Unraveling Additive from Nonadditive Effects Using Genomic Relationship Matrices

The application of quantitative genetics in plant and animal breeding has largely focused on additive models, which may also capture dominance and epistatic effects. Partitioning genetic variance into its additive and nonadditive components using pedigree-based models (P-genomic best linear unbiased predictor) (P-BLUP) is difficult with most commonly available family structures. However, the availability of dense panels of molecular markers makes possible the use of additive- and dominance-realized genomic relationships for the estimation of variance components and the prediction of genetic values (G-BLUP). We evaluated height data from a multifamily population of the tree species Pinus taeda with a systematic series of models accounting for additive, dominance, and first-order epistatic interactions (additive by additive, dominance by dominance, and additive by dominance), using either pedigree- or marker-based information. We show that, compared with the pedigree, use of realized genomic relationships in marker-based models yields a substantially more precise separation of additive and nonadditive components of genetic variance. We conclude that the marker-based relationship matrices in a model including additive and nonadditive effects performed better, improving breeding value prediction. Moreover, our results suggest that, for tree height in this population, the additive and nonadditive components of genetic variance are similar in magnitude. This novel result improves our current understanding of the genetic control and architecture of a quantitative trait and should be considered when developing breeding strategies.     

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.     

The change in quantitative genetic variation with inbreeding

Inbreeding is known to reduce heterozygosity of neutral genetic markers, but its impact on quantitative genetic variation is debated. Theory predicts a linear decline in additive genetic variance (V(A)) with increasing inbreeding coefficient (F) when loci underlying the trait act additively, but a nonlinear hump-shaped relationship when dominance and epistasis are important. Predictions for heritability (h2) are similar, although the exact shape depends on the value of h2 in the absence of inbreeding. We located 22 published studies in which the level of genetic variation in experimentally inbred populations (measured by V(A) or h2) was compared with that in outbred control populations. For life-history traits, the data strongly supported a nonlinear change in genetic variation with increasing F. V(A) and h2 were, respectively, 244% and 50% higher at F = 0.4 than in outbred populations, and dominance plus epistatic variance together exceeded additive variance by a factor of four. For nonfitness traits the decline was linear and estimates of nonadditive variance were small. These results confirm that population bottlenecks frequently increase V(A) in some traits, and imply that life-history traits are underlain by substantial dominance or epistasis. However, the importance of drift-induced genetic variation in conservation or evolutionary biology is questionable, in part because inbreeding depression usually accompanies inbreeding.     

Genetics of tassel branch number in maize and its implications for a selection program for small tassel size

Summary Tassel branch numbers of six crosses of maize (Zea mays L.) were analyzed to determine inheritance of this trait. Generation mean analyses were used to estimate genetic effects, and additive and nonadditive components of variance were calculated and evaluated for bias due to linkage. Both narrow-sense and broad-sense heritabilities were estimated. Additive genetic variance estimates were significant in five of the six crosses, whereas estimates of variance due to nonadditive components were significant in only three crosses. Additionally, estimates of additive variance components usually were larger than corresponding nonadditive components. There was no evidence for linkage bias in these estimates. Estimates of additive genetic effects were significant in four of six crosses, but significant dominance, additive × additive and additive × dominance effects also were detected. Additive, dominance, and epistatic gene action, therefore, all influenced the inheritance of tassel branch number, but additive gene action was most important. Both narrow-sense and broadsense heritability estimates were larger than those reported for other physiological traits of maize and corroborated conclusions concerning the importance of additive gene action inferred from analyses of genetic effects and variances. We concluded that selection for smalltasseled inbreds could be accomplished most easily through a mass-selection and/or pedigree-selection system. Production of a small-tasseled hybrid would require crossing of two small-tasseled inbreds. We proposed two genetic models to explain unexpected results obtained for two crosses. One model involved five interacting loci and the other employed two loci displaying only additive and additive × additive gene action.Journal Paper No. J-9231 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa 50011. Project No. 2152     

Variations in morphological and life-history traits under extreme temperatures in <Emphasis Type="Italic">Drosophila ananassae</Emphasis>

