Sensitivity of Codispersion to Noise and Error in Ecological and Environmental Data

Understanding relationships among tree species, or between tree diversity, distribution, and underlying environmental gradients, is a central concern for forest ecologists, managers, and management agencies. The spatial processes underlying observed spatial patterns of trees or edaphic variables often are complex and violate two fundamental assumptions-isotropy and stationarity-of spatial statistics. Codispersion analysis is a new statistical method developed to assess spatial covariation between two spatial processes that may not be isotropic or stationary. Its application to data from large forest plots has provided new insights into mechanisms underlying observed patterns of species distributions and the relationship between individual species and underlying edaphic and topographic gradients. However, these data are not collected without error, and the performance of the codispersion coefficient when there is noise or measurement error ("contamination") in the data heretofore has been addressed only theoretically. Here, we use Monte Carlo simulations and real datasets to investigate the sensitivity of codispersion to four types of contamination commonly seen in many forest datasets. Three of these involved comparing codispersion of a spatial dataset with a contaminated version of itself. The fourth examined differences in codispersion between tree species and soil variables, where the estimates of soil characteristics were based on complete or thinned datasets. In all cases, we found that estimates of codispersion were robust when contamination was relatively low ( < 15%), but were sensitive to larger percentages of contamination. We also present a useful method for imputing missing spatial data and discuss several aspects of the codispersion coefficient when applied to noisy data to gain more insight about the performance of codispersion in practice.