Food security is a key facet of a sustainable society, while some threats, such as climate change and food riots may unsettle any society. Some aspects of food security such as food production and distribution are inherently spatial, thus requiring spatialized methods to study it. In this study, we introduce Discrete Ecosystem Evolution Rules (DEER), which is a spatial generalization of the EDEN framework developed in environmental sciences. Based on extensive expert knowledge and literature, we developed both spatially implicit and explicit models to assess the impacts of climate change on food security dynamics in a complex West-African social-ecological system (Dano, Burkina Faso). Comparing these two models allowed highlighting the role of spatial structure on food security degradation and recovery over the long term. Results showed that the impacts of climate change on food security were mediated by water availability and soil degradation. The spatial model provided a finer understanding of food security dynamics by highlighting unexpected sequences of events. These insights highlight the relevance of a spatial modeling framework to get a proper understanding of food security and, more generally, of social-ecological dynamics.

As the advancing autonomy of vehicles requires increasing assistance from the surrounding infrastructure, it becomes clear that the potential for cyberattacks necessitates a sophisticated implementation of resilience, capable of detecting and responding to both internal and external threats. Therefore, threat analysis and risk assessment, including careful modelling of resilience, are essential to prepare against cybersecurity risks. In this context, we extend our method of an automatic discovery of cost-ranked cyberattack scenarios by monitoring/fallback mechanisms. We then demonstrate that this extension allows an analysis of a realistic resilient model of cybersecurity aspects of a level 2 autonomous vehicle in a connected environment.

Trophic interaction networks are notoriously difficult to understand and to diagnose (i.e., to identify contrasted network functioning regimes). Such ecological networks have many direct and indirect connections between species, and these connections are not static but often vary over time. These topological changes, as opposed to a dynamic on a static (frozen) network, can be triggered by natural forcings (e.g., seasons) and/or by human influences (e.g., nutrient or pollution inputs). Aquatic trophic networks are especially dynamic and versatile, thus suggesting new approaches for identifying network structures and functioning in a comprehensive manner.In this study, a qualitative model was devised for this purpose. Applying discrete-event models from theoretical computer science, a mechanistic and qualitative model was developed that allowed computation of the exhaustive dynamics of a given trophic network and its environment. Once the model definition is assumed, it provides all possible trajectories of the network from a chosen initial state. In a rigorous and analytical approach, for the first time, we validated the model on one theoretical and two observed trajectories recorded at freshwater stations in the La Rochelle region (Western France). The model appears to be easy to build and intuitive, and it provides additional relevant trajectories to the expert community. We hope this formal approach will open a new avenue in identifying and predicting trophic (and non-trophic) ecological networks.

CONTEXT Smallholder farmers in sub-Saharan Africa seek to improve their livelihoods by investing in new assets. These investments and their effectiveness are constrained by current capital and management practices. Therefore, to understand farm trajectories, the combined effects of different management practices and the timing of investments and losses must be considered. OBJECTIVE The present study aimed to determine, under 128 distinct scenarios, which ones enable a poorly endowed farm to develop and maintain a sustainable agropastoralism in southwestern Burkina Faso. METHODS For this purpose, we used the Ecological Discrete-Event Network (EDEN) modelling framework. This framework includes a formalism based on if-then rules describing economic and ecological events (e.g. investments and losses) that affect qualitative variables. The model rules were built from a literature review, expert interviews, and direct observations. Based on this model, the software then computes all trajectories the farm can take. Based on empirically-reported farm types and trajectories, we then attempted to falsify the modelled dynamics using model-checking techniques. RESULTS AND CONCLUSIONS Model predictions matched all observed farm types and trajectories, thus not falsifying the model. Results highlighted that, for this system, livelihood improvement relied on the ability of the farm to to increase its cultivated area, workforce, livestock and fodder resources, all while producing and applying organic inputs to maintain or recover soil fertility. Although qualitative, model predictions are consistent with available observations and provide explanations about farm trajectories in southwestern Burkina Faso. SIGNIFICANCE The EDEN modelling framework, through its qualitative — yet rigorous — exploration of all possible trajectories, can help the decision-making process by highlighting the far-reaching consequences of management actions.

We present a method for an automatic discovery of cyberattacks in a distributed information system. The method creates a formal model of branching propagation of the attacker from the specification of software and hardware architecture enriched with multi-faceted access control information. The ensuing network of automata, decorated with unitary attack costs, enables a vast range of model checking techniques, in particular the search for the most efficient attack strategies. The model is expressive enough to cover a wide range of attack and defence approaches, like false data injection or redundant data sources.

