Topological data analysis reveals a core heteroblastic program embedded in leaves of grapevine and maracuya

Leaves have a single shape. However, embedded in that shape are 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 maracuya (Passifloraceae) species, we apply a technique from the mathematical field of topological data analysis to comparatively visualize the structure of heteroblastic effects on leaf shape in each group. Consistent with a morphologically closer relationship, members of the grapevine dataset possess a strong core heteroblasty program with little deviation between species. Remarkably, we found that most members of the maracuya family also share a core heteroblasty program despite dramatic species-to-species leaf shape differences. This conservation was not detected using traditional analyses. We also identify two morphotypes of maracuya that deviate from the core structure, suggesting the evolution of new heteroblastic properties in this phylogenetically related 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.