A Review of Lagrangian Formalism in Biology: Recent Advances and Perspectives

TL;DR

This paper reviews the application of Lagrangian formalism in biology over the past 50 years, highlighting methods to derive Lagrangians for population models and discussing future perspectives in biological research.

Contribution

It provides a comprehensive overview of how Lagrangian formalism has been adapted for biological systems and details methods to derive and utilize Lagrangians in population dynamics.

Findings

Derived Lagrangians for five population models

Demonstrated how to gain biological insights without solving equations

Discussed future applications of Lagrangian formalism in biology

Abstract

The Lagrangian formalism has attracted the attention of mathematicians and physicists for more than 250 years and has played significant roles in establishing modern theoretical physics. The history of the Lagrangian formalism in biology is much shorter, spanning only the last 50 years. In this paper, a broad review of the Lagrangian formalism in biology is presented in the context of both its historical and modern developments. Detailed descriptions of different methods to derive Lagrangians for five selected population dynamics models are given and the resulting Lagrangians are presented and discussed. The procedure to use the obtained Lagrangians to gain new biological insights into the evolution of the populations without solving the equations of motion is described and applied to the models. Finally, perspectives of the Lagrangian formalism in biology are discussed.