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.     

Influence of Gene Interaction on Complex Trait Variation with Multilocus Models

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

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

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

Identifying quantitative trait locus by genetic background interactions in association studies

Association studies are designed to identify main effects of alleles across a potentially wide range of genetic backgrounds. To control for spurious associations, effects of the genetic background itself are often incorporated into the linear model, either in the form of subpopulation effects in the case of structure or in the form of genetic relationship matrices in the case of complex pedigrees. In this context epistatic interactions between loci can be captured as an interaction effect between the associated locus and the genetic background. In this study I developed genetic and statistical models to tie the locus by genetic background interaction idea back to more standard concepts of epistasis when genetic background is modeled using an additive relationship matrix. I also simulated epistatic interactions in four-generation randomly mating pedigrees and evaluated the ability of the statistical models to identify when a biallelic associated locus was epistatic to other loci. Under additive-by-additive epistasis, when interaction effects of the associated locus were quite large (explaining 20% of the phenotypic variance), epistasis was detected in 79% of pedigrees containing 320 individuals. The epistatic model also predicted the genotypic value of progeny better than a standard additive model in 78% of simulations. When interaction effects were smaller (although still fairly large, explaining 5% of the phenotypic variance), epistasis was detected in only 9% of pedigrees containing 320 individuals and the epistatic and additive models were equally effective at predicting the genotypic values of progeny. Epistasis was detected with the same power whether the overall epistatic effect was the result of a single pairwise interaction or the sum of nine pairwise interactions, each generating one ninth of the epistatic variance. The power to detect epistasis was highest (94%) at low QTL minor allele frequency, fell to a minimum (60%) at minor allele frequency of about 0.2, and then plateaued at about 80% as alleles reached intermediate frequencies. The power to detect epistasis declined when the linkage disequilibrium between the DNA marker and the functional polymorphism was not complete.     

Mapping single-locus and epistatic quantitative trait loci for plant architectural traits in chrysanthemum

Plant architecture is important for chrysanthemum cultivation and breeding. To determine the genetic basis of plant architectural traits in chrysanthemum, a population of 142 F1 plants derived from a cross between the creeping ground-cover chrysanthemum cultivar Yuhualuoying and the erect potted cultivar Aoyunhanxiao was used to detect quantitative trait loci (QTL) associated with plant height, plant width, inter-node length and flower neck length. The broad-sense heritability h _B ² for the four plant architectural traits ranged from 0.33 to 0.83, and transgressive segregation was observed. Single-locus QTL analysis revealed a total of five QTL, accounting for 6.0?C16.1% of the phenotypic variation. Additionally, 11 pairs of epistatic QTL were identified, explaining 3.5?C14.5% of the phenotypic variations. The majority of the interactions detected occurred between background loci. These results indicate that both additive and epistatic effects contribute to phenotypic variation in the plant architecture of chrysanthemum. It is expected that the identified markers associated with the additive QTL and epistatic QTL detected in this study will be of importance in future breeding programs to develop chrysanthemum cultivars exhibiting desirable plant architecture.     

The Multi-allelic Genetic Architecture of a Variance-Heterogeneity Locus for Molybdenum Concentration in Leaves Acts as a Source of Unexplained Additive Genetic Variance

Genome-wide association (GWA) analyses have generally been used to detect individual loci contributing to the phenotypic diversity in a population by the effects of these loci on the trait mean. More rarely, loci have also been detected based on variance differences between genotypes. Several hypotheses have been proposed to explain the possible genetic mechanisms leading to such variance signals. However, little is known about what causes these signals, or whether this genetic variance-heterogeneity reflects mechanisms of importance in natural populations. Previously, we identified a variance-heterogeneity GWA (vGWA) signal for leaf molybdenum concentrations in Arabidopsis thaliana. Here, fine-mapping of this association reveals that the vGWA emerges from the effects of three independent genetic polymorphisms that all are in strong LD with the markers displaying the genetic variance-heterogeneity. By revealing the genetic architecture underlying this vGWA signal, we uncovered the molecular source of a significant amount of hidden additive genetic variation or “missing heritability”. Two of the three polymorphisms underlying the genetic variance-heterogeneity are promoter variants for Molybdate transporter 1 (MOT1), and the third a variant located ~25 kb downstream of this gene. A fourth independent association was also detected ~600 kb upstream of MOT1. Use of a T-DNA knockout allele highlights Copper Transporter 6; COPT6 (AT2G26975) as a strong candidate gene for this association. Our results show that an extended LD across a complex locus including multiple functional alleles can lead to a variance-heterogeneity between genotypes in natural populations. Further, they provide novel insights into the genetic regulation of ion homeostasis in A. thaliana, and empirically confirm that variance-heterogeneity based GWA methods are a valuable tool to detect novel associations of biological importance in natural populations.     

