Joint modeling of additive and non-additive (genetic line) effects in multi-environment trials

A statistical approach for the analysis of multi-environment trials (METs) is presented, in which selection of best performing lines, best parents, and best combination of parents can be determined. The genetic effect of a line is partitioned into additive, dominance and residual non-additive effects. The dominance effects are estimated through the incorporation of the dominance relationship matrix, which is presented under varying levels of inbreeding. A computationally efficient way of fitting dominance effects is presented which partitions dominance effects into between family dominance and within family dominance line effects. The overall approach is applicable to inbred lines, hybrid lines and other general population structures where pedigree information is available.     

Epistasis and the conversion of non-additive to additive genetic variance at population bottlenecks

The effect of population bottlenecks on the mean and the additive variance generated by two neutral independent epistatic loci has been studied theoretically. Six epistatic models, used in the analysis of binary disease traits, were considered. Ancestral values in an infinitely large panmictic population were compared with their expectations at equilibrium, after t consecutive bottlenecks of equal size N (derived values). An increase in the additive variance after bottlenecks (inversely related to N and t) will occur only if the frequencies of the negative allele at each locus are: (1) low, invariably associated to strong inbreeding depression; (2) high, always accompanied by an enhancement of the mean with inbreeding. The latter is an undesirable property, making the pertinent models unsuitable for the genetic analysis of disease. For the epistatic models considered, it is unlikely that the rate of evolution may be accelerated after population bottlenecks, in spite of occasional increments of the derived additive variance over its ancestral value.     

Genome-wide scan reveals important additive and non-additive genetic effects associated with resistance to Haemonchus contortus in Florida Native sheep

Florida Native sheep is among the sheep breeds best adapted to humid and hot climatic conditions such as those of Florida, USA, and have shown a superior ability to regulate nematode burdens. This is one of the oldest sheep breeds in North America and is an endangered species. To ensure genetic diversity and long-term survival of the breed, protection of the current genetic stock is critical and conservation efforts are required to promote its breeding and production. The objective of the present study was to investigate the importance of additive and non-additive genetic effects on resistance to natural Haemonchus contortus infections in Florida Native sheep using a whole genome scan. A total of 200 sheep were evaluated in the present study. Phenotypic records included faecal egg count (FEC, eggs/gram), FAMACHA® score, packed cell volume (PCV, %), body condition score and average daily gain (ADG, kg). Sheep were genotyped using the GGP Ovine 50K SNP chip and 45.2 k single nucleotide polymorphism (SNP) markers spanning the entire genome were available for quality control procedures. Mixed models were used to analyse the response variables and included the identity by state matrix to control for population structure. Bonferroni correction was used to control for multiple testing and a second arbitrary threshold (0.1 × 10^?3) was used. Fifteen SNPs with additive and non-additive genetic effects and located in Ovis aries chromosome OAR1, 2, 3, 6, 8, 10, 11, 12, 13 and 21 were associated with FEC, FAMACHA® score, PCV and ADG. These SNPs could be potential genetic markers for resistance to natural H. contortus exposure in Florida Native sheep.     

Genetic models to estimate additive and non-additive effects of marker-associated QTL using multiple regression techniques

Summary The development of molecular markers has recently raised expectations for their application in selection programs. However, some questions related to quantitative trait loci (QTL) identification are still unanswered. The objectives of this paper are (1) to develop statistical genetic models for detecting and locating on the genome multi-QTL with additive, dominance and epistatic effects using multiple linear regression analysis in the backcross and F_n generations from the cross of two inbred lines; and (2) to discuss the bias caused by linked and unlinked QTL on the genetic estimates. Non-linear models were developed for different backcross and F_n generations when both epistasis and no epistasis were assumed. Generation analysis of marked progenies is suggested as a way of increasing the number of observations for the estimates without additional cost for molecular scoring. Some groups of progenies can be created in different generations from the same scored individuals. The non-linear models were transformed into approximate multivariate linear models to which combined stepwise and standard regression analysis could be applied. Expressions for the biases of the marker classes from linked QTL were obtained when no epistasis was assumed. When epistasis was assumed, these expressions increased in complexity, and the biases were caused by both linked and unlinked QTL.     

