Morphological plant modeling: Unleashing geometric and topological potential within the plant sciences

Abstract

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

Architectural and anatomical responses of maize roots to agronomic practices in a semi‐arid environment

“…Some of the observed effects of plastic film mulching are similar to the effects of N fertilization, yet being the result of presumably hypoxic soil conditions and high soil temperature. Hence, future challenges remain to measure, describe, and understand the multivariate effects of treatments on root architecture and aerenchyma variation ( Bucksch et al, ; Puttonen et al, ) in greater detail.…”

Plant science decadal vision 2020–2030: Reimagining the potential of plants for a healthy and sustainable future

“…These would be accessed via the most innovative aspect of the Transparent Plant—a scalable and interactive simulation in which a researcher could visualize and predict the consequences of a stimulus such as light, a hormone, or a pathogen through molecular, cellular, and whole‐plant animations (Iwasa, 2016; Nayak & Iwasa, 2019). This interface will require advancements in virtual reality technology and graphics processing capabilities that go well beyond currently available predictive models of root biology (Hartmann, Šimůnek, Aidoo, Seidel, & Lazarovitch, 2018; Jiang et al., 2019), C 4 leaf development (Bogart & Myers, 2016), plant–insect interactions (Pearse, Harris, Karban, & Sih, 2013; Pineda, Kaplan, & Bezemer, 2017), and other processes (Bucksch et al., 2017; Fatichi, Pappas, & Ivanov, 2016; Martinez et al., 2017). Simplified versions of the interface could be developed for learning purposes (Goal 6) in the same way the high school‐appropriate DNA Subway (2020) on CyVerse complements the sophisticated and data‐intensive gene comparison tools used by researchers.…”

Machine Learning Approaches to Improve Three Basic Plant Phenotyping Tasks Using Three-Dimensional Point Clouds

“…The next challenge is to transform the stem points into an underlying skeleton (a graph-theoretic tree) that captures the essential shape of the plant. Deriving skeleton graphs of plants is commonly used to perform morphological analysis of plant architectures (Bucksch et al, 2017;Conn et al, 2017b;Prusinkiewicz and Lindenmayer, 1996).…”