Genetics of Callous-Unemotional Behavior in Children

Callous-unemotional behavior (CU) is currently under consideration as a subtyping index for conduct disorder diagnosis. Twin studies routinely estimate the heritability of CU as greater than 50%. It is now possible to estimate genetic influence using DNA alone from samples of unrelated individuals, not relying on the assumptions of the twin method. Here we use this new DNA method (implemented in a software package called Genome-wide Complex Trait Analysis, GCTA) for the first time to estimate genetic influence on CU. We also report the first genome-wide association (GWA) study of CU as a quantitative trait. We compare these DNA results to those from twin analyses using the same measure and the same community sample of 2,930 children rated by their teachers at ages 7, 9 and 12. GCTA estimates of heritability were near zero, even though twin analysis of CU in this sample confirmed the high heritability of CU reported in the literature, and even though GCTA estimates of heritability were substantial for cognitive and anthropological traits in this sample. No significant associations were found in GWA analysis, which, like GCTA, only detects additive effects of common DNA variants. The phrase ‘missing heritability’ was coined to refer to the gap between variance associated with DNA variants identified in GWA studies versus twin study heritability. However, GCTA heritability, not twin study heritability, is the ceiling for GWA studies because both GCTA and GWA are limited to the overall additive effects of common DNA variants, whereas twin studies are not. This GCTA ceiling is very low for CU in our study, despite its high twin study heritability estimate. The gap between GCTA and twin study heritabilities will make it challenging to identify genes responsible for the heritability of CU.     

A variational Bayes algorithm for fast and accurate multiple locus genome-wide association analysis

Background  

The success achieved by genome-wide association (GWA) studies in the identification of candidate loci for complex diseases has been accompanied by an inability to explain the bulk of heritability. Here, we describe the algorithm V-Bay, a variational Bayes algorithm for multiple locus GWA analysis, which is designed to identify weaker associations that may contribute to this missing heritability.     

Characterisation of genome-wide association epistasis signals for serum uric acid in human population isolates

Genome-wide association (GWA) studies have identified a number of loci underlying variation in human serum uric acid (SUA) levels with the SLC2A9 gene having the largest effect identified so far. Gene-gene interactions (epistasis) are largely unexplored in these GWA studies. We performed a full pair-wise genome scan in the Italian MICROS population (n = 1201) to characterise epistasis signals in SUA levels. In the resultant epistasis profile, no SNP pairs reached the Bonferroni adjusted threshold for the pair-wise genome-wide significance. However, SLC2A9 was found interacting with multiple loci across the genome, with NFIA - SLC2A9 and SLC2A9 - ESRRAP2 being significant based on a threshold derived for interactions between GWA significant SNPs and the genome and jointly explaining 8.0% of the phenotypic variance in SUA levels (3.4% by interaction components). Epistasis signal replication in a CROATIAN population (n = 1772) was limited at the SNP level but improved dramatically at the gene ontology level. In addition, gene ontology terms enriched by the epistasis signals in each population support links between SUA levels and neurological disorders. We conclude that GWA epistasis analysis is useful despite relatively low power in small isolated populations.     

Effect on linkage disequilibrium of selection for a quantitative character with epistasis

Summary Selection for a character controlled by additive genes induces linkage disequilibrium which reduces the additive genetic variance usable for further selective gains. Additive x additive epistasis contributes to selection response through development of linkage disequilibrium between interacting loci. To investigate the relative importance of the two effects of linkage disequilibrium, formulae are presented and results are reported of simulations using models involving additive, additive x additive and dominance components. The results suggest that so long as epistatic effects are not large relative to additive effects, and the proportion of pairs of loci which show epistasis is not very high, the predominant effect of linkage disequilibrium will be to reduce the rate of selection response.     

Effect of inter- and intragenic epistasis on the heritability of oil content in rapeseed (Brassica napus L.)

The loci detected by association mapping which are involved in the expression of important agronomic traits in crops often explain only a small proportion of the total genotypic variance. Here, 17 SNPs derived from 9 candidate genes from the triacylglycerol biosynthetic pathway were studied in an association analysis in a population of 685 diverse elite rapeseed inbred lines. The 685 lines were evaluated for oil content, as well as for glucosinolates, yield, and thousand-kernel weight in field trials at 4 locations. We detected main effects for most of the studied genes illustrating that genetic diversity for oil content can be exploited by the selection of favorable alleles. In addition to main effects, both intergenic and intragenic epistasis was detected that contributes to a considerable amount to the genotypic variance observed for oil content. The proportion of explained genotypic variance was doubled when in addition to main effects epistasis was considered. Therefore, a knowledge-based improvement of oil content in rapeseed should also take such favorable epistatic interactions into account. Our results suggest, that the observed high contribution of epistasis may to some extent explain the missing heritability in genome-wide association studies.     

Epistatic interaction is an important genetic basis of grain yield and its components in maize

A population of 294 recombinant inbred lines (RIL) derived from Yuyu22, an elite maize hybrid extending broadly in China, has been constructed to investigate the genetic basis of grain yield, and associated yield components in maize. The main-effect quantitative trait loci (QTL), digenic epistatic interactions, and their interactions with the environment for grain yield and its three components were identified by using the mixed linear model approach. Thirty-two main-effect QTL and forty-four pairs of digenic epistatic interactions were detected for the four measured traits in four environments. Our results suggest that both additive effects and epistasis (additive × additive) effects are important genetic bases of grain yield and its components in the RIL population. Only 30.4% of main-effect QTL for ear length were involved in epistatic interactions. This implies that many loci in epistatic interactions may not have significant effects for traits alone but may affect trait expression by epistatic interaction with the other loci.     