Using half-sib analysis, we analysed the consequences of extreme rearing temperatures on genetic and phenotypic variations in the morphological and life-history traits of Drosophila ananassae. Paternal half-sib covariance contains a relatively small proportion of the epistatic variance and lacks the dominance variance and variance due to maternal effect, which provides more reliable estimates of additive genetic variance. Experiments were performed on a mass culture population of D. ananassae collected from Kanniyakumari (India). Two extremely stressful temperatures (18°C and 32°C) and one standard temperature (25°C) were used to examine the effect of stressful and non-stressful environments on the morphological and life-history traits in males and females. Mean values of various morphological traits differed significantly among different temperature regimens in both males and females. Rearing at 18°C and 32°C resulted in decreased thorax length, wing-to-thorax (w/t) ratio, sternopleural bristle number, ovariole number, sex comb-tooth number and testis length. Phenotypic variances increased under stressful temperatures in comparison with non-stressful temperatures. Heritability and evolvability based on among-sires (males), among-dams (females), and the sum of the two components (sire + dam) showed higher values at both the stressful temperatures than at the non-stressful temperature. These differences reflect changes in additive genetic variance. Viability was greater at the high than the low extreme temperature. As viability is an indicator of stress, we can assume that stress was greater at 18°C than at 32°C in D. ananassae. The genetic variations for all the quantitative and life-history traits were higher at low temperature. Variation in sexual traits was more pronounced as compared with other morphometric traits, which shows that sexual traits are more prone to thermal stress. Our results agree with the hypothesis that genetic variation is increased in stressful environments.     

THE EVOLUTIONARY GENETICS OF MALE LIFE-HISTORY CHARACTERS IN DROSOPHILA MELANOGASTER

Alternative models of the maintenance of genetic variability, theories of life-history evolution, and theories of sexual selection and mate choice can be tested by measuring additive and nonadditive genetic variances of components of fitness. A quantitative genetic breeding design was used to produce estimates of genetic variances for male life-history traits in Drosophila melanogaster. Additive genetic covariances and correlations between traits were also estimated. Flies from a large, outbred, laboratory population were assayed for age-specific competitive mating ability, age-specific survivorship, body mass, and fertility. Variance-component analysis then allowed the decomposition of phenotypic variation into components associated with additive genetic, nonadditive genetic, and environmental variability. A comparison of dominance and additive components of genetic variation provides little support for an important role for balancing selection in maintaining genetic variance in this suite of traits. The results provide support for the mutation-accumulation theory, but not the antagonistic-pleiotropy theory of senescence. No evidence is found for the positive genetic correlations between mating success and offspring quality or quantity that are predicted by “good genes” models of sexual selection. Additive genetic coefficients of variation for life-history characters are larger than those for body weight. Finally, this set of male life-history characters exhibits a very low correspondence between estimates of genetic and phenotypic correlations.     

Genetic divergence in adaptive characters between sympatric species of stickleback

This study explored the genetic basis of phenotypic differences between two sympatric species of ecologically and morphologically divergent sticklebacks (Gasterosteus aculeatus complex). The aim was to understand how many loci determine the differences and to what extent the differences are due to additive or nonadditive gene action. I reared the two parental species, F1 and F2 hybrids, and both backcrosses in the laboratory and measured the following quantitative characters: gill raker number and length (both involved in feeding), lateral plate number and pelvic spine length (both involved in predator defense), and growth (a fitness component). I then applied joint-scaling regression models to estimate composite additive, dominance and epistatic effects, and their contribution to divergence of parental lines. A simple additive model was sufficient for gill raker number and growth; additive and dominance effects contributed significantly to divergence in plate number and pelvic spine length; and additive, dominance, and epistatic effects contributed significantly to divergence in gill raker length. Wright's estimator for the number of loci for the four morphological characters ranged from 1 to 50. My results suggest that adaptive divergence between limnetic and benthic sticklebacks has taken place through a variety of genetic mechanisms specific to different traits. Though interspecific hybrids are completely fertile and viable in the laboratory, they are selected against in the wild. The pattern of inheritance for the traits examined here directly influences how well hybrids can exploit the two major resource environments in the wild.     

