A Unified and Comprehensible View of Parametric and Kernel Methods for Genomic Prediction with Application to Rice

Salinity stress tolerance prediction for biomass-related traits in maize (Zea mays L.) using genome-wide markers

Maize (Zea mays L.) is the third most important cereal crop after rice (Oryza sativa) and wheat (Triticum aestivum). Salinity stress significantly affects vegetative biomass and grain yield and, therefore, reduces the food and silage productivity of maize. Selecting salt-tolerant genotypes is a cumbersome and time-consuming process that requires meticulous phenotyping. To predict salt tolerance in maize, we estimated breeding values for four biomass-related traits, including shoot length, shoot weight, root length, and root weight under salt-stressed and controlled conditions. A five-fold cross-validation method was used to select the best model among genomic best linear unbiased prediction (GBLUP), ridge-regression BLUP (rrBLUP), extended GBLUP, Bayesian Lasso, Bayesian ridge regression, BayesA, BayesB, and BayesC. Examination of the effect of different marker densities on prediction accuracy revealed that a set of low-density single nucleotide polymorphisms obtained through filtering based on a combination of analysis of variance and linkage disequilibrium provided the best prediction accuracy for all the traits. The average prediction accuracy in cross-validations ranged from 0.46 to 0.77 across the four derived traits. The GBLUP, rrBLUP, and all Bayesian models except BayesB demonstrated comparable levels of prediction accuracy that were superior to the other modeling approaches. These findings provide a roadmap for the deployment and optimization of genomic selection in breeding for salt tolerance in maize.

Integrated Genomic Selection for Accelerating Breeding Programs of Climate-Smart Cereals

Rapidly rising population and climate changes are two critical issues that require immediate action to achieve sustainable development goals. The rising population is posing increased demand for food, thereby pushing for an acceleration in agricultural production. Furthermore, increased anthropogenic activities have resulted in environmental pollution such as water pollution and soil degradation as well as alterations in the composition and concentration of environmental gases. These changes are affecting not only biodiversity loss but also affecting the physio-biochemical processes of crop plants, resulting in a stress-induced decline in crop yield. To overcome such problems and ensure the supply of food material, consistent efforts are being made to develop strategies and techniques to increase crop yield and to enhance tolerance toward climate-induced stress. Plant breeding evolved after domestication and initially remained dependent on phenotype-based selection for crop improvement. But it has grown through cytological and biochemical methods, and the newer contemporary methods are based on DNA-marker-based strategies that help in the selection of agronomically useful traits. These are now supported by high-end molecular biology tools like PCR, high-throughput genotyping and phenotyping, data from crop morpho-physiology, statistical tools, bioinformatics, and machine learning. After establishing its worth in animal breeding, genomic selection (GS), an improved variant of marker-assisted selection (MAS), has made its way into crop-breeding programs as a powerful selection tool. To develop novel breeding programs as well as innovative marker-based models for genetic evaluation, GS makes use of molecular genetic markers. GS can amend complex traits like yield as well as shorten the breeding period, making it advantageous over pedigree breeding and marker-assisted selection (MAS). It reduces the time and resources that are required for plant breeding while allowing for an increased genetic gain of complex attributes. It has been taken to new heights by integrating innovative and advanced technologies such as speed breeding, machine learning, and environmental/weather data to further harness the GS potential, an approach known as integrated genomic selection (IGS). This review highlights the IGS strategies, procedures, integrated approaches, and associated emerging issues, with a special emphasis on cereal crops. In this domain, efforts have been taken to highlight the potential of this cutting-edge innovation to develop climate-smart crops that can endure abiotic stresses with the motive of keeping production and quality at par with the global food demand.

Genomic Prediction: Progress and Perspectives for Rice Improvement

Genomic prediction can be a powerful tool to achieve greater rates of genetic gain for quantitative traits if thoroughly integrated into a breeding strategy. In rice as in other crops, the interest in genomic prediction is very strong with a number of studies addressing multiple aspects of its use, ranging from the more conceptual to the more practical. In this chapter, we review the literature on rice (Oryza sativa) and summarize important considerations for the integration of genomic prediction in breeding programs. The irrigated breeding program at the International Rice Research Institute is used as a concrete example on which we provide data and R scripts to reproduce the analysis but also to highlight practical challenges regarding the use of predictions. The adage "To someone with a hammer, everything looks like a nail" describes a common psychological pitfall that sometimes plagues the integration and application of new technologies to a discipline. We have designed this chapter to help rice breeders avoid that pitfall and appreciate the benefits and limitations of applying genomic prediction, as it is not always the best approach nor the first step to increasing the rate of genetic gain in every context.

