Epistasis interaction of QTL effects as a genetic parameter influencing estimation of the genetic additive effect

Epistasis, an additive-by-additive interaction between quantitative trait loci, has been defined as a deviation from the sum of independent effects of individual genes. Epistasis between QTLs assayed in populations segregating for an entire genome has been found at a frequency close to that expected by chance alone. Recently, epistatic effects have been considered by many researchers as important for complex traits. In order to understand the genetic control of complex traits, it is necessary to clarify additive-by-additive interactions among genes. Herein we compare estimates of a parameter connected with the additive gene action calculated on the basis of two models: a model excluding epistasis and a model with additive-by-additive interaction effects. In this paper two data sets were analysed: 1) 150 barley doubled haploid lines derived from the Steptoe × Morex cross, and 2) 145 DH lines of barley obtained from the Harrington × TR306 cross. The results showed that in cases when the effect of epistasis was different from zero, the coefficient of determination was larger for the model with epistasis than for the one excluding epistasis. These results indicate that epistatic interaction plays an important role in controlling the expression of complex traits.     

Non-additive gene effects in populations under different methods of selection

Summary The genetic parameters of two quantitative traits, 13-day larval weight and pupal weight, in Tribolium populations developed by reciprocal recurrent selection (RRS) and by within-line purebred selection (WLS) were compared each with the other and also with the parameters of the unselected base populations using the genetic model of Carbonell, Nyquist and Bell. The variability for two and three-way crosses of inbred lines derived from companion populations (two strains, breeds, or varieties used for a terminal cross or hybrid) was analyzed into genetic effects: autosomal additivity (^* g), autosomal heterosis (^* s), sex-linked additivity (L), sex-linked heterosis (LL), general maternal (m), specific maternal or reciprocal (r), additive by additive epistasis (aa), and deviations from the model due, among other causes, to higher order epistasis (dev). One series of crosses involved companion populations with diverse origins. For contrast, a second series of crosses involved companion populations originating from a common heterogenous base population. For the heterotic trait larval weight, ^* g and ^* s effects were equally important and accounted for over 50% of the total variation. The aa epistasis contributed another 20% and was followed in importance by higher order epistasis and general maternal effects. For the more highly heritable trait, pupal weight, ^* g effects were most important with ^* s, aa, and m effects having smaller but significant influences. Sex-linked and reciprocal effects were statistically significant for many crosses, but they were relatively unimportant overall. In general, the unselected base populations showed higher ^* g variation than either RRS or WLS populations with the reverse true for ^* s effects. In agreement with theoretical expectations, RRS was more effective than WLS in exploiting ^* s effects. The aa epistatic effects for larval weight were of major importance in the unselected populations, but RRS and WLS did not differ significantly for exploiting superior aa gene combinations. Companion populations with diverse origins revealed significantly larger variation due to ^* g and ^* s effects in crosses than did populations initiated from a common heterogeneous base.Journal Paper No. 11559 from Purdue University Agricultural Experimental Station     

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.     

Unraveling epistasis with triple testcross progenies of near-isogenic lines

Libraries of near-isogenic lines (NILs) are a powerful plant genetic resource to map quantitative trait loci (QTL). Nevertheless, QTL mapping with NILs is mostly restricted to genetic main effects. Here we propose a two-step procedure to map additive-by-additive digenic epistasis with NILs. In the first step, a generation means analysis of parents, their F₁ hybrid, and one-segment NILs and their triple testcross (TTC) progenies is used to identify in a one-dimensional scan loci exhibiting QTL-by-background interactions. In a second step, one-segment NILs with significant additive-by-additive background interactions are used to produce particular two-segment NILs to test for digenic epistatic interactions between these segments. We evaluated our approach by analyzing a random subset of a genomewide Arabidopsis thaliana NIL library for growth-related traits. The results of our experimental study illustrated the potential of the presented two-step procedure to map additive-by-additive digenic epistasis with NILs. Furthermore, our findings suggested that additive main effects as well as additive-by-additive digenic epistasis strongly influence the genetic architecture underlying growth-related traits of A. thaliana.     

