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Persistent homology and the branching topologies of plants
Author(s) -
Li Mao,
Duncan Keith,
Topp Christopher N.,
Chitwood Daniel H.
Publication year - 2017
Publication title -
american journal of botany
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.218
H-Index - 151
eISSN - 1537-2197
pISSN - 0002-9122
DOI - 10.3732/ajb.1700046
Subject(s) - biology , branching (polymer chemistry) , evolutionary biology , homology (biology) , network topology , computational biology , genetics , computer science , gene , materials science , composite material , operating system
In On the Nature of Th ings , Lucretius speculates on the necessity of plant development: Branching trees simply do not “leap” from the turf, rather, the branching patterns of shoots and roots develop over time, “slowly increas[sing] from [their] lawful seed” ( Leonard, 2015 ). Over 2000 years ago, the essence of the plant phenotype was written in a poem; plants are four-dimensional beings, branching structures that emerge through time. Th is qualitative realization of the nature of plant phenotype is self-apparent, but quantitative models of plant morphology are less forthcoming. Plant morphology should be quantifi ed comprehensively. Conventional analyses of phenotypic traits consider specifi c plant features and assess only a small proportion of overall morphological variation. Th ere is a critical need for methods to quantify the complete morphology of a plant, including the growing branching structures of both the root and shoot. Plant morphology can be considered across scales; for example, the main trunks of a tree defi ne its coarse architecture, but local branching patterns of twigs distributed throughout the tree also contribute to the overall morphology. Th e branching patterns of plants can be considered from the perspective of topology. Topology is a fi eld of mathematics concerned with the connectedness, or contiguousness, of structures. Smaller branches split from larger branches, creating a hierarchy of connectedness appropriate for topological analysis. Th e ability to quantify and compare the total branching structures of plants across scales has implications for studies of plant genetics, development, evolution, and environmental response, all of which currently rely on traits that measure facets of overall plant morphology. Persistent homology, a mathematical method that captures topological features across scales, is well suited to quantify the growing branching architectures of plants. We begin by considering existing models and morphometric methods used to quantify and compare plant morphology before introducing persistent homology and its applications.