Insight into Genome-Wide Associations of Growth Trajectories Using a Hierarchical Non-Linear Mixed Model

In applying a hierarchical mixed model to genome-wide association analysis (GWAS) of longitudinal data, dimensionality reduction through modeling repeated measurements improves both computational efficiency and statistical power. Legendre polynomials can flexibly fit population growth trajectories, but higher orders substantially increase computational complexity. Instead of using Legendre polynomials, we first estimated fewer individual-specific parameters using biologically meaningful non-linear models and then associated these phenotypic regressions with genetic markers using a multivariate linear mixed model (mvLMM). After performing a canonical transformation of the regressions based on the pre-estimated covariance matrices under the null genomic mvLMM, we decomposed the mvLMM into mutually independent univariate models and incorporated EMMAX to enable rapid genome-wide mixed-model associations for each transformed phenotype. Simulations for longitudinal association analysis in maize and GWAS for the growth trajectories of body weights in mice demonstrated the advantages of hierarchical non-linear mixed models in computing efficiency and statistical power for detecting quantitative trait loci (QTL), compared with mvLMM for multiple growth points and the hierarchical random regression model using Legendre polynomials as sub-models.