Heritability estimation for a linear combination of phenotypes via ridge regression

MOTIVATIONThe joint analysis of multiple phenotypes is important in many biological studies, such as plant and animal breeding. The heritability estimation for a linear combination of phenotypes is designed to account for correlation information. Existing methods for estimating heritability mainly focus on single phenotypes under random-effect models. These methods also require some stringent conditions, which calls for a more flexible and interpretable method for estimating heritability. Fixed-effect models emerge as a useful alternative. RESULTSIn this article, we propose a novel heritability estimator based on multivariate ridge regression for linear combinations of phenotypes, yielding accurate estimates in both sparse and dense cases. Under mild conditions in the high-dimensional setting, the proposed estimator appears to be consistent and asymptotically normally distributed. Simulation studies show that the proposed estimator is promising under different scenarios. Compared with independently combined heritability estimates in the case of multiple phenotypes, the proposed method significantly improves the performance by considering correlations among those phenotypes. We further demonstrate its application in heritability estimation and correlation analysis for the Oryza sativa rice dataset. AVAILABILITY AND IMPLEMENTATIONAn R package implementing the proposed method is available at https://github.com/xg-SUFE1/MultiRidgeVar, where covariance estimates are also given together with heritability estimates. SUPPLEMENTARY INFORMATIONSupplementary data are available at Bioinformatics online.