Quantifying barley morphology using Euler characteristic curves

Shape is data and data is shape. Biologists are accustomed to thinking about how the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. Less often do we consider that data itself has shape and structure, or that it is possible to measure the shape of data and analyze it. Topological Data Analysis is a novel mathematical discipline that uses principles from algebraic topology to comprehensively measure shape in datasets. Using a function that relates the similarity of data points to each other, we can monitor the evolution of topological features—connected components, loops, and voids. This evolution, a topological signature, concisely summarizes large, complex datasets. Here, we focus on quantifying the morphology of barley spikes and seeds using topological descriptors based on the Euler characteristic and relate the output back to genetic information. The vision of TDA, that data is shape and shape is data, will be relevant as biology transitions into a data-driven era where meaningful interpretation of large datasets is a limiting factor.