Aggregating Fine‐Scale Ecological Knowledge to Model Coarser‐Scale Attributes of Ecosystems

As regional and global scales become more important to ecologists, methods must be developed for the application of existing fine—scale knowledge to predict coarser—scale ecosystem properties. This generally involves some form of model in which fine—scale components are aggregated. This aggregation is necessary to avoid the cumulative error associated with the estimation of a large number of parameters. However, aggregation can itself produce errors that arise because of the variation among the aggregated components. The statistical expectation operator can be used as a rigorous method for translating fine—scale relationships to coarser scales without aggregation errors. Unfortunately this method is too cumbersome to be applied in most cases, and alternative methods must be used. These alternative methods are typically partial corrections for the variation in only a few of the fine—scale attributes. Therefore, for these methods to be effective, the attributes that are the most severe sources of error must be identified a priori. We present a procedure for making these identifications based on a Monte Carlo sampling of the fine—scale attributes. We then present four methods of translating fine—scale knowledge so it can be applied at coarser scales: (1) partial transformations using the expectation operator, (2) moment expansions, (3) partitioning, and (4) calibration. These methods should make it possible to apply the vast store of fine—scale ecological knowledge to model coarser—scale attributes of ecosystems.