Mapping,genetic effects,and epistatic interaction of two bacterial canker resistance QTLs from<Emphasis Type="Italic"> Lycopersicon hirsutum</Emphasis>

Two quantitative trait loci (QTL) from Lycopersicon hirsutum, Rcm 2.0 and Rcm 5.1, control resistance to Clavibacter michiganensis subsp. michiganensis (Cmm). To precisely map both loci, we applied interval mapping techniques to 1,056 individuals in three populations exhibiting F₂ segregation. Based on a 1-LOD confidence interval, Rcm 2.0 mapped to a 14.9-cM interval on chromosome 2 and accounted for 25.7–34.0% of the phenotypic variation in disease severity. Rcm 5.1 mapped to a 4.3-cM interval on chromosome 5 and accounted for 25.8–27.9% of the phenotypic variation. Progeny testing of recombinant plants narrowed the QTL location for Rcm 2.0 to a 4.4-cM interval between TG537-TG091 and to a 2.2-cM interval between CT202-TG358 for Rcm 5.1. A population of 750 individuals exhibiting F₂ segregation was used to detect epistasis between both loci using ANOVA and orthogonal contrasts (P=0.027), suggesting that resistance was determined by additive gene action and an additive-by-additive epistatic interaction. A partial diallel mating design was used to confirm epistasis, advance superior genotypes, randomize genetic backgrounds, and create recombination opportunities. This crossing scheme created a more balanced population (n=112) containing the nine F₂ genotypic classes. Parents in the diallel were selected from the previous population based on resistance, genotype at the Rcm 2.0 and Rcm 5.1 loci, and horticultural traits. A replicated trial using the diallel population confirmed additive-by-additive epistasis (P<0.0001). These results validate the gene action, intra -locus interaction, and map position of two loci controlling resistance to Cmm.Communicated by G. Wenzel     

Epistasis and maternal effects in experimental adaptation to chronic nutritional stress in Drosophila

Based on ecological and metabolic arguments, some authors predict that adaptation to novel, harsh environments should involve alleles showing negative (diminishing return) epistasis and/or that it should be mediated in part by evolution of maternal effects. Although the first prediction has been supported in microbes, there has been little experimental support for either prediction in multicellular eukaryotes. Here we use a line‐cross design to study the genetic architecture of adaptation to chronic larval malnutrition in a population of Drosophila melanogaster that evolved on an extremely nutrient‐poor larval food for 84 generations. We assayed three fitness‐related traits (developmental rate, adult female weight and egg‐to‐adult viability) under the malnutrition conditions in 14 crosses between this selected population and a nonadapted control population originally derived from the same base population. All traits showed a pattern of negative epistasis between alleles improving performance under malnutrition. Furthermore, evolutionary changes in maternal traits accounted for half of the 68% increase in viability and for the whole of 8% reduction in adult female body weight in the selected population (relative to unselected controls). These results thus support both of the above predictions and point to the importance of nonadditive effects in adaptive microevolution.     

Diallel and generation means analyses for the components of resistance to Cercospora arachidicola in peanut

Summary The inheritance of the components of partial resistance to Cercospora arachidicola Hori in peanut (Arachis hypogaea L.) was examined in two five-parent diallels and in the six generations of two single crosses in greenhouse tests. The Griffing (1956) analysis indicated general combining ability (GCA) to be of most importance, yet large ratios of SCA/GCA sum of squares suggested nonadditive genetic variance as well. Reciprocal effects were found for lesion area and lesion number/10 cm² leaf area. The importance of nonadditive genetic variance was substantiated by the lack of fit for the additive-dominance model in the Hayman's analysis (1954 a, b). Further evidence from the Hayman's analysis indicated that epistasis may be important in determining the inheritance of some of the components of resistance. Additive gene effects alone accounted for the genetic variability observed among the generation means from two single crosses for all components of resistance except latent period. There was evidence that epistasis was an important mode of gene action for the inheritance of latent period.Paper No. 10172 of the Journal Series of the North Carolina Agricultural Research Service, Raleigh, NC 27601, USA     

Genetic variation in Solanum tuberosum group Andigena haploids

Summary A random sample of haploids, derived from 28 parental introductions from Solarium tuberosum Gp. Andigena, was used to estimate the quantitative genetic variation for six traits within this group. The six traits analyzed on a plot mean basis were: total tuber weight, fresh vine weight, total fresh weight (tuber+vine), dry vine weight, total dry matter (tuber+vine) and specific gravity. Progenies were obtained following the North Carolina mating Design I and were evaluated along with the female parental clones at two locations. Components of variance and narrow sense heritabilities were calculated by two methods: Design I and female parent-offspring regression. Heritability estimates calculated by the two procedures were in close agreement for most traits. The estimates for total tuber weight from the Design I procedure were twice that from parent offspring regression. The genetic coefficient of variation for these traits indicated a large amount of total genetic variance in this population. Genetic variability for total tuber weight was mostly additive, while both additive and dominant genetic variances were equally important for the remaining traits.     

