Joint prediction of multiple quantitative traits using a Bayesian multivariate antedependence model

Predicting organismal phenotypes from genotype data is important for preventive and personalized medicine as well as plant and animal breeding. Although genome-wide association studies (GWAS) for complex traits have discovered a large number of trait- and disease-associated variants, phenotype prediction based on associated variants is usually in low accuracy even for a high-heritability trait because these variants can typically account for a limited fraction of total genetic variance. In comparison with GWAS, the whole-genome prediction (WGP) methods can increase prediction accuracy by making use of a huge number of variants simultaneously. Among various statistical methods for WGP, multiple-trait model and antedependence model show their respective advantages. To take advantage of both strategies within a unified framework, we proposed a novel multivariate antedependence-based method for joint prediction of multiple quantitative traits using a Bayesian algorithm via modeling a linear relationship of effect vector between each pair of adjacent markers. Through both simulation and real-data analyses, our studies demonstrated that the proposed antedependence-based multiple-trait WGP method is more accurate and robust than corresponding traditional counterparts (Bayes A and multi-trait Bayes A) under various scenarios. Our method can be readily extended to deal with missing phenotypes and resequence data with rare variants, offering a feasible way to jointly predict phenotypes for multiple complex traits in human genetic epidemiology as well as plant and livestock breeding.     

Comparison of whole-genome prediction models for traits with contrasting genetic architecture in a diversity panel of maize inbred lines

ABSTRACT: BACKGROUND: There is increasing empirical evidence that whole-genome prediction (WGP) is a powerful tool for predicting line and hybrid performance in maize. However, there is a lack of knowledge about the sensitivity of WGP models towards the genetic architecture of the trait. Whereas previous studies exclusively focused on highly polygenic traits, important agronomic traits such as disease resistances, nutrifunctional or climate adaptational traits have a genetic architecture which is either much less complex or unknown. For such cases, information about model robustness and guidelines for model selection are lacking. Here, we compared five WGP models with different assumptions about the distribution of the underlying genetic effects. As contrasting model traits, we chose three highly polygenic agronomic traits and three metabolites each with a major QTL explaining 22 to 30 % of the genetic variance in a panel of 289 diverse maize inbred lines genotyped with 56,110 SNPs. RESULTS: We found the five WGP models to be remarkable robust towards trait architecture with the largest differences in prediction accuracies ranging between 0.05 and 0.14 for the same trait, most likely as the result of the high level of linkage disequilibrium prevailing in elite maize germplasm. Whereas RR-BLUP performed best for the agronomic traits, it was inferior to LASSO or elastic net for the three metabolites. We found the approach of genome partitioning of genetic variance, first applied in human genetics, as useful in guiding the breeder which model to choose, if prior knowledge of the trait architecture is lacking. CONCLUSIONS: Our results suggest that in diverse germplasm of elite maize inbred lines with a high level of LD, WGP models differ only slightly in their accuracies, irrespective of the number and effects of QTL found in previous linkage or association mapping studies. However, small gains in prediction accuracies can be achieved if the WGP model is selected according to the genetic architecture of the trait. If the trait architecture is unknown e.g. for novel traits which only recently received attention in breeding, we suggest to inspect the distribution of the genetic variance explained by each chromosome for guiding model selection in WGP.     

