Partial Dominance,Overdominance and Epistasis as the Genetic Basis of Heterosis in Upland Cotton (Gossypium hirsutum L.)

Determination of genetic basis of heterosis may promote hybrid production in Upland cotton (Gossypium hirsutum L.). This study was designed to explore the genetic mechanism of heterosis for yield and yield components in F_{2: 3} and F_{2: 4} populations derived from a hybrid ‘Xinza No. 1’. Replicated yield field trials of the progenies were conducted in 2008 and 2009. Phenotypic data analyses indicated overdominance in F₁ for yield and yield components. Additive and dominance effects at single-locus level and digenic epistatic interactions at two-locus level were analyzed by 421 marker loci spanning 3814 cM of the genome. A total of 38 and 49 QTLs controlling yield and yield components were identified in F_{2: 3} and F_{2: 4} populations, respectively. Analyses of these QTLs indicated that the effects of partial dominance and overdominance contributed to heterosis in Upland cotton simultaneously. Most of the QTLs showed partial dominance whereas 13 QTLs showing overdominance in F_2:3 population, and 19 QTLs showed overdominance in F_2:4. Among them, 21 QTLs were common in both F_{2: 3} and F_{2: 4} populations. A large number of two-locus interactions for yield and yield components were detected in both generations. AA (additive × additive) epistasis accounted for majority portion of epistatic effects. Thirty three complementary two-locus homozygotes (11/22 and 22/11) were the best genotypes for AA interactions in terms of bolls per plant. Genotypes of double homozygotes, 11/22, 22/11 and 22/22, performed best for AD/DA interactions, while genotype of 11/12 performed best for DD interactions. These results indicated that (1) partial dominance and overdominance effects at single-locus level and (2) epistasis at two-locus level elucidated the genetic basis of heterosis in Upland cotton.     

Environmentally dependent expression of heritable variation on early recruitment traits induced by light conditions and provenance in the columnar cactus Pilosocereus leucocephalus

Response to selection depends on heritable genetic variation, which is affected by environmental conditions. The present study experimentally assessed whether the effect of light-related stress and the attenuating effect of shade as a facilitator of seedling germination, survival and growth affect the expression of heritable variation and the potential for a response to selection in the columnar cactus Pilosocereus leucocephalus. A reciprocal transplant experiment combined with the artificial manipulation of light/shade conditions within greenhouses was performed using seeds from controlled crosses of two natural populations (demes PN and SI). Additive genetic variance (V_A), heritability (h²) and the coefficient of variation of additive variance (CV_A) were estimated for per cent of germination, per cent of seedling survival and growth (biomass) under each treatment combination. Although all three recruitment traits showed evidence of different from zero heritability, this result was highly dependent upon the particular transplant site, deme and light treatment combination. The deme that is still not locally adapted (SI) showed significant heritability for all traits and much more potential for a response selection as indicated by a higher CV_A than the locally adapted deme PN. The effect of light conditions on the expression of V_A, h² and CV_A depended on whether the deme was grown in its native or an alien site, but this interaction was only detected for the less adapted deme of SI. Shade conditions promoted by facilitation reduced the evolutionary potential for germination of both demes through an attenuation of genetic differences among genotypes.     

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.     

Contribution of genetic effects to genetic variance components with epistasis and linkage disequilibrium

Background

Cockerham genetic models are commonly used in quantitative trait loci (QTL) analysis with a special feature of partitioning genotypic variances into various genetic variance components, while the F_∞ genetic models are widely used in genetic association studies. Over years, there have been some confusion about the relationship between these two type of models. A link between the additive, dominance and epistatic effects in an F_∞ model and the additive, dominance and epistatic variance components in a Cockerham model has not been well established, especially when there are multiple QTL in presence of epistasis and linkage disequilibrium (LD).

Results

In this paper, we further explore the differences and links between the F_∞ and Cockerham models. First, we show that the Cockerham type models are allelic based models with a special modification to correct a confounding problem. Several important moment functions, which are useful for partition of variance components in Cockerham models, are also derived. Next, we discuss properties of the F_∞ models in partition of genotypic variances. Its difference from that of the Cockerham models is addressed. Finally, for a two-locus biallelic QTL model with epistasis and LD between the loci, we present detailed formulas for calculation of the genetic variance components in terms of the additive, dominant and epistatic effects in an F_∞ model. A new way of linking the Cockerham and F_∞ model parameters through their coding variables of genotypes is also proposed, which is especially useful when reduced F_∞ models are applied.

