To understand and manage (social-)ecological systems, we need an intuitive and rigorous way to represent them. Recent ecological studies propose to represent interaction networks into modular graphs, multiplexes and higher-order interactions. Along these lines, we argue here that non-dyadic (non-pairwise) interactions are common in ecology and environmental sciences, necessitating fresh concepts and tools for handling them. In addition, such interaction networks often change sharply, due to appearing and disappearing species and components. We illustrate in a simple example that any ecosystem can be represented by a single hypergraph, here called the ecosystem hypernetwork. Moreover, we highlight that any ecosystem hypernetwork exhibits a changing topology summarizing its long term dynamics (e.g., species extinction/invasion, pollutant or human arrival/migration). Qualitative and discrete-event models developed in computer science appear suitable for modeling hypergraph (topological) dynamics. Hypernetworks thus also provide a conceptual foundation for theoretical as well as more applied studies in ecology (at large), as they form the qualitative backbone of ever-changing ecosystems.

The EDEN framework provides formal modelling and analysis tools to study ecosystems. At the heart of the framework is the reaction rules (RR) modelling language, that is equipped with an operational semantics and can be translated into Petri nets with equivalent semantics. In this paper, we formally define the RR language and its semantics, detailing the initial definition from Gaucherel et al, 2019 and extending it with a notion of constraints that allows to model mandatory events. Then, we consider in turn two classes of Petri nets: priority Petri nets (PPN), which are safe place/transition Petri nets equipped with transitions priorities, and extended Petri nets (EPN) which are PPN further extended with read arcs, inhibitor arcs, and reset arcs. For each of these classes, we define the translation of an RR system into a Petri net and prove that the state-space generated with the RR operational semantics is equivalent to the marking graph of the Petri net resulting from the translation. We use a very strong notion of equivalence by considering labelled transition systems (LTS) isomophism with states and labels matching.

Understanding ecosystems is crucial, in particular to take conservation actions. One way to do so is formal modelling and analysis. In this paper, we present the EDEN (Ecological Discrete-Event Networks) framework that provides ecologists with discrete modelling languages and dedicated analysis tools. These tools are based on well-known techniques in computer science, like symbolic state-spaces or model-checking, but used in quite a different way. Indeed, most formal analysis techniques provide yes/no answers to well-defined questions, possibly with a witness execution, which is good to assess whether a system exhibits or not a given property. However, most questions in ecology are not stated as “Does the system have such behaviour?” but rather as “Why does the system sometimes has such behaviour and how can we prevent it from happening?” Moreover, these questions are often hard to express formally. With EDEN, we propose an exploratory way to build progressively a representation of this behaviour that is suitable to answer such questions. The question itself being formalised on the way, together with the model exploration. This approach is based on a hybrid representation of the state-space that can be incrementally split into a graph of components (symbolic sets of states) linked by transitions. The goal is thus to provide the users with a human-readable representation of the state-space that can be fine-tuned with respect to the questions of interest, resulting in an object that constitutes by itself the expected explanation. While EDEN is rather specific to ecology, we advocate that its analysis method and tools could be beneficial for other domains.

Ecosystems are complex systems still waiting for a convenient and flexible way to model them. This article extends the rule-based discrete-event modeling approach for ecosystems developed by Gaucherel et al. Here, we propose the systematic use of (1-safe) reset Petri nets for the analysis of such systems.

Sub-Saharan social-ecological systems are undergoing changes in environmental conditions, including modifications in rainfall pattern and biodiversity loss. Consequences of such changes depend on complex causal chains which call for integrated management strategies whose efficiency could benefit from ecosystem dynamic modeling. However, ecosystem models often require lots of quantitative information for estimating parameters, which is often unavailable. Alternatively, qualitative modeling frameworks have proved useful for explaining ecosystem responses to perturbations, while only requiring qualitative information about social-ecological interactions and events and providing more general predictions due to their validity for wide ranges of parameter values. In this paper, we propose the Ecological Discrete-Event Network (EDEN), an innovative qualitative dynamic modeling framework based on “if-then” rules generating non-deterministic dynamics. Based on expert knowledge, observations, and literature, we use EDEN to assess the effect of permanent changes in surface water and herbivores diversity on vegetation and socio-economic transitions in an East African savanna. Results show that water availability drives changes in vegetation and socio-economic transitions, while herbivore functional groups have highly contrasted effects depending on the group. This first use of EDEN in a savanna context is promising for bridging expert knowledge and ecosystem modeling.

