This $769,770 Project Grant from the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049) will fund research at Ball State University from September 2022 through August 2025. The research aims to develop rigorous mathematical models describing the coordinated changes in form and function that occur through ontogeny in arboreal lizards. Researchers will conduct biomechanical experiments and morphological analysis on mourning geckos and three additional arboreal lizard species. They will integrate this data with mathematical modeling and machine learning to derive differential equations describing biomechanical transformations and nonlinear maps between shapes modeling morphological changes during growth. The goal is to establish a unified framework quantifying how morphology, behavior, locomotion and ecology interact and evolve through development. In addition to advancing understanding of developmental biology and ecomorphology, this work is expected to stimulate new applied mathematics research on modeling complex multi-scale nonlinear systems.