The Genetic Architecture of Quantitative Traits Cannot Be Inferred from Variance Component Analysis

Classical quantitative genetic analyses estimate additive and non-additive genetic and environmental components of variance from phenotypes of related individuals without knowing the identities of quantitative trait loci (QTLs). Many studies have found a large proportion of quantitative trait variation can be attributed to the additive genetic variance (V_A), providing the basis for claims that non-additive gene actions are unimportant. In this study, we show that arbitrarily defined parameterizations of genetic effects seemingly consistent with non-additive gene actions can also capture the majority of genetic variation. This reveals a logical flaw in using the relative magnitudes of variance components to indicate the relative importance of additive and non-additive gene actions. We discuss the implications and propose that variance component analyses should not be used to infer the genetic architecture of quantitative traits.     

Assumptions and Properties of Limiting Pathway Models for Analysis of Epistasis in Complex Traits

For most complex traits, results from genome-wide association studies show that the proportion of the phenotypic variance attributable to the additive effects of individual SNPs, that is, the heritability explained by the SNPs, is substantially less than the estimate of heritability obtained by standard methods using correlations between relatives. This difference has been called the “missing heritability”. One explanation is that heritability estimates from family (including twin) studies are biased upwards. Zuk et al. revisited overestimation of narrow sense heritability from twin studies as a result of confounding with non-additive genetic variance. They propose a limiting pathway (LP) model that generates significant epistatic variation and its simple parametrization provides a convenient way to explore implications of epistasis. They conclude that over-estimation of narrow sense heritability from family data (‘phantom heritability’) may explain an important proportion of missing heritability. We show that for highly heritable quantitative traits large phantom heritability estimates from twin studies are possible only if a large contribution of common environment is assumed. The LP model is underpinned by strong assumptions that are unlikely to hold, including that all contributing pathways have the same mean and variance and are uncorrelated. Here, we relax the assumptions that underlie the LP model to be more biologically plausible. Together with theoretical, empirical, and pragmatic arguments we conclude that in outbred populations the contribution of additive genetic variance is likely to be much more important than the contribution of non-additive variance.     

Sexual selection in the cricket <Emphasis Type="Italic">Gryllus bimaculatus</Emphasis>: no good genes?

Recent studies have suggested that females of the field cricket Gryllus bimaculatus exercise post-copulatory choice over the paternity of their offspring. There is evidence that these choices are made in relation to the genetic compatibility of mates rather than their absolute quality, but the magnitude of heritable differences in males has not been thoroughly examined. Using a half-sib breeding design we measured additive genetic variance and dam effects in a suite of reproductive and non-reproductive traits. Both components explained relatively little of the phenotypic variance across traits. The dam component in our design contains variance caused by both maternal effects and dominance. If maternal effects are negligible as suggested by previous studies, our data suggest that dominance variance is an important source of variation in these traits. The lack of additive genetic variation, but possible existence of large amounts of non-additive genetic variation is consistent with the idea that female mate choice and multiple mating may be driven by differences in genetic compatibility between potential mates rather than by differences in genetic quality.     

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 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.     

Estimating Additive and Non-Additive Genetic Variances and Predicting Genetic Merits Using Genome-Wide Dense Single Nucleotide Polymorphism Markers

Non-additive genetic variation is usually ignored when genome-wide markers are used to study the genetic architecture and genomic prediction of complex traits in human, wild life, model organisms or farm animals. However, non-additive genetic effects may have an important contribution to total genetic variation of complex traits. This study presented a genomic BLUP model including additive and non-additive genetic effects, in which additive and non-additive genetic relation matrices were constructed from information of genome-wide dense single nucleotide polymorphism (SNP) markers. In addition, this study for the first time proposed a method to construct dominance relationship matrix using SNP markers and demonstrated it in detail. The proposed model was implemented to investigate the amounts of additive genetic, dominance and epistatic variations, and assessed the accuracy and unbiasedness of genomic predictions for daily gain in pigs. In the analysis of daily gain, four linear models were used: 1) a simple additive genetic model (MA), 2) a model including both additive and additive by additive epistatic genetic effects (MAE), 3) a model including both additive and dominance genetic effects (MAD), and 4) a full model including all three genetic components (MAED). Estimates of narrow-sense heritability were 0.397, 0.373, 0.379 and 0.357 for models MA, MAE, MAD and MAED, respectively. Estimated dominance variance and additive by additive epistatic variance accounted for 5.6% and 9.5% of the total phenotypic variance, respectively. Based on model MAED, the estimate of broad-sense heritability was 0.506. Reliabilities of genomic predicted breeding values for the animals without performance records were 28.5%, 28.8%, 29.2% and 29.5% for models MA, MAE, MAD and MAED, respectively. In addition, models including non-additive genetic effects improved unbiasedness of genomic predictions.     