Ecosystems are complex and data-intensive systems, and the ecologists still struggle to understand them in an integrated manner. Models that miss key dynamics can possibly lead to fallacious conclusions about the ecosystem fate. To address these limits and encompass whole and realistic ecosystems, we develop here a qualitative model with the help of discrete-event models. This model, based on formal Petri nets, was able to integrate biotic, abiotic and human-related components (e.g. grazing) along with their processes into the same interaction network. The model was also able to grasp ecosystem development, as defined by sharp changes of the interaction network structure itself. Furthermore, the model was possibilistic and thus rigorously computed all possible ecosystem states reached after a specific (present-day) initial state. This innovative approach in ecology then allows to rigorously and exhaustively identifying all possible ecosystem trajectories and to study their impacts and outcomes. For the first time in a realistic ecosystem, we illustrated such discrete and qualitative models in the case study of temporary marshes in the Mediterranean part of France, the Camargue delta. The model demonstrated that when marshes are exposed to extensive grazing the presence of marsh heritage species (i.e. with a conservation value) is facilitated by opening up the vegetation through various trajectories. This supports the commonly used management practices of extensive grazing to conserve certain protected habitats. The detailed analysis of the computed ecosystem trajectories allows exploring a range of recommendations for management strategies.

Monitoring the provision of multiple ecosystem services (ES) in social-ecological systems is a major challenge. Most tools usually tackle the problem by modelling individual ES, but do not perform a holistic analysis of a dynamic and integrated system. We developed a discrete-event model (DORIAN) and explored its potential for assessing biodiversity and multifunctionality of a mountain ski resort subjected to a changing climate. We represented this social-ecological system as a network comprising 16 binary components and 51 processes that define component interactions. We identified 22 economy- and ecology-related ES, depending on the presence/absence of components. We simulated six scenarios representing different economic, environmental and climatic situations and calculated a score (the sum of proxies for biodiversity or ES), corresponding to the level of biodiversity and multifunctionality. Results showed that climate change reduced the system’s multifunctionality and increased the number of degraded states, as well as the trajectories from healthy to degraded states. With increasing levels of biodiversity, only ecology-related ES were boosted at low biodiversity levels, while both high levels of ecology- and economy-related ES were maintained at high biodiversity levels. This result demonstrates the importance of conserving high biodiversity in a social ecological system, for an optimal “biodiversity – multifunctionality” win-win strategy.

Ecosystems are complex objects, simultaneously combining biotic, abiotic, and human components and processes. Ecologists still struggle to understand ecosystems, and one main method for achieving an understanding consists in computing potential surfaces based on physical dynamical systems. We argue in this conceptual paper that the foundations of this analogy between physical and ecological systems are inappropriate and aim to propose a new method that better reflects the properties of ecosystems, especially complex, historical nonergodic systems, to which physical concepts are not well suited. As an alternative proposition, we have developed rigorous possibilistic, process-based models inspired by the discrete-event systems found in computer science and produced a panel of outputs and tools to analyze the system dynamics under examination. The state space computed by these kinds of discrete ecosystem models provides a relevant concept for a holistic understanding of the dynamics of an ecosystem and its abovementioned properties. Taking as a specific example an ecosystem simplified to its process interaction network, we show here how to proceed and why a state space is more appropriate than a corresponding potential surface.

In this paper we consider discrete qualitative models of ecosystems viewed as collections of interacting living (animals, plants…) and nonliving entities (air, water, soil…), whose conditions of appearance/disappearance are controlled by a set of formal rules (i.e., processes). We present here a rule-based method allowing to compare ecosystems. The method relies on a measure of similarity and on an optimization algorithm. In addition, the proposed method allows to detect patterns (i.e., ecological processes or sets of processes) in ecosystems. We have validated the method by applying it against a set of models and patterns provided by ecologists.