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.     

Genetic analysis of agronomic characters in chickpea. II. Estimates of genetic variances from line × tester mating designs

Summary Thirty line x tester experiments involving diverse chickpea (Cicer arietinum L.) germplasm were conducted over 8 years and three locations to determine the nature of the genetic variance for grain yield and related characters, and the effects of generation and environment on these genetic parameters. Days-to-flowering, 100-seed mass, and seeds per pod were predominantly under the control of additive genetic variance, while both additive and non-additive genetic components of variance were important for days-to-maturity, plant height, primary and secondary branches, pods per plant, and seed yield. The F₁ and F₂ generations were found equally useful in estimating the genetic variances for different characters because the generation did not significantly interact with genetic parameters in the majority of cases. Sites or seasons, on the other hand, showed significant interaction with genetic components of variances; additive variance showed a larger interaction with environments than non-additive variance. This indicated the importance of more than one site and/ or season for unbiased estimation of the genetic components of variance. The results were compared with previous findings from diallel analyses.ICRISAT Journal Article No. 1200     

Predicting evolutionary responses to selection on polyandry in the wild: additive genetic covariances with female extra-pair reproduction

The evolutionary forces that underlie polyandry, including extra-pair reproduction (EPR) by socially monogamous females, remain unclear. Selection on EPR and resulting evolution have rarely been explicitly estimated or predicted in wild populations, and evolutionary predictions are vulnerable to bias due to environmental covariances and correlated selection through unmeasured traits. However, evolutionary responses to (correlated) selection on any trait can be directly predicted as additive genetic covariances (cov_A) with appropriate components of relative fitness. I used comprehensive life-history, paternity and pedigree data from song sparrows (Melospiza melodia) to estimate cov_A between a female''s liability to produce extra-pair offspring and two specific fitness components: relative annual reproductive success (ARS) and survival to recruitment. All three traits showed non-zero additive genetic variance. Estimates of cov_A were positive, predicting evolution towards increased EPR, but 95% credible intervals overlapped zero. There was therefore no conclusive prediction of evolutionary change in EPR due to (correlated) selection through female ARS or recruitment. Negative environmental covariance between EPR and ARS would have impeded evolutionary prediction from phenotypic selection differentials. These analyses demonstrate an explicit quantitative genetic approach to predicting evolutionary responses to components of (correlated) selection on EPR that should be unbiased by environmental covariances and unmeasured traits.     

Genetic studies of yield contributing traits in Amaranthus

Summary Genetical studies on grain yield and its contributing traits were made in a six parent complete diallel in the F₁ and F₂ generations of one of the most widely grown grain species of grain amaranths (Amaranthus hypochondriacus L.). Graphical analysis indicated that epistasis exists for 1,000-grain weight in the F₁. Grain weight/panicle, yield/plant and harvest index indicated absence of non-allelic gene interaction. The harvest index in the F₁ and F₂ and grain weight/ panicle, 1,000-grain weight, yield/plant in the F₂ appeared to be controlled by overdominance effects. Higher grain yield appeared to be associated with dominant genes. Both additive and non-additive gene effects were responsible for the genetic variation in the diallel population. However, dominance variance was more important than additive variance in grain yield/ plant and harvest index in the F₁ and F₂. For 1,000-grain weight additive genetic variance was more important in the F₁ and non-additive in F₂. There was overdominance of a consistent nature in the two analyses for harvest index in the F₁ and F₂, grain weight/ panicle, 1,000-grain weight and yield/plant in the F₂ and partial dominance for 1,000-grain weight in the F₁.     

Maintenance of genetic variation in quantitative traits of a woodland rodent during generations of captive breeding

Breeding programs to conserve diversity are predicated on the assumption that genetic variation in adaptively important traits will be lost in parallel to the loss of variation at neutral loci. To test this assumption, we monitored quantitative traits across 18 generations of Peromyscus leucopus mice propagated with protocols that mirror breeding programs for threatened species. Ears, hind feet, and tails became shorter, but changes were reversible by outcrossing and therefore were due to accumulated inbreeding. Heritability of ear length decreased, because of an increase in phenotypic variance rather than the expected decrease in additive genetic variance. Additive genetic variance in hind foot length increased. This trait initially had low heritability but large dominance or common environmental variance contributing to resemblance among full-sibs. The increase in the additive component indicates that there was conversion of interaction variances to additive variance. For no trait did additive genetic variation decrease significantly across generations. These findings indicate that the restructuring of genetic variance that occurs with genetic drift and novel selection in captivity can prevent or delay the loss of phenotypic and heritable variation, providing variation on which selection can act to adapt populations to captivity and perhaps later to readapt to more natural habitats after release. Therefore, the importance of minimizing loss of gene diversity from conservation breeding programs for threatened wildlife species might lie in preventing immediate reduction in individual fitness due to inbreeding and protecting allelic diversity for long-term evolutionary change, more so than in protecting variation in quantitative traits for rapid re-adaptation to wild environments.     

