Learning genetic values from incomplete pedigree, genomic and phenotypic data

Abstract

Prediction is important in agricultural breeding. Prediction machines can be built from phenotypes, genealogies, and molecular markers. Information is incomplete: there may be individuals lacking at least one input. For instance, all possess pedigree, but a fraction has molecular markers. A solution is "single-step best linear unbiased prediction" (SS-BLUP). In a more general setting, some subjects have genomic data but lack genealogy, with or without phenotypes. We present a Bayesian method that accommodates wider incompleteness than SS-BLUP. Hy-BLUP ("Hy" for "hybrid") combines prior knowledge captured by pedigree and by markers, as if the two sources were independent. The Bayesian logic weights sources implicitly, but additional weights on pedigree and genomic information may be introduced as tuning parameters. The prior induces a precision matrix automatically, without cumbersome matrix algebra or approximations. The prior is combined with the data, and the "mixed model" equations are built directly. The method was evaluated using 599 fully pedigreed inbred lines of wheat genotyped for binary markers; the target was grain yield. We simulated patterns of incompleteness and used a training-testing layout supplemented by bootstrapping and random reconstruction of sets. There were minor differences between SS-BLUP and Hy-BLUP in predictive ability. From an inferential perspective, the weights and the variance components are not separable in the likelihood function. However, given the variance components, Bayesian learning about weights takes place. The discussion offers a multiple-trait generalization of Hy-BLUP that may be useful when some individuals are not phenotyped for some trait (e.g., carcass weight in a breeding nucleus) while others (not pedigreed) are genotyped, scored, and destroyed for commercial purposes. We provide a proof-of-concept of the usefulness of Hy-BLUP for genome-enabled prediction under irregular patterns of information.