RUI: Collaborative Research: DMS/NIGMS 1: The mathematical laws of morphology and biomechanics through ontogeny

Although fruitful interactions between mathematical theory and scientific experimentation were plentiful in the 20th century, even now the integration of math into biology is still in its infancy and mostly limited to fine scales. Already 100-years ago, D’Arcy Thompson developed critical concepts and tools for the analysis of form and function as organisms develop, yet nevertheless, we continue to lack a solid, mathematical theory of how macroscopic, fully 3D shapes and functions evolve through growth in animals.

To thoroughly understand the mechanisms of changes in form and function through growth, it is necessary to derive rigorous mathematical laws that govern both morphology and locomotion through development. This project will concentrate on arboreal lizards, a model system in many fields of biology, and will combine biomechanical experiments and morphological analysis, together with mathematical modeling and machine learning.

By capitalizing on the rapid growth and extraordinary diversity of body forms and locomotor behaviors of arboreal lizards, this research will build an integrative picture of how their form and function transform through development with mathematical rigor. This will provide a tangible contribution to our understanding of the mechanisms underlying the flexibility and resilience of species that face an ever-changing environment, while at the same time stimulating new research in applied mathematics such as the modeling of increasingly complex, multi-scale, and nonlinear systems.

This project will have broad community and societal impacts through the education and training of highly qualified personnel (undergraduate, graduate, and postdoctoral scholars), particularly those from underrepresented groups in STEM. Through outreach initiatives, this project will educate school children, especially those from disadvantaged populations, and the public on the ways that math and biology can work together to contribute to our understanding of animal form and movement, climate change, population aging, and conservation.

This project will bring new theoretical and methodological foundations to the understanding of the biology of arboreal lizards via the data-driven discovery of the mathematical laws that govern 1) their biomechanical transformation through ontogeny, in the form of differential equations describing the coupled motion of joints/limbs; 2) their transformations in morphology through ontogeny, via smooth group transformations in the form of nonlinear maps between shapes; and 3) how their shape and mechanics are related to each other, via explainable statistical and machine learning models and low-dimensional transformations across age-groups. Experiments will be conducted to collect comprehensive biomechanical and morphological data that will empower mathematical and machine learning models and will occur in two phases.

Phase 1 will capitalize on a parthenogenic arboreal lizard (mourning gecko) and a common garden design to construct models that will allow us to quantify the coordinated changes of form and function through growth; Phase 2 will test the generality of our models on three additional arboreal lizard species. The longitudinal data produced will be unparalleled in its scale and scope in functional morphology and comparative biomechanics, making it a benchmark dataset and enabling and stimulating the investigation of further questions related to developmental biology, animal behavior, and ecomorphology.

This work will provide a unifying perspective to how ontogeny, morphology, behavior, locomotion, community ecology, and evolution interact and merge by producing a common mathematical and computational framework that will become of broad use at the intersection of these disciplines.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.