AUTHOR=Li Mao , An Hong , Angelovici Ruthie , Bagaza Clement , Batushansky Albert , Clark Lynn , Coneva Viktoriya , Donoghue Michael J. , Edwards Erika , Fajardo Diego , Fang Hui , Frank Margaret H. , Gallaher Timothy , Gebken Sarah , Hill Theresa , Jansky Shelley , Kaur Baljinder , Klahs Phillip C. , Klein Laura L. , Kuraparthy Vasu , Londo Jason , Migicovsky Zoë , Miller Allison , Mohn Rebekah , Myles Sean , Otoni Wagner C. , Pires J. C. , Rieffer Edmond , Schmerler Sam , Spriggs Elizabeth , Topp Christopher N. , Van Deynze Allen , Zhang Kuang , Zhu Linglong , Zink Braden M. , Chitwood Daniel H. TITLE=Topological Data Analysis as a Morphometric Method: Using Persistent Homology to Demarcate a Leaf Morphospace JOURNAL=Frontiers in Plant Science VOLUME=9 YEAR=2018 URL=https://www.frontiersin.org/journals/plant-science/articles/10.3389/fpls.2018.00553 DOI=10.3389/fpls.2018.00553 ISSN=1664-462X ABSTRACT=

Current morphometric methods that comprehensively measure shape cannot compare the disparate leaf shapes found in seed plants and are sensitive to processing artifacts. We explore the use of persistent homology, a topological method applied as a filtration across simplicial complexes (or more simply, a method to measure topological features of spaces across different spatial resolutions), to overcome these limitations. The described method isolates subsets of shape features and measures the spatial relationship of neighboring pixel densities in a shape. We apply the method to the analysis of 182,707 leaves, both published and unpublished, representing 141 plant families collected from 75 sites throughout the world. By measuring leaves from throughout the seed plants using persistent homology, a defined morphospace comparing all leaves is demarcated. Clear differences in shape between major phylogenetic groups are detected and estimates of leaf shape diversity within plant families are made. The approach predicts plant family above chance. The application of a persistent homology method, using topological features, to measure leaf shape allows for a unified morphometric framework to measure plant form, including shapes, textures, patterns, and branching architectures.