Genetic architecture of survival and fitness-related traits in two populations of Atlantic salmon

The additive genetic effects of traits can be used to predict evolutionary trajectories, such as responses to selection. Non-additive genetic and maternal environmental effects can also change evolutionary trajectories and influence phenotypes, but these effects have received less attention by researchers. We partitioned the phenotypic variance of survival and fitness-related traits into additive genetic, non-additive genetic and maternal environmental effects using a full-factorial breeding design within two allopatric populations of Atlantic salmon (Salmo salar). Maternal environmental effects were large at early life stages, but decreased during development, with non-additive genetic effects being most significant at later juvenile stages (alevin and fry). Non-additive genetic effects were also, on average, larger than additive genetic effects. The populations, generally, did not differ in the trait values or inferred genetic architecture of the traits. Any differences between the populations for trait values could be explained by maternal environmental effects. We discuss whether the similarities in architectures of these populations is the result of natural selection across a common juvenile environment.     

An experimental method for evaluating the contribution of deleterious mutations to quantitative trait variation.

Unconditionally deleterious mutations could be an important source of variation in quantitative traits. Deleterious mutations should be rare (segregating at low frequency in the population) and at least partially recessive. In this paper, I suggest that the contribution of rare, partially recessive alleles to quantitative trait variation can be assessed by comparing the relative magnitudes of two genetic variance components: the covariance of additive and homozygous dominance effects (Cad) and the additive genetic variance (Va). If genetic variation is due to rare recessives, then the ratio of Cad to Va should be equal to or greater than 1. In contrast, Cad/Va should be close to zero or even negative if variation is caused by alleles at intermediate frequencies. The ratio of Cad to Va can be estimated from phenotypic comparisons between inbred and outbred relatives, but such estimates are likely to be highly imprecise. Selection experiments provide an alternative estimator for Cad/Va, one with favourable statistical properties. When combined with other biometrical analyses, the ratio test can provide an incisive test of the deleterious mutation model.     

Admixture mapping of quantitative traits in Populus hybrid zones: power and limitations

Uncovering the genetic architecture of species differences is of central importance for understanding the origin and maintenance of biological diversity. Admixture mapping can be used to identify the number and effect sizes of genes that contribute to the divergence of ecologically important traits, even in taxa that are not amenable to laboratory crosses because of their long generation time or other limitations. Here, we apply admixture mapping to naturally occurring hybrids between two ecologically divergent Populus species. We map quantitative trait loci for eight leaf morphological traits using 77 mapped microsatellite markers from all 19 chromosomes of Populus. We apply multivariate linear regression analysis allowing the modeling of additive and non-additive gene action and identify several candidate genomic regions associated with leaf morphology using an information-theoretic approach. We perform simulation studies to assess the power and limitations of admixture mapping of quantitative traits in natural hybrid populations for a variety of genetic architectures and modes of gene action. Our results indicate that (1) admixture mapping has considerable power to identify the genetic architecture of species differences if sample sizes and marker densities are sufficiently high, (2) modeling of non-additive gene action can help to elucidate the discrepancy between genotype and phenotype sometimes seen in interspecific hybrids, and (3) the genetic architecture of leaf morphological traits in the studied Populus species involves complementary and overdominant gene action, providing the basis for rapid adaptation of these ecologically important forest trees.     

