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

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.