Qualitative mathematical modeling for resilience assessment and management

Resumen

Since the 1970s resilience has been a lively discussed concept in ecology and
environmental management. Resilience refers to “a measure of the persistence
of systems and of their ability to absorb change and disturbance and still
maintain the same relationships between populations or state variables”.
Despite important theoretical and empirical developments, the assessment of
resilience of environmental systems has remained an unsolved challenge.
Relevant variables and relations cannot always be immediately studied through
exact equations or numerical methods. Variables usually differ in nature (e.g.,
natural, social), can be numerous, and might not be readily measured. The
available data is commonly partial and not always quantitative. In this paper,
assessing resilience of regimes of an environmental system will be based on
the feasibility of representing regimes with loop models, which are developed
with the qualitative mathematical modeling method of loop analysis. The
importance of persistence in the definition of resilience calls attention to a
mathematical treatment of stability in order to assess resilience. The present
paper proposes that if a regime is resilient, the loop model representing the
regime is stable. Correspondingly, if the regime is not resilient, the loop model
representing the regime is not stable. In environmental management, promoting
the persistence (resilience) of a desired regime, and the change of non desired
ones, can be supported by analyzing what the influences (links) between the
components of the regime are, or should be, so that the regime remains, or
becomes, resilient and thus representable by a stable loop model. The
approach introduced in the paper is explained with empirical evidences from
three regimes observed in a wetland environment. It is shown that loop models
can be obtained from scarce empirical data. Loop analysis allows alternative
interpretations of the environmental system of interest, and addressing
manifestations of non linearity.