Abstract
Heterosis, also known as the hybrid vigor, occurs when the mean phenotype of hybrid off-spring is superior to that of its two inbred parents. The heterosis phenomenon is extensively utilized in agriculture though the molecular basis is still unknown. In an effort to understand phenotypic heterosis at the molecular level, researchers have begun to compare expression levels of thousands of genes between parental inbred lines and their hybrid offspring to search for evidence of gene expression heterosis. Standard statistical approaches for separately analyzing expression data for each gene can produce biased and highly variable estimates and unreliable tests of heterosis. To address these shortcomings, we develop a hierarchical model to borrow information across genes. Using our modeling framework, we derive empirical Bayes estimators and an inference strategy to identify gene expression heterosis. Simulation results show that our proposed method outperforms the more traditional strategy used to detect gene expression heterosis. This article has supplementary material online.
Highlights
Heterosis, or hybrid vigor, refers to the enhanced phenotype of hybrid progeny relative to their inbred parents
The reported numbers of genes exhibiting each of the three types of gene expression heterosis identified by the sample average method and the empirical Bayes method, respectively, are listed in Table 2 where false discovery rates (FDRs) was controlled at the 0.05 level
A shrinkage method based on the sample average estimators can improve inferences on gene expression heterosis by sharing information across genes
Summary
We model αj , the half parental difference, as a draw from a mixture of a point-mass-at-0 distribution and a normal distribution. The point-mass distribution in the mixture model represents the case where the parental gene expression levels are equal, whereas the normal component corresponds to genes whose expression levels differ between the two parental lines. We model δj , the difference between the offspring mean and the average of the parental means, with another mixture model that has normal and point-mass-at-0 component distributions. Under an empirical Bayes framework, we derive posterior distributions of αj and δj and draw inferences about gene expression heterosis from estimates of these posteriors. We compare the empirical Bayes method with the sample average method through simulation studies where datasets were generated based on real heterosis microarray experiments or hypothetical probability models. R code and C code for the analysis of real experiments in Section 4, the simulation studies in Section 5, and the implementation of all our algorithms is available upon request
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