Stochastic Simulation for Characterizing Ecological Spatial Patterns and Appraising Risk.

The theory and a case study are presented for a class of techniques known as stochastic simulation. Stochastic simulations can characterize the certainty of estimates of spatially and/or temporally correlated ecological variables. Rather than merely providing a unique estimate, a conditional probability distribution is built for the unsampled location. This distribution provides the researcher with any summary statistic or confidence limit desired. Moreover, the techniques are flexible enough to incorporate expected economic losses into the analysis. A simple analogy of a jigsaw puzzle is used first to introduce key concepts. Then, the mathematical highlights of two leading stochastic simulation procedures are presented. Finally, one simulation method, known as sequential Gaussian conditional simulation, is used to generate multiple, equally probable images of adult corn rootworm densities over a large (225 x 150 km) area in northwestern Iowa during the summer of 1989. The results show the simulated density of rootworms to be influenced strongly by the choice of summary statistic and density threshold. Economic risk is appraised from the point of view of the farmer by incorporating the expected economic losses due to the use of a soil insecticide. Since the cost to the farmer of not using an insecticide when in fact it is needed is over three times greater than the cost of using one when it is not needed, the area identified as potentially requiring treatment is much larger than when a summary statistic like the mean or median is used. Stochastic simulation allows the environmental researcher, policy-maker, or manager the opportunity to characterize uncertainty and economic or other losses, and to determine areas requiring treatment and additional samples. © 1993 by the Ecological Society of America.