Transmutation and functional representation of heterogeneous landscapes

Models of local small-scale ecological processes can be used to describe related processes at larger spatial scales if the influences of increased scale and heterogeneity are carefully considered. In this paper we consider the changes in the functional representation of an ecological process that can occur as one moves from a local small-scale model to a model of the aggregate expression of that process for a larger spatial extent. We call these changes spatial transmutation. We specifically examine landscape heterogeneity as a cause of transmutation. Spatial transmutation as a consequence of landscape heterogeneity is a source of error in the prediction of aggregate landscape behavior from smaller scale models. However, we also demonstrate a procedure for taking advantage of spatial transmutation to develop appropriately scaled landscape functions. First a mathematical function describing the process of interest as a local function of local variables is defined. The spatial heterogeneity of the local variables is described by their statistical distribution in the landscape. The aggregate landscape expression of the local process is then predicted by calculating the expected value of the local function, explicitly integrating landscape heterogeneity. Monte Carlo simulation is used to repeat the local-to-landscape extrapolation for a variety of landscape patterns. Finally, the extrapolated landscape results are regressed on landscape variables to define response functions that explain a useful fraction of the total variation in landscape behavior. The response functions are hypotheses about the functional representation of the local process at the larger spatial scale.