Canadian regulatory aspects of gene editing technologies

The development of gene editing techniques, capable of producing plants and animals with new and improved traits, is revolutionizing the world of plant and animal breeding and rapidly advancing to commercial reality. However, from a regulatory standpoint the Government of Canada views gene editing as another tool that will join current methods used to develop desirable traits in plants and animals. This is because Canada focusses on the potential risk resulting from the novelty of the trait, or plant or animal product entering the Canadian environment or market place, rather than the process or method by which it was created. The Canadian Food Inspection Agency is responsible for the regulation of the environmental release of plants with novel traits, and novel livestock feeds, while Health Canada is responsible for the regulation of novel foods. Environment and Climate Change Canada, in partnership with Health Canada, regulates modified animals for entry into the environment. In all cases, these novel products may be the result of conventional breeding, mutagenesis, recombinant DNA techniques or other methods of plant or animal breeding such as gene editing. This novelty approach allows the Canadian regulatory system to efficiently adjust to any new developments in the science of plant and animal breeding and allows for risk-appropriate regulatory decisions. This approach encourages innovation while maintaining science-based regulatory expertise. Canadian regulators work cooperatively with proponents to determine if their gene editing-derived product meets the definition of a novel product, and whether it would be subject to a pre-market assessment. Therefore, Canada’s existing regulatory system is well positioned to accommodate any new innovations or technologies in plant or animal breeding, including gene editing.

     

Genomic models with genotype × environment interaction for predicting hybrid performance: an application in maize hybrids

Key message

A new genomic model that incorporates genotype?×?environment interaction gave increased prediction accuracy of untested hybrid response for traits such as percent starch content, percent dry matter content and silage yield of maize hybrids.

Abstract

The prediction of hybrid performance (HP) is very important in agricultural breeding programs. In plant breeding, multi-environment trials play an important role in the selection of important traits, such as stability across environments, grain yield and pest resistance. Environmental conditions modulate gene expression causing genotype?×?environment interaction (G?×?E), such that the estimated genetic correlations of the performance of individual lines across environments summarize the joint action of genes and environmental conditions. This article proposes a genomic statistical model that incorporates G?×?E for general and specific combining ability for predicting the performance of hybrids in environments. The proposed model can also be applied to any other hybrid species with distinct parental pools. In this study, we evaluated the predictive ability of two HP prediction models using a cross-validation approach applied in extensive maize hybrid data, comprising 2724 hybrids derived from 507 dent lines and 24 flint lines, which were evaluated for three traits in 58 environments over 12 years; analyses were performed for each year. On average, genomic models that include the interaction of general and specific combining ability with environments have greater predictive ability than genomic models without interaction with environments (ranging from 12 to 22%, depending on the trait). We concluded that including G?×?E in the prediction of untested maize hybrids increases the accuracy of genomic models.

     

From Genotype �� Environment Interaction to Gene �� Environment Interaction

Historically in plant breeding a large number of statistical models has been developed and used for studying genotype × environment interaction. These models have helped plant breeders to assess the stability of economically important traits and to predict the performance of newly developed genotypes evaluated under varying environmental conditions. In the last decade, the use of relatively low numbers of markers has facilitated the mapping of chromosome regions associated with phenotypic variability (e.g., QTL mapping) and, to a lesser extent, revealed the differetial response of these chromosome regions across environments (i.e., QTL × environment interaction). QTL technology has been useful for marker-assisted selection of simple traits; however, it has not been efficient for predicting complex traits affected by a large number of loci. Recently the appearance of cheap, abundant markers has made it possible to saturate the genome with high density markers and use marker information to predict genomic breeding values, thus increasing the precision of genetic value prediction over that achieved with the traditional use of pedigree information. Genomic data also allow assessing chromosome regions through marker effects and studying the pattern of covariablity of marker effects across differential environmental conditions. In this review, we outline the most important models for assessing genotype × environment interaction, QTL × environment interaction, and marker effect (gene) × environment interaction. Since analyzing genetic and genomic data is one of the most challenging statistical problems researchers currently face, different models from different areas of statistical research must be attempted in order to make significant progress in understanding genetic effects and their interaction with environment.     