Modeling additive and non-additive effects in a hybrid population using genome-wide genotyping: prediction accuracy implications

Hybrids are broadly used in plant breeding and accurate estimation of variance components is crucial for optimizing genetic gain. Genome-wide information may be used to explore models designed to assess the extent of additive and non-additive variance and test their prediction accuracy for the genomic selection. Ten linear mixed models, involving pedigree- and marker-based relationship matrices among parents, were developed to estimate additive (A), dominance (D) and epistatic (AA, AD and DD) effects. Five complementary models, involving the gametic phase to estimate marker-based relationships among hybrid progenies, were developed to assess the same effects. The models were compared using tree height and 3303 single-nucleotide polymorphism markers from 1130 cloned individuals obtained via controlled crosses of 13 Eucalyptus urophylla females with 9 Eucalyptus grandis males. Akaike information criterion (AIC), variance ratios, asymptotic correlation matrices of estimates, goodness-of-fit, prediction accuracy and mean square error (MSE) were used for the comparisons. The variance components and variance ratios differed according to the model. Models with a parent marker-based relationship matrix performed better than those that were pedigree-based, that is, an absence of singularities, lower AIC, higher goodness-of-fit and accuracy and smaller MSE. However, AD and DD variances were estimated with high s.es. Using the same criteria, progeny gametic phase-based models performed better in fitting the observations and predicting genetic values. However, DD variance could not be separated from the dominance variance and null estimates were obtained for AA and AD effects. This study highlighted the advantages of progeny models using genome-wide information.     

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.     

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.     

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.     

Maternal effects and additive genetic inheritance in the collared lemming Dicrostonyx groenlandicus

We examined patterns of inheritance of size, growth and behavioural traits of collared lemmings (Dicrostonyx groenlandicus). Work was conducted on field-caught parents from the Canadian Arctic and their lab-born progeny. We partitioned inherited variance in traits into additive genetic and maternal effects components by using a half-sib breeding experiment in which each sire was mated to two dams. We found no evidence of statistically significant amounts of additive genetic variance in any of the traits measured. However, significant maternal effects were detected for several size- and growth-related traits. Three behavioural traits involving aggression, dispersal and activity showed no statistically significant inheritance of any kind. The presence of maternal effects may have consequences for population dynamics by causing lags resulting in inappropriate phenotypes being produced under regimes of fluctuating selection pressure. We recommend that maternal effects should be investigated as a potential general cause of population cycles in small mammals.     

Hierarchical spatial modeling of additive and dominance genetic variance for large spatial trial datasets

Summary .  This article expands upon recent interest in Bayesian hierarchical models in quantitative genetics by developing spatial process models for inference on additive and dominance genetic variance within the context of large spatially referenced trial datasets. Direct application of such models to large spatial datasets are, however, computationally infeasible because of cubic-order matrix algorithms involved in estimation. The situation is even worse in Markov chain Monte Carlo (MCMC) contexts where such computations are performed for several iterations. Here, we discuss approaches that help obviate these hurdles without sacrificing the richness in modeling. For genetic effects, we demonstrate how an initial spectral decomposition of the relationship matrices negate the expensive matrix inversions required in previously proposed MCMC methods. For spatial effects, we outline two approaches for circumventing the prohibitively expensive matrix decompositions: the first leverages analytical results from Ornstein–Uhlenbeck processes that yield computationally efficient tridiagonal structures, whereas the second derives a modified predictive process model from the original model by projecting its realizations to a lower-dimensional subspace, thereby reducing the computational burden. We illustrate the proposed methods using a synthetic dataset with additive, dominance, genetic effects and anisotropic spatial residuals, and a large dataset from a Scots pine ( Pinus sylvestris L.) progeny study conducted in northern Sweden. Our approaches enable us to provide a comprehensive analysis of this large trial, which amply demonstrates that, in addition to violating basic assumptions of the linear model, ignoring spatial effects can result in downwardly biased measures of heritability.     

