Organismal biology

What mathematical laws govern morphology and biomechanics of animals through ontogeny?

Background

Although it's already over 100 years since D'Arcy Thompson's work started to look at growth and form through a quantitative lens, we still lack a satisfactory understanding of the mathematical principles underpinning how shape and function are related through growth.

Goals

This project aims to uncover the mathematical and physical laws that describe variations in shapes and behaviour of lizards across species and through growth via the use of differential equations and modern machine learning tools.

Broader Impacts

This project will provide new quantitative methodologies widely applicable in organismal biology. 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.

Relevant Publications

Selvitella, A.M and Foster, K.L. (2025). Sharp conditions for the existence of smooth periodic solutions to a hybrid dynamical system for human running via algebraic geometric tools. To appear in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.
A.M. Selvitella and E. Allen (2025). On the effectiveness of sparse identification methods to detect nonlinear models of oscillatory dynamics in psychology and the life sciences. To appear in Nonlinear Dynamics, Psychology, and Life Sciences.
Selvitella, A.M. and K.L. Foster. (2024). Some comments on the paper ``Is human height based on a Lucas sequence relationship between the foot height, tibial length, femur length and upper body length?" and an alternative analysis. Journal of Anatomy, 246(4), 631-632.
Selvitella, A.M. and Foster, K.L. (2024). An approximate solution of the SLIP model under the regime of linear angular dynamics during stance and the stability of symmetric periodic running gaits. Journal of Theoretical Biology, 595, 111934.
Selvitella, A.M. and Foster, K.L. (2023). On the variability and dependence of human leg stiffness across strides during running and some consequences for the analysis of locomotion data. Royal Society Open Science, 10, 230597. https://doi.org/10.1098/rsos.230597.

Selvitella, A.M. and Foster, K.L. (2022). The spring-mass model and other reductionist models of bipedal locomotion on inclines. Integrative and Comparative Biology, 62(5), 1320-1334. https://doi.org/10.1093/icb/icac047.

Foster, K.L. and Selvitella, A.M. (2022). Transfer of Anolis locomotor behavior across environments and species. Integrative and Comparative Biology, 62 (3), 774–790. https://doi.org/10.1093/icb/icac015.

Foster, K.L. and Selvitella, A.M. (2020). Learning the locomotion behaviour of lizards transfers across environments. International Conference on Machine Learning 2020 Workshop on Computational Biology. July 17th, 2020. https://icml-compbio.github.io/2020/papers/WCBICML2020_paper_2.pdf

Student Publications

D.T. Brown. (2023). Model selection through Cross Validation for Supervised Learning Tasks with Manifold Data. Journal of Purdue Undergraduate Research, 13 (41). Supervisor: Selvitella, A.M.
K. Wijesooriya. (2024). The mathematical laws of morphology and biomechanics through ontogeny. To appear in the Journal of Purdue Undergraduate Research. Supervisor: Selvitella, A.M.

Grants

NSF Award # 2152789 on RUI: Collaborative Research: DMS/NIGMS 1: The mathematical laws of morphology and biomechanics through ontogeny. PIs: Prof. Alessandro Maria Selvitella (Purdue University) and Prof. Kathleen Lois Foster (Ball State University).

NSF-Simons Center for Quantitative Biology - Northwestern University Pilot Project Grant: On the mathematical and physical laws of the morphology and biomechanics of mourning geckos through ontogeny. PIs: Prof. Alessandro Maria Selvitella (Purdue University) and Prof. Kathleen Lois Foster (Ball State University).

Major Events

Thematic Program on The Mathematical Laws of Morphology and Biomechanics: Biological Principles, Mathematical Models, and Data. 2021/2022 - ongoing. Co-organizer: K.L. Foster, Ball State University. Website.

Midwest Workshop on Women in Experimental Biology: Towards and Integration of Modern Machine Learning Methods to The Biological Sciences. 2022. Co-organizer: K.L. Foster, Ball State University.

Workshop in Mathematical and Computational Biology. 2021 and 2022. Co-organizers: K.L. Foster, Ball State University, and D. Kihara, Purdue University.

Main Collaborators

Kathleen Lois Foster - Ball State University Lab page

Student Team

Elliot Allen - Purdue University Fort Wayne
Umair Ali Wani - University of New Mexico
Tanisha Raskar - Purdue University Fort Wayne
Prisha Joshi - Purdue University Fort Wayne
Elizabeth Strong - Purdue University Fort Wayne
Nasiru Nurudeen - Purdue University Fort Wayne
Hikmat Sanusi - Purdue University Fort Wayne

Alumni

Derek Brown - Purdue University Fort Wayne
Rishikesh Fulari - Purdue University Fort Wayne
Aman Bajpayee - Purdue University Fort Wayne
Kisal Wijesooriya - Purdue University
Duncan Andrews - Pennsylvania State University

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