Estimation in a multiplicative mixed model involving a genetic relationship matrix

Genetic models partitioning additive and non-additive genetic effects for populations tested in replicated multi-environment trials (METs) in a plant breeding program have recently been presented in the literature. For these data, the variance model involves the direct product of a large numerator relationship matrix A, and a complex structure for the genotype by environment interaction effects, generally of a factor analytic (FA) form. With MET data, we expect a high correlation in genotype rankings between environments, leading to non-positive definite covariance matrices. Estimation methods for reduced rank models have been derived for the FA formulation with independent genotypes, and we employ these estimation methods for the more complex case involving the numerator relationship matrix. We examine the performance of differing genetic models for MET data with an embedded pedigree structure, and consider the magnitude of the non-additive variance. The capacity of existing software packages to fit these complex models is largely due to the use of the sparse matrix methodology and the average information algorithm. Here, we present an extension to the standard formulation necessary for estimation with a factor analytic structure across multiple environments.     

Multi-trait and multi-environment QTL analyses of yield and a set of physiological traits in pepper

Key message

A mixed model framework was defined for QTL analysis of multiple traits across multiple environments for a RIL population in pepper. Detection power for QTLs increased considerably and detailed study of QTL by environment interactions and pleiotropy was facilitated.

Abstract

For many agronomic crops, yield is measured simultaneously with other traits across multiple environments. The study of yield can benefit from joint analysis with other traits and relations between yield and other traits can be exploited to develop indirect selection strategies. We compare the performance of three multi-response QTL approaches based on mixed models: a multi-trait approach (MT), a multi-environment approach (ME), and a multi-trait multi-environment approach (MTME). The data come from a multi-environment experiment in pepper, for which 15 traits were measured in four environments. The approaches were compared in terms of number of QTLs detected for each trait, the explained variance, and the accuracy of prediction for the final QTL model. For the four environments together, the superior MTME approach delivered a total of 47 regions containing putative QTLs. Many of these QTLs were pleiotropic and showed quantitative QTL by environment interaction. MTME was superior to ME and MT in the number of QTLs, the explained variance and accuracy of predictions. The large number of model parameters in the MTME approach was challenging and we propose several guidelines to help obtain a stable final QTL model. The results confirmed the feasibility and strengths of novel mixed model QTL methodology to study the architecture of complex traits.     

烤烟主要农艺性状的遗传与相关分析

利用包括基因型与环境互作的加性-显性遗传模型,对14个烤烟品种(系)及其配制的41个杂交组合在4个环境下的7个农艺性状表现进行遗传分析。结果表明,株高、节距、腰叶宽主要受加性效应控制,叶数、腰叶长受显性×环境互作效应影响最大,茎围以加性×环境互作效应、显性×环境互作效应为主,产量以加性效应、显性×环境互作效应为主。适应当地生态条件的品种（系）具有较高的正向加性效应。许多组合的显性主效应及在各试验点的显性×环境互作效应在方向上不尽一致,杂交组合的选配宜针对特定的生态环境进行。性状相关分析表明,大多数成对性状的各项相关系数为正值,且多以加性遗传相关为主,可利用株高对产量进行间接选择。
     

A Comprehensive Genetic Approach for Improving Prediction of Skin Cancer Risk in Humans

Prediction of genetic risk for disease is needed for preventive and personalized medicine. Genome-wide association studies have found unprecedented numbers of variants associated with complex human traits and diseases. However, these variants explain only a small proportion of genetic risk. Mounting evidence suggests that many traits, relevant to public health, are affected by large numbers of small-effect genes and that prediction of genetic risk to those traits and diseases could be improved by incorporating large numbers of markers into whole-genome prediction (WGP) models. We developed a WGP model incorporating thousands of markers for prediction of skin cancer risk in humans. We also considered other ways of incorporating genetic information into prediction models, such as family history or ancestry (using principal components, PCs, of informative markers). Prediction accuracy was evaluated using the area under the receiver operating characteristic curve (AUC) estimated in a cross-validation. Incorporation of genetic information (i.e., familial relationships, PCs, or WGP) yielded a significant increase in prediction accuracy: from an AUC of 0.53 for a baseline model that accounted for nongenetic covariates to AUCs of 0.58 (pedigree), 0.62 (PCs), and 0.64 (WGP). In summary, prediction of skin cancer risk could be improved by considering genetic information and using a large number of single-nucleotide polymorphisms (SNPs) in a WGP model, which allows for the detection of patterns of genetic risk that are above and beyond those that can be captured using family history. We discuss avenues for improving prediction accuracy and speculate on the possible use of WGP to prospectively identify individuals at high risk.     