Understanding the Effectiveness of Genomic Prediction in Tetraploid Potato

Use of genomic prediction (GP) in tetraploid is becoming more common. Therefore, we think it is the right time for a comparison of GP models for tetraploid potato. GP models were compared that contrasted shrinkage with variable selection, parametric vs. non-parametric models and different ways of accounting for non-additive genetic effects. As a complement to GP, association studies were carried out in an attempt to understand the differences in prediction accuracy. We compared our GP models on a data set consisting of 147 cultivars, representing worldwide diversity, with over 39 k GBS markers and measurements on four tuber traits collected in six trials at three locations during 2 years. GP accuracies ranged from 0.32 for tuber count to 0.77 for dry matter content. For all traits, differences between GP models that utilised shrinkage penalties and those that performed variable selection were negligible. This was surprising for dry matter, as only a few additive markers explained over 50% of phenotypic variation. Accuracy for tuber count increased from 0.35 to 0.41, when dominance was included in the model. This result is supported by Genome Wide Association Study (GWAS) that found additive and dominance effects accounted for 37% of phenotypic variation, while significant additive effects alone accounted for 14%. For tuber weight, the Reproducing Kernel Hilbert Space (RKHS) model gave a larger improvement in prediction accuracy than explicitly modelling epistatic effects. This is an indication that capturing the between locus epistatic effects of tuber weight can be done more effectively using the semi-parametric RKHS model. Our results show good opportunities for GP in 4x potato.

Epistasis Detection and Modeling for Genomic Selection in Cowpea (Vigna unguiculata L. Walp.)

Genetic architecture reflects the pattern of effects and interaction of genes underlying phenotypic variation. Most mapping and breeding approaches generally consider the additive part of variation but offer limited knowledge on the benefits of epistasis which explains in part the variation observed in traits. In this study, the cowpea multiparent advanced generation inter-cross (MAGIC) population was used to characterize the epistatic genetic architecture of flowering time, maturity, and seed size. In addition, consideration for epistatic genetic architecture in genomic-enabled breeding (GEB) was investigated using parametric, semi-parametric, and non-parametric genomic selection (GS) models. Our results showed that large and moderate effect-sized two-way epistatic interactions underlie the traits examined. Flowering time QTL colocalized with cowpea putative orthologs of Arabidopsis thaliana and Glycine max genes like PHYTOCLOCK1 (PCL1 [Vigun11g157600]) and PHYTOCHROME A (PHY A [Vigun01g205500]). Flowering time adaptation to long and short photoperiod was found to be controlled by distinct and common main and epistatic loci. Parametric and semi-parametric GS models outperformed non-parametric GS model, while using known quantitative trait nucleotide(s) (QTNs) as fixed effects improved prediction accuracy when traits were controlled by large effect loci. In general, our study demonstrated that prior understanding of the genetic architecture of a trait can help make informed decisions in GEB.

Selection of trait-specific markers and multi-environment models improve genomic predictive ability in rice

