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.

Long term development of a realistic and integrated socio-ecological system

“…at least one process impacts it, and at least one process depends on it). We call such connected nodes characterized components (Gaucherel and Pommereau 2019). In our temporary marsh model, the best described components are those associated with the central question addressed ( i.e.…”

“…The resulting model handles Boolean components (i.e. being functionally present or absent) and qualitative processes (being executed or not, not to be confused with Boolean functions), to ultimately explore all possible ecosystem developments in the future from an initial ecosystem composition called the initial state (Gaucherel and Pommereau 2019; Gaucherel et al 2017).…”

“…2). Additional details on the principle and uses of Petri nets can be found in literature (Gaucherel and Pommereau 2019; Pommereau 2010; Reisig 2013) and in Appendix 2. The ecosystem Petri net itself is developed in three successive steps: a) an intuitive graph (i.e.…”

“…To handle potentially huge and complex interaction networks, new kinds of models and/or methods of simplifications are required. Here, we demonstrate two different ways to simplify the study of ecosystem trajectories: first, we model qualitative interaction networks, as already explored in biology (Reisig 2013); secondly, we focus only on the structural changes of this network (Gaucherel and Pommereau 2019; Gaucherel et al 2017). In other words, we model network (topological) changes instead of dynamics (fluxes) within a frozen network.…”

“…Petri nets belong to the wide category of discrete modelling formalisms (Giavitto and Michel 2003; Pommereau 2010). Such models have proven powerful when applied to biological networks but, to our knowledge, are almost absent in ecology (but see Baldan et al 2015; Gaucherel and Pommereau 2019; Gaucherel et al 2017). We demonstrate the ability of Petri nets to integrate abiotic, biotic and human components of a system and to handle its sharp changes over the long term.…”