Topological Data Analysis as a Morphometric Method: Using Persistent Homology to Demarcate a Leaf Morphospace.

Area of Science:

• Botany
• Computational Biology
• Topology

Background:

• Current morphometric techniques struggle to compare diverse seed plant leaf shapes and are susceptible to processing errors.
• A need exists for a robust method to quantify and compare a wide range of plant forms.

Purpose of the Study:

• To introduce and validate persistent homology as a unified framework for measuring seed plant leaf shape.
• To establish a comprehensive morphospace for all seed plant leaves.
• To analyze leaf shape diversity across major phylogenetic groups and plant families.

Main Methods:

• Applied persistent homology, a topological data analysis method, to quantify shape features across varying spatial resolutions.
• Analyzed a dataset of 182,707 leaves from 141 plant families worldwide.
• Isolated shape features and measured spatial relationships of pixel densities within leaf outlines.

Main Results:

• Demarcated a defined morphospace encompassing all analyzed seed plant leaves.
• Detected significant shape differences among major phylogenetic groups.
• Estimated leaf shape diversity within plant families and successfully predicted plant family membership.
• Demonstrated the method's ability to capture shape, texture, pattern, and architecture.

Conclusions:

• Persistent homology provides a unified and robust morphometric framework for analyzing diverse plant forms.
• This topological approach overcomes limitations of traditional methods, enabling large-scale comparative studies of plant shape.
• The method has significant potential for biodiversity assessment and evolutionary studies.