Prediction of genetic values has been a focus of applied quantitative genetics since the beginning of the 20th century, with renewed interest following the advent of the era of whole genome-enabled prediction. Opportunities offered by the emergence of high-dimensional genomic data fueled by post-Sanger sequencing technologies, especially molecular markers, have driven researchers to extend Ronald Fisher and Sewall Wright's models to confront new challenges. In particular, kernel methods are gaining consideration as a regression method of choice for genome-enabled prediction. Complex traits are presumably influenced by many genomic regions working in concert with others (clearly so when considering pathways), thus generating interactions. Motivated by this view, a growing number of statistical approaches based on kernels attempt to capture non-additive effects, either parametrically or non-parametrically. This review centers on whole-genome regression using kernel methods applied to a wide range of quantitative traits of agricultural importance in animals and plants. We discuss various kernel-based approaches tailored to capturing total genetic variation, with the aim of arriving at an enhanced predictive performance in the light of available genome annotation information. Connections between prediction machines born in animal breeding, statistics, and machine learning are revisited, and their empirical prediction performance is discussed. Overall, while some encouraging results have been obtained with non-parametric kernels, recovering non-additive genetic variation in a validation dataset remains a challenge in quantitative genetics.

Precision animal agriculture is poised to rise to prominence in the livestock enterprise in the domains of management, production, welfare, sustainability, health surveillance, and environmental footprint. Considerable progress has been made in the use of tools to routinely monitor and collect information from animals and farms in a less laborious manner than before. These efforts have enabled the animal sciences to embark on information technology-driven discoveries to improve animal agriculture. However, the growing amount and complexity of data generated by fully automated, high-throughput data recording or phenotyping platforms, including digital images, sensor and sound data, unmanned systems, and information obtained from real-time noninvasive computer vision, pose challenges to the successful implementation of precision animal agriculture. The emerging fields of machine learning and data mining are expected to be instrumental in helping meet the daunting challenges facing global agriculture. Yet, their impact and potential in “big data” analysis have not been adequately appreciated in the animal science community, where this recognition has remained only fragmentary. To address such knowledge gaps, this article outlines a framework for machine learning and data mining and offers a glimpse into how they can be applied to solve pressing problems in animal sciences.

The accessibility of high‐throughput phenotyping platforms in both the greenhouse and field, as well as the relatively low cost of unmanned aerial vehicles, has provided researchers with an effective means to characterize large populations throughout the growing season. These longitudinal phenotypes can provide important insight into plant development and responses to the environment. Despite the growing use of these new phenotyping approaches in plant breeding, the use of genomic prediction models for longitudinal phenotypes is limited in major crop species. The objective of this study was to demonstrate the utility of random regression ( RR ) models using Legendre polynomials for genomic prediction of shoot growth trajectories in rice ( Oryza sativa ). An estimate of shoot biomass, projected shoot area ( PSA ), was recorded over a period of 20 days for a panel of 357 diverse rice accessions using an image‐based greenhouse phenotyping platform. A RR that included a fixed second‐order Legendre polynomial, a random second‐order Legendre polynomial for the additive genetic effect, a first‐order Legendre polynomial for the environmental effect, and heterogeneous residual variances was used to model PSA trajectories. The utility of the RR model over a single time point ( TP ) approach, where PSA is fit at each time point independently, is shown through four prediction scenarios. In the first scenario, the RR and TP approaches were used to predict PSA for a set of lines lacking phenotypic data. The RR approach showed a 11.6% increase in prediction accuracy over the TP approach. Much of this improvement could be attributed to the greater additive genetic variance captured by the RR approach. The remaining scenarios focused forecasting future phenotypes using a subset of early time points for known lines with phenotypic data, as well new lines lacking phenotypic data. In all cases, PSA could be predicted with high accuracy ( r : 0.79 to 0.89 and 0.55 to 0.58 for known and unknown lines, respectively). This study provides the first application of RR models for genomic prediction of a longitudinal trait in rice and demonstrates that RR models can be effectively used to improve the accuracy of genomic prediction for complex traits compared to a TP approach.

Recent work has suggested that the performance of prediction models for complex traits may depend on the architecture of the target traits. Here we compared several prediction models with respect to their ability of predicting phenotypes under various statistical architectures of gene action: (1) purely additive, (2) additive and dominance, (3) additive, dominance, and two-locus epistasis, and (4) purely epistatic settings. Simulation and a real chicken dataset were used. Fourteen prediction models were compared: BayesA, BayesB, BayesC, Bayesian LASSO, Bayesian ridge regression, elastic net, genomic best linear unbiased prediction, a Gaussian process, LASSO, random forests, reproducing kernel Hilbert spaces regression, ridge regression (best linear unbiased prediction), relevance vector machines, and support vector machines. When the trait was under additive gene action, the parametric prediction models outperformed non-parametric ones. Conversely, when the trait was under epistatic gene action, the non-parametric prediction models provided more accurate predictions. Thus, prediction models must be selected according to the most probably underlying architecture of traits. In the chicken dataset examined, most models had similar prediction performance. Our results corroborate the view that there is no universally best prediction models, and that the development of robust prediction models is an important research objective.

Core Ideas Random regression models are an appealing framework for genome‐wide association studies (GWAS) of longitudinal traits This approach provides improvements over conventional single time point analyses for GWAS. We identify quantitative trait loci with transient and persistent effects on shoot growth in rice. This is the first application of random regression models for GWAS of longitudinal traits in crops. Understanding the genetic basis of dynamic plant phenotypes has largely been limited because of a lack of space and labor resources needed to record dynamic traits, often destructively, for a large number of genotypes. However, the recent advent of image‐based phenotyping platforms has provided the plant science community with an effective means to nondestructively evaluate morphological, developmental, and physiological processes at regular, frequent intervals for a large number of plants throughout development. The statistical frameworks typically used for genetic analyses (e.g., genome‐wide association mapping, linkage mapping, and genomic prediction) in plant breeding and genetics are not particularly amenable for repeated measurements. Random regression (RR) models are routinely used in animal breeding for the genetic analysis of longitudinal traits and provide a robust framework for modeling trait trajectories and performing genetic analysis simultaneously. We recently used a RR approach for genomic prediction of shoot growth trajectories in rice (Oryza sativa L.) from 33,674 single nucleotide polymorphisms. In this study, we have extended this approach for genetic inference by leveraging genomic breeding values derived from RR models for rice shoot growth during early vegetative development. This approach provides improvements over conventional single time point analyses for discovering loci associated with shoot growth trajectories. The RR approach uncovers persistent as well as time‐specific transient quantitative trait loci. This methodology can be widely applied to understand the genetic architecture of other complex polygenic traits with repeated measurements.