# Probability and Statistics Seminar

### A robust mixed linear model for heritability estimation in plant studies

Heritability ($H^2$) refers to the extent of how much a certain phenotype is genetically determined. Knowledge of $H^2$ is crucial in plant studies to help perform effective selection. Once a trait is known to be high heritable, association studies are performed so that the SNPs underlying those traits’ variation may be found. Here, regression models are used to test for associations between phenotype and candidate SNPs. SNP imputation ensures that marker information is complete, so both the coefficient of determination ($R^2$) and $H^2$ are equivalent. One popular model used in these studies is the animal model, which is a linear mixed model (LMM) with a specific layout. However, when the normality assumption is violated, as other likelihood-based models, this model may provide biased results in the association analysis and greatly affect the classical $R^2$. Therefore, a robust version of the REML estimates for linear LMM to be used in this context is proposed, as well as a robust version of a recently proposed $R^2$. The performance of both classical and robust approaches for the estimation of $H^2$ is thus evaluated via simulation and an example of application with a maize data set is presented.

Joint work with P.C. Rodrigues, M.S. Fonseca and A.M. Pires