Weighted mean patch size: a robust index for quantifying landscape structure

Variables such as number of patches and mean patch size have been widely used to describe landscape structure. However, these simple, independent measurements often fail to adequately represent or track offsetting or reinforcing changes that occur from interactions between patch number, size and shape. Here, we present a synthetic `weighted mean patch sizeʹ (WMPS) index which combines information represented in patch size and number. The utility of the WMPS index, which was based on percolation theory, is demonstrated using two data sets. The first data set consisted of output from a cellular automata-based simulation of landscape response to disturbance that varied in intensity and scale. Unlike simple estimates of mean patch size, the WMPS index was highly sensitive to disturbance and varied in a consistent fashion with both intensity and scale of disturbance. The second application involved the use of historical aerial photography to compare the dynamics of tree/shrub clusters (=patches) in a subtropical savanna parkland during a period of drought (1941–1960) and a period of normal to above-normal annual rainfall (1960–1983). Contrary to expectations, mean cluster (=patch) size increased in both periods. In addition, greatest increases in mean patch size occurred during the drought period, apparently the result of higher mortality among small clusters relative to large clusters. In contrast, climate-induced vegetation dynamics indicated by the WMPS index (decrease during drought period; increase in subsequent pluvial period) tracked those of other structural measurements (cluster density, total cover, cluster growth rate) and appeared to reflect dynamic, rainfall-induced changes in patch structure associated with changes in tree and shrub canopy area and plant numbers. These examples suggest the WMPS index, by combining information on patch size and number, can preserve process-level ecological information and provide robust, functionally relevant numerical representations of landscape structure over time and in response to disturbance.