Model-checking ecological state-transition graphs

Abstract

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.

A single changing hypernetwork to represent (social-)ecological dynamics

“…This is precisely what we modeled in several studies from a chosen EN of temperate and tropical social-ecological systems (Mao et al 2021, Cosme et al 2022). By using specific tools, it is also possible to formalize specific questions about the dynamics displayed in the STG, without explicitly computing them, a relevant advantage when it becomes too large to be fully computed (Fages et al 2004, Largouët et al 2012, Thomas et al 2022). In addition to an intelligible visualization of ecosystem structure and dynamics, we now have the benefit of the whole toolbox associated with such representations (Fig.…”

“…Such models automatically produce STGs comparable to those already developed in many empirical ecological studies (Stringham et al 2003, Bestelmeyer et al 2017). Looking ahead, several computing tools are even able to automatically detect various kinds of topological structures and regularities/invariants directly within the EN (Rodríguez and Schwoon 2013, Thomas et al 2022). For example, in theory, individuals or populations that may exhibit cycles or that may collapse could be detected by such invariants directly within the EN representation (Fig.…”

“…Such models automatically produce STGs comparable to those already developed in many empirical ecological studies (Stringham et al, 2003; Bestelmeyer et al, 2017). Looking ahead, several computing tools are even able to automatically detect various kinds of topological structures and regularities/invariants directly within the EN (Rodríguez & Schwoon, 2013; C. Thomas et al, 2022).…”

Formal Verification of Ecosystem Restoration Requirements using UML and Alloy

“…For instance, in [19], Thomas et al discuss the application of model-checking within ecosystems, automatically assessing the dynamics of ecological systems by verifying whether a state-transition graph satisfies a dynamical property expressed as a temporal logic for -mula. This article offers an inventory of existing ecological state-transition graphs and a clear presentation of the model-checking methodology, using ecosystem vegetation models as examples.…”

On the History of Ecosystem Dynamical Modeling: The Rise and Promises of Qualitative Models

“…The EDEN framework has already succeeded in representing and modeling realistic social-ecological systems and their dynamics in specific case studies. EDEN models have already helped in understanding terrestrial temperate [132], tropical [133,134] and aquatic ( [111], submitted) ecosystems, either for applied [133,134] or theoretical objectives [15]. In each of these case studies, the ecosystem is represented as an interaction network, then handled by the EDEN rules formalizing the way this network could change over time (see pre-mentioned references for detailed modeling steps).…”