Prediction of genetic values of quantitative traits with epistatic effects in plant breeding populations

Though epistasis has long been postulated to have a critical role in genetic regulation of important pathways as well as provide a major source of variation in the process of speciation, the importance of epistasis for genomic selection in the context of plant breeding is still being debated. In this paper, we report the results on the prediction of genetic values with epistatic effects for 280 accessions in the Nebraska Wheat Breeding Program using adaptive mixed least absolute shrinkage and selection operator (LASSO). The development of adaptive mixed LASSO, originally designed for association mapping, for the context of genomic selection is reported. The results show that adaptive mixed LASSO can be successfully applied to the prediction of genetic values while incorporating both marker main effects and epistatic effects. Especially, the prediction accuracy is substantially improved by the inclusion of two-locus epistatic effects (more than onefold in some cases as measured by cross-validation correlation coefficient), which is observed for multiple traits and planting locations. This points to significant potential in using non-additive genetic effects for genomic selection in crop breeding practices.     

Using numerical plant models and phenotypic correlation space to design achievable ideotypes

Numerical plant models can predict the outcome of plant traits modifications resulting from genetic variations, on plant performance, by simulating physiological processes and their interaction with the environment. Optimization methods complement those models to design ideotypes, that is, ideal values of a set of plant traits, resulting in optimal adaptation for given combinations of environment and management, mainly through the maximization of performance criteria (e.g. yield and light interception). As use of simulation models gains momentum in plant breeding, numerical experiments must be carefully engineered to provide accurate and attainable results, rooting them in biological reality. Here, we propose a multi‐objective optimization formulation that includes a metric of performance, returned by the numerical model, and a metric of feasibility, accounting for correlations between traits based on field observations. We applied this approach to two contrasting models: a process‐based crop model of sunflower and a functional–structural plant model of apple trees. In both cases, the method successfully characterized key plant traits and identified a continuum of optimal solutions, ranging from the most feasible to the most efficient. The present study thus provides successful proof of concept for this enhanced modelling approach, which identified paths for desirable trait modification, including direction and intensity.     

Leaf herbivory and drought stress affect floral attractive and defensive traits in Nicotiana quadrivalvis

Adaptive phenotypic plasticity allows sessile organisms such as plants to match trait expression to the particular environment they experience. Plasticity may be limited, however, by resources in the environment, by responses to prior environmental cues, or by previous interactions with other species, such as competition or herbivory. Thus, understanding the expression of plastic traits and their effects on plant performance requires evaluating trait expression in complex environments, rather than across levels of a single variable. In this study, we tested the independent and combined effects of two components of a plant’s environment, herbivory and water availability, on the expression of attractive and defensive traits in Nicotiana quadrivalvis in the greenhouse. Damage and drought did not affect leaf nicotine concentrations but had additive and non-additive effects on floral attractive and defensive traits. Plants in the high water treatment produced larger flowers with more nectar than in the low water treatment. Leaf damage induced greater nectar volumes in the high water treatment only, suggesting that low water limited plastic responses to herbivore damage. Leaf damage also tended to induce higher nicotine concentrations in nectar, consistent with other studies showing that leaf damage can induce floral defenses. Our results suggest that there are separate and synergistic effects of leaf herbivory and drought on floral trait expression, and thus plasticity in response to complex environments may influence plant fitness via effects on floral visitation and defense.     

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.     

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.     

