main effects is strongly affected by the distance between epistatic QTLs. The closer they are (≤11.5 cM), the higher the probability of detecting false-positive main-effect QTLs and the lower the probability of detecting epistatic effects. In this case, the presence of main-effect QTLs is due to the deviation of the heterozygote from the homozygotes at each linked interacting QTL and is algebraically explained by the joint effect of the linkage and the additive-by-additive interaction, resulting in a heterosis at a single genomic region in the absence of simulated dominant genetic effects. The number of false-positive main effects only reached nominal levels at about 100 cM. For RIL populations, the number of false positives or the detection of existing epistasis does not depend on the distance, and the power to detect epistatic QTLs is much higher even with small sample sizes and low contributions to the trait. RIL populations are highly recommended to detect epistatic QTLs and to better infer the genetic architecture of a quantitative trait.     

Minor quantitative trait loci underlie floral traits associated with mating system divergence in Mimulus

The genetic basis of species differences provides insight into the mode and tempo of phenotypic divergence. We investigate the genetic basis of floral differences between two closely related plant taxa with highly divergent mating systems, Mimulus guttatus (large-flowered outcrosser) and M. nasutus (small-flowered selfer). We had previously constructed a framework genetic linkage map of the hybrid genome containing 174 markers spanning approximately 1800 cM on 14 linkage groups. In this study, we analyze the genetics of 16 floral, reproductive, and vegetative characters measured in a large segregating M. nasutus x M. guttatus F2 population (N = 526) and in replicates of the parental lines and F1 hybrids. Phenotypic analyses reveal strong genetic correlations among floral traits and epistatic breakdown of male and female fertility traits in the F2 hybrids. We use multitrait composite interval mapping to jointly locate and characterize quantitative trait loci (QTLs) underlying interspecific differences in seven floral traits. We identified 24 floral QTLs, most of which affected multiple traits. The large number of QTLs affecting each trait (mean = 13, range = 11-15) indicates a strikingly polygenic basis for floral divergence in this system. In general, QTL effects are small relative to both interspecific differences and environmental variation within genotypes, ruling out QTLs of major effect as contributors to floral divergence between M. guttatus and M. nasutus. QTLs show no pattern of directional dominance. Floral characters associated with pollinator attraction (corolla width) and self-pollen deposition (stigma-anther distance) share several pleiotropic or linked QTLs, but unshared QTLs may have allowed selfing to evolve independently from flower size. We discuss the polygenic nature of divergence between M. nasutus and M. guttatus in light of theoretical work on the evolution of selfing, genetics of adaptation, and maintenance of variation within populations.