Secondary sexual ornamentation and non-additive genetic benefits of female mate choice

Ornamental secondary sexual traits are hypothesized to evolve in response to directional mating preferences for more ornamented mates. Such mating preferences may themselves evolve partly because ornamentation indicates an individual's additive genetic quality (good genes). While mate choice can also confer non-additive genetic benefits (compatible genes), the identity of the most 'compatible' mate is assumed to depend on the choosy individual's own genotype. It is therefore unclear how choice for non-additive genetic benefits could contribute to directional mating preferences and consequently the evolution of ornamentation. In free-living song sparrows (Melospiza melodia), individual males varied in their kinship with the female population. Furthermore, a male's song repertoire size, a secondary sexual trait, was negatively correlated with kinship such that males with larger repertoires were less closely related to the female population. After excluding close relatives as potential mates, individual females were on average less closely related to males with larger repertoires. Therefore, female song sparrows expressing directional preferences for males with larger repertoires would on average acquire relatively unrelated mates and produce relatively outbred offspring. Such non-additive genetic fitness benefits of directional mating preferences, which may reflect genetic dominance variance expressed in structured populations, should be incorporated into genetic models of sexual selection.     

Priority effects produced by plant litter result in non-additive competitive effects

Litter may indirectly affect competitive interactions. It is not clear whether these changes are additive or non-additive indirect effects. Non-additivity could result from: (1) changes in biomass allocation patterns by competitors towards organs not directly involved in resource acquisition (e.g., longer hypocotyls); (2) changes in the proportion of different functional groups (e.g., grasses and forbs) that possess different competitive abilities; or (3) through priority effects caused by subtle changes in timing of emergence. We used a combination of field and glasshouse experiments in which Eucalyptus obliqua seedlings were grown either with or without leaf litter (grass litter/eucalypt litter), and with or without competitors. Eucalypt species growing in the field and in pots attained more biomass with litter than without when competitors were absent. Competition substantially decreased the biomass of eucalypt seedlings. Competitive intensity was heavily influenced by litter type and was most intense in the presence of grass litter. Litter produced a small change in patterns of biomass allocation in the competing herbaceous vegetation, and there was a slight (marginally non-significant) indication of a change in the proportion of grasses relative to forbs when litter was present. However, when the integral of competitor biomass over time was used to calculate competitive intensity, the combined effects of the experimental factors (litter and competition) became additive, suggesting that the effect of leaf litter on the timing of germination and establishment in the grasses and forbs, relative to that of Eucalyptus seedlings, was the principal mechanism by which leaf litter altered the interaction strength of the species studied.     

Ontogeny of additive and maternal genetic effects: lessons from domestic mammals

Evolution of size and growth depends on heritable variation arising from additive and maternal genetic effects. Levels of heritable (and nonheritable) variation might change over ontogeny, increasing through "variance compounding" or decreasing through "compensatory growth." We test for these processes using a meta-analysis of age-specific weight traits in domestic ungulates. Generally, mean standardized variance components decrease with age, consistent with compensatory growth. Phenotypic convergence among adult sheep occurs through decreasing environmental and maternal genetic variation. Maternal variation similarly declines in cattle. Maternal genetic effects are thus reduced with age (both in absolute and relative terms). Significant trends in heritability (decreasing in cattle, increasing in sheep) result from declining maternal and environmental components rather than from changing additive variation. There was no evidence for increasing standardized variance components. Any compounding must therefore be masked by more important compensatory processes. While extrapolation of these patterns to processes in natural population is difficult, our results highlight the inadequacy of assuming constancy in genetic parameters over ontogeny. Negative covariance between direct and maternal genetic effects was common. Negative correlations with additive and maternal genetic variances indicate that antagonistic pleiotropy (between additive and maternal genetic effects) may maintain genetic variance and limit responses to selection.     

