lme4breeding: enabling genetic evaluation in the era of genomic data

Mixed models are a cornerstone in quantitative genetics to study the genetics of complex traits. A standard quantitative genetic model assumes that the effects of some random effects (e.g., individuals) are correlated based on their identity by descent and state. In addition, other relationships arise in the genotype by environment interactions (i.e., covariance structures). Open-source mixed model routines are available but do not account for complex covariance structures and are able to fit big genomic models. The lme4breeding R package was developed as an extension of the lme4 package and allows correlated random effects and complex covariance structures to be fitted for Gaussian, binary, and count responses. The correlation between levels of the random effect (e.g., individuals) is accounted for by post-multiplying the incidence matrix of the levels of this random factor by the Cholesky factor of the corresponding (co)variance matrix (e.g., the genomic relationship matrix). To enable big genomic models the eigen decomposition of relationship matrices is enabled. Maximum likelihood and REML estimation are available in lme4breeding. This note describes the type of models that can be fitted using lme4breeding and presents some examples.