Bayesian hierarchical modeling of yield in incomplete diallel crosses of the Pacific oyster Crassostrea gigas

Abstract

Identifying elite inbred parent lines that produce high-performing hybrid Pacific oyster seed requires diallel or factorial test crosses among lines, each acting as both a male and a female parent. Previously, we used the generalized linear model with fixed effects (i.e. GLM) to partition variance in yield, among hybrid families produced by a diallel cross, into causal genetic components—principally, general combining ability (GCA), specific combining ability (SCA), and reciprocal effect (R). However, GLM is extremely sensitive to missing information, which arises from loss of hybrid families for random environmental causes or from variation in the reproductive success of parent lines. To resolve this issue, we apply a Bayesian hierarchical model, which partitions yield variance into the familiar causal genetic components, while providing Bayesian shrinkage estimates incorporating the uncertainty of missing data. Our study suggests that correlation between observed yields and those predicted by the Bayesian model is high (r2 ≥ 0.99), for observed offspring, regardless of diallel completeness. Additionally, in analyses of complete diallel crosses, line-specific GCA rankings from GLM and Bayesian models are consistent for parent lines. Finally, comparing simulated complete and incomplete diallel datasets, we show the accuracy of predicted yield for families that are present and of parent-line ranking by GCA and the reliability of parent-line selection for double-cross hybrids, especially when non-parental lines (i.e. the four hybrid parents used to predict the yield of double-cross hybrids) are present. Our study demonstrates that the Bayesian hierarchical model performs as well as GLM in analyzing complete diallel crosses and can properly deal with incomplete diallel crosses for which GLM does not work. Therefore, the Bayesian hierarchical model is powerful in diallel analysis to select superior parent lines for producing high-yielding, hybrid, Pacific oyster seed.