Sexual selection in the cricket <Emphasis Type="Italic">Gryllus bimaculatus</Emphasis>: no good genes?

Recent studies have suggested that females of the field cricket Gryllus bimaculatus exercise post-copulatory choice over the paternity of their offspring. There is evidence that these choices are made in relation to the genetic compatibility of mates rather than their absolute quality, but the magnitude of heritable differences in males has not been thoroughly examined. Using a half-sib breeding design we measured additive genetic variance and dam effects in a suite of reproductive and non-reproductive traits. Both components explained relatively little of the phenotypic variance across traits. The dam component in our design contains variance caused by both maternal effects and dominance. If maternal effects are negligible as suggested by previous studies, our data suggest that dominance variance is an important source of variation in these traits. The lack of additive genetic variation, but possible existence of large amounts of non-additive genetic variation is consistent with the idea that female mate choice and multiple mating may be driven by differences in genetic compatibility between potential mates rather than by differences in genetic quality.     

Assumption-free estimation of heritability from genome-wide identity-by-descent sharing between full siblings

The study of continuously varying, quantitative traits is important in evolutionary biology, agriculture, and medicine. Variation in such traits is attributable to many, possibly interacting, genes whose expression may be sensitive to the environment, which makes their dissection into underlying causative factors difficult. An important population parameter for quantitative traits is heritability, the proportion of total variance that is due to genetic factors. Response to artificial and natural selection and the degree of resemblance between relatives are all a function of this parameter. Following the classic paper by R. A. Fisher in 1918, the estimation of additive and dominance genetic variance and heritability in populations is based upon the expected proportion of genes shared between different types of relatives, and explicit, often controversial and untestable models of genetic and non-genetic causes of family resemblance. With genome-wide coverage of genetic markers it is now possible to estimate such parameters solely within families using the actual degree of identity-by-descent sharing between relatives. Using genome scans on 4,401 quasi-independent sib pairs of which 3,375 pairs had phenotypes, we estimated the heritability of height from empirical genome-wide identity-by-descent sharing, which varied from 0.374 to 0.617 (mean 0.498, standard deviation 0.036). The variance in identity-by-descent sharing per chromosome and per genome was consistent with theory. The maximum likelihood estimate of the heritability for height was 0.80 with no evidence for non-genetic causes of sib resemblance, consistent with results from independent twin and family studies but using an entirely separate source of information. Our application shows that it is feasible to estimate genetic variance solely from within-family segregation and provides an independent validation of previously untestable assumptions. Given sufficient data, our new paradigm will allow the estimation of genetic variation for disease susceptibility and quantitative traits that is free from confounding with non-genetic factors and will allow partitioning of genetic variation into additive and non-additive components.     

Marker-assisted prediction of non-additive genetic values

It has become increasingly clear from systems biology arguments that interaction and non-linearity play an important role in genetic regulation of phenotypic variation for complex traits. Marker-assisted prediction of genetic values assuming additive gene action has been widely investigated because of its relevance in artificial selection. On the other hand, it has been less well-studied when non-additive effects hold. Here, we explored a nonparametric model, radial basis function (RBF) regression, for predicting quantitative traits under different gene action modes (additivity, dominance and epistasis). Using simulation, it was found that RBF had better ability (higher predictive correlations and lower predictive mean square errors) of predicting merit of individuals in future generations in the presence of non-additive effects than a linear additive model, the Bayesian Lasso. This was true for populations undergoing either directional or random selection over several generations. Under additive gene action, RBF was slightly worse than the Bayesian Lasso. While prediction of genetic values under additive gene action is well handled by a variety of parametric models, nonparametric RBF regression is a useful counterpart for dealing with situations where non-additive gene action is suspected, and it is robust irrespective of mode of gene action.     

