AUTHOR=Bucksch Alexander , Atta-Boateng Acheampong , Azihou Akomian F. , Battogtokh Dorjsuren , Baumgartner Aly , Binder Brad M. , Braybrook Siobhan A. , Chang Cynthia , Coneva Viktoirya , DeWitt Thomas J. , Fletcher Alexander G. , Gehan Malia A. , Diaz-Martinez Diego Hernan , Hong Lilan , Iyer-Pascuzzi Anjali S. , Klein Laura L. , Leiboff Samuel , Li Mao , Lynch Jonathan P. , Maizel Alexis , Maloof Julin N. , Markelz R. J. Cody , Martinez Ciera C. , Miller Laura A. , Mio Washington , Palubicki Wojtek , Poorter Hendrik , Pradal Christophe , Price Charles A. , Puttonen Eetu , Reese John B. , Rellán-Álvarez Rubén , Spalding Edgar P. , Sparks Erin E. , Topp Christopher N. , Williams Joseph H. , Chitwood Daniel H. TITLE=Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences JOURNAL=Frontiers in Plant Science VOLUME=8 YEAR=2017 URL=https://www.frontiersin.org/journals/plant-science/articles/10.3389/fpls.2017.00900 DOI=10.3389/fpls.2017.00900 ISSN=1664-462X 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.