Developing high yielding rice varieties that are tolerant to drought stress is crucial for the sustainable livelihood of rice farmers in rainfed rice cropping ecosystems. Genomic selection (GS) promises to be an effective breeding option for these complex traits. We evaluated the effectiveness of two rather new options in the implementation of GS: trait and environment-specific marker selection and the use of multi-environment prediction models. A reference population of 280 rainfed lowland accessions endowed with 215k SNP markers data was phenotyped under a favorable and two managed drought environments. Trait-specific SNP subsets (28k) were selected for each trait under each environment, using results of GWAS performed with the complete genotype dataset. Performances of single-environment and multi-environment genomic prediction models were compared using kernel regression based methods (GBLUP and RKHS) under two cross validation scenarios: availability (CV2) or not (CV1) of phenotypic data for the validation set, in one of the environments. Trait-specific marker selection strategy achieved predictive ability (PA) of genomic prediction up to 22% higher than markers selected on the bases of neutral linkage disequilibrium (LD). Tolerance to drought stress was up to 32% better predicted by multi-environment models (especially RKHS based models) under CV2 strategy. Under the less favorable CV1 strategy, the multi-environment models achieved similar PA than the single-environment predictions. We also showed that reasonable PA could be obtained with as few as 3,000 SNP markers, even in a population of low LD extent, provided marker selection is based on pairwise LD. The implications of these findings for breeding for drought tolerance are discussed. The most resource sparing option would be accurate phenotyping of the reference population in a favorable environment and under a managed drought, while the candidate population would be phenotyped only under one of those environments.

Genomic Prediction of Breeding Values Using a Subset of SNPs Identified by Three Machine Learning Methods

The analysis of large genomic data is hampered by issues such as a small number of observations and a large number of predictive variables (commonly known as “large P small N”), high dimensionality or highly correlated data structures. Machine learning methods are renowned for dealing with these problems. To date machine learning methods have been applied in Genome-Wide Association Studies for identification of candidate genes, epistasis detection, gene network pathway analyses and genomic prediction of phenotypic values. However, the utility of two machine learning methods, Gradient Boosting Machine (GBM) and Extreme Gradient Boosting Method (XgBoost), in identifying a subset of SNP makers for genomic prediction of breeding values has never been explored before. In this study, using 38,082 SNP markers and body weight phenotypes from 2,093 Brahman cattle (1,097 bulls as a discovery population and 996 cows as a validation population), we examined the efficiency of three machine learning methods, namely Random Forests (RF), GBM and XgBoost, in (a) the identification of top 400, 1,000, and 3,000 ranked SNPs; (b) using the subsets of SNPs to construct genomic relationship matrices (GRMs) for the estimation of genomic breeding values (GEBVs). For comparison purposes, we also calculated the GEBVs from (1) 400, 1,000, and 3,000 SNPs that were randomly selected and evenly spaced across the genome, and (2) from all the SNPs. We found that RF and especially GBM are efficient methods in identifying a subset of SNPs with direct links to candidate genes affecting the growth trait. In comparison to the estimate of prediction accuracy of GEBVs from using all SNPs (0.43), the 3,000 top SNPs identified by RF (0.42) and GBM (0.46) had similar values to those of the whole SNP panel. The performance of the subsets of SNPs from RF and GBM was substantially better than that of evenly spaced subsets across the genome (0.18–0.29). Of the three methods, RF and GBM consistently outperformed the XgBoost in genomic prediction accuracy.

Rice diversity panel provides accurate genomic predictions for complex traits in the progenies of biparental crosses involving members of the panel

KEY MESSAGE

Rice breeding programs based on pedigree schemes can use a genomic model trained with data from their working collection to predict performances of progenies produced through rapid generation advancement. So far, most potential applications of genomic prediction in plant improvement have been explored using cross validation approaches. This is the first empirical study to evaluate the accuracy of genomic prediction of the performances of progenies in a typical rice breeding program. Using a cross validation approach, we first analyzed the effects of marker selection and statistical methods on the accuracy of prediction of three different heritability traits in a reference population (RP) of 284 inbred accessions. Next, we investigated the size and the degree of relatedness with the progeny population (PP) of sub-sets of the RP that maximize the accuracy of prediction of phenotype across generations, i.e., for 97 F5-F7 lines derived from biparental crosses between 31 accessions of the RP. The extent of linkage disequilibrium was high (r 2 = 0.2 at 0.80 Mb in RP and at 1.1 Mb in PP). Consequently, average marker density above one per 22 kb did not improve the accuracy of predictions in the RP. The accuracy of progeny prediction varied greatly depending on the composition of the training set, the trait, LD and minor allele frequency. The highest accuracy achieved for each trait exceeded 0.50 and was only slightly below the accuracy achieved by cross validation in the RP. Our results thus show that relatively high accuracy (0.41-0.54) can be achieved using only a rather small share of the RP, most related to the PP, as the training set. The practical implications of these results for rice breeding programs are discussed.