Prediction of non-equilibrium dynamics in ecosystems: from dogs and fleas to moleculesand organisms

Abstract

Ecosystems are systems made up of large collections of interacting microscopic entities.Therefore, a statistical mechanical approach to these systems may yield reliable predictionsof their macroscopic properties. Here we examine the predictions of an ecosystem modelwhich assigns to each possible macroscopic trajectory of the system, during a given timeinterval, a probability which is proportional to its microscopic multiplicity, that is thenumber of ways it can be realized microscopically. We show that, for sufficiently largesystems, this model predicts quasi-deterministic macroscopic dynamics, eventhough all microscopic trajectories are equiprobable. We give an explicit formalismfor these most probable dynamics and point out some of its strikingly realisticproperties. We argue that the interplay of microscopic multiplicities reflected in ourmodel could provide a sufficient and basic explanation for macroscopic ecosystemdynamics.