Hierarchical and factorial mating designs for quantitative genetic analysis in tetrasomic potato

Plant breeders need to quantify additive and non-additive components of genetic variance in order to determine appropriate selection methods to improve quantitative characteristics. Hierarchical and factorial mating designs (also known as North Carolina mating designs I and II, respectively) allow one to determine these variance components. The relative advantages of these two designs in the quantitative genetics of tuber yield in tetrasomic potato were investigated. Likewise, the number of female parents to include in design I was also investigated. Data were collected from two independent experiments at two contrasting Peruvian locations: La Molina in the dry coast and San Ramon in the humid mid-altitude. In the first experiment, although design I gave a negative digenic variance (σ² _D), this design provided almost the same estimate of narrow-sense heritability (h²) for tuber yield as that obtained in design II (0.291 and 0.260, respectively). Therefore, design I appears to be appropriate for quantitative genetics research in tetrasomic potato, a crop in which some clones are male sterile. The easy handling of crosses (distinct random females included in the crossing scheme) is another advantage of design I relative to design II. In the second experiment, 12 males were crossed with either two or four females following a design-I mating scheme. The additive genetic variance (σ² _A) was zero (or negative) when two females per male were included but was positive with four females. These results suggest that two females per male may not be enough for design I in tetrasomic potato. Four females per male are preferable to determine σ² _A in design I for this tetrasomic crop. Received: 19 March 2001 / Accepted: 3 July 2001     

Genetic variants and underlying mechanisms influencing variance heterogeneity in maize

Traditional genetic studies focus on identifying genetic variants associated with the mean difference in a quantitative trait. Because genetic variants also influence phenotypic variation via heterogeneity, we conducted a variance‐heterogeneity genome‐wide association study to examine the contribution of variance heterogeneity to oil‐related quantitative traits. We identified 79 unique variance‐controlling single nucleotide polymorphisms (vSNPs) from the sequences of 77 candidate variance‐heterogeneity genes for 21 oil‐related traits using the Levene test (P < 1.0 × 10^?5). About 30% of the candidate genes encode enzymes that work in lipid metabolic pathways, most of which define clear expression variance quantitative trait loci. Of the vSNPs specifically associated with the genetic variance heterogeneity of oil concentration, 89% can be explained by additional linked mean‐effects genetic variants. Furthermore, we demonstrated that gene × gene interactions play important roles in the formation of variance heterogeneity for fatty acid compositional traits. The interaction pattern was validated for one gene pair (GRMZM2G035341 and GRMZM2G152328) using yeast two‐hybrid and bimolecular fluorescent complementation analyses. Our findings have implications for uncovering the genetic basis of hidden additive genetic effects and epistatic interaction effects, and we indicate opportunities to stabilize efficient breeding and selection of high‐oil maize (Zea mays L.).     

Unifying Genetic Canalization,Genetic Constraint,and Genotype-by-Environment Interaction: QTL by Genomic Background by Environment Interaction of Flowering Time in Boechera stricta

Natural populations exhibit substantial variation in quantitative traits. A quantitative trait is typically defined by its mean and variance, and to date most genetic mapping studies focus on loci altering trait means but not (co)variances. For single traits, the control of trait variance across genetic backgrounds is referred to as genetic canalization. With multiple traits, the genetic covariance among different traits in the same environment indicates the magnitude of potential genetic constraint, while genotype-by-environment interaction (GxE) concerns the same trait across different environments. While some have suggested that these three attributes of quantitative traits are different views of similar concepts, it is not yet clear, however, whether they have the same underlying genetic mechanism. Here, we detect quantitative trait loci (QTL) influencing the (co)variance of phenological traits in six distinct environments in Boechera stricta, a close relative of Arabidopsis. We identified nFT as the QTL altering the magnitude of phenological trait canalization, genetic constraint, and GxE. Both the magnitude and direction of nFT''s canalization effects depend on the environment, and to our knowledge, this reversibility of canalization across environments has not been reported previously. nFT''s effects on trait covariance structure (genetic constraint and GxE) likely result from the variable and reversible canalization effects across different traits and environments, which can be explained by the interaction among nFT, genomic backgrounds, and environmental stimuli. This view is supported by experiments demonstrating significant nFT by genomic background epistatic interactions affecting phenological traits and expression of the candidate gene, FT. In contrast to the well-known canalization gene Hsp90, the case of nFT may exemplify an alternative mechanism: Our results suggest that (at least in traits with major signal integrators such as flowering time) genetic canalization, genetic constraint, and GxE may have related genetic mechanisms resulting from interactions among major QTL, genomic backgrounds, and environments.     

