A General Approach to the Modelling of Trophic Chains

Based on the law of mass action (and its microscopic foundation) and mass conservation, we present here a method to derive consistent dynamic models for the time evolution of systems with an arbitrary number of species. Equations are derived through a mechanistic description, ensuring that all parameters have ecological meaning. After discussing the biological mechanisms associated to the logistic and Lotka-Volterra equations, we show how to derive general models for trophic chains, including the effects of internal states at fast time scales. We show that conformity with the mass action law leads to different functional forms for the Lotka-Volterra and trophic chain models. We use mass conservation to recover the concept of carrying capacity for an arbitrary food chain.