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Abstract Persian walnuts (Juglans regiaL.) are the second most produced and consumed tree nut, with over 2.6 million metric tons produced in the 2022–2023 harvest cycle alone. The United States is the second largest producer, accounting for 25% of the total global supply. Nonetheless, producers face an ever‐growing demand in a more uncertain climate landscape, which requires effective and efficient walnut selection and breeding of new cultivars with increased kernel content and easy‐to‐open shells. Past and current efforts select for these traits using hand‐held calipers and eye‐based evaluations. Yet there is plenty of morphology that meets the eye but goes unmeasured, such as the volume of inner air or the convexity of the kernel. Here, we study the shape of walnut fruits based on X‐ray computed tomography three‐dimensional reconstructions. We compute 49 different morphological phenotypes for 1264 individual nuts comprising 149 accessions. These phenotypes are complemented by traits of breeding interest such as ease of kernel removal and kernel‐to‐nut weight ratio. Through allometric relationships, relative growth of one tissue to another, we identify possible biophysical constraints at play during development. We explore multiple correlations between all morphological and commercial traits and identify which morphological traits can explain the most variability of commercial traits. We show that using only volume‐ and thickness‐based traits, especially inner air content, we can successfully encode several of the commercial traits. 

Abstract 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. Here, we review applications of topological data analysis (TDA) to biology in a way accessible to biologists and applied mathematicians alike. TDA uses principles from algebraic topology to comprehensively measure shape in data sets. 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 data sets. We first provide a TDA primer for biologists before exploring the use of TDA across biological sub‐disciplines, spanning structural biology, molecular biology, evolution, and development. We end by comparing and contrasting different TDA approaches and the potential for their use in biology. The vision of TDA, that data are shape and shape is data, will be relevant as biology transitions into a data‐driven era where the meaningful interpretation of large data sets is a limiting factor.