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Resilience, vulnerability and adaptive capacity to environmental change in a dynamical system, and application to a nonlinear lake model

Abstract : We use the mathematical framework of viability theory to give operational definitions to the concepts of resilience, vulnerability and adaptive capacity in a context of environmental change. These three concepts are widely used to describe the problem of managing a social and / or ecological system submitted to such a change. Resilience and vulnerability are two complementary notions which respectively refer to the possibility of maintaining or recovering a set of properties and functions after a disturbance, and to the cost of losing them, whether temporarily or permanently. Adaptive capacity, which is concerned with the capacity of the system to cope with or recover from a change, is an essential determinant of both resilience and vulnerability. The operational definitions we propose can apply to any stochastic controlled discrete-time dynamical system, and are especially useful for nonlinear systems. The goal is to use these concepts to describe the adaptation of the management strategy of a social-ecological system in the presence of environmental change. Such a strategy must keep or recover the desirable properties of that system. To define it, we thereby introduce a concept of baseline management, using a subset of the state space for which the decision taken is uniform and stationary. This baseline decision is implemented provided such management does not endanger the system’s core properties. Thus, this is the way it is managed unless these properties are threatened, leading to an emergency situation, for which other decisions must be taken. Stochastic viability theory then uses stochastic dynamic programming to find the baseline strategies, which both incorporate the baseline management and maximize the viability of the system: its probability of maintaining its desirable properties over the planning period. The set of states for which this probability tops a given confidence level is called the stochastic viability kernel, and such strategies are called viable baseline strategies if the states for which the baseline decision is taken belong to the stochastic viability kernel. Indeed, the latter represents the set of safe states, and the baseline decision only applies to such states. Viable baseline strategies are valid under given environmental conditions, i.e., under a given set of system parameters. When environmental change occurs, the baseline strategy may not be adequate to allow for the continuing functioning of the system, and may need to be modified. Adaptive management is simply defined as a change of the set of the available baseline strategies. It is not instantaneous, and is characterized by its rate as well by its total magnitude. Thus, it consists in a temporal sequence in which the set of available baseline strategies changes at each time step. In this context, dynamic programming can be used to maximize resilience, defined as the probability to eventually reach the stochastic viability kernel of a new viable baseline strategy. It can also be used to minimize vulnerability, a statistic defined on the distribution of possible costs. Adaptive capacity then measures the impact of adaptive management in terms of resilience and vulnerability. We provide an illustration to a nonlinear model of lake eutrophication, in which phosphorus inputs to the lake originating from economic activities have to be limited to keep it in a desirable, clear water state. Adaptive management of an abrupt shift in the lake dynamics through a reduction in phosphorus inputs illustrates how our framework helps determine the determinants adaptive capacity. Results suggest that strengthening adaptation rates is more important than reducing the lag in implementing adaptation to a change of the lake system, and show nonlinear shifts of the resilience and adaptation depending on the values of the adaptation parameters.
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Contributor : Migration Irstea Publications <>
Submitted on : Saturday, May 16, 2020 - 1:01:46 AM
Last modification on : Tuesday, September 7, 2021 - 3:54:57 PM


  • HAL Id : hal-02598921, version 1
  • IRSTEA : PUB00039260



Charlène Rougé, Jean-Denis Mathias, Guillaume Deffuant. Resilience, vulnerability and adaptive capacity to environmental change in a dynamical system, and application to a nonlinear lake model. Sep 2013, Barcelone, Spain. ⟨hal-02598921⟩



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