A two-stage approach for the spatio-temporal analysis of high-throughput phenotyping data

Abstract

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.

Figure 1

Overview of the two high-throughput phenotyping platforms. (a) PhenoArch platform at INRAE Montpellier (image source: INRAE). (b) FIP platform at ETH Zürich (image source: ETH crop science)

Figure 2

Results of the first stage of analysis for the PhenoArch platform: Spatial distribution of the (a) raw and (b) spatially corrected leaf area at four different measurements times ($t=108,112,115,117$ DOY). The white areas denote missing data. The colour scale is different for each time point.

Figure 3

Results of the first stage of analysis for the PhenoArch platform: Evolution over time of the raw (grey lines) and spatially corrected (blue lines) leaf area for the plants (replicates) of two genotypes, one per panel, under the two water regimes (as illustration). WD stands for water deficit and WW for well watered.

Figure 4

Results of the second stage of analysis for the PhenoArch platform: (a) Estimated population growth curves (continuous blue lines) with 95% pointwise confidence intervals (blue shaded areas), (b) estimated genotype-specific deviations for all genotypes, (c) estimated genotype-specific deviations for two genotypes per population (as illustration) with 95% pointwise confidence intervals (shaded areas); and (d) estimated plant- (dotted blue lines) and genotype- (red continuous lines) specific growth curves with 95% pointwise confidence intervals (red shaded areas) for two genotypes, one per panel, under the two water regimes (as illustration). WD stands for water deficit and WW for well watered. In (a) and (d) the grey lines represent the spatially corrected leaf area at the plant level (first stage).

Figure 5

Results of the first stage of analysis for the ETH field phenotyping platform: Spatial distribution of the (a) raw and (b) spatially corrected canopy height at four different measurement days ($t=103,114,129,138$ DOY). The white areas denote missing data. The colour scale is different for each day.

Figure 6

Results of the second stage of analysis for the ETH field phenotyping platform: (a) estimated region (orange) and genotype-specific (blue) growth curves, (b) estimated region (orange) and genotype-specific (blue) first-order derivatives, and (c) estimated genotype-specific deviations. In (a) and (b) the orange shaded areas denote 95% pointwise confidence intervals at the region level. AT/CZ: Austria/Czechia; CH: Switzerland; DE: Germany; FR: France; GB: Great Britain; PL: Poland; SE/DK: Sweden/Denmark.

Figure 7

Results of the second stage for the ETH field phenotyping platform: (a) region-specific growth curves (coloured lines) vs. mean temperature (grey line), and (b) region-specific first-order derivatives; blue and red points indicate (local) minima and maxima, respectively. AT/CZ: Austria/Czechia; CH: Switzerland; DE: Germany; FR: France; GB: Great Britain; PL: Poland; SE/DK: Sweden/Denmark.

Figure 8

Scatterplots matrix with the extracted attributes at the genotype level for the ETH field phenotyping platform. The lower off diagonal depicts bivariate scatterplots, the diagonal shows the conditional densities of each attribute per region, the upper off diagonal indicates the bivariate Pearson correlation (marginal and by region; “***” p-value < 0.001, “**” p-value < 0.01, “*” p-value < 0.05, “.” p-value < 0.10 and “” otherwise), the last column displays the boxplots of each attribute per region, the last row depicts the conditional histograms of each attribute per region, and the bottom right barplot shows the number of genotypes per region. AT/CZ: Austria/Czechia; CH: Switzerland; DE: Germany; FR: France; GB: Great Britain; PL: Poland; SE/DK: Sweden/Denmark.