Lagrangian Formalism in Biology: I. Standard Lagrangians and their Role in Population Dynamics

TL;DR

This paper develops a Lagrangian formalism for population dynamics, using standard Lagrangians to analyze models of interacting species and explore their physical analogies.

Contribution

It introduces a method to derive standard Lagrangians for population models, linking biological dynamics with physical energy concepts.

Findings

Derived Lagrangians reveal energy-like terms in population models

Standard Lagrangians help identify similarities between different population dynamics

The formalism provides a new perspective on biological interactions

Abstract

The Lagrangian formalism is developed for the population dynamics of interacting species that are described by several well-known models. The formalism is based on standard Lagrangians, which represent differences between the physical kinetic and potential energy-like terms. A method to derive these Lagrangians is presented and applied to selected theoretical models of the population dynamics. The role of the derived Lagrangians and the energy-like terms in the population dynamics is investigated and discussed. It is suggested that the obtained standard Lagrangians can be used to identify physical similarities between different population models.