José Crossa

Prediction of genetic values of quantitative traits in plant breeding using pedigree and molecular markers

The availability of dense molecular markers has made possible the use of genomic selection (GS) for plant breeding. However, the evaluation of models for GS in real plant populations is very limited. This article evaluates the performance of parametric and semiparametric models for GS using wheat (Triticum aestivum L.) and maize (Zea mays) data in which different traits were measured in several environmental conditions. The findings, based on extensive cross-validations, indicate that models including marker information had higher predictive ability than pedigree-based models. In the wheat data set, and relative to a pedigree model, gains in predictive ability due to inclusion of markers ranged from 7.7 to 35.7%. Correlation between observed and predictive values in the maize data set achieved values up to 0.79. Estimates of marker effects were different across environmental conditions, indicating that genotype × environment interaction is an important component of genetic variability. These results indicate that GS in plant breeding can be an effective strategy for selecting among lines whose phenotypes have yet to be observed.

Predicting Quantitative Traits With Regression Models for Dense Molecular Markers and Pedigree

The availability of genomewide dense markers brings opportunities and challenges to breeding programs. An important question concerns the ways in which dense markers and pedigrees, together with phenotypic records, should be used to arrive at predictions of genetic values for complex traits. If a large number of markers are included in a regression model, marker-specific shrinkage of regression coefficients may be needed. For this reason, the Bayesian least absolute shrinkage and selection operator (LASSO) (BL) appears to be an interesting approach for fitting marker effects in a regression model. This article adapts the BL to arrive at a regression model where markers, pedigrees, and covariates other than markers are considered jointly. Connections between BL and other marker-based regression models are discussed, and the sensitivity of BL with respect to the choice of prior distributions assigned to key parameters is evaluated using simulation. The proposed model was fitted to two data sets from wheat and mouse populations, and evaluated using cross-validation methods. Results indicate that inclusion of markers in the regression further improved the predictive ability of models. An R program that implements the proposed model is freely available.

Association analysis of historical bread wheat germplasm using additive genetic covariance of relatives and population structure

Linkage disequilibrium can be used for identifying associations between traits of interest and genetic markers. This study used mapped diversity array technology (DArT) markers to find associations with resistance to stem rust, leaf rust, yellow rust, and powdery mildew, plus grain yield in five historical wheat international multienvironment trials from the International Maize and Wheat Improvement Center (CIMMYT). Two linear mixed models were used to assess marker–trait associations incorporating information on population structure and covariance between relatives. An integrated map containing 813 DArT markers and 831 other markers was constructed. Several linkage disequilibrium clusters bearing multiple host plant resistance genes were found. Most of the associated markers were found in genomic regions where previous reports had found genes or quantitative trait loci (QTL) influencing the same traits, providing an independent validation of this approach. In addition, many new chromosome regions for disease resistance and grain yield were identified in the wheat genome. Phenotyping across up to 60 environments and years allowed modeling of genotype × environment interaction, thereby making possible the identification of markers contributing to both additive and additive × additive interaction effects of traits.

Statistical Analyses of Multilocation Trials

Publisher Summary This chapter presents the statistical analysis of multilocation trials. Multilocation trials play an important role in plant breeding and agronomic research. Data from such trials have three main agricultural objectives—to accurately estimate and predict yield based on limited experimental data; to determine yield stability and the pattern of response of genotypes or agronomic treatments across environments; and to provide reliable guidance for selecting the best genotypes or agronomic treatments for planting in future years and at new sites. Agronomists use multilocation trials to compare combinations of agronomic factors, such as fertilizer levels and plant density, and on this basis make recommendations for farmers. Breeders compare different improved genotypes to identify the superior ones. Data collected in multilocation trials are intrinsically complex, having three fundamental aspects—namely, structural patterns; nonstructural noise; and relationships among genotypes, environments, and genotypes and environments considered jointly. Pattern implies that a number of genotypes respond to certain environments in a systematic, significant, and interpretable manner, whereas noise suggests that the responses are unpredictable and uninterpretable.

Genomic Selection in Wheat Breeding using Genotyping-by-Sequencing

Genomic selection (GS) uses genomewide molecular markers to predict breeding values and make selections of individuals or breeding lines prior to phenotyping. Here we show that genotyping‐by‐sequencing (GBS) can be used for de novo genotyping of breeding panels and to develop accurate GS models, even for the large, complex, and polyploid wheat (Triticum aestivum L.) genome. With GBS we discovered 41,371 single nucleotide polymorphisms (SNPs) in a set of 254 advanced breeding lines from CIMMYTs semiarid wheat breeding program. Four different methods were evaluated for imputing missing marker scores in this set of unmapped markers, including random forest regression and a newly developed multivariate‐normal expectation‐maximization algorithm, which gave more accurate imputation than heterozygous or mean imputation at the marker level, although no significant differences were observed in the accuracy of genomic‐estimated breeding values (GEBVs) among imputation methods. Genomic‐estimated breeding value prediction accuracies with GBS were 0.28 to 0.45 for grain yield, an improvement of 0.1 to 0.2 over an established marker platform for wheat. Genotyping‐by‐sequencing combines marker discovery and genotyping of large populations, making it an excellent marker platform for breeding applications even in the absence of a reference genome sequence or previous polymorphism discovery. In addition, the flexibility and low cost of GBS make this an ideal approach for genomics‐assisted breeding.