Epistasis in Measured Genotypes: Drosophila P-Element Insertions

Transposon tagging provides an opportunity to construct large numbers of strains of organisms that differ by single insertional mutations. By scoring the phenotypes of these ``measured genotypes,' powerful tests of effects of mutations on phenotypic expression have been performed. Here we extend this approach by constructing with simple crosses all possible two-locus genotypes for each of eight pairs of P-element insertions. Analysis of metabolic phenotypes (fat and glycogen contents, enzyme activities, total protein, and body weight) of the resulting nine genotypes provides direct estimates of additive, dominance, and epistatic effects of the mutations. Nested two-way analysis of variance identified significant epistatic effects in 27% of the tests (35/128 of the trait X P-element combinations). Posterior contrasts were performed to partition the epistatic variance into the four orthogonal components of COCKERHAM, and the data exhibit a tendency toward additive X dominance and dominance X dominance epistasis. Mutations in this study have epistatic effects on metabolic traits that are on the same order of magnitude as main (additive and dominance) effects. Measured genotypes have been used in other contexts to quantify epistatic effects on phenotypic expression, and these results are also briefly reviewed.     

Estimates of genetic variance in an F2 maize population

Maize (Zea mays L.) breeders have used several genetic-statistical models to study the inheritance of quantitative traits. These models provide information on the importance of additive, dominance, and epistatic genetic variance for a quantitative trait. Estimates of genetic variances are useful in understanding heterosis and determining the response to selection. The objectives of this study were to estimate additive and dominance genetic variances and the average level of dominance for an F2 population derived from the B73 x Mo17 hybrid and use weighted least squares to determine the importance of digenic epistatic variances relative to additive and dominance variances. Genetic variances were estimated using Design III and weighted least squares analyses. Both analyses determined that dominance variance was more important than additive variance for grain yield. For other traits, additive genetic variance was more important than dominance variance. The average level of dominance suggests either overdominant gene effects were present for grain yield or pseudo-overdominance because of linkage disequilibrium in the F2 population. Epistatic variances generally were not significantly different from zero and therefore were relatively less important than additive and dominance variances. For several traits estimates of additive by additive epistatic variance decreased estimates of additive genetic variance, but generally the decrease in additive genetic variance was not significant.     

WILL POPULATION BOTTLENECKS AND MULTILOCUS EPISTASIS INCREASE ADDITIVE GENETIC VARIANCE?

We apply new analytical methods to understand the consequences of population bottlenecks for expected additive genetic variance. We analyze essentially all models for multilocus epistasis that have been numerically simulated to demonstrate increased additive variance. We conclude that for biologically plausible models, large increases in expected additive variance--attributable to epistasis rather than dominance--are unlikely. Naciri-Graven and Goudet (2003) found that as the number of epistatically interacting loci increases, additive variance tends to be inflated more after a bottleneck. We argue that this result reflects biologically unrealistic aspects of their models. Specifically, as the number of loci increases, higher-order epistatic interactions become increasingly important in these models, with an increasing fraction of the genetic variance becoming nonadditive, contrary to empirical observations. As shown by Barton and Turelli (2004), without dominance, conversion of nonadditive to additive variance depends only on the variance components and not on the number of loci per se. Numerical results indicating that more inbreeding is needed to produce maximal release of additive variance with more loci follow directly from our analytical results, which show that high levels of inbreeding (F > 0.5) are needed for significant conversion of higher-order components. We discuss alternative approaches to modeling multilocus epistasis and understanding its consequences.     

