Functional Modeling of Plant Growth Dynamics

Recent advances in automated plant phenotyping have enabled the collection of time series measurements from the same plants of a wide range of traits at different developmental time scales. The availability of time series phenotypic datasets has increased interest in statistical approaches for comparing patterns of change among different plant genotypes and different treatment conditions. Two widely used methods of modeling growth with time are pointwise analysis of variance (ANOVA) and parametric sigmoidal curve fitting. Pointwise ANOVA yields discontinuous growth curves, which do not reflect the true dynamics of growth patterns in plants. In contrast, fitting a parametric model to a time series of observations does capture the trend of growth; however, these models require assumptions regarding the true pattern of plant growth. Depending on the species, treatment regime, and subset of the plant life cycle sampled, these assumptions will not always hold true. We have developed a different approach—functional ANOVA—which yields continuous growth curves without requiring assumptions regarding patterns of plant growth. We compared and validated this approach using data from an experiment measuring the growth of two maize ( L. ssp. ) genotypes under two water availability treatments during a 21-d period. Functional ANOVA enables a nonparametric estimation of the dynamics of changes in plant traits with time without assumptions regarding curve shape. In addition to estimating smooth curves of trait values with time, functional ANOVA also estimates the derivatives of these curves, e.g., growth rates, simultaneously. Using two different subsampling strategies, we demonstrate that this functional ANOVA method enables the comparison of growth curves among plants phenotyped on non-overlapping days with little reduction in estimation accuracy. This means that functional ANOVA based approaches can allow larger numbers of samples and biological replicates to be scored in a single experiment given fixed amounts of phenotyping infrastructure and personnel