Conclusion

The Cockerham type models are allele-based models with a focus on partition of genotypic variances into various genetic variance components, which are contributed by allelic effects and their interactions. By contrast, the F_∞ regression models are genotype-based models focusing on modeling and testing of within-locus genotypic effects and locus-by-locus genotypic interactions. When there is no need to distinguish the paternal and maternal allelic effects, these two types of models are transferable. Transformation between an F_∞ model's parameters and its corresponding Cockerham model's parameters can be established through a relationship between their coding variables of genotypes. Genetic variance components in terms of the additive, dominance and epistatic genetic effects in an F_∞ model can then be calculated by translating formulas derived for the Cockerham models.

     

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.     

The effect of trait type and strength of selection on heritability and evolvability in an island bird population

The heritability (h²) of fitness traits is often low. Although this has been attributed to directional selection having eroded genetic variation in direct proportion to the strength of selection, heritability does not necessarily reflect a trait's additive genetic variance and evolutionary potential (“evolvability”). Recent studies suggest that the low h² of fitness traits in wild populations is caused not by a paucity of additive genetic variance (V_A) but by greater environmental or nonadditive genetic variance (V_R). We examined the relationship between h² and variance‐standardized selection intensities (i or β_σ), and between evolvability (I_A:V_A divided by squared phenotypic trait mean) and mean‐standardized selection gradients (β_μ). Using 24 years of data from an island population of Savannah sparrows, we show that, across diverse traits, h² declines with the strength of selection, whereas I_A and I_R (V_R divided by squared trait mean) are independent of the strength of selection. Within trait types (morphological, reproductive, life‐history), h², I_A, and I_R are all independent of the strength of selection. This indicates that certain traits have low heritability because of increased residual variance due to the age at which they are expressed or the multiple factors influencing their expression, rather than their association with fitness.     

Genotype x environment interaction for male attractiveness in an acoustic moth: evidence for plasticity and canalization

The lek paradox arises when choosy females deplete the genetic variance for male display traits from a population, yet substantial additive genetic variation (V_A) in male traits persists. Thus, the lek paradox can be more generally stated as one of the most fundamental evolutionary questions: What maintains genetic variation in natural populations? One solution to this problem may be found in the condition‐dependent nature of many sexually selected traits. Genotype × environment (G × E) interactions can maintain V_A under conditions of environmental heterogeneity provided certain restrictions are met, although antagonistic pleiotropy has also been proposed as a mechanism. Here, we provide evidence for G × E interactions and against the role of antagonistic pleiotropy in the maintenance of V_A for sexually selected traits. Using inbred lines of the lesser waxmoth Achroia grisella, we measured V_A for song attractiveness, condition and development rate under different competitive environments and found that genotypes differed in their plasticity. We argue that variation persists in natural populations because G × E interactions prevent any one variant from producing the optimal phenotype across all environments.     

Morphological differentiation following experimental bottlenecks in the butterfly Bicyclus anynana (Nymphalidae)

The consequences of population bottlenecks for morphological differentiation were investigated experimentally in the Afrotropical butterfly Bicyclus anynana (Satyrinae). A genetically variable laboratory population was used to establish daughter populations differing in the severity of the founding bottleneck (two, six, 20 and c. 300 individuals), with four to six replicate lines per treatment. Nine quantitative traits of the hind wing were measured (wing area and eight wing pattern characters) in the founders, F₁, F₂ and F₃ generations. A tenth character, egg weight, was measured in all lines in F₃. The validity of the neutral additive model was tested by regressing the observed phenotypic variance among replicate lines (V_d) at F₃ against the expected additive genetic variance among lines (2F_tV_A0, where F_t is the coefficient of inbreeding at generation t and V_A0 is the additive genetic variance in the base population). This analysis was performed for the first six principal components of the wing character set, and using two series of F_t estimates, one obtained from demographic parameters, the other from molecular markers. Overall, V_d was slightly less than expected, perhaps as a result of some characters being subject to weak stabilizing selection, but the general picture was one of close concordance with the prediction of the neutral additive model. Plots of phenotypic line means, from the parental generation through to F₃, illustrate that the observed differentiation was essentially entirely due to the initial sampling event. Egg weight showed a similar pattern of differentiation. © 2006 The Linnean Society of London, Biological Journal of the Linnean Society, 2006, 89 , 107–115.     

