Topological data analysis reveals core heteroblastic and ontogenetic programs embedded in leaves of grapevine (Vitaceae) and maracuy (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 maracuya (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 maracuya 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 maracuya 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. Questions in biology are increasingly driven by large datasets comprised of disparate types of data obtained through ecological, morphological, and molecular measurements. A key challenge in the field is thus to make biologically meaningful sense of this enormous amount of data. Methods in topological data analysis offer a flexible and powerful solution to this challenge. To illustrate this, we interrogated datasets of grapevine and maracuya (passion-flower) leaves using the Mapper algorithm, a method of topological data analysis that presents hidden relationships in an easily visualizable graph or network. Our analyses identified core, deeply conserved developmental signatures in all species of grapevine and most species of maracuya that were not detected using traditional analyses. We also found two interesting exceptions to this trend in the maracuya family. These species showed a 'reverse hourglass' effect, suggesting their developmental programs have been modified but only at nodes near the middle of the leaf series. As these exceptions cluster phylogenetically, we propose an independently evolving heteroblasty program may be at play in this subclade. Our analyses illustrate the power of topological data analysis to isolate signatures normally hidden within high-dimensional datasets, and to identify biologically relevant exceptions to those specific signatures.