Quantitative genetic variation of leaf size and shape in a mixed diploid and triploid population of Populus

In the interspecific cross of Populus trichocarpa x P. deltoides, unexpected simultaneous occurrence of diploid hybrids and triploid hybrids (with two alleles from the female parent and one from the male parent at each locus) led us to examine the evolutionary genetic significance of this phenomenon. As expected, leaf size and shape of the triploid progeny are closer to the female P. trichocarpa than male P. deltoides parent. Although the pure triploid progeny population did not have higher genetic variance in leaf traits than the pure diploid population, the former appears to hide much non-additive genetic variance and display strong genetic control over the phenotypic plasticity of leaf traits. It is suggested that the cryptic non-additive variance, especially epistasis, can be released when a population is disturbed by changes in the environment. A mixed diploid and triploid progeny population combines phenotypic and genetic characteristics of both pure hybrids and is considered to be of adaptive significance for populars to survive and evolve in a fluctuating environment. The significant effect due to general and specific combining ability differences at the population level suggests that the population divergence of these two species is under additive and non-additive genetic control.     

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.     

Beyond mean allelic effects: A locus at the major color gene MC1R associates also with differing levels of phenotypic and genetic (co)variance for coloration in barn owls

The mean phenotypic effects of a discovered variant help to predict major aspects of the evolution and inheritance of a phenotype. However, differences in the phenotypic variance associated to distinct genotypes are often overlooked despite being suggestive of processes that largely influence phenotypic evolution, such as interactions between the genotypes with the environment or the genetic background. We present empirical evidence for a mutation at the melanocortin‐1‐receptor gene, a major vertebrate coloration gene, affecting phenotypic variance in the barn owl, Tyto alba. The white MC1R allele, which associates with whiter plumage coloration, also associates with a pronounced phenotypic and additive genetic variance for distinct color traits. Contrarily, the rufous allele, associated with a rufous coloration, relates to a lower phenotypic and additive genetic variance, suggesting that this allele may be epistatic over other color loci. Variance differences between genotypes entailed differences in the strength of phenotypic and genetic associations between color traits, suggesting that differences in variance also alter the level of integration between traits. This study highlights that addressing variance differences of genotypes in wild populations provides interesting new insights into the evolutionary mechanisms and the genetic architecture underlying the phenotype.     

Y-chromosomes can constrain adaptive evolution via epistatic interactions with other chromosomes

Background

Variation in the non-coding regions of Y-chromosomes have been shown to influence gene regulation throughout the genome in some systems; a phenomenon termed Y-linked regulatory variation (YRV). This type of sex-specific genetic variance could have important implications for the evolution of male and female traits. If YRV contributes to the additive genetic variation of an autosomally coded trait shared between the sexes (e.g. body size), then selection could facilitate sexually dimorphic evolution via the Y-chromosome. In contrast, if YRV is entirely non-additive (i.e. interacts epistatically with other chromosomes), then Y-chromosomes could constrain trait evolution in both sexes whenever they are selected for the same trait value. The ability for this phenomenon to influence such fundamental evolutionary dynamics remains unexplored.

Results

Here we address the evolutionary contribution of Y-linked variance by selecting for improved male geotaxis in populations possessing multiple Y-chromosomes (i.e. possessed Y-linked additive and/or epistatic variation) or a single Y-chromosome variant (i.e. possessed no Y-linked variation). We found that males from populations possessing Y-linked variation did not significantly respond to selection; however, males from populations with no Y-linked variation did respond. These patterns suggest the presence of a large quantity of Y-linked epistatic variance in the multi-Y population that dramatically slowed its response.

Conclusions

Our results imply that YRV is unlikely to facilitate the evolution of sexually dimorphic traits (at least for the trait examined here), but can interfere with the rate of trait evolution in both males and females. This result could have real biological implications as it suggests that YRV can affect how quickly a population responds to new selective pressures (e.g. invasive species, novel pathogens, or climate change). Considering that YRV influences hundreds of genes and is likely typical of other independently-evolved hemizygous chromosomes, YRV-like phenomena may represent common and significant costs to hemizygous sex determination.