The effect of non-additive genetic interactions on selection in multi-locus genetic models

Additive genetic variance might usually be expected to decrease in a finite population because of genetic drift. However, both theoretical and empirical studies have shown that the additive genetic variance of a population could, in some cases, actually increase owing to the action of genetic drift in presence of non-additive effects. We used Monte-Carlo simulations to address a less-well-studied issue: the effects of directional truncation selection on a trait affected by non-additive genetic variation. We investigated the effects on genetic variance and the response to selection. We compared two different genetic models, representing various numbers of loci. We found that the additive genetic variance could also increase in the case of truncation selection, when dominance and epistasis was present. Additive-by-additive epistatic effects generally gave a higher increase in additive variance compared to dominance. However, the magnitude of the increase differed depending on the particular model and on the number of loci.     

The importance and type of non-additive genetic effects for growth in Eucalyptus globulus

The paper investigates the importance of additive and non-additive genetic variances for growth in Eucalyptus globulus (Tasmanian Blue Gum), based on a large collection of diameter growth data covering 40 sites and more than 4,200 genotypes, most of them cloned, and spanning three generations of breeding. The variance estimates were based on a model accounting for additive, full-sib family and clone within full-sib family terms. The results indicated a small amount of additive genetic variance for diameter ( [^(h)]² = 0.10 ) \left( {{{\widehat{h}}^2} = 0.10} \right) and although non-additive genetic variance was also small, it accounted for a significant proportion of the total genetic variance present, corresponding to 80% of the additive variance. The interpretation of these non-additive effects is difficult. The results suggest, however, a possible role of epistasis. The evidence for this came from a strong observed bias in additive variance when clone effects were removed from the model and a larger than expected variance due to full-sib families relative to the variance due to clones within family. The relatively large proportion of genetic variance for growth that seems to be due to non-additive genetic effects has obvious implications in the breeding and deployment options in eucalypts, and these are briefly discussed.     

Condition dependence and the maintenance of genetic variance in a sexually dimorphic black scavenger fly

The maintenance of genetic variation in traits under strong sexual selection is a longstanding problem in evolutionary biology. The genic capture model proposes that this problem can be explained by the evolution of condition dependence in exaggerated male traits. We tested the predictions that condition dependence should be more pronounced in male sexual traits and that genetic variance in expression of these traits should increase under stress as among‐genotype variation in overall condition is exposed. Genetic variance in female and nonsexual traits should, by contrast, be similar across environments as a result of stabilizing selection on trait expression. The relationship between the degree of sexual dimorphism, condition dependence and additive genetic variance (V_a) was assessed for two morphological traits (body size and relative fore femur width) affecting male mating success in the black scavenger fly Sepsis punctum (Diptera: Sepsidae) and for development time (a nonsexual trait often correlated with body size). We compared trait expression between the sexes for two cross‐continental populations that differ in degree of sexual dimorphism (Ottawa and Zurich). Condition dependence was indeed most pronounced in males of the strongly dimorphic Zurich population (males larger), and V_a was similar for males and females unless the trait was strongly sex specific and condition dependent. Contrary to prediction, however, V_a primarily increased under food limitation in both sexes, and genetic variance in fore femur width was low to nil, perhaps depleted by putatively strong sexual selection. Solely for body size of Zurich males, V_a increased more in males than females at limited food, in accordance with the predictions of the genic capture model. Overall therefore, quantitative genetic evidence in support of the model was inconsistent and weak at best.     

Genetic architecture and phenotypic plasticity of thermally-regulated traits in an eruptive species, <Emphasis Type="Italic">Dendroctonus ponderosae</Emphasis>

Phenotypic plasticity in thermally-regulated traits enables close tracking of changing environmental conditions, and can thereby enhance the potential for rapid population increase, a hallmark of outbreak insect species. In a changing climate, exposure to conditions that exceed the capacity of existing phenotypic plasticity may occur. Combining information on genetic architecture and trait plasticity among populations that are distributed along a latitudinal cline can provide insight into how thermally-regulated traits evolve in divergent environments and the potential for adaptation. Dendroctonus ponderosae feed on Pinus species in diverse climatic regimes throughout western North America, and show eruptive population dynamics. We describe geographical patterns of plasticity in D. ponderosae development time and adult size by examining reaction norms of populations from multiple latitudes. The relative influence of additive and non-additive genetic effects on population differences in the two phenotypic traits at a single temperature is quantified using line-cross experiments and joint-scaling tests. We found significant genetic and phenotypic variation among D. ponderosae populations. Simple additive genetic variance was not the primary source of the observed variation, and dominance and epistasis contributed greatly to the genetic divergence of the two thermally-regulated traits. Hybrid breakdown was also observed in F₂ hybrid crosses between northern and southern populations, further indication of substantial genetic differences among clinal populations and potential reproductive isolation within D. ponderosae. Although it is unclear what maintains variation in the life-history traits, observed plasticity in thermally-regulated traits that are directly linked to rapid numerical change may contribute to the outbreak nature of D. ponderosae, particularly in a changing climate.     