AMMI adjustment for statistical analysis of an international wheat yield trial

SummaryMultilocation trials are important for the CIMMYT Bread Wheat Program in producing high-yielding, adapted lines for a wide range of environments. This study investigated procedures for improving predictive success of a yield trial, grouping environments and genotypes into homogeneous subsets, and determining the yield stability of 18 CIMMYT bread wheats evaluated at 25 locations. Additive Main effects and Multiplicative Interaction (AMMI) analysis gave more precise estimates of genotypic yields within locations than means across replicates. This precision facilitated formation by cluster analysis of more cohesive groups of genotypes and locations for biological interpretation of interactions than occurred with unadjusted means. Locations were clustered into two subsets for which genotypes with positive interactions manifested in high, stable yields were identified. The analyses highlighted superior selections with both broad and specific adaptation.

Semi-parametric genomic-enabled prediction of genetic values using reproducing kernel Hilbert spaces methods

Prediction of genetic values is a central problem in quantitative genetics. Over many decades, such predictions have been successfully accomplished using information on phenotypic records and family structure usually represented with a pedigree. Dense molecular markers are now available in the genome of humans, plants and animals, and this information can be used to enhance the prediction of genetic values. However, the incorporation of dense molecular marker data into models poses many statistical and computational challenges, such as how models can cope with the genetic complexity of multi-factorial traits and with the curse of dimensionality that arises when the number of markers exceeds the number of data points. Reproducing kernel Hilbert spaces regressions can be used to address some of these challenges. The methodology allows regressions on almost any type of prediction sets (covariates, graphs, strings, images, etc.) and has important computational advantages relative to many parametric approaches. Moreover, some parametric models appear as special cases. This article provides an overview of the methodology, a discussion of the problem of kernel choice with a focus on genetic applications, algorithms for kernel selection and an assessment of the proposed methods using a collection of 599 wheat lines evaluated for grain yield in four mega environments.

Genomic-Enabled Prediction Based on Molecular Markers and Pedigree Using the Bayesian Linear Regression Package in R

The availability of dense molecular markers has made possible the use of genomic selection in plant and animal breeding. However, models for genomic selection pose several computational and statistical challenges and require specialized computer programs, not always available to the end user and not implemented in standard statistical software yet. The R‐package BLR (Bayesian Linear Regression) implements several statistical procedures (e.g., Bayesian Ridge Regression, Bayesian LASSO) in a unified framework that allows including marker genotypes and pedigree data jointly. This article describes the classes of models implemented in the BLR package and illustrates their use through examples. Some challenges faced when applying genomic‐enabled selection, such as model choice, evaluation of predictive ability through cross‐validation, and choice of hyper‐parameters, are also addressed.

High-throughput phenotyping and genomic selection: The frontiers of crop breeding converge

Genomic selection (GS) and high-throughput phenotyping have recently been captivating the interest of the crop breeding community from both the public and private sectors world-wide. Both approaches promise to revolutionize the prediction of complex traits, including growth, yield and adaptation to stress. Whereas high-throughput phenotyping may help to improve understanding of crop physiology, most powerful techniques for high-throughput field phenotyping are empirical rather than analytical and comparable to genomic selection. Despite the fact that the two methodological approaches represent the extremes of what is understood as the breeding process (phenotype versus genome), they both consider the targeted traits (e.g. grain yield, growth, phenology, plant adaptation to stress) as a black box instead of dissecting them as a set of secondary traits (i.e. physiological) putatively related to the target trait. Both GS and high-throughput phenotyping have in common their empirical approach enabling breeders to use genome profile or phenotype without understanding the underlying biology. This short review discusses the main aspects of both approaches and focuses on the case of genomic selection of maize flowering traits and near-infrared spectroscopy (NIRS) and plant spectral reflectance as high-throughput field phenotyping methods for complex traits such as crop growth and yield.

Genomic prediction in CIMMYT maize and wheat breeding programs.

Genomic selection (GS) has been implemented in animal and plant species, and is regarded as a useful tool for accelerating genetic gains. Varying levels of genomic prediction accuracy have been obtained in plants, depending on the prediction problem assessed and on several other factors, such as trait heritability, the relationship between the individuals to be predicted and those used to train the models for prediction, number of markers, sample size and genotype × environment interaction (GE). The main objective of this article is to describe the results of genomic prediction in International Maize and Wheat Improvement Center’s (CIMMYT’s) maize and wheat breeding programs, from the initial assessment of the predictive ability of different models using pedigree and marker information to the present, when methods for implementing GS in practical global maize and wheat breeding programs are being studied and investigated. Results show that pedigree (population structure) accounts for a sizeable proportion of the prediction accuracy when a global population is the prediction problem to be assessed. However, when the prediction uses unrelated populations to train the prediction equations, prediction accuracy becomes negligible. When genomic prediction includes modeling GE, an increase in prediction accuracy can be achieved by borrowing information from correlated environments. Several questions on how to incorporate GS into CIMMYT’s maize and wheat programs remain unanswered and subject to further investigation, for example, prediction within and between related bi-parental crosses. Further research on the quantification of breeding value components for GS in plant breeding populations is required.