Growth dynamics and heritability for plant high-throughput phenotyping studies using hierarchical functional data analysis.

In modern high-throughput plant phenotyping, images of plants of different genotypes are repeatedly taken throughout the growing season, and phenotypic traits of plants (e.g., plant height) are extracted through image processing. It is of interest to recover whole trait trajectories and their derivatives at both genotype and plant levels based on observations made at irregular discrete time points. We propose to model trait trajectories using hierarchical functional principal component analysis (HFPCA) and show that the problem of recovering derivatives of the trajectories is reduced to estimating derivatives of eigenfunctions, which is solved by differentiating eigenequations. Based on HFPCA, we also propose a new measure for the broad-sense heritability by allowing it to vary over time during plant growth. Simulation studies show that the proposed procedure performs better than its competitors in terms of recovering both trait trajectories and their derivatives. Interesting characteristics of plant growth and heritability dynamics are revealed in the application to a modern plant phenotyping study.