家蚕茧质性状的QTL定位研究

采用QTLMapper 2．0 QTL作图软件,对F2群体的家蚕全茧量、茧层量、茧层率和蛹体重等性状进行了QTL定位分析,分别检测出7个、6个、2个、8个有显著效应分量的QTLs,分布于7个、5个、2个、7个不同的连锁群。控制全茧量、茧层量的QTLs一般存在复杂的上位性效应。对全茧量性状,有3对QTLs存在显著的加加上位性效应,其中1对还存在加显、显显互作;共有3个QTLs存在显著的显性效应,1个存在显著的加性效应。对茧层量QTLs,发现1对QTLs存在极显著的各项遗传效应,包括上位性效应;1对QTLs被检测到显著的显显互作,1个QTL具有显著的显性效应,并与另一个QTL存在显著的加加互作。茧层率、蛹体重主要受加性或显性的QTLs作用,没有发现茧层率QTLs的上位性效应,蛹体重的有效QTL大都呈现显著的负向显性效应,只有一对QTLs存在显著的加加上位性效应。第2、3、4、11、13、24、34、37、40连锁群是两个或多个性状QTLs分布的共同连锁群。全茧量和茧层量存在共同的QTL或染色体区域,育种上可通过适当选配,利用基因的互作效应,同步改良这两个性状。     

Additive and non-additive genetic parameters from clonally replicated and seedling progenies of<Emphasis Type="Italic"> Eucalyptus globulus</Emphasis>

The first estimates of the importance of epistatic effects within Eucalyptus globulus were obtained from analysis of clonally replicated full-sib progeny tests grown in Portugal. Parents comprised diverse selections from the Portuguese landrace. Variance components were estimated for 4-year-old diameter growth and pilodyn penetration, an indirect measure of wood density, both key traits in the pulpwood breeding objective. The experimental components of variance were used to estimate heritabilities and proportions of the phenotypic variance due to dominance and epistasis. The additive variance was the only significant genetic component affecting either diameter or pilodyn. Estimates of the additive, dominance and epistatic effects accounted for 8–10%, 0–4% and 0.4% of the phenotypic variance in diameter, and for 11–17%, 0% and 5% of the phenotypic variance in pilodyn, respectively. A comparison of residual coefficients of variation within seedling and cloned progenies indicated that C effects within clones were not a serious source of random variability. Despite the test sites encompassing a diverse range of locations, no important genotype by environment interaction was detected. The results suggested that an improvement strategy combining both recurrent selection for additive genetic merit and clonal testing may be adequate for optimizing genetic gains from this genetic base.Communicated by O. Savolainen     

Nonadditive genetic components in resistance of the red flour beetle Tribolium castanaeum against parasite infection

Genetically coupled antagonistic coevolution between host and parasites can select for the maintenance of recombination in the host. Mechanistically, maintenance of recombination relies on epistatic interactions between resistance genes creating linkage disequilibria (LD). The role of epistasis in host resistance traits is however only partly understood. Therefore, we applied the joint scaling principle to assess epistasis and other nonadditive genetic components of two resistance traits, survival, and parasite spore load, in population crosses of the red flour beetle Tribolium castanaeum under infections with the microsporidian Nosema whitei. We found nonadditive components only in infected populations but not in control populations. The genetic architecture underlying survival under parasite infection was more complex than that of spore load. Accordingly, the observed negative correlation between survival and spore load was mainly based on a correlation between shared additive components. Breakdown of resistance was especially strong in F2 crosses between resistant lines indicating that multiple epistatic routes can lead to the same adaptation. In general, the wide range of nonoverlapping genetic components between crosses indicated that parasite resistance in T. castanaeum can be understood as a multi peaked fitness landscape with epistasis contributing substantially to phenotypic differentiation in resistance.     

The Expression of Additive and Nonadditive Genetic Variation under Stress

Experimental lines of Drosophila melanogaster derived from a natural population, which had been isolated in the laboratory for ~70 generations, were crossed to determine if the expression of additive, dominance and epistatic genetic variation in development time and viability was associated with the environment. No association was found between the level of additive genetic effects and environmental value for either trait, but nonadditive genetic effects increased at both extremes of the environmental range for development time. The expression of high levels of dominance and epistatic genetic variation at environmental extremes may be a general expectation for some traits. The disruption of the epistatic gene complexes in the parental lines resulted in hybrid breakdown toward faster development and there was some indication of hybrid breakdown toward higher viability. A combination of genetic drift and natural selection had therefore resulted in different epistatic gene complexes being selected after ~70 generations from a common genetic base. After crossing, the hybrid populations were observed for 10 generations. Epistasis contributed on average 12 hr in development time. Fluctuating asymmetry in sternopleural bristle number also evolved in the hybrid populations, decreasing by >18% in the first seven generations after hybridization.     