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.     

Percent of oxygen saturation of arterial hemoglobin among Bolivian Aymara at 3,900–4,000 m

A range of variation in percent of oxygen saturation of arterial hemoglobin (SaO₂) among healthy individuals at a given high altitude indicates differences in physiological hypoxemia despite uniform ambient hypoxic stress. In populations native to the Tibetan plateau, a significant portion of the variance is attributable to additive genetic factors, and there is a major gene influencing SaO₂. To determine whether there is genetic variance in other high-altitude populations, we designed a study to test the hypothesis that additive genetic factors contribute to phenotypic variation in SaO₂ among Aymara natives of the Andean plateau, a population geographically distant from the Tibetan plateau and with a long, separate history of high-altitude residence. The average SaO₂ of 381 Aymara at 3,900–4,000 m was 92 ± 0.15% (SEM) with a range of 84–99%. The average was 2.6% higher than the average SaO₂ of a sample of Tibetans at 3,800–4,065 m measured with the same techniques. Quantitative genetic analyses of the Aymara sample detected no significant variance attributable to genetic factors. The presence of genetic variance in SaO₂ in the Tibetan sample and its absence in the Aymara sample indicate there is potential for natural selection on this trait in the Tibetan but not the Aymara population. Am J Phys Anthropol 108:41–51, 1999. © 1999 Wiley-Liss, Inc.     

Dominance Genetic Variance for Traits Under Directional Selection in Drosophila serrata

In contrast to our growing understanding of patterns of additive genetic variance in single- and multi-trait combinations, the relative contribution of nonadditive genetic variance, particularly dominance variance, to multivariate phenotypes is largely unknown. While mechanisms for the evolution of dominance genetic variance have been, and to some degree remain, subject to debate, the pervasiveness of dominance is widely recognized and may play a key role in several evolutionary processes. Theoretical and empirical evidence suggests that the contribution of dominance variance to phenotypic variance may increase with the correlation between a trait and fitness; however, direct tests of this hypothesis are few. Using a multigenerational breeding design in an unmanipulated population of Drosophila serrata, we estimated additive and dominance genetic covariance matrices for multivariate wing-shape phenotypes, together with a comprehensive measure of fitness, to determine whether there is an association between directional selection and dominance variance. Fitness, a trait unequivocally under directional selection, had no detectable additive genetic variance, but significant dominance genetic variance contributing 32% of the phenotypic variance. For single and multivariate morphological traits, however, no relationship was observed between trait–fitness correlations and dominance variance. A similar proportion of additive and dominance variance was found to contribute to phenotypic variance for single traits, and double the amount of additive compared to dominance variance was found for the multivariate trait combination under directional selection. These data suggest that for many fitness components a positive association between directional selection and dominance genetic variance may not be expected.     

Mate choice for non-additive genetic benefits: a resolution to the lek paradox

In promiscuous mating systems, females often show a consistent preference to mate with one or a few males, presumably to acquire heritable genetic benefits for their offspring. However, strong directional selection should deplete additive genetic variation in fitness and consequently any benefit to expressing the preference by females (referred to as the lek paradox). Here, we provide a novel resolution that examines non-additive genetic benefits, such as overdominance or inbreeding, as a source of genetic variation. Focusing on the inbreeding coefficient f and overdominance effects, we use dynamic models to show that (1) f can be inherited from sire to offspring, (2) populations with females that express a mating preferences for outbred males (low f) maintain higher genetic variation than populations with females that mate randomly, and (3) preference alleles for outbred males can invade populations even when the alleles are associated with a fecundity cost. We show that non-additive genetic variation due to overdominance can be converted to additive genetic variation and becomes “heritable” when the frequencies of alternative homozygous genotypes at fitness loci deviate from equality. Unlike previous models that assume an infinite population size, we now show that genetic drift in finite populations can lead to the necessary deviations in the frequencies of homozygous genotypes. We also show that the “heritability of f,” and hence the benefit to a mating preference for non-additive genetic benefits, is highest in small populations and populations in which a smaller number of loci contribute to fitness via overdominance. Our model contributes to the solution of the lek paradox.     

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.