Topological data analysis reveals core heteroblastic and ontogenetic programs embedded in leaves of grapevine (Vitaceae) and maracuyá (Passifloraceae)

Leaves are often described in language that evokes a single shape. However, embedded in that descriptor is a multitude of latent shapes arising from evolutionary, developmental, environmental, and other effects. These confounded effects manifest at distinct developmental time points and evolve at different tempos. Here, revisiting datasets comprised of thousands of leaves of vining grapevine (Vitaceae) and maracuyá (Passifloraceae) species, we apply a technique from the mathematical field of topological data analysis to comparatively visualize the structure of heteroblastic and ontogenetic effects on leaf shape in each group. Consistent with a morphologically closer relationship, members of the grapevine dataset possess strong core heteroblasty and ontogenetic programs with little deviation between species. Remarkably, we found that most members of the maracuyá family also share core heteroblasty and ontogenetic programs despite dramatic species-to-species leaf shape differences. This conservation was not initially detected using traditional analyses such as principal component analysis or linear discriminant analysis. We also identify two morphotypes of maracuyá that deviate from the core structure, suggesting the evolution of new developmental properties in this phylogenetically distinct sub-group. Our findings illustrate how topological data analysis can be used to disentangle previously confounded developmental and evolutionary effects to visualize latent shapes and hidden relationships, even ones embedded in complex, high-dimensional datasets.