GEO-MATHEMATICAL MODELLING OF SPATIAL-ECOLOGICAL COMPLEX SYSTEMS: AN EVALUATION

摘要

Assessing the complexity of landscapes is one of the top research priorities for Physical Geography and Ecology. This paper aims at a methodological evaluation of the discrete and analytical mathematical models hitherto available for quantitative assessments of spatial ecological complex systems. These models are derived from cellular automata and nonlinear dynamics. They describe complex features and processes in landscapes, such as spatial ecological nonlinear interactions, unpredictability and chaos, self-organization and pattern formation. Beginning with a distinction between two basic types of spatial ecological complexity (structural, functional), and after reviewing the quantitative methods so far available to assess it, the areas where the major challenges (and hence, difficulties) for future research arise are identified. These are: a) to develop measures of structural spatial-ecological complexity, b) to find Lyapunov functions for dynamical systems describing spatial interactions on the landscape (and related attractors), and c) to combine discrete time and continuous spatial data and models.