Hierarchy and Scaling : Extrapolating Information along a Scaling

The large number of components, nonlinear interactions, time delays and feedbacks, and spatial heterogeneity together often make ecological systems overwhelmingly complex. This complexity must be effectively dealt with for understanding and scaling. Hierarchy theory suggests that ecological systems are nearly completely decomposable (or nearly decomposable) systems because of their loose vertical and horizontal coupling in structure and function. Such systems can thus be simplified based on the principle of time-space decomposition. Patch dynamics provides a powerful way of dealing explicitly with spatial heterogeneity, and has emerged as a unifying concept across different fields of earth sciences. The integration between hierarchy theory and patch dynamics has led to the emergence of the hierarchical patch dynamics paradigm (HPDP). In this paper, I shall discuss some major elements of ecological complexity, hierarchy theory, and hierarchical patch dynamics, and then present a hierarchical scaling strategy. The strategy consists of three stages, each of which may involve a number of steps and methods: (1) identifying appropriate patch hierarchies, (2) making observations and developing models of patterns and processes around focal levels, and (3) extrapolation across the domains of scale using a hierarchy of models. Identifying and taking advantage of the hierarchical structure and near-decomposability of complex ecological systems are essential to understanding and prediction because a hierarchical approach can greatly facilitate simplification and scaling. It is hardly justifiable theoretically and overwhelmingly difficult technically to translate information directly between two distant levels (or corresponding scales), when ignoring intervening levels that are relevant to the phenomenon under study. Although it may be possible to scale up from the cell to globe, or vice versa, successful approaches most likely have to be hierarchical. In this paper I shall describe one of such approaches in which patch hierarchies are used as “scaling ladders”. This scaling ladder approach can help simplify the complexity of systems under study, enhance ecological understanding, and, in the same time, minimize the danger of intolerable error propagation in translating information across multiple scales.