Genetic control of the opaque-2 gene and background polygenes over some kernel traits in maize (Zea mays L.)

Some kernel traits of agronomical importance in maize are affected by the opaque-2 (o2) gene and background polygenes, which express in different genetic systems such as embryo, endosperm, cytoplasm and maternal plant. A genetic model for seed quantitative traits with the o2 gene effects and polygenic effects as well as their GE interactions was used for protein content, lysine content, oil content and kernel density in maize. The results suggested that the o2 gene was involved in the traits investigated but the effects of the o2 gene were distinctive on various traits. The effects of the o2 gene were large on lysine content and protein content while minor on oil content. There was a substantially wide quantitative variation from polygenes expressing in different genetic systems for the traits evaluated. Significant GE interactions of the o2 gene and background polygenes declared that not only the main effects but also specific expressions depending on environments were responsible for variation of the traits studied. There seemed to have strong maternal heterosis and slight embryo heterosis for kernel density.     

Sex-linked and maternal effects in the Eberhart-Gardner general genetics model

To deal with differences between reciprocal crosses found in many animal breeding experiments, an extension of the general model for genetic effects, given by Eberhart and Gardner (1966, Biometrics 22, 864-881), is presented. In this extension, reciprocal differences between crosses are defined in terms of several maternal and sex-linked parameters, the latter being expressed as functions of gene values and their frequencies. Models are given for several kinds of crosses. Experimental setups or designs of increasing complexity are presented for the estimation of some of the parameters in the models, particularly the sex-linked and maternal ones, as well as the interpopulation heterotic additive-by-additive epistasis. For prediction purposes, different analyses are suggested for the model with highly correlated variables. If the genetic architecture of a trait in different populations is to be compared, the analysis of variance will provide enough degrees of freedom to allow the investigation of the importance of each kind of genetic effect. An example which uses all possible two-way crosses and a partial set of three-way crosses applied to two quantitative traits in the flour beetle, Tribolium castaneum, is included merely as a guide for computations. Population means given by Eberhart and Gardner are extended to incorporate the inbreeding coefficient.     

Variation in seed and seedling traits in Pithecellobium pedicellare,a tropical rain forest tree

Summary Pithecellobium pedicellare, a mimosoid legume, is a large canopy tree in the tropical rain forests of Costa Rica. We examined the pattern of variation in seed weight, germination date, hypocotyl length (stem), and rachis length (the first leaf) of the seedlings in this species. Seeds collected from widely dispersed individual trees at the La Selva Biological Station, Costa Rica, were randomly planted in blocks, and grown under controlled, indoor conditions for about 2 weeks. There-fore, we were able to quantify the effects of maternal family on mean seed weight and the effects of maternal family and microenvironment on the remaining traits examined. A significant effect of maternal family was detected for all traits. In particular, the maternal effects on germination date and seedling size traits which were consistently significant even after controlling the initial seed weight may indicate that the maternal effects reflect, at least to some extent, maternal genetic control over these traits. Despite overall strong maternal effects, the performance of maternal siblings, such as the rachis length, differed among blocks. The sensitivity of maternal siblings to the local environments may contribute to the maintenance of genetic variability in this highly outcrossing tropical species.     

EFFECTS OF DIFFERENT LEVELS OF INBREEDING ON PROGENY FITNESS IN PLANTAGO CORONOPUS

Inbreeding depression (δ) is a major selective force favoring outcrossing in flowering plants. Many phenotypic and genetic models of the evolution of selfing conclude that complete outcrossing should evolve whenever inbreeding depression is greater than one-half, otherwise selfing should evolve. Recent theoretical work, however, has challenged this view and emphasized (1) the importance of variation in inbreeding depression among individuals within a population; and (2) the nature of gene action between deleterious mutations at different loci (epistasis) as important determinants for the evolution of plant mating systems. The focus of this study was to examine the maintenance of inbreeding depression and the relationship between inbreeding level and inbreeding depression at both the population and the individual level in one population of the partially self-fertilizing plant Plantago coronopus (L.). Maternal plants, randomly selected from an area of about 50 m² in a natural population, were used to establish lines with expected inbreeding coefficients (f) of 0, 0.25, 0.50, 0.75, and 0.875. Inbreeding depression was estimated both in the greenhouse and at the site of origin of the maternal plants by comparing growth, survival, flowering, and seed production of the progeny with different inbreeding coefficients. No significant inbreeding depression for these fitness traits was detected in the greenhouse after 16 weeks. This was in strong contrast to the field, where the traits all displayed significant inbreeding depression and declined with increased inbreeding. The results were consistent with the view that mutation to mildly deleterious alleles is the primary cause of inbreeding depression. At the family level, significantly different maternal line responses (maternal parent × inbreeding level interaction) provide a mechanism for the invasion of a selfing variant into the population through any maternal line exhibiting purging of its genetic load. At the population level, evidence for synergistic epistasis was detected for the probability of flowering, but not for total seed production. At the family level, however, a significant interaction between inbreeding level and maternal families for both traits was observed, indicating that epistasis could play a role in the expression of inbreeding depression among maternal lines.     

