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Spatially explicit individual-based models are used more often in forest modeling, especially because they take into account the influence of the spatial structure on the dynamics. However, they are potentially very sensitive to the initial spatial structure used for a simulation, which can be problematic if the initial state is not known or is simulated in an unrealistic way.The aim of this article is to study this sensitivity to initial spatial structure in the case of the "Mountain" model, an individual-based model of irregular spruce stands implemented in the Capsis platform. To characterize the influence of the initial spatial structure on the dynamics of the model, the authors simulated different initial spatial structures and compared the results of long-term simulations. They showed that the initial spatial structure can highly influence the dynamics of the model, not only during the first cycle of the evolution but also in the very long term in the evolution of the next generations. They also illustrated how some disturbances, such as a periodic gap opening through storms, can modify both the long-term dynamics of the stand and the duration of the influence of the initial spatial structure.

International audienceAbstract Background Agri-food is one of the most important sectors of the industry in Europe and potentially a major contributor to the global warming. Sustainability issues in this context pose a huge challenge for several reasons: the variety of considered scales, the number of disciplines involved, the uncertainties, the out-of-equilibrium states, the complex quantitative and qualitative factors, the normative issues and the availability of data. Although important insight and breakthroughs have been attained in different scientific domains, an overarching and integrated analysis of these complex problems have yet to be realized. Scope and Approach This context creates huge opportunities for research in interaction with mathematical programming, integrative models and decision-support tools. The paper propose a computational viewpoint including questions of holistic approach, multiscale reconstruction and optimization. Some directions are discussed. Key Findings and Conclusions Several research questions based on a mathematical programming framework are emerging: how can such a framework manage uncertainty, cope with complex qualitative and quantitative information essential for social and environmental considerations, encompass diverse scales in space and time, cope with a multivariable dynamic environment and with scarcity of data. Moreover, how can it deal with different perspectives, types of models, research goals and data produced by conceptually disjoint scientific disciplines, ranging from physics and physiology to sociology and ethics? Building models is essential, but highly difficult; it will need a strong iterative interaction combining computational intensive methods, formal reasoning and the experts of the different fields. Some future research directions are proposed, involving all those dimensions: mathematical resilience, human-machine interactive learning and optimization techniques

With the increasing pressure on natural resources, the sustainability study of socio-ecological systems has become a crucial scientific issue. In this paper we emphasize that transient behaviors have to be taken into account in sustainability analysis. We illustrate their impact with a model of tourism development from the literature, where the sustainability study is based on asymptotic properties. In order to evaluate relevant space and time characteristics of transient dynamics, we propose to use the concepts and tools of the mathematical viability theory. We also extend this analysis to controlled dynamical systems, which are particularly appropriate to model socio-ecological systems when management issues are at stake.

This paper addresses the issue of managing urban pigeon population using some possible actions that makes it reach a density target with respect to socio-ecological constraints. A mathematical model describing the dynamic of this population is introduced. This model incorporates the effect of some regulatory actions on the dynamic of this population. We then used mathematical viability theory, which provides a framework to study compatibility between dynamics and state constraints. The viability study shows when and how it is possible to regulate the pigeon population with respect to the constraints.