A bstract 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.

A risk assessment for disasters is usually composed of hazard, vulnerability and exposure variables, which are hardly studied and modeled simultaneously. In volcanology, it remains ambitious to anticipate risk trajectories of pre- and post-eruption regimes. The interdependencies and feedback loops of the system's components, between geological, ecological, social and economic ones, give rise to trade-offs and synergies that should be disentangled for supporting decisionmakers and helping local communities to face the risks. We developed here an innovative discrete-event and possibilistic model based on a dynamical network representation to assess volcanological multi-risk and long term post-eruption impacts of such a multifactorial system. We illustrated our method with the region around Mount Meru (Northern Tanzania), a strato-volcano with various eruption styles, located in a growing economic and touristic region (>1 M.inh.).We used qualitative and rule-based Petri nets, largely unused in environmental sciences, for an integrated assessment of the overall system dynamics and associated risks. As a central result, we showed that the region could recover from a blast eruption, irrespective of the timescale. Our study highlights the fact that agriculture and pastoralism remain key activities to favour the recovery of this region. Yet, as soon as subsidies from governmental and non-governmental organizations are lacking, the modeled region remains isolated from national and international activities and shifts to rural dynamics. Our case study can equip environmental risk assessment with innovative models, new dynamical indices (e.g. desirable and non-desirable trajectories), and rigorous reasoning for an ultimate integrated management of social-ecological systems at stake.

CONTEXT: Smallholder farmers in sub-Saharan Africa seek to improve their livelihoods by investing in new assets. These investments and their effectiveness are constrained by current capital and management practices. Therefore, to understand farm trajectories, the combined effects of different management practices and the timing of investments and losses must be considered.OBJECTIVE: The present study aimed to determine, under 64 distinct scenarios, which ones enable a poorly endowed farm to develop and maintaina sustainable agropastoralism in southwestern Burkina Faso.METHODS: For this purpose, we used the Ecological Discrete-Event Network (EDEN) modelling framework. This framework includes a formalismbased on if-then rules describing economic and ecological events (e.g. investments and losses) that affect qualitative variables. The model rules werebuilt from a literature review, expert interviews, and direct observations. Based on this model, the software then computes all trajectories the farmcan take. Based on empirically-reported farm types and trajectories, we then attempted to falsify the modelled dynamics using model-checking techniques.RESULTS AND CONCLUSIONS: Model predictions matched all observed farm types and trajectories, thus not falsifying the model. In addition,results highlighted the crucial role of livestock and agricultural equipment for small farmers to develop sustainable agropastoralism. Although qualitative,model predictions are consistent with available observations and provide economic and ecological explanations about farm trajectories in southwesternBurkina Faso. SIGNIFICANCE: The EDEN modelling framework, through its qualitative - yet rigorous - exploration of all possible trajectories, can help thedecision-making process by highlighting the far-reaching consequences of management actions.

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.

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 [8] 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 (Errs) isomophism with states and labels matching.

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 [8] 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.

A risk assessment for natural disasters is usually composed of hazard, vulnerability and exposure variables, which are hardly considered and modeled simultaneously. In volcanology, it becomes ambitious predicting its trajectories of pre- and post-eruption regimes. The interdependencies and feedback loops of the system’s geological, ecological, social and economic components give rise to trade-offs and synergies that have to be disentangled for supporting decision-makers and helping local communities to face the risks. We developed here an innovative discrete-event and possibilistic model based on a dynamical network representation to assess volcanological multi-risk and long term post-eruption impacts of such a multifactorial system. We illustrated our method with the region around Mount Meru (Northern Tanzania), a strato-volcano with various eruption styles, located in a growing economic and touristic region (>1M.inh.).We used qualitative and rule-based Petri nets, still largely unused in environmental sciences, for an integrated assessment of the overall system dynamics and associated risks. As a central result, we showed that the region could recover from a blast eruption, irrespective of the timescale. Our study highlights the fact that agriculture and pastoralism remain key activities to reinforce the recovery of this region. Yet, as soon as subsidies from governmental and non-governmental organizations are lacking, the modeled region remains isolated from national and international systems and shifts to rural dynamics. Our case study can equip environmental risk assessment with innovative models, new dynamical indices (e.g. desirable and non-desirable trajectories), and rigorous reasoning for an ultimate integrated management of social-ecological systems at stake.

