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.

Shape is foundational to biology. Observing and documenting shape has fueled biological understanding as the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. The vision of Topological Data Analysis (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. We focus on quantifying the morphology of X-ray CT scans of a diverse panel of citrus and their tissues. In total, we have access to 146 different citrus samples comprising 58 different species, 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 exocarp compared to the mesocarp or the endocarp. Second, using Persistent Homology we focus on characterizing the size and distribution of oil glands across different citrus species, and the relation of such distribution to other phenotypes such as exocarp surface area. This shape characterization will allow us later to link genotype with phenotype, furthering our understanding on how the physical shape is genetically coded in DNA.

Observing and documenting shape has fueled biological understanding as the shape of biomolecules, cells, tissues, and organisms arise from the effects of genetics, development, and the environment. The vision of Topological Data Analysis (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. We focus first on quantifying the morphology of X-ray CT scans of barley spikes and seeds using topological descriptors based on the Euler Characteristic Transform. We then successfully train a support vector machine to distinguish and classify 28 different varieties of barley based solely on the 3D shape of their grains. This shape characterization will allow us later to link genotype with phenotype, furthering our understanding on how the physical shape is genetically coded in DNA.