Non-additive genetic variation in growth,carcass and fertility traits of beef cattle

Background

A better understanding of non-additive variance could lead to increased knowledge on the genetic control and physiology of quantitative traits, and to improved prediction of the genetic value and phenotype of individuals. Genome-wide panels of single nucleotide polymorphisms (SNPs) have been mainly used to map additive effects for quantitative traits, but they can also be used to investigate non-additive effects. We estimated dominance and epistatic effects of SNPs on various traits in beef cattle and the variance explained by dominance, and quantified the increase in accuracy of phenotype prediction by including dominance deviations in its estimation.

Methods

Genotype data (729 068 real or imputed SNPs) and phenotypes on up to 16 traits of 10 191 individuals from Bos taurus, Bos indicus and composite breeds were used. A genome-wide association study was performed by fitting the additive and dominance effects of single SNPs. The dominance variance was estimated by fitting a dominance relationship matrix constructed from the 729 068 SNPs. The accuracy of predicted phenotypic values was evaluated by best linear unbiased prediction using the additive and dominance relationship matrices. Epistatic interactions (additive × additive) were tested between each of the 28 SNPs that are known to have additive effects on multiple traits, and each of the other remaining 729 067 SNPs.

Results

The number of significant dominance effects was greater than expected by chance and most of them were in the direction that is presumed to increase fitness and in the opposite direction to inbreeding depression. Estimates of dominance variance explained by SNPs varied widely between traits, but had large standard errors. The median dominance variance across the 16 traits was equal to 5% of the phenotypic variance. Including a dominance deviation in the prediction did not significantly increase its accuracy for any of the phenotypes. The number of additive × additive epistatic effects that were statistically significant was greater than expected by chance.

Conclusions

Significant dominance and epistatic effects occur for growth, carcass and fertility traits in beef cattle but they are difficult to estimate precisely and including them in phenotype prediction does not increase its accuracy.     

Inbreeding and the genetic variance in floral traits of Mimulus guttatus

The additive genetic variance, V(A), is frequently used as a measure of evolutionary potential in natural plant populations. Many plants inbreed to some extent; a notable observation given that random mating is essential to the model that predicts evolutionary change from V(A). With inbreeding, V(A) is not the only relevant component of genetic variation. Several nonadditive components emerge from the combined effects of inbreeding and genetic dominance. An important empirical question is whether these components are quantitatively significant. We use maximum likelihood estimation to extract estimates for V(A) and the nonadditive 'inbreeding components' from an experimental study of the wildflower Mimulus guttatus. The inbreeding components contribute significantly to four of five floral traits, including several measures of flower size and stigma-anther separation. These results indicate that inbreeding will substantially alter the evolutionary response to natural selection on floral characters.     

Gene actions at loci underlying several quantitative traits in two elite rice hybrids

To understand the gene activities controlling nine important agronomic quantitative traits in rice, we applied a North Carolina design 3 (NC III design) analysis to recombinant inbred lines (RILs) in highly heterotic inter- (IJ) and intra-subspecific (II) hybrids by performing the following tasks: (1) investigating the relative contribution of additive, dominant, and epistatic effects for performance traits by generation means analysis and variance component estimates; (2) detecting the number, genomic positions, and genetic effects of QTL for phenotypic traits; and (3) characterizing their mode of gene action. Under an F∞-metric, generation means analysis and variance components estimates revealed that epistatic effects prevailed for the majority of traits in the two hybrids. QTL analysis identified 48 and 66 main-effect QTL (M-QTL) for nine traits in IJ and II hybrids, respectively. In IJ hybrids, 20 QTL (41.7%) showed an additive effect of gene actions, 20 (41.7%) showed partial-to-complete dominance, and 8 (16.7%) showed overdominance. In II hybrids, 34 QTL (51.5%) exhibited additive effects, 14 (21.2%) partial-to-complete dominance, and 18 (27.3%) overdominance. There were 153 digenic interactions (E-QTL) in the IJ hybrid and 252 in the II hybrid. These results suggest that additive effects, dominance, overdominance, and particularly epistasis attribute to the genetic basis of the expression of traits in the two hybrids. Additionally, we determined that the genetic causes of phenotypic traits and their heterosis are different. In the plants we studied, the phenotypic traits investigated and their heterosis were conditioned by different M-QTL and E-QTL, respectively, and were mainly due to non-allelic interactions (epistasis).     

