In this talk, we look at the problem of classifying the algebraic relations between the solutions of the Lotka-Volterra System. This quadratic system of differential equations was first studied in ecology, independently by Lotka and Volterra in the early 1900’s, as a model for the interaction between two species - a predator and its prey. It has since appeared in several other scientific areas such as chemistry and physics.

We explain some recent result, joint with Y. Duan, where we prove the algebraic independence of the solutions of the system (and their derivatives) in the general case of linearly independent coefficients. The proof uses techniques from the model theory of differential fields, and in particular goes via establishing the irreducibility/strong minimality of the system.