Inheritance of resistance in cucumber to race 2 of Colletotrichum lagenarium

Summary The resistant breeding line, AR79-95, and the susceptible cultivar, Model, were crossed to develop F₁, F₂, F₃, and backcross populations for genetic analysis of resistance in cucumbers to race 2 of Colletotrichum lagenarium (Pass.) Ellis & Halsted., the causal agent of cucurbit anthracnose. There was no maternal effect on resistance and a small amount of F₁ heterosis toward the susceptible parent. Generation means analysis showed that there was additive and dominance but no epistatic gene action detected on the scale used. Additive and dominance genetic variances were estimated, and narrow-sense heritability was low to moderate. Based on effective factor formulae, at least five effective factors contrtolled the resistance. Some of these factors were dominant and others recessive. Implications for breeding procedures are discussed.     

Genetic variance in fitness and its cross-sex covariance predict adaptation during experimental evolution

The additive genetic variation (V_A) of fitness in a population is of particular importance to quantify its adaptive potential and predict its response to rapid environmental change. Recent statistical advances in quantitative genetics and the use of new molecular tools have fostered great interest in estimating fitness V_A in wild populations. However, the value of V_A for fitness in predicting evolutionary changes over several generations remains mostly unknown. In our study, we addressed this question by combining classical quantitative genetics with experimental evolution in the model organism Tribolium castaneum (red flour beetle) in three new environmental conditions (Dry, Hot, Hot-Dry). We tested for potential constraints that might limit adaptation, including environmental and sex genetic antagonisms captured by negative genetic covariance between environments and female and male fitness, respectively. Observed fitness changes after 20 generations mainly matched our predictions. Given that body size is commonly used as a proxy for fitness, we also tested how this trait and its genetic variance (including nonadditive genetic variance) were impacted by environmental stress. In both traits, genetic variances were sex and condition dependent, but they differed in their variance composition, cross-sex and cross-environment genetic covariances, as well as in the environmental impact on V_A.     

EPISTASIS AND THE EVOLUTION OF ADDITIVE GENETIC VARIANCE IN POPULATIONS THAT PASS THROUGH A BOTTLENECK

Traditional models of genetic drift predict a linear decrease in additive genetic variance for populations passing through a bottleneck. This perceived lack of heritable variance limits the scope of founder-effect models of speciation. We produced 55 replicate bottleneck populations maintained at two male-female pairs through four generations of inbreeding (average F = 0.39). These populations were formed from an F₂ intercross of the LG/J and SM/J inbred mouse strains. Two contemporaneous control strains maintained with more than 60 mating pairs per generation were formed from this same source population. The average level of within-strain additive genetic variance for adult body weight was compared between the control and experimental lines. Additive genetic variance for adult body weight within experimental bottleneck strains was significantly higher than expected under an additive genetic model This enhancement of additive genetic variance under inbreeding is likely to be due to epistasis, which retards or reverses the loss of additive genetic variance under inbreeding for adult body weight in this population. Therefore, founder-effect speciation processes may not be constrained by a loss of heritable variance due to population bottlenecks.     

EFFECTS OF POSTGLACIAL RANGE EXPANSION ON ALLOZYME AND QUANTITATIVE GENETIC VARIATION OF THE PITCHER-PLANT MOSQUITO,WYEOMYIA SMITHII

We determined allozyme variability of 34 populations of the pitcher-plant mosquito, Wyeomyia smithii, from Florida (30°N) to northern Manitoba (54°N) and compared allozyme variability with the additive genetic variance for preadult development time and photoperiodic response determined previously for six populations over a similar range (30–50°N). Phylogenetic analysis of allozymes shows a well-defined split between Gulf Coast and lowland North Carolina populations, similar to previously observed phylogeographic patterns in a wide variety of taxa. A deeper split in the phylogeny of W. smithii coincides with the location of the maximum extent of the Laurentide Ice Sheet. Furthermore, both average heterozygosity and patterns of isolation-by-distance decline in populations north of the former glacial border. It is likely that northern populations are the result of a range expansion that occurred subsequent to the late-Wisconsin retreat of the Laurentide Ice Sheet and that these populations have not yet reached a drift-migration equilibrium. The northern decline in allozyme heterozygosity contrasts sharply with the northern increase in additive genetic variance of development time and photoperiodic response found in previous studies. These previous studies also showed that the genetic divergence of populations has involved stochastic variation in the contribution of dominance and epistasis to the genetic architecture underlying demographic traits, including preadult development time, and photoperiodic response. When taken together, the present and prior studies identify the genetic processes underlying the lack of concordance between geographic patterns of allozyme and quantitative genetic variation in natural populations of W. smithii. In the presence of nonadditive genetic variation, isolation and drift can result in opposite patterns of genetic variation for structural genes and quantitative traits.     

