Abstract. For the foreseeable future, plant breeding methodology will continue to unfold as a practical application of the scaling of quantitative biology. These efforts to increase the effective scale of breeding programs will focus on the immediate and long-term needs of society. The foundations of the quantitative dimension will be integration of quantitative genetics, statistics, gene-to-phenotype knowledge of traits embedded within crop growth and development models. The integration will be enabled by advances in quantitative genetics methodology and computer simulation. The foundations of the biology dimension will be integrated experimental and functional gene-to-phenotype modelling approaches that advance our understanding of functional germplasm diversity, and gene-to-phenotype trait relationships for the native and transgenic variation utilised in agricultural crops. The trait genetic knowledge created will span scales of biology, extending from molecular genetics to multi-trait phenotypes embedded within evolving genotype-environment systems. The outcomes sought and successes achieved by plant breeding will be measured in terms of sustainable improvements in agricultural production of food, feed, fibre, biofuels and other desirable plant products that meet the needs of society. In this review, examples will be drawn primarily from our experience gained through commercial maize breeding. Implications for other crops, in both the private and public sectors, will be discussed.

Genomic selection, enabled by whole genome prediction (WGP) methods, is revolutionizing plant breeding. Existing WGP methods have been shown to deliver accurate predictions in the most common settings, such as prediction of across environment performance for traits with additive gene effects. However, prediction of traits with non-additive gene effects and prediction of genotype by environment interaction (G×E), continues to be challenging. Previous attempts to increase prediction accuracy for these particularly difficult tasks employed prediction methods that are purely statistical in nature. Augmenting the statistical methods with biological knowledge has been largely overlooked thus far. Crop growth models (CGMs) attempt to represent the impact of functional relationships between plant physiology and the environment in the formation of yield and similar output traits of interest. Thus, they can explain the impact of G×E and certain types of non-additive gene effects on the expressed phenotype. Approximate Bayesian computation (ABC), a novel and powerful computational procedure, allows the incorporation of CGMs directly into the estimation of whole genome marker effects in WGP. Here we provide a proof of concept study for this novel approach and demonstrate its use with synthetic data sets. We show that this novel approach can be considerably more accurate than the benchmark WGP method GBLUP in predicting performance in environments represented in the estimation set as well as in previously unobserved environments for traits determined by non-additive gene effects. We conclude that this proof of concept demonstrates that using ABC for incorporating biological knowledge in the form of CGMs into WGP is a very promising and novel approach to improving prediction accuracy for some of the most challenging scenarios in plant breeding and applied genetics.

High throughput genotyping, phenotyping, and envirotyping applied within plant breeding multienvironment trials (METs) provide the data foundations for selection and tackling genotype × environment interactions (GEIs) through whole‐genome prediction (WGP). Crop growth models (CGM) can be used to enable predictions for yield and other traits for different genotypes and environments within a MET if genetic variation for the influential traits and their responses to environmental variation can be incorporated into the CGM framework. Furthermore, such CGMs can be integrated with WGP to enable whole‐genome prediction with crop growth models (CGM‐WGP) through use of computational methods such as approximate Bayesian computation. We previously used simulated data sets to demonstrate proof of concept for application of the CGM‐WGP methodology to plant breeding METs. Here the CGM‐WGP methodology is applied to an empirical maize (Zea mays L.) drought MET data set to evaluate the steps involved in reduction to practice. Positive prediction accuracy was achieved for hybrid grain yield in two drought environments for a sample of doubled haploids (DHs) from a cross. This was achieved by including genetic variation for five component traits into the CGM to enable the CGM‐WGP methodology. The five component traits were a priori considered to be important for yield variation among the maize hybrids in the two target drought environments included in the MET. Here, we discuss lessons learned while applying the CGM‐WGP methodology to the empirical data set. We also identify areas for further research to improve prediction accuracy and to advance the CGM‐WGP for a broader range of situations relevant to plant breeding.

Genomic selection, enabled by whole genome prediction (WGP) methods, is revolutionizing plant breeding. Existing WGP methods have been shown to deliver accurate predictions in the most common settings, such as prediction of across environment performance for traits with additive gene effects. However, prediction of traits with non-additive gene effects and prediction of genotype by environment interaction (G×E), continues to be challenging. Previous attempts to increase prediction accuracy for these particularly difficult tasks employed prediction methods that are purely statistical in nature. Augmenting the statistical methods with biological knowledge has been largely overlooked thus far. Crop growth models (CGMs) attempt to represent the impact of functional relationships between plant physiology and the environment in the formation of yield and similar output traits of interest. Thus, they can explain the impact of G×E and certain types of non-additive gene effects on the expressed phenotype. Approximate Bayesian computation (ABC), a novel and powerful computational procedure, allows the incorporation of CGMs directly into the estimation of whole genome marker effects in WGP. Here we provide a proof of concept study for this novel approach and demonstrate its use with synthetic data sets. We show that this novel approach can be considerably more accurate than the benchmark WGP method GBLUP in predicting performance in environments represented in the estimation set as well as in previously unobserved environments for traits determined by non-additive gene effects. We conclude that this proof of concept demonstrates that using ABC for incorporating biological knowledge in the form of CGMs into WGP is a very promising and novel approach to improving prediction accuracy for some of the most challenging scenarios in plant breeding and applied genetics.

The objective of this project was to determine the genetic control of conception rate, or pregnancy percentage in Angus beef heifers. Producers from 6 herds in 5 states provided 3,144 heifer records that included breeding dates, breeding contemporary groups, service sires, and pregnancy check information. Two hundred fourteen sires of the heifers were represented; with 104 sires having less than 5 progeny, and 14 sires having greater than 50 progeny. These data were combined with performance and pedigree information, including actual and adjusted birth weights, weaning weights, and yearling weights, from the American Angus Association database. Heifer pregnancy rate varied from 75 to 95% between herds, and from 65 to 100% between sires, with an overall pregnancy rate of 93%, measured as the percentage of heifers pregnant at pregnancy check after the breeding season. Pregnancy was analyzed as a threshold trait with an underlying continuous distribution. A generalized linear animal model, using a relationship matrix, was fitted. This model included the fixed effects of contemporary group, age of dam, and first AI service sire, and the covariates of heifer age at the beginning of breeding, adjusted birth weight, adjusted weaning weight, and adjusted yearling weight. The relationship matrix included 4 generations of pedigree. The heritability of pregnancy and first-service conception rates on the underlying scale was 0.13 +/- 0.07 and 0.03 +/- 0.03, respectively. Estimated breeding values for pregnancy rate on the observed scale ranged from -0.02 to 0.05 for sires of heifers. Including growth traits with pregnancy rate as 2-trait analyses did not change the heritability of pregnancy rate. As expected for a reproductive trait, the heritability of pregnancy rate was low. Because of its low heritability, genetic improvement in fertility by selection on heifer pregnancy rate would be expected to be slow.