On prediction of genetic values in marker-assisted selection.

We suggest a new approximation for the prediction of genetic values in marker-assisted selection. The new approximation is compared to the standard approach. It is shown that the new approach will often provide substantially better prediction of genetic values; furthermore the new approximation avoids some of the known statistical problems of the standard approach. The advantages of the new approach are illustrated by a simulation study in which the new approximation outperforms both the standard approach and phenotypic selection.     

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.     

Genome-enabled prediction of genetic values using radial basis function neural networks

The availability of high density panels of molecular markers has prompted the adoption of genomic selection (GS) methods in animal and plant breeding. In GS, parametric, semi-parametric and non-parametric regressions models are used for predicting quantitative traits. This article shows how to use neural networks with radial basis functions (RBFs) for prediction with dense molecular markers. We illustrate the use of the linear Bayesian LASSO regression model and of two non-linear regression models, reproducing kernel Hilbert spaces (RKHS) regression and radial basis function neural networks (RBFNN) on simulated data and real maize lines genotyped with 55,000 markers and evaluated for several trait-environment combinations. The empirical results of this study indicated that the three models showed similar overall prediction accuracy, with a slight and consistent superiority of RKHS and RBFNN over the additive Bayesian LASSO model. Results from the simulated data indicate that RKHS and RBFNN models captured epistatic effects; however, adding non-signal (redundant) predictors (interaction between markers) can adversely affect the predictive accuracy of the non-linear regression models.     

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.     

Predicting genetic values: a kernel-based best linear unbiased prediction with genomic data

Genomic data provide a valuable source of information for modeling covariance structures, allowing a more accurate prediction of total genetic values (GVs). We apply the kriging concept, originally developed in the geostatistical context for predictions in the low-dimensional space, to the high-dimensional space spanned by genomic single nucleotide polymorphism (SNP) vectors and study its properties in different gene-action scenarios. Two different kriging methods ["universal kriging" (UK) and "simple kriging" (SK)] are presented. As a novelty, we suggest use of the family of Matérn covariance functions to model the covariance structure of SNP vectors. A genomic best linear unbiased prediction (GBLUP) is applied as a reference method. The three approaches are compared in a whole-genome simulation study considering additive, additive-dominance, and epistatic gene-action models. Predictive performance is measured in terms of correlation between true and predicted GVs and average true GVs of the individuals ranked best by prediction. We show that UK outperforms GBLUP in the presence of dominance and epistatic effects. In a limiting case, it is shown that the genomic covariance structure proposed by VanRaden (2008) can be considered as a covariance function with corresponding quadratic variogram. We also prove theoretically that if a specific linear relationship exists between covariance matrices for two linear mixed models, the GVs resulting from BLUP are linked by a scaling factor. Finally, the relation of kriging to other models is discussed and further options for modeling the covariance structure, which might be more appropriate in the genomic context, are suggested.     

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.     

Joint modeling of additive and non-additive genetic line effects in single field trials

A statistical approach is presented for selection of best performing lines for commercial release and best parents for future breeding programs from standard agronomic trials. The method involves the partitioning of the genetic effect of a line into additive and non-additive effects using pedigree based inter-line relationships, in a similar manner to that used in animal breeding. A difference is the ability to estimate non-additive effects. Line performance can be assessed by an overall genetic line effect with greater accuracy than when ignoring pedigree information and the additive effects are predicted breeding values. A generalized definition of heritability is developed to account for the complex models presented.     

Marker-assisted estimation of quantitative genetic parameters in rainbow trout,Oncorhynchus mykiss

Estimation of quantitative genetic parameters conventionally requires known pedigree structure. However, several methods have recently been developed to circumvent this requirement by inferring relationship structure from molecular marker data. Here, two such marker-assisted methodologies were used and compared in an aquaculture population of rainbow trout (Oncorhynchus mykiss). Firstly a regression-based model employing estimates of pairwise relatedness was applied, and secondly a Markov Chain Monte Carlo (MCMC) procedure was employed to reconstruct full-sibships and hence an explicit pedigree. While both methods were effective in detecting significant components of genetic variance and covariance for size and spawning time traits, the regression model resulted in estimates that were quantitatively unreliable, having both significant bias and low precision. This result can be largely attributed to poor performance of the pairwise relatedness estimator. In contrast, genetic parameters estimated from the reconstructed pedigree showed close agreement with ideal values obtained from the true pedigree. Although not significantly biased, parameters based on the reconstructed pedigree were underestimated relative to ideal values. This was due to the complex structure of the true pedigree in which high numbers of half-sibling relationships resulted in inaccurate partitioning of full-sibships, and additional unrecognized relatedness between families.     