Breeding new varieties for controlled environments

Agricultural production in controlled environments is increasingly feasible, and may play an important role in providing nutrition and choice to growing urban centres. New technologies in lighting, ventilation, robotics and irrigation are just a few of the innovations that enable production of high‐value specialty crops outside of a traditional field setting. However, despite all of the advances in the hardware within the plant factory operation, innovation of the most complex machine has been neglected – the plant itself. Indoor agricultural operations typically rely on legacy varieties, plants selected and bred for field conditions. In the field, phenotypic stability is paramount, as production must be consistent in an unpredictable and changing environment. However, the controlled environment affords focus on different breeding priorities as environmental flux, pests, pathogens and post‐harvest quality are less formidable barriers to production. On the contrary, breeding for controlled environments shifts the focus to a completely different set of plant traits, such as rapid growth, performance in low light environments and active manipulation of plant stature. Instead of breeding for phenotypic stability, plants may be bred to maximise genetic plasticity, allowing specific traits to be presented as a function of the quality of the ambient light spectrum. In this scenario plant varieties may be grown with optimal size, supporting a focus on consumer traits like flavour or accumulation of health‐related compounds. Gene editing may be a central technology in the production of designer plants for controlled environments. This review considers the opportunity for breeding for controlled environments, with a focus on a revision of priorities for controlled‐environment breeders.     

Prediction of expected years of life using whole-genome markers

Genetic factors are believed to account for 25% of the interindividual differences in Years of Life (YL) among humans. However, the genetic loci that have thus far been found to be associated with YL explain a very small proportion of the expected genetic variation in this trait, perhaps reflecting the complexity of the trait and the limitations of traditional association studies when applied to traits affected by a large number of small-effect genes. Using data from the Framingham Heart Study and statistical methods borrowed largely from the field of animal genetics (whole-genome prediction, WGP), we developed a WGP model for the study of YL and evaluated the extent to which thousands of genetic variants across the genome examined simultaneously can be used to predict interindividual differences in YL. We find that a sizable proportion of differences in YL-which were unexplained by age at entry, sex, smoking and BMI-can be accounted for and predicted using WGP methods. The contribution of genomic information to prediction accuracy was even higher than that of smoking and body mass index (BMI) combined; two predictors that are considered among the most important life-shortening factors. We evaluated the impacts of familial relationships and population structure (as described by the first two marker-derived principal components) and concluded that in our dataset population structure explained partially, but not fully the gains in prediction accuracy obtained with WGP. Further inspection of prediction accuracies by age at death indicated that most of the gains in predictive ability achieved with WGP were due to the increased accuracy of prediction of early mortality, perhaps reflecting the ability of WGP to capture differences in genetic risk to deadly diseases such as cancer, which are most often responsible for early mortality in our sample.     

Genetic by environment interactions affect plant–soil linkages

The role of plant intraspecific variation in plant–soil linkages is poorly understood, especially in the context of natural environmental variation, but has important implications in evolutionary ecology. We utilized three 18‐ to 21‐year‐old common gardens across an elevational gradient, planted with replicates of five Populus angustifolia genotypes each, to address the hypothesis that tree genotype (G), environment (E), and G × E interactions would affect soil carbon and nitrogen dynamics beneath individual trees. We found that soil nitrogen and carbon varied by over 50% and 62%, respectively, across all common garden environments. We found that plant leaf litter (but not root) traits vary by genotype and environment while soil nutrient pools demonstrated genotype, environment, and sometimes G × E interactions, while process rates (net N mineralization and net nitrification) demonstrated G × E interactions. Plasticity in tree growth and litter chemistry was significantly related to the variation in soil nutrient pools and processes across environments, reflecting tight plant–soil linkages. These data overall suggest that plant genetic variation can have differential affects on carbon storage and nitrogen cycling, with implications for understanding the role of genetic variation in plant–soil feedback as well as management plans for conservation and restoration of forest habitats with a changing climate.     

