Functional Principal Component Analysis: A Robust Method for Time-Series Phenotypic Data

Molecular breeding relies on careful assessment of phenotypic traits linked to DNA markers so that causal genes can be identified and desirable crop alleles selected. Over the past decade, DNA markers have become abundant with the rapid advancement of next-generation sequencing technology, including whole-genome sequencing and genome-wide marker profiles in diverse germplasms. However, the labor-intensive job of phenotyping, which traditionally depends on the experienced eye of breeders, remains a bottleneck to taking advantage of the massive amount of genomic information. In recent years, high-throughput phenotyping, also known as phenomics, has emerged and thrived. Phenomics brings together imaging and sensor technology, robotics, high-performance computing, and artificial intelligence to characterize plant structure and function in various environmental conditions (Tardieu et al., 2017; Zhao et al., 2019). Algorithms and software convert image data into measurable plant traits that can be analyzed accordingly (Gehan et al., 2017; Li et al., 2018; Zhao et al., 2019). The increasing complexity of phenotypic data also demands appropriate statistical methodology (Xu et al., 2018; York, 2019).

In this issue of Plant Physiology, Miao et al. (2020) investigate hypertemporal image data in a genome-wide association study (GWAS). They demonstrate that compared with the analysis of individual time points, functional principal component analysis (FPCA) is a robust statistical approach to analyze phenotypic changes over time. As their focal species, Miao et al. (2020) chose sorghum (Sorghum bicolor), a drought-tolerant bioenergy crop in the grass family. They focused on plant height as the phenotypic trait, for which several causal loci have been identified, including Dwarf1 (Dw1; encoding a protein in the brassinosteroid signaling pathway), Dw2 (encoding a protein kinase), and Dw3 (encoding an auxin-related transporter). Dw2 is also genetically linked with the flowering-time gene Maturity1 (Ma1).

Using a collection of sorghum germplasms, Miao et al. (2020) compared three approaches for plant height measurement and analysis, with each method followed by GWAS (Fig. 1A). They first manually measured plant height at maturity in the field from the base of the plant to the top of panicle using 357 lines and identified Dw1, Dw2-Ma1, and another known plant-height locus, KHL1. After removing lines that could not be measured under greenhouse conditions (described below), either due to limitations of the maximum height of their imaging facility or poor plant growth, GWAS using the remaining 292 lines retrieved only Dw1 as a significant locus. Neither the full panel nor the remaining population identified Dw3 (Miao et al., 2020).

Figure 1.

FPCA is a powerful method to identify genes in time-series GWAS. A, Diagram summarizing the loci identified by GWAS with different experimental conditions. DAP, Days after planting; DAPE, days after panicle emergence. B, Distribution of principal components and growth curves of selected genotypes. Adapted from Miao et al. (2020), figure 6.

Next, the authors performed GWAS using greenhouse-grown and automated phenotyped plants in a time point-by-time point manner. Due to the limited capacity of the imaging facility, the set of plants was divided in half and measured on alternate days. Nonparametric regression was employed to infer missing data and compare height at each time point. Miao et al. (2020) explored two approaches in plant height measurement: whole-plant segmentation and organ-level segmentation. The former method identifies plant and nonplant pixels and measures height from the base to the top of the plant even if the highest point is a leaf tip, whereas the latter method separates different organs and measures the length from the base to the top of the stalk or inflorescence. Since sorghum leaf angle changes during leaf expansion, whole-plant segmentation may measure different parts of the leaf blade at different developmental stages and thus may be inaccurate. Accordingly, organ-level segmentation was used in subsequent experiments. The authors further compared plant age calculated as days after planting versus that calculated as days after panicle emergence. Combining results from different time points, they identified Dw1, Dw3, and a photoperiod-sensitive gene, Ma3 (Childs et al., 1997), with the days-after-planting method. With the days-after-panicle-emergence method, they identified Dw1, Dw2-Ma1, and another known locus, WAK, on chromosome 3 (Fig. 1A; Miao et al., 2020).

Last but not least, FPCA was employed to decompose the variation among the nonparametric curves. The first two functional principal components explained more than 97% of total variation and thus were used for GWAS. The first principal component (PC1) describes height variation that is consistent over time, while PC2 reflects growth rates that vary between developmental stages (Fig. 1B). While the GWAS using PC1 data identified Dw1, Dw2-Ma1, and WAK, GWAS with PC2 identified Dw3 and novel loci on chromosomes 5 and 9. Together, the FPCA method identified most of the known loci controlling sorghum height and additional novel loci (Fig. 1A). The fact that different loci were recovered from different principal components may reflect distinctive mechanisms of these genes controlling plant height. Furthermore, the single-nucleotide polymorphisms nearest to the significant loci are generally closer to the known responsible genes, further supporting greater accuracy and precision of the FPCA method.

In conclusion, time-series data are crucial for studying plant developmental dynamics and plant-environment interactions and become easier to acquire with the advance of high-throughput phenotyping. Compared with single-time-point comparisons, FPCA confers greater power in gene identification in time-series GWAS regardless of missing data and may be applicable in a wide range of time-series phenotypic data analyses.