     

Partitioning of genetic variance and selection efficiency for alternative vegetative deployment strategies for white spruce in Eastern Canada

Genetic variances and selection efficiencies for growth traits of white spruce (Picea glauca (Moench) Voss) were estimated from clonally replicated full-sib progeny tests established both in nursery and field environments in New Brunswick, Canada. The available data included heights at 4, 5, and 6 years in the nursery test; height at 9 years, height, DBH, and volume at 14 years in the field test. Estimated variance components were interpreted according to an additive-dominance-epistasis model. For heights in the nursery test, while both non-additive and additive variances were important sources of genetic variation, the former decreased but the latter increased with age; among the non-additive genetic variance, the epistatic variance was much more important than the dominance variance. Different from the nursery traits, for traits in the field test, additive variance accounted for an average of 81% of the total genetic variance, whereas dominance variance explained most of the remaining genetic variance. Genetic parameters and selection efficiencies for three vegetative deployment strategies: deploying half-sib families (VD_FAM_HS), full-sib families (VD_FAM_FS), and multi-varietal forestry (MVF), were compared. Heritability estimates were moderate for VD_FAM_HS and VD_FAM_FS (0.61–0.72), high for MVF (>0.82) for the nursery heights, and high (>0.79) for the field traits for all strategies. Genetic correlations of volume at age 14 in the field test, the target trait for improvement, were strong (>0.85) with other field traits. Genetic correlations of VOL14 with the nursery heights were also strong (>0.71) at the half-sib and full-sib family levels, but were only moderate (>0.59) for MVF. Overall, practicing MVF is the most effective deployment strategy, yielding the highest genetic gains, followed by VD_FAM_FS and VD_FAM_HS, regardless of traits and selection methods. Furthermore, early selections for HT9 or for HT4–HT6 were very encouraging, resulting in higher gain in volume at age 14 on a per year basis.     

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 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.     

Exploitation of heterosis for carotenoid content in African marigold (<Emphasis Type="Italic">Tagetes erecta</Emphasis> L.) and its correlation with esterase polymorphism

African marigold (Tagetes erecta L.), a major source of carotenoids, is also grown as a cut flower and a garden flower in addition to being grown for its medicinal values. We studied gene action, combining ability and heterosis, aiming at genetic improvement of T. erecta for enhanced carotenoid content in petals, and report for the first time that heterosis can be exploited for total carotenoids and its commercially important fractions. Total content of carotenoids and lutein appears to be governed by dominance (or non-additive) gene action, while content of xanthophyll esters is governed by both additive and dominance (or non-additive) gene actions. Specific combining ability variance was predominant for all the three traits. General and specific combining abilities and heterosis were highly significant. Heterobeltiosis was also positive. General combining ability (GCA) variances were not significantly correlated to performance per se. There was also no correlation between performance per se of normal petalled pollen parents and the performance of crosses made between male-sterile (female) and male-fertile (pollen) parents. These findings suggest that carotenoid content should not be the only criterion considered in the selection of parental lines. Studies on esterase in seeds and peroxidase in seedlings revealed a relatively high level of polymorphism in esterase with a total of 14 isoforms, whereas peroxidase showed low polymorphism. Similarity indices between different parental combinations, calculated based on seed esterase polymorphism, showed a significant negative correlation (r = -0.479, P = 0.05) with heterosis for carotenoid content. This indicates that the selection of parents with wider variation in their esterase profiles may possibly be exploited for genetic enhancement of carotenoids in T. erecta.     

Do bottlenecks increase additive genetic variance?

Because of anthropogenic factors many populations have been at least temporarily reduced to a very small population size. Such reductions could potentially decrease genetic variation and increase the probability of extinction. Analysis of molecular markers has shown a decrease in genetic variation but in many cases this has not reduced the ability of the population to recover from the bottleneck. This apparent paradox is resolved by a consideration of how population bottlenecks can affect additive genetic variance, the relevant measure of ability to respond to selective factors. A bottleneck has the potential to increase additive genetic variance in a population. This may result in an increase in fitness, particularly in populations of conservation concern that are small and lack genetic variation. Here we present a meta-analysis of experimental tests of this prediction using models designed to fit data that is strictly additive and data that has non-additive components. This analysis shows that additive genetic variance in a dataset dominated by morphological traits increases, on average, after a bottleneck event when the inbreeding coefficient is less than 0.3, but neither of the theoretical models alone can adequately explain this result. Because of our inability at present to predict the results of a population bottleneck in a specific case and the probability of extinction associated with small population size we caution against using bottlenecks to increase genetic variance, and thus the fitness, of endangered populations.     

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.     

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.