Using Bayesian Multilevel Whole Genome Regression Models for Partial Pooling of Training Sets in Genomic Prediction.

Training set size is an important determinant of genomic prediction accuracy. Plant breeding programs are characterized by a high degree of structuring, particularly into populations. This hampers the establishment of large training sets for each population. Pooling populations increases training set size but ignores unique genetic characteristics of each. A possible solution is partial pooling with multilevel models, which allows estimating population-specific marker effects while still leveraging information across populations. We developed a Bayesian multilevel whole-genome regression model and compared its performance with that of the popular BayesA model applied to each population separately (no pooling) and to the joined data set (complete pooling). As an example, we analyzed a wide array of traits from the nested association mapping maize population. There we show that for small population sizes (e.g., <50), partial pooling increased prediction accuracy over no or complete pooling for populations represented in the training set. No pooling was superior; however, when populations were large. In another example data set of interconnected biparental maize populations either partial or complete pooling was superior, depending on the trait. A simulation showed that no pooling is superior when differences in genetic effects among populations are large and partial pooling when they are intermediate. With small differences, partial and complete pooling achieved equally high accuracy. For prediction of new populations, partial and complete pooling had very similar accuracy in all cases. We conclude that partial pooling with multilevel models can maximize the potential of pooling by making optimal use of information in pooled training sets.