Smoothing and extraction of traits in the growth analysis of noninvasive phenotypic data

Non-destructive high-throughput plant phenotyping is becoming increasingly used and various methods for growth analysis have been proposed. Traditional longitudinal or repeated measures analyses that model growth using statistical models are common. However, often the variation in the data is inappropriately modelled, in part because the required models are complicated and difficult to fit. We provide a novel, computationally efficient technique that is based on smoothing and extraction of traits (SET), which we compare with the alternative traditional longitudinal analysis methods.

The SET-based and longitudinal analyses were applied to a tomato experiment to investigate the effects on plant growth of zinc (Zn) addition and growing plants in soil inoculated with arbuscular mycorrhizal fungi (AMF). Conclusions from the SET-based and longitudinal analyses are similar, although the former analysis results in more significant differences. They showed that added Zn had little effect on plants grown in inoculated soils, but that growth depended on the amount of added Zn for plants grown in uninoculated soils. The longitudinal analysis of the unsmoothed data fitted a mixed model that involved both fixed and random regression modelling with splines, as well as allowing for unequal variances and autocorrelation between time points.

A SET-based analysis can be used in any situation in which a traditional longitudinal analysis might be applied, especially when there are many observed time points. Two reasons for deploying the SET-based method are (i) biologically relevant growth parameters are required that parsimoniously describe growth, usually focussing on a small number of intervals, and/or (ii) a computationally efficient method is required for which a valid analysis is easier to achieve, while still capturing the essential features of the exhibited growth dynamics. Also discussed are the statistical models that need to be considered for traditional longitudinal analyses and it is demonstrated that the oft-omitted unequal variances and autocorrelation may be required for a valid longitudinal analysis. With respect to the separate issue of the subjective choice of mathematical growth functions or splines to characterize growth, it is recommended that, for both SET-based and longitudinal analyses, an evidence-based procedure is adopted.