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.     

EPISTASIS AND THE EFFECT OF FOUNDER EVENTS ON THE ADDITIVE GENETIC VARIANCE

Models of founder events have focused on the reduction in the genetic variation following a founder event. However, recent work (Bryant et al., 1986; Goodnight, 1987) suggests that when there is epistatic genetic variance in a population, the total genetic variance within demes may actually increase following a founder event. Since the additive genetic variance is a statistical property of a population and can change with the level of inbreeding, some of the epistatic genetic variance may be converted to additive genetic variance during a founder event. The model presented here demonstrates that some of the additive-by-additive epistatic genetic variance is converted to additive genetic variance following a founder event. Furthermore, the amount of epistasis converted to additive genetic variance is a function of the recombination rate and the propagule size. For a single founder event of two individuals, as much as 75% of the epistatic variance in the ancestral population may become additive genetic variance following the founder event. For founder events involving two individuals with free recombination, the relative contribution of epistasis to the additive genetic variance following a founder event is equal to its proportion of the total genetic variance prior to the founder event. Traits closely related to fitness are expected to have relatively little additive genetic variance but may have substantial nonadditive genetic variance. Founder events may be important in the evolution of fitness traits, not because they lead to a reduction in the genetic variance, but rather because they lead to an increase in the additive genetic variance.     

Mapping the epistatic network underlying murine reproductive fatpad variation

Genome-wide mapping analyses are now commonplace in many species and several networks of interacting loci have been reported. However, relatively few details regarding epistatic interactions and their contribution to complex trait variation in multicellular organisms are available and the identification of positional candidate loci for epistatic QTL (epiQTL) is hampered, especially in mammals, by the limited genetic resolution inherent in most study designs. Here we further investigate the genetic architecture of reproductive fatpad weight in mice using the F(10) generation of the LG,SM advanced intercross (AI) line. We apply multiple mapping techniques including a single-locus model, locus-specific composite interval mapping (CIM), and tests for multiple QTL per chromosome to the 12 chromosomes known to harbor single-locus QTL (slQTL) affecting obesity in this cross. We also perform a genome-wide scan for pairwise epistasis. Using this combination of approaches we detect 199 peaks spread over all 19 autosomes, which potentially contribute to trait variation including all eight original F(2) loci (Adip1-8), novel slQTL peaks on chromosomes 7 and 9, and several novel epistatic loci. Extensive epistasis is confirmed involving both slQTL confidence intervals (C.I.) as well as regions that show no significant additive or dominance effects. These results provide important new insights into mapping complex genetic architectures and the role of epistasis in complex trait variation.     

WILL POPULATION BOTTLENECKS AND MULTILOCUS EPISTASIS INCREASE ADDITIVE GENETIC VARIANCE?

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

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.     

Genetic expectations of quantitative trait loci main and interaction effects obtained with the triple testcross design and their relevance for the analysis of heterosis

Interpretation of experimental results from quantitative trait loci (QTL) mapping studies on the predominant type of gene action can be severely affected by the choice of statistical model, experimental design, and provision of epistasis. In this study, we derive quantitative genetic expectations of (i) QTL effects obtained from one-dimensional genome scans with the triple testcross (TTC) design and (ii) pairwise interactions between marker loci using two-way analyses of variance (ANOVA) under the F(2)- and the F(infinity)-metric model. The theoretical results show that genetic expectations of QTL effects estimated with the TTC design are complex, comprising both main and epistatic effects, and that genetic expectations of two-way marker interactions are not straightforward extensions of effects estimated in one-dimensional scans. We also demonstrate that the TTC design can partially overcome the limitations of the design III in separating QTL main effects and their epistatic interactions in the analysis of heterosis and that dominance x additive epistatic interactions of individual QTL with the genetic background can be estimated with a one-dimensional genome scan. Furthermore, we present genetic expectations of variance components for the analysis of TTC progeny tested in a split-plot design, assuming digenic epistasis and arbitrary linkage.     

Epistasis and Its Contribution to Genetic Variance Components

We present a new parameterization of physiological epistasis that allows the measurement of epistasis separate from its effects on the interaction (epistatic) genetic variance component. Epistasis is the deviation of two-locus genotypic values from the sum of the contributing single-locus genotypic values. This parameterization leads to statistical tests for epistasis given estimates of two-locus genotypic values such as can be obtained from quantitative trait locus studies. The contributions of epistasis to the additive, dominance and interaction genetic variances are specified. Epistasis can make substantial contributions to each of these variance components. This parameterization of epistasis allows general consideration of the role of epistasis in evolution by defining its contribution to the additive genetic variance.