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.     

Data and theory point to mainly additive genetic variance for complex traits

The relative proportion of additive and non-additive variation for complex traits is important in evolutionary biology, medicine, and agriculture. We address a long-standing controversy and paradox about the contribution of non-additive genetic variation, namely that knowledge about biological pathways and gene networks imply that epistasis is important. Yet empirical data across a range of traits and species imply that most genetic variance is additive. We evaluate the evidence from empirical studies of genetic variance components and find that additive variance typically accounts for over half, and often close to 100%, of the total genetic variance. We present new theoretical results, based upon the distribution of allele frequencies under neutral and other population genetic models, that show why this is the case even if there are non-additive effects at the level of gene action. We conclude that interactions at the level of genes are not likely to generate much interaction at the level of variance.     

Systemic properties of metabolic networks lead to an epistasis-based model for heterosis

The genetic and molecular approaches to heterosis usually do not rely on any model of the genotype–phenotype relationship. From the generalization of Kacser and Burns’ biochemical model for dominance and epistasis to networks with several variable enzymes, we hypothesized that metabolic heterosis could be observed because the response of the flux towards enzyme activities and/or concentrations follows a multi-dimensional hyperbolic-like relationship. To corroborate this, we used the values of systemic parameters accounting for the kinetic behaviour of four enzymes of the upstream part of glycolysis, and simulated genetic variability by varying in silico enzyme concentrations. Then we “crossed” virtual parents to get 1,000 hybrids, and showed that best-parent heterosis was frequently observed. The decomposition of the flux value into genetic effects, with the help of a novel multilocus epistasis index, revealed that antagonistic additive-by-additive epistasis effects play the major role in this framework of the genotype–phenotype relationship. This result is consistent with various observations in quantitative and evolutionary genetics, and provides a model unifying the genetic effects underlying heterosis.     

ANTAGONISTIC PLEIOTROPIC EFFECT OF SECOND-CHROMOSOME INVERSIONS ON BODY SIZE AND EARLY LIFE-HISTORY TRAITS IN DROSOPHILA BUZZATII

A simple way to think of evolutionary trade-offs is to suppose genetic effects of opposed direction that give rise to antagonistic pleiotropy. Maintenance of additive genetic variability for fitness related characters, in association with negative correlations between these characters, may result. In the cactophilic species Drosophila buzzatii, there is evidence that second-chromosome polymorphic inversions affect size-related traits. Because a trade-off between body size and larval developmental time has been reported in Drosophila, we study here whether or not these inversions also affect larva-adult viability and developmental time. In particular, we expect that polymorphic inversions make a statistically significant contribution to the genetic correlation between body size (as measured by thorax length) and larval developmental time. This contribution is expected to be in the direction predicted by the trade-off, namely, those flies whose karyotypes cause them to be genetically larger should also have a longer developmental time than flies with other karyotypes. Using two different experimental approaches, a statistically significant contribution of the second-chromosome inversions to the phenotypic variances of body size and developmental time in D. buzzatii was found. Further, these inversions make a positive contribution to the total genetic correlation between the traits, as expected by the suggested trade-off. The data do not provide evidence as to whether the genetic correlation is due to antagonistic pleiotropic gene action or to gametic disequilibrium of linked genes that affect one or both traits. The results do suggest, however, a possible explanation for the maintenance of inversion polymorphism in this species.     

