Topological data analysis expands the genotype to phenotype map for 3D maize root system architecture.

A central goal of biology is to understand how genetic variation produces phenotypic variation, which has been described as a genotype to phenotype (G to P) map. The plant form is continuously shaped by intrinsic developmental and extrinsic environmental inputs, and therefore plant phenomes are highly multivariate and require comprehensive approaches to fully quantify. Yet a common assumption in plant phenotyping efforts is that a few pre-selected measurements can adequately describe the relevant phenome space. Our poor understanding of the genetic basis of root system architecture is at least partially a result of this incongruence. Root systems are complex 3D structures that are most often studied as 2D representations measured with relatively simple univariate traits. In prior work, we showed that persistent homology, a topological data analysis method that does not pre-suppose the salient features of the data, could expand the phenotypic trait space and identify new G to P relations from a commonly used 2D root phenotyping platform. Here we extend the work to entire 3D root system architectures of maize seedlings from a mapping population that was designed to understand the genetic basis of maize-nitrogen relations. Using a panel of 84 univariate traits, persistent homology methods developed for 3D branching, and multivariate vectors of the collective trait space, we found that each method captures distinct information about root system variation as evidenced by the majority of non-overlapping QTL, and hence that root phenotypic trait space is not easily exhausted. The work offers a data-driven method for assessing 3D root structure and highlights the importance of non-canonical phenotypes for more accurate representations of the G to P map.