Wednesday 7
Which Mathematical Formalizations of Resilience and What For?
Guillaume Deffuant, Jean Denis Mathias
› 14:35 - 15:30 (55min)
› Antigone 1
Adaptation and transformation from a complex systems perspective
Steven Lade  1, 2, *@  
1 : Stockholm Resilience Centre  (SRC)  -  Website
Stockholm University, Kräftriket 2B, 114 19 Stockholm -  Suède
2 : Nordic Institute for Theoretical Physics  (NORDITA)  -  Website
* : Corresponding author

At the origins of resilience thinking lie mathematical concepts from dynamical systems theory such as attractors, basins of attraction, potential landscapes, and so on. These served as an excellent basis from which to conceptualise resilience as the ability of an ecological system to withstand shocks. In recent years, however, the focus of resilience research has shifted towards social-ecological systems (SESs) and the ability of these systems to adapt and transform in response to changing conditions. Although some descriptive frameworks have been developed and applied (such as the three phases of transformation, Olsson et al., Ecology and Society 9:2 2004), corresponding developments in mathematical models have so far been lacking. Furthermore, one of the chief criticisms of modern resilience thinking is that it is not easily able to incorporate the human qualities of actors such as agency and power.

Network conceptualisations of SESs are particularly suited to the study of adaptation and transformation. Within a network perspective, an adaptation, for example a fishing community switching target species, appears as the creation, deletion or re-wiring of a single link. A transformation appears as a larger-scale re-organisation of the system. Indeed, there have been several successful applications of network approaches to social-ecological systems in recent years. These approaches, however, usually consider static networks, or at best when the network is changing a series of snapshots of the network. To properly understand the resilience of an SES, I contend that the dynamics of the structure of the SES must be considered, not only through a series of static snapshots, but through a consideration of the mechanisms that drive the evolution of the network.

Another characteristic feature of social-ecological systems is that they operate over multiple scales and that they involve a diverse range of entities and interactions between them. The SES framework of Elinor Ostrom and others provides a natural starting point for the types of nodes (such as resources, harvesters, governance systems) and links (such as harvesting, monitoring, sanctioning, provisioning) and the properties of those nodes and links that should be included in the network representation. Furthermore, consideration of some basic transformation scenarios such as escape from a poverty trap shows that one crucial factor for transformation is the ability of actors within the system to change existing links and create new links: in other words, the power held by the system's actors.

This presentation will therefore culminate in a tentative sketch of a combined network and dynamical systems modelling framework, in which adaptation and transformation can be represented and in which the power of an actor also plays a central role.

I emphasise that this modelling framework is still under development. Furthermore, it emphasises rule making and interactions among actors and resources, rather than transformation of individual organisations. Nevertheless, it is hoped that this framework will provide a basis for conceptualising, modelling, and even testing general hypotheses regarding possible trajectories of social-ecological systems, in turn assisting policy and practice related to transformation and development

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