Persistent homology: a tool to universally measure plant morphologies across organs and scales

Genetic contributions to plant morphology are not partitioned between shoots and roots. Yet, shoot and root architectures are rarely measured in the same plants. Even if shoot and root architectures are both studied, the application of mathematical methods flexible enough to accommodate the disparate topologies and shapes within a plant, and across scales, are lacking. Here, we advocate the use of persistent homology, a mathematical method robust to noise, invariant with respect to orientation, capable of application across diverse scales, and importantly, compatible with diverse functions to quantify disparate plant morphologies, architectures, and textures. To demonstrate the usefulness of this method, we apply persistent homology approaches to the shape of leaves, serrations, and root architecture as measured in the same plants of a domesticated tomato Solanum pennellii near-isogenic introgression line population under field conditions. We find that genetic contributions to morphology affect the plant in a concerted fashion, affecting both the shoot and root, revealing a pleiotropic basis to natural variation in tomato.