Genetic architecture of differences between populations of cowpea weevil (Callosobruchus maculatus) evolved in the same environment

We investigated the genetic architecture underlying differentiation in fitness-related traits between two pairs of populations of the seed beetle Callosobruchus maculatus (Coleoptera: Bruchidae). These populations had geographically distant (> 2000 km) origins but evolved in a uniform laboratory environment for 120 generations. For each pair of populations (Nigeria x Yemen and Cameroon x Uganda) we estimated the means of five fitness-related characters and a measure of fitness (net reproductive rate R0) in each of the parental populations and 12 types of hybrids (two F1 and two F2 lines and eight backcrosses). Models containing up to nine composite genetic parameters were fitted to the means of the 14 lines. The patterns of line means for all traits in the Nigeria x Yemen cross and for four traits (larval survival, developmental rate, female body weight, and fecundity) in the Cameroon x Uganda cross were best explained by models including additive, dominance, and maternal effects, but excluding epistasis. We did not find any evidence for outbreeding depression for any trait. An epistatic component of divergence was detected for egg hatching success and R0 in the Cameroon x Uganda cross, but its sign was opposite to that expected under outbreeding depression, that is, additive x additive epistasis had a positive effect on the performance of F2 hybrids. All traits except fecundity showed a pattern of heterosis. A large difference of egg-hatching success between the two reciprocal F1 lines in that cross was best explained as fertilization incompatibility between Cameroon females and sperm carrying Uganda genes. The results suggest that these populations have not converged to the same life-history phenotype and genetic architecture, despite 120 generations of uniform natural selection. However, the absence of outbreeding depression implies that they did not evolve toward different adaptive peaks.     

The genetical basis of hybrid vigour in a highly heterotic cross of Nicotiana tabacum

The genetical control of F₁ heterosis, observed in a cross of desirable Nicotiana tabacum varieties, was investigated by analysing the data of the basic generations, triple test cross-families and random samples of doubled haploids (DH) and single-seed descent (SSD) lines. Analyses of the first-degree statistics revealed a complex control underlying the genetic variation, including the presence of epistasis, linkage, maternal effects and their interactions, in addition to the additive and dominance effects of the genes segregating in the cross. These analyses identified gene dispersion, directional dominance, and duplicate epistasis, as the main causes of heterosis. The triple test-cross analysis also confirmed the presence of non-allelic interactions and indicated that the dominance ratio, although inflated by epistasis, is consistently partial for all the traits. The extent of transgression in the recombinant inbred lines finally established unequivocally that, as in numerous other crosses, gene dispersion and unidirectional, but partial, dominance are the true causes of heterosis in this cross too.     

Genetic basis of variation of yield, and yield components in mungbean (Vigna radiata (L.) Wilczek)

Additive, dominance, and epistasis genetic basis of seed yield per plant, number of pods per plant, number of seeds per pod, and 1000 seed weight in mungbean (Vigna radiata (L.) Wilczek) have been examined, using Triple Test Cross (TTC) analysis. The material for TTC test was evaluated in two seasons i.e., kharif (July-October) and spring/summer (March-June), at the research station of the Nuclear Institute for Agriculture and Biology (NIAB), Faisalabad, Pakistan. Epistasis was present significantly for number of pods per plant and number of seeds per pod when grown in the spring/summer season (March to June). Partition of epistasis showed that additive x additive ('i' type) interaction was an important component of number of pods per plant, and number of seeds per pod was found to be of both types 'i' type, and additive x dominance, and dominance x dominance ('j' and 'l' type) interactions. This indicated that epistasis might be a non-trivial factor in the inheritance of pods per plant, and seeds per pod in mungbean. The expression of epistasis was influenced differentially by particular genotypes, indicating that a limited number of genotypes may not be sufficient to detect non-allelic interactions for a trait in mungbean. Additive and dominance genetic components were significant for all four traits in kharif season (July to October) but only for seed yield and 1000 seed weight in spring/summer season. This suggests that the genes controlling seed yield per plant, and 1000 seed weight are equally sensitive to the environment. The predominance additive gene action in those traits is not significantly influenced by epistasis, suggesting that improvement of the traits can be achieved through standard selection procedures.     

Epistasis,inbreeding depression,and the evolution of self-fertilization

Inbreeding depression resulting from partially recessive deleterious alleles is thought to be the main genetic factor preventing self-fertilizing mutants from spreading in outcrossing hermaphroditic populations. However, deleterious alleles may also generate an advantage to selfers in terms of more efficient purging, while the effects of epistasis among those alleles on inbreeding depression and mating system evolution remain little explored. In this article, we use a general model of selection to disentangle the effects of different forms of epistasis (additive-by-additive, additive-by-dominance, and dominance-by-dominance) on inbreeding depression and on the strength of selection for selfing. Models with fixed epistasis across loci, and models of stabilizing selection acting on quantitative traits (generating distributions of epistasis) are considered as special cases. Besides its effects on inbreeding depression, epistasis may increase the purging advantage associated with selfing (when it is negative on average), while the variance in epistasis favors selfing through the generation of linkage disequilibria that increase mean fitness. Approximations for the strengths of these effects are derived, and compared with individual-based simulation results.