Host genetic architecture in single and multiple infections

Hosts are often target to multiple simultaneous infections by genetically diverse parasite strains. The interaction among these strains and the interaction of each strain with the host was shown to have profound effects on the evolution of parasite traits. Host factors like genetic architecture of resistance have so far been largely neglected. To see whether genetic architecture differs between different kinds of infections we used joint scaling analysis to compare the genetic components of resistance in the red flour beetle Tribolium castaneum exposed to single and multiple strains of the microsporidian Nosema whitei. Our results indicate that additive, dominance and epistatic components were more important in single infections whereas maternal components play a decisive role in multiple infections. In detail, parameter estimates of additive, dominance and epistatic components correlated positively between single and multiple infections, whereas maternal components correlated negatively. These findings may suggest that specificity of host–parasite interactions are mediated by genetic and especially epistatic components whereas maternal effects constitute a more general form of resistance.     

Quantitative genetics of speciation: additive and non-additive genetic differentiation between <Emphasis Type="Italic">Drosophila madeirensis</Emphasis> and <Emphasis Type="Italic">Drosophila subobscura</Emphasis>

The role of dominance and epistasis in population divergence has been an issue of much debate ever since the neoDarwinian synthesis. One of the best ways to dissect the several genetic components affecting the genetic architecture of populations is line cross analysis. Here we present a study comparing generation means of several life history-traits in two closely related Drosophila species: Drosophila subobscura, D. madeirensis as well as their F ₁ and F ₂ hybrids. This study aims to determine the relative contributions of additive and non-additive genetic parameters to the differentiation of life-history traits between these two species. The results indicate that both negative dominance and epistatic effects are very important in the differentiation of most traits. We end with considerations about the relevance of these findings for the understanding of the role of non-additive effects in speciation.     

Epistasis for fitness-related quantitative traits in Arabidopsis thaliana grown in the field and in the greenhouse

The extent to which epistasis contributes to adaptation, population differentiation, and speciation is a long-standing and important problem in evolutionary genetics. Using recombinant inbred (RI) lines of Arabidopsis thaliana grown under natural field conditions, we have examined the genetic architecture of fitness-correlated traits with respect to epistasis; we identified both single-locus additive and two-locus epistatic QTL for natural variation in fruit number, germination, and seed length and width. For fruit number, we found seven significant epistatic interactions, but only two additive QTL. For seed germination, length, and width, there were from two to four additive QTL and from five to eight epistatic interactions. The epistatic interactions were both positive and negative. In each case, the magnitude of the epistatic effects was roughly double that of the effects of the additive QTL, varying from -41% to +29% for fruit number and from -5% to +4% for seed germination, length, and width. A number of the QTL that we describe participate in more than one epistatic interaction, and some loci identified as additive also may participate in an epistatic interaction; the genetic architecture for fitness traits may be a network of additive and epistatic effects. We compared the map positions of the additive and epistatic QTL for germination, seed width, and seed length from plants grown in both the field and the greenhouse. While the total number of significant additive and epistatic QTL was similar under the two growth conditions, the map locations were largely different. We found a small number of significant epistatic QTL x environment effects when we tested directly for them. Our results support the idea that epistatic interactions are an important part of natural genetic variation and reinforce the need for caution in comparing results from greenhouse-grown and field-grown plants.