Genetic structure and differentiation of four populations of Afghan Pika (Ochotona rufescens) in Iran based on mitochondrial cytochrome b gene

The population genetics of the Afghan Pika (Ochotona rufescens) was studied in Northern Khorasan Province, Iran. For prediction of the genetic differentiation of four populations, the DNA of mitochondrial cytochrome b of 32 individuals from four areas was sequenced and a Bayesian analysis based on the HKY model was constructed. In total, 15 polymorphic sites, 1125 conserved sites (98.7%) and 14 different haplotypes were found. The phylogenetic tree resulting from the Bayesian analysis and network analysis showed that all samples were clustered in two major groups and the haplotypes of the four populations did not separate geographically. An analysis of molecular variance (AMOVA) indicated that a large majority of the genetic variance was due to the variance within populations. The results of fixation indices showed significant genetic structure among populations in both methods. The pairwise F_st revealed that two northern populations have a significant genetic differentiation from two southern populations, but no significance pairwise F_st value was demonstrated between the closed populations. Nei's genetic distances between closed populations were not significant, while significant values occurred between distant populations. It seems that there is not a major discontinuity between populations of Afghan Pika based on cyt-b mitochondrial gene. However, phylogenetic analysis did not separate populations and a large majority of the genetic variance was found within populations. However, AMOVA analysis showed a significant level of genetic structure among populations (p?<?0.001) and between groups (p?<?0.5). It seems that these results suggest shallow genetic differentiation between populations of different geographic groups.     

LOCAL VARIATION IN THE GENETIC BASIS OF PAEDOMORPHOSIS IN THE SALAMANDER AMBYSTOMA TALPOIDEUM

The hypothesis that local isolated populations differed in the genetic basis for life-history traits was tested in the salamander Ambystoma talpoideum. Genetic basis was defined as the specific genetic architecture (additive and nonadditive) that contributes, along with maternal and environmental factors, to the phenotype. All crosses within and between three populations were made to produce nine F₁ populations. Nine within-population crosses produced the F₂ generation. This design does not permit an estimation of the exact nature of the genetic basis (e.g., additive, nonadditive) for any trait within populations. However, hybrid dissimilarity in the F₂ generation was taken as evidence of a different genetic basis for a trait in each population. The genetic basis of life-history pathway (metamorphosis vs. paedomorphosis) and per capita fecundity differed between two populations. The genetic basis of life-history pathway, per capita fecundity, survival, and growth rate was similar between the remaining sets of populations. This study and related ones (Semlitsch and Wilbur, 1989; Semlitsch et al., 1990) suggest that a heterochronic shift that causes rapid morphological evolution between metamorphosis and paedomorphosis (a macroevolutionary pattern) can evolve independently and does not require a macromutation or other nonmicroevolutionary mechanisms.     

Comparative QTL mapping of resistance to Ustilago maydis across four populations of European flint-maize

 We mapped and characterized quantitative trait loci (QTLs) for resistance to Ustilago maydis and investigated their consistency across different flint-maize populations. Four independent populations, comprising 280 F₃ lines (A×B^I), 120 F₅ lines (A×B^II), 131 F₄ lines (A×C) and 133 F₄ lines (C×D), were produced from four European elite flint inbreds (A, B, C, D) and genotyped at 89, 151, 104, and 122 RFLP marker loci, respectively. All F_n lines were evaluated in field trials with two replications in five German environments. Genotypic variances were highly significant for the percentage of U. maydis infected plants (UST) in all populations, and heritabilities exceeded 0.69. Between five and ten QTLs were detected in individual populations by composite interval mapping, explaining between 39% and 58% of the phenotypic variance. These 19 different QTLs were distributed over all ten chromosomes without any clustering on certain chromosomes. In most cases, gene action was dominant or overdominant. Fourteen pairs of the detected QTLs for UST displayed significant digenic epistatic interactions, but only two of them did so after arcsin √UST/100 transformation. Significant QTL× environment interactions occurred frequently. Between two to four QTLs were common between pairs of populations. Population C×D was also grown in Chartres, a location with a high U. maydis incidence. Two out of six QTLs identified for Chartres were in common with QTLs detected across five German environments for C×D. Consequently, marker-assisted or phenotypic selection based on results from natural infection seem to be suitable breeding strategies for improving the resistance of maize to U. maydis. Received: 3 July 1998 / Accepted: 24 July 1998     

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.     

