Using discrete systems to exhaustively characterize the dynamics of an integrated ecosystem

Abstract

To understand long-term ecosystem dynamics, several concepts have been recently proposed that consider ‘basins of attraction’ to express resilience and ‘tipping points’ that express sharp change in an ecosystem's behaviour. However, these temporal features remain difficult to identify and quantify because current models usually focus only on a part of the whole ecosystem behaviour, whereas a holistic approach should be preferred. We propose an original family of models based on discrete systems and designed to comprehensively characterize ecosystem dynamics holistically and over the long term. We developed a qualitative model based on Petri nets, made up of a relational graph (interaction network) that was then rigorously handled using transition rules. Unlike traditional modelling and graph theory approaches, transition rules can strongly modify the graph structure (i.e. a dynamic topology occurs). We examined the value of Petri nets when applied to the simple ecosystem of a termite colony. A termite colony comprises of abiotic and biotic components and processes that we explored along all of their possible trajectories. Several temporal features, such as basins of attraction (i.e. strongly connected states), tipping points (critical transitions along trajectories) and various kinds of collapses (functioning systems whose structures were nevertheless fixed), were easily detected and quantified. We propose that Petri nets developed for more complex ecosystems will provide original insights into their holistic behaviour.