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.     

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.     

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.     

Comparison of GWAS models to identify non-additive genetic control of flowering time in sunflower hybrids

Key message

This study compares five models of GWAS, to show the added value of non-additive modeling of allelic effects to identify genomic regions controlling flowering time of sunflower hybrids.

Abstract

Genome-wide association studies are a powerful and widely used tool to decipher the genetic control of complex traits. One of the main challenges for hybrid crops, such as maize or sunflower, is to model the hybrid vigor in the linear mixed models, considering the relatedness between individuals. Here, we compared two additive and three non-additive association models for their ability to identify genomic regions associated with flowering time in sunflower hybrids. A panel of 452 sunflower hybrids, corresponding to incomplete crossing between 36 male lines and 36 female lines, was phenotyped in five environments and genotyped for 2,204,423 SNPs. Intra-locus effects were estimated in multi-locus models to detect genomic regions associated with flowering time using the different models. Thirteen quantitative trait loci were identified in total, two with both model categories and one with only non-additive models. A quantitative trait loci on LG09, detected by both the additive and non-additive models, is located near a GAI homolog and is presented in detail. Overall, this study shows the added value of non-additive modeling of allelic effects for identifying genomic regions that control traits of interest and that could participate in the heterosis observed in hybrids.

     

Genome-based prediction of testcross values in maize

This is the first large-scale experimental study on genome-based prediction of testcross values in an advanced cycle breeding population of maize. The study comprised testcross progenies of 1,380 doubled haploid lines of maize derived from 36 crosses and phenotyped for grain yield and grain dry matter content in seven locations. The lines were genotyped with 1,152 single nucleotide polymorphism markers. Pedigree data were available for three generations. We used best linear unbiased prediction and stratified cross-validation to evaluate the performance of prediction models differing in the modeling of relatedness between inbred lines and in the calculation of genome-based coefficients of similarity. The choice of similarity coefficient did not affect prediction accuracies. Models including genomic information yielded significantly higher prediction accuracies than the model based on pedigree information alone. Average prediction accuracies based on genomic data were high even for a complex trait like grain yield (0.72–0.74) when the cross-validation scheme allowed for a high degree of relatedness between the estimation and the test set. When predictions were performed across distantly related families, prediction accuracies decreased significantly (0.47–0.48). Prediction accuracies decreased with decreasing sample size but were still high when the population size was halved (0.67–0.69). The results from this study are encouraging with respect to genome-based prediction of the genetic value of untested lines in advanced cycle breeding populations and the implementation of genomic selection in the breeding process.     

Marker-assisted rationalisation of genetic resource collections: a case study in flax using AFLPs

Removing redundant germplasm from collections is one of the options for genebanks to increase the efficiency of their genetic resource management. Molecular characterisation of germplasm is thereby becoming more and more important to verify suspected duplication. AFLPs were used to characterise 29 flax accessions of material derived from research activities (hereafter termed ’’breeder’s line”). Based on similar accession names, the breeder’s lines could be classified into three series (’M 25’, ’Ru’ and ’Rm’) that were expected to contain redundancies. In addition, 12 reference cultivars were analysed. A total number of 144 polymorphic bands (59.8%) were scored among the 164 individuals investigated. In general, relatively high levels of intra-accession variation were found, even for the cultivars examined. This finding was not in line with the low outcrossing rates reported for flax. A cluster analysis grouped the ’Ru’ and ’Rm’ series together, indicating their close genetic relationship. An analysis of molecular variance (AMOVA) showed a significant group effect (fibre/oil flax) only for ’M 25’, explaining 34% of the variation observed within this series. For the cultivars 40.5% of the variation was distributed among accessions within groups and all pairwise comparisons were significantly different, except for one case. Both for the series of breeder’s lines and the cultivars the major part of the variation was distributed among individuals within accessions. This component constituted 80.7% and 83.6% of the total variation for the ’Ru’ and ’Rm’ series, respectively. Pairwise comparisons of accessions were performed by AMOVA in order to identify redundant germplasm. Stepwise bulking of accessions until all remaining accessions were significantly different showed that the 29 accessions of breeder’s lines could be reduced to 14. Only a small negative effect of this bulking approach on the among-population component of variance was observed, showing a reduction of 2.6%. Results are discussed in relation to improving the efficiency of collection management. Received: 25 June 2000 / Accepted: 27 October 2000     