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

Model-checking is a methodology developed in computer science to automatically assess the dynamics of discrete systems, by checking if a system modelled as a state-transition graph satisfies a dynamical property written as a temporal logic formula. The dynamics of ecosystems have been drawn as state-transition graphs for more than a century, ranging from state-and-transition models to assembly graphs. Model-checking can provide insights into both empirical data and theoretical models, as long as they sum up into state-transition graphs. While model-checking proved to be a valuable tool in systems biology, it remains largely underused in ecology apart from precursory applications. This article proposes to address this situation, through an inventory of existing ecological STGs and an accessible presentation of the model-checking methodology. This overview is illustrated by the application of model-checking to assess the dynamics of a vegetation pathways model. We select management scenarios by model-checking Computation Tree Logic formulas representing management goals and built from a proposed catalogue of patterns. In discussion, we sketch bridges between existing studies in ecology and available model-checking frameworks. In addition to the automated analysis of ecological state-transition graphs, we believe that defining ecological concepts with temporal logics could help clarify and compare them.

maker; foresight; process-based model. Abstract Food security is a key aspect of a sustainable society, and some threats as climate change and food riots may unsettle any social-ecological system such as the Dano’s region in Burkina Faso. Some facets of food security such as food production and food distribution are inherently spatial, and taking space into account may refine our region understanding. We developed both spatialized and non-spatialized discrete event models to address food security dynamics in the Dano social-ecological system. The comparison of these two models allowed estimating the influence of spatialization in modelling dynamics. Results showed that water cycle and soil components are critical features of the landscape’s food security. Space refined the region’s understanding in highlighting unexpected slide-cascades the system is exposed to and revealing high sensitivity of the region’s food security to dam water presence. As food security spreading in space, to explicit spatial processes in models appears critical to get a proper understanding of most processes Abstract Food security is a key aspect of a sustainable society, and some threats as climate change and food riots may unsettle any social-ecological system such as the Dano’s region in Burkina Faso. Some facets of food security such as food production and food distribution are inherently spatial, and taking space into account may refine our region understanding. We developed both spatialized and non-spatialized discrete event models to address food security dynamics in the Dano social-ecological system. The comparison of these two models allowed estimating the influence of spatialization in modelling dynamics. Results showed that water cycle and soil components are critical features of the landscape’s food security. Space refined the region’s understanding in highlighting unexpected slide-cascades the system is exposed to and revealing high sensitivity of the region’s food security to dam water presence. As food security spreading in space, to explicit spatial processes in models appears critical to get a proper understanding of most processes in social ecological systems.

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.

Sub-Saharan savanna ecosystems are undergoing transitions such as bush encroachment, desertification or agricultural expansion. Such shifts and persistence of land cover are increasingly well understood, especially bush encroachment which is of major concern in pastoral systems. Although dominant factors can explain such transformations, they often result from intertwined causes in which human activities play a significant role. Therefore, in this latter case, these issues may require integrated solutions, involving many interacting components. Ecosystem modelling has proved appropriate to support decision-makers in such complex situations. However, ecosystem models often require lots of quantitative information for estimating parameters and the precise functional form of interactions is often unknown. Alternatively, in rangeland management, States-and-Transitions Models (STMs) have been developed to organize knowledge about system transitions and to help decision-makers. However, these conceptual diagrams often lack mathematical analyzing tools, which strongly constrains their complexity. In this paper, we introduce the Ecological Discrete-Event Network (EDEN) modelling approach for representing the qualitative dynamics of an East-African savanna as a set of discrete states and transitions generated from empirical rules. These rules are derived from local knowledge, field observations and scientific literature. In contrast with STMs, EDEN generates automatically every possible states and transitions, thus enabling the prediction of novel ecosystem structures. Our results show that the savanna is potentially resilient to the disturbances considered. Moreover, the model highlights all transitions between vegetation types and socio-economic profiles under various climatic scenarios. The model also suggests that wildlife diversity may increase socio-economic resistance to seasonal drought. Tree-grass coexistence and agropastoralism have the widest ranges of conditions of existence of all vegetation types and socio-economic profiles, respectively. As this is a preliminary use of EDEN for applied purpose, analysis tools should be improved to enable finer investigation of desirable trajectories. By translating local knowledge into ecosystem dynamics, the EDEN approach seems promising to build a new bridge between managers and modellers.

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.