Walnuts are the second most produced and consumed tree nut, with over 2.6 million metric tons produced in the 2022-23 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 CT (Computed Tomography) 3D reconstructions. We compute 49 different morphological phenotypes for 1264 individuals comprising 149 accessions. These phenotypes are complemented by traits of breeding interest such as ease of kernel removal and kernel weight. 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.

As collections of data grow in size, it is increasingly important to have an efficient means of analyzing large data sets. Topological data analysis (TDA) applies concepts from the mathematical field of topology to not only efficiently examine large data sets, but to make inferences related to the overall “shape” of data. In this project, we use Mapper, a tool from TDA that summarizes data into a graph, to discover an underlying structure relating the shapes of more than 3,300 Passiflora leaves from 40 different species. We choose to study leaves of the Passiflora species in particular due to their extraordinary diversity of shape. As the Mapper graph has a structure, or “shape” of its own, we think of it as a “shape of shapes” that provides information on the interplay between the developmental processes determining leaf shape within a single plant and the evolutionary processes between species. In particular, we examine the interactions between leaf species and both heteroblasty and leaf area by constructing a Mapper graph for each measure. For each node in the resulting graphs, we then compute the average leaf shape to obtain a graph structure that reveals how morphometric differences between species relate to the developmental changes that must occur for those shapes to be realized.

From preventing scurvy to being part of religious rituals, citrus are intrinsically connected to human health and perception. From tiny mandarins to head-sized pummelos, citrus capability of hybridization provides a vastly diverse array of fruit sizes and shapes, which in turn corresponds to a diversity of flavors and aromas. These sensory qualities are tightly linked to oil glands in the citrus skin. The oil glands are also key to understanding fruit development, and the essential oils contained by them are fundamental in the food and perfume industries. We study the shape of citrus based on 3D X-ray CT scan reconstruction of 163 different citrus samples comprising 58 different species and cultivars, including samples of all fundamental citrus species. First, using the power of X-rays and image processing, we are able to compare and contrast size ratios between different tissues, such as the size of the skin compared to the rind or the flesh. Second, we model the fruit shape as an ellipsoidal surface, and later we study and infer possible oil gland distributions on this surface using principles of directional statistics. We finally compare and contrast these overall fruit shape models along their gland distributions across different citrus species. This morphological modeling will allow us later to link genotype with phenotype, furthering our insight on how the physical shape is genetically specified in DNA.