Genome-based prediction of test cross performance in two subsequent breeding cycles

Genome-based prediction of genetic values is expected to overcome shortcomings that limit the application of QTL mapping and marker-assisted selection in plant breeding. Our goal was to study the genome-based prediction of test cross performance with genetic effects that were estimated using genotypes from the preceding breeding cycle. In particular, our objectives were to employ a ridge regression approach that approximates best linear unbiased prediction of genetic effects, compare cross validation with validation using genetic material of the subsequent breeding cycle, and investigate the prospects of genome-based prediction in sugar beet breeding. We focused on the traits sugar content and standard molasses loss (ML) and used a set of 310 sugar beet lines to estimate genetic effects at 384 SNP markers. In cross validation, correlations >0.8 between observed and predicted test cross performance were observed for both traits. However, in validation with 56 lines from the next breeding cycle, a correlation of 0.8 could only be observed for sugar content, for standard ML the correlation reduced to 0.4. We found that ridge regression based on preliminary estimates of the heritability provided a very good approximation of best linear unbiased prediction and was not accompanied with a loss in prediction accuracy. We conclude that prediction accuracy assessed with cross validation within one cycle of a breeding program can not be used as an indicator for the accuracy of predicting lines of the next cycle. Prediction of lines of the next cycle seems promising for traits with high heritabilities.     

Identification of QTLs for seed and pod traits in soybean and analysis for additive effects and epistatic effects of QTLs among multiple environments

Soybean seed and pod traits are important yield components. Selection for high yield style in seed and pod along with agronomic traits is a goal of many soybean breeders. The intention of this study was to identify quantitative trait loci (QTL) underlying seed and pod traits in soybean among eleven environments in China. 147 recombinant inbred lines were advanced through single-seed-descent method. The population was derived from a cross between Charleston (an American high yield soybean cultivar) and DongNong594 (a Chinese high yield soybean cultivar). A total of 157 polymorphic simple sequence repeat markers were used to construct a genetic linkage map. The phenotypic data of seed and pod traits [number of one-seed pod, number of two-seed pod, number of three-seed pod, number of four-seed pod, number of (two plus three)-seed pod, number of (three plus four)-seed pod, seed weight per plant, number of pod per plant] were recorded in eleven environments. In the analysis of single environment, fourteen main effect QTLs were identified. In the conjoint analysis of multiple environments, twenty-four additive QTLs were identified, and additive QTLs by environments interactions (AE) were evaluated and analyzed at the same time among eleven environments; twenty-three pairs of epistatic QTLs were identified, and epistasis (additive by additive) by environments interactions (AAE) were also analyzed and evaluated among eleven environments. Comparing the results of identification between single environment mapping and multiple environments conjoint mapping, three main effect QTLs with positive additive values and another three main effect QTLs with negative additive values, had no interactions with all environments, supported that these QTLs could be used in molecular assistant breeding in the future. These different effect QTLs could supply a good foundation to the gene clone and molecular asisstant breeding of soybean seed and pod traits.     

Impacts of QTL × Environment Interactions on Genetic Response to Marker-Assisted Selection

Genotype × environment (GE) interaction is a common characteristic for quantitative traits, and has been a subject of great concern for breeding programs. Simulation studies were conducted to investigate the effects of GE interaction on genetic response to marker-assisted selection (MAS). In our study we demonstrated that MAS is generally more efficient than phenotypic selection in the presence of GE interaction, and this trend is more pronounced for developing broadly adaptable varieties. The utilization of different QTL information dramatically influences MAS efficiency. When MAS is based on QTLs evaluated in a single environment, the causal QTL × environment (QE) interactions usually reduce general response across environments, and the reduction in the cumulative general response is a function of the proportion of QE interactions for the trait studied. However, MAS using QTL information evaluated in multiple environments not only yields higher general response, but the general response obtained is also reasonably robust to QE interactions. The total response achieved by MAS in a specific environment depends largely on the total heritability of traits and is slightly subject to relative changes between general heritability and GE interaction heritability. Two breeding strategies, breeding experiments conducted in one environment throughout and in two environments alternately, were also examined for the implementation of marker-based selection. It was thus concluded that plant breeders should be cautious to utilize QTL information from only one environment and execute breeding studies in another.