Joint effect of selection, linkage and partial inbreeding on additive genetic variance in an infinite population

Under the inifinitesimal model of gene effects, selection reduces the additive genetic variance by inducing negative linkage disequilibrium among selected genes. If the selected genes are linked, the decay of linkage disequilibrium is delayed, and the reduction of additive genetic variance is enhanced. Inbreeding in an infinite population also alters the additive genetic variance through the generation of positive association among genes within a locus. In the present study, the joint effect of selection, linkage and partial inbreeding (partial selfing or partial full-sib mating) on the additive genetic variance was modeled. The recurrence relations of the additive genetic variance between successive generations and the prediction equation of the asymptotic additive genetic variance were derived. Numerical computation showed that although partially inbred populations initially maintain larger genetic variances, the accumulated effect of selection overrides the effect of inbreeding. Stochastic simulation was carried out to check the precision of prediction, showing that the obtained equations give a satisfactory prediction during initial generations. However, the predicted values always overestimate the simulated values, especially in later generations. Based on these results, possible extensions and perspectives of the assumed model were discussed.     

Preponderance of additive and non-additive variances for growth,ecophysiological and wood traits in Eucalyptus hybrid genotype-by-spacing interaction

Tree Genetics & Genomes - A clonal trial, including 124 hybrid poplars, was planted in the center of Chile in 2014 and Septoria canker was detected in 2016. We propose a new approach to...     

Joint effects of genetic hitchhiking and background selection on neutral variation

Due to relatively high rates of strongly selected deleterious mutations, directional selection on favorable alleles (causing hitchhiking effects on linked neutral polymorphisms) is expected to occur while a deleterious mutation-selection balance is present in a population. We analyze this interaction of directional selection and background selection and study their combined effects on neutral variation, using a three-locus model in which each locus is subjected to either deleterious, favorable, or neutral mutations. Average heterozygosity is measured by simulations (1) at the stationary state under the assumption of recurrent hitchhiking events and (2) as a transient level after a single hitchhiking event. The simulation results are compared to theoretical predictions. It is shown that known analytical solutions describing the hitchhiking effect without background selection can be modified such that they accurately predict the joint effects of hitchhiking and background on linked, neutral variation. Generalization of these results to a more appropriate multilocus model (such that background selection can occur at multiple sites) suggests that, in regions of very low recombination rates, stationary levels of nucleotide diversity are primarily determined by hitchhiking, whereas in regions of high recombination, background selection is the dominant force. The implications of these results on the identification and estimation of the relevant parameters of the model are discussed.     

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

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

The consequences of including non-additive effects on the genetic evaluation of harvest body weight in Coho salmon (Oncorhynchus kisutch)

Background

In this study, we used different animal models to estimate genetic and environmental variance components on harvest weight in two populations of Oncorhynchus kisutch, forming two classes i.e. odd- and even-year spawners.

Methods

The models used were: additive, with and without inbreeding as a covariable (A + F and A respectively); additive plus common environmental due to full-sib families and inbreeding (A + C + F); additive plus parental dominance and inbreeding (A + D + F); and a full model (A + C + D + F). Genetic parameters and breeding values obtained by different models were compared to evaluate the consequences of including non-additive effects on genetic evaluation.

Results

Including inbreeding as a covariable did not affect the estimation of genetic parameters, but heritability was reduced when dominance or common environmental effects were included. A high heritability for harvest weight was estimated in both populations (even = 0.46 and odd = 0.50) when simple additive models (A + F and A) were used. Heritabilities decreased to 0.21 (even) and 0.37 (odd) when the full model was used (A + C + D + F). In this full model, the magnitude of the dominance variance was 0.19 (even) and 0.06 (odd), while the magnitude of the common environmental effect was lower than 0.01 in both populations. The correlation between breeding values estimated with different models was very high in all cases (i.e. higher than 0.98). However, ranking of the 30 best males and the 100 best females per generation changed when a high dominance variance was estimated, as was the case in one of the two populations (even).

Conclusions

Dominance and common environmental variance may be important components of variance in harvest weight in O. kisutch, thus not including them may produce an overestimation of the predicted response; furthermore, genetic evaluation was seen to be partially affected, since the ranking of selected animals changed with the inclusion of non-additive effects in the animal model.