Marker-assisted dissection of genetic influences on motor and neuroendocrine sensitization to cocaine in rats

This study investigated genetic influences on behavioral and neuroendocrine responses to cocaine sensitization. We used male and female rats of the inbred strains Lewis (LEW) and spontaneously hypertensive rats (SHR), which display genetic differences in stress-related responses. The influence of two quantitative trait loci (QTL; Ofil1 and Ofil2 on chromosomes 4 and 7), which modulate stress reactivity in rats, on the effects of cocaine was also investigated through the use of recombinant lines (derived from a LEW   ×   SHR intercross) selected by their genotype at Ofil1 and Ofil2 . Animals were given repeated cocaine or saline injections and tested for locomotion (induction of sensitization). Two weeks later, all animals were challenged with cocaine, and locomotion and corticosterone levels were measured (expression of sensitization). Results indicated that male SHR rats showed more behavioral sensitization than LEW rats, whereas no strain differences in sensitization were seen among females. When challenged with cocaine, LEW and SHR rats of both sexes pretreated with cocaine showed behavioral sensitization compared with saline pretreated animals; however, only LEW rats displayed an increase in the corticosterone levels. Ofil1 was found to influence the induction of sensitization in males and Ofil2 modulated the locomotor effect of cocaine in females. This study provides evidence of a genotype-dependent relationship between the induction and expression of cocaine sensitization, and between the behavioral and neuroendocrine responses induced by cocaine. Moreover, the Ofil1 and Ofil2 loci may contain one or more genes that control the behavioral effects of cocaine in rats.     

Marker-assisted selection and evaluation of the QTL for stigma exsertion under japonica rice genetic background

Stigma exsertion is one of the important traits which contribute to the efficient improvement of commercial seed production in hybrid rice. In order to understand the genetic factors involved in the stigma exsertion of an indica variety—IR24—a QTL analysis was conducted using the F₂ population between a japonica variety—Koshihikari—and a breeding line showing exserted stigma selected from the backcross population between IR24 as a donor and japonica varieties. As a result, a highly significant QTL (qES3), which had been predicted in the recombinant inbred population of IR24, was confirmed at the centromeric region on chromosome 3. qES3 increases about 20% of the frequency of the exserted stigmas at the IR24 allele and explains about 32% of the total phenotypic variance. A QTL near-isogenic line for qES3 increased the frequency of the exserted stigma by 36% compared to that of Koshihikari in a field evaluation, which suggests that qES3 is a promising QTL for the development of a maternal line for hybrid rice. Electronic supplementary material Supplementary material is available in the online version of this article at and is accessible for authorized users. Maiko Miyata and Toshio Yamamoto contributed equally to this study.     

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.     

Estimation of genetic parameters and prediction of breeding values for apple fruit-quality traits using pedigreed plant material in Europe

Genetic parameters for apple (Malus x domestica) fruit external traits (fruit size, ground colour, proportion of over colour and attractiveness) and sensory traits (firmness, crispness, texture, juiciness, flavour, sugar, acidity and global taste) were estimated using 2,207 pedigreed genotypes from breeding programmes in six European countries. Data were scored for 3 years and four periods during storage. Analyses were performed with a restricted maximum likelihood method using VCE 5.1.2 software. Heritability estimates ranged from medium to high for instrumental traits. Genetic correlations between firmness and sugar were medium and low between firmness and acidity. Sensory traits showed low to high heritability, acidity and flavour being, respectively, the most and the less heritable. Global taste was strongly correlated with texture, juiciness, and flavour and relatively less correlated with crispness and acidity. Sensory sugar and acidity showed highly negative correlations whereas their instrumental measurements showed low and increasing positive correlations from harvest to 4 months post-harvest. Sugar exhibited a higher sensory/instrumental divergence. Conversely, instrumental and sensory firmness were highly correlated. Fruit external characteristics had medium heritability. Fruit attractiveness had highest and lowest correlations with fruit size and ground colour, respectively. Best linear unbiased predictors of breeding values were computed for all genotypes with the software PEST. The results were analysed with regard to the dynamic and the reliability of genetic parameters according to the scoring dates. Original issues of the study and the importance of the obtained results for efficient designs of further apple fruit quality breeding programmes were discussed.