p.1 Although adaptive capacity is a frequent topic of study in the resilience literature, there are few formal models. This paper introduces such a model and uses it to explore adaptive capacity by contrast with the opposite condition, or traps... The model... is general and flexible, so it can be used as a building block in more specific and detailed models of adaptive capacity for a particular region. [JLJ - Ok, got my attention, so I decide to read on...]

p.1 How do transformation and persistence coexist in living systems? This paradox is addressed by the concept of resilience (Holling 1973, Folke 2006). Resilience is not about an equilibrium of transformation and persistence. Instead, it explains how transformation and persistence work together, allowing living systems to assimilate disturbance, innovation, and change, while at the same time maintaining characteristic structures and processes (Westley et al. 2006).

p.2 Adaptive capacity, the ability of a system to adjust to changing internal demands and external circumstances, is a central feature of resilience... It is useful to have models for adaptive capacity that can be applied in a wide range of contexts... Here, we propose such a model.
A minimal model for adaptice capacity is suggested by the physiological concept of allostasis (Sterling 2004)... Allostasis... proposes that organisms persist by varying physiological conditions and matching them appropriately to fluctuating inputs or internal demands.

p.3 Our model [JLJ - of adaptive capacity] is motivated by consideration of an adaptive system in a variable environment, where long-term success depends on maintaining the capacity to adapt through change... the model connects adaptive capacity to stress experienced by the system... Stress, as used in our paper, represents the cumulative effort expended by the system to adapt its internal conditions to external forces as well as changing internal demands.

p.6 [Rigidity Trap example] If the cumulative stress is decreased, then adaptive capacity can grow.

p.11 If stress accumulates, then adaptive capacity can grow out of the poverty trap.

p.11 Just as a whole photographic image emerges from the contrast of dark and light, understanding of social-ecological systems can emerge from the contrast of adaptive dynamics across a range of scenarios.... the model focuses on changes in the capacity to adapt... In a poverty trap, fluctuations are not harnessed for adaptation, although there are lurches toward the adaptive range... a poverty trap is unrealized potential. By contrast, in the rigidity trap, the expanding fluctuations due to overuse of control are likely to lead to a breakdown in some dimension of the system, perhaps leading to a more general collapse... Understanding the pathways out of traps, and how complex systems can be guided onto one pathway or another, is another topic for ongoing research.

p.11 The model was designed to be simple (representing adaptive capacity with relatively few equations and parameters...) and general (applicable to generic features of poverty and rigidity traps) for synthetic understanding of common features of broad classes of traps... It is a quite general representation of adaptive control for a system that undergoes changes in controllability. A model for a specific social-ecological system would almost certainly require a more complicated set of equations in order to represent the important details of that particular context.

p.12 Many case studies of regional ecosystem management could be modeled within the general framework that we propose... Much of control theory that focuses on the general features of integral and proportional controllers (e.g., Yi et al. 2000) was not designed to display the features of traps that we explore here.

p.13 our paper is an initial attempt to combine ideas on nonlinear control problems... with a set of dynamics where controllability decays if the system is not used very much, and also decays if the system is used too much... The effects of adaptive capacity resemble the effects of algorithmic complexity in modeling behavior of human agents in economics (Velupillai 2000): an agent is an effective adaptor when its algorithmic complexity is relatively high... the model can be used as a building block of more detailed models used to study adaptive capacity in particular regions.