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This work is motivated by the need to accurately estimate genetic effects over time when analysing data from high-throughput phenotyping (HTP) experiments. The HTP data we deal with here are characterised by phenotypic traits measured multiple times in the presence of spatial and temporal noise and a hierarchical organisation at three levels (populations, genotypes within populations, and plants within genotypes). We propose a feasible one-stage spatio-temporal P-spline-based hierarchical approach to model the evolution of the genetic signal over time on a given phenotype while accounting for spatio-temporal noise and experimental design and/or post-blocking factors. We provide the user with appealing tools that take advantage of the sparse model matrices structure to reduce computational complexity. We illustrate the performance of our method using spatio-temporal simulated data and data from the PhenoArch greenhouse platform at INRAE Montpellier. In the plant breeding context, we show that information extracted for selection purposes from our fitted genotypic curves is similar to that obtained using a comparable two-stage P-spline-based approach.Supplementary materials accompanying this paper appear on-line. [ABSTRACT FROM AUTHOR]

High throughput phenotyping (HTP) platforms and devices are increasingly used for the characterization of growth and developmental processes for large sets of plant genotypes. Such HTP data require challenging statistical analyses in which longitudinal genetic signals need to be estimated against a background of spatio-temporal noise processes. We propose a two-stage approach for the analysis of such longitudinal HTP data. In a first stage, we correct for design features and spatial trends per time point. In a second stage, we focus on the longitudinal modelling of the spatially corrected data, thereby taking advantage of shared longitudinal features between genotypes and plants within genotypes. We propose a flexible hierarchical three-level P-spline growth curve model, with plants/plots nested in genotypes, and genotypes nested in populations. For selection of genotypes in a plant breeding context, we show how to extract new phenotypes, like growth rates, from the estimated genotypic growth curves and their first-order derivatives. We illustrate our approach on HTP data from the PhenoArch greenhouse platform at INRAE Montpellier and the outdoor Field Phenotyping platform at ETH Zürich. [ABSTRACT FROM AUTHOR]