Modelling temporal genetic and spatio-temporal residual effects for high-throughput phenotyping data*

High-throughput phenomics data are being collected in both the laboratory and the field. The data are often collected at many time points and there may be spatial variation in the laboratory or field that impacts on the growth of the plants, and that may influence the traits of interest. Modelling the genetic effects is of primary interest in such studies, but these effects might be biased if non-genetic effects present in the experiment are ignored. With data that are collected both in time and space, there may be a need to jointly model these multi-dimensional non-genetic effects. Thus both modelling of genetic effects over time and non-genetic effects over time and space in a one-stage analysis is considered. An experiment that involves field phenomics data with four dimensions, two in space and two in time, provides the vehicle to examine the models. Factor analytic (FA) models are often used for genetic effects for different environments to provide reliable estimates of genetic variances and correlations. As the time dimension defines the environments, FA models are examined for the phenomics data. Reduced rank tensor smoothing splines are presented as a possible approach for modelling the spatio-temporal effects, although an additional term is included for heterogeneity over the two time dimensions. This approach is feasible, although very time-consuming. The process of model selection for the genetic effects is presented including tests, information criteria and diagnostics. Comparisons of more simplistic models are made with the reduced rank tensor spline. This also shows the interplay between the genetic and residual models in model selection.