Heritability and evolvability of fitness and nonfitness traits: Lessons from livestock

Data from natural populations have suggested a disconnection between trait heritability (variance standardized additive genetic variance, V_A) and evolvability (mean standardized V_A) and emphasized the importance of environmental variation as a determinant of trait heritability but not evolvability. However, these inferences are based on heterogeneous and often small datasets across species from different environments. We surveyed the relationship between evolvability and heritability in >100 traits in farmed cattle, taking advantage of large sample sizes and consistent genetic approaches. Heritability and evolvability estimates were positively correlated (r = 0.37/0.54 on untransformed/log scales) reflecting a substantial impact of V_A on both measures. Furthermore, heritabilities and residual variances were uncorrelated. The differences between this and previously described patterns may reflect lower environmental variation experienced in farmed systems, but also low and heterogeneous quality of data from natural populations. Similar to studies on wild populations, heritabilities for life‐history and behavioral traits were lower than for other traits. Traits having extremely low heritabilities and evolvabilities (17% of the studied traits) were almost exclusively life‐history or behavioral traits, suggesting that evolutionary constraints stemming from lack of genetic variability are likely to be most common for classical “fitness” (cf. life‐history) rather than for “nonfitness” (cf. morphological) traits.     

Selection,structure and the heritability of behaviour

Characters which are closely linked to fitness often have low heritabilities (V_A/V_P). Low heritabilities could be because of low additive genetic variation (V_A), that had been depleted by directional selection. Alternatively, low heritabilities may be caused by large residual variation (V_R=V_P – V_A) compounded at a disproportionately higher rate than V_A across integrated characters. Both hypotheses assume that each component of quantitative variation has an independent effect on heritability. However, V_A and V_R may also covary, in which case differences in heritability cannot be fully explained by the independent effects of elimination‐selection or compounded residual variation. We compared the central tendency of published behavioural heritabilities (mean=0.31, median=0.23) with morphological and life history data collected by 26 ). Average behavioural heritability was not significantly different from average life history heritability, but both were smaller than average morphological heritability. We cross‐classified behavioural traits to test whether variation in heritability was related to selection (dominance, domestic/wild) or variance compounding (integration level). There was a significant three‐way interaction between indices of selection and variance compounding, related to the absence of either effect at the highest integration level. At lower integration levels, high dominance variance indicated effects of selection. It was also indicated by the low CV_A of domestic species. At the same time CV_R increased disproportionately faster than CV_A across integration levels, demonstrating variance compounding. However, neither CV_R nor CV_A had a predominant effect on heritability. The partial regression coefficients of CV_R and CV_A on heritability were similar and a path analysis indicated that their (positive) correlation was also necessary to explain variation in heritability. These results suggest that relationships between additive genetic and residual components of quantitative genetic variation can constrain their independent direct effects on behavioural heritability.     

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     

Influence of Gene Interaction on Complex Trait Variation with Multilocus Models

Although research effort is being expended into determining the importance of epistasis and epistatic variance for complex traits, there is considerable controversy about their importance. Here we undertake an analysis for quantitative traits utilizing a range of multilocus quantitative genetic models and gene frequency distributions, focusing on the potential magnitude of the epistatic variance. All the epistatic terms involving a particular locus appear in its average effect, with the number of two-locus interaction terms increasing in proportion to the square of the number of loci and that of third order as the cube and so on. Hence multilocus epistasis makes substantial contributions to the additive variance and does not, per se, lead to large increases in the nonadditive part of the genotypic variance. Even though this proportion can be high where epistasis is antagonistic to direct effects, it reduces with multiple loci. As the magnitude of the epistatic variance depends critically on the heterozygosity, for models where frequencies are widely dispersed, such as for selectively neutral mutations, contributions of epistatic variance are always small. Epistasis may be important in understanding the genetic architecture, for example, of function or human disease, but that does not imply that loci exhibiting it will contribute much genetic variance. Overall we conclude that theoretical predictions and experimental observations of low amounts of epistatic variance in outbred populations are concordant. It is not a likely source of missing heritability, for example, or major influence on predictions of rates of evolution.