Gaussian Analysis: Identifying Environmental Factors Influencing Bell‐Shaped Species Distributions

In seeking to identify environmental factors controlling the distribution of individual species, ecologists have most commonly used techniques which assume a linear relationship between an environmental factor value and species response (e.g., canonical correlation analysis, multiple linear regression analysis, discriminant analysis). Many species assume nonmonotonic, curvilinear response curves along a variety of environmental axes, however. A method is presented to help identify environmental factors controlling species distributions when the latter species response occurs. The technique builds on theoretical and empirical observations indicating that the distribution of species importance values is most often approximately bell—shaped when arrayed along an axis representing linear change in an environment factor strongly influencing the growth and survival of the species. The method consists of identifying those environmental factor axes along which a species distribution curve best fits a Gaussian form. The method is illustrated using coastal sage scrub vegetation and habitat data from southern California. The "Gaussian analysis" technique described here will not identify all of the important predictors of species response, for reasons arising largely from the multifactorial nature of influences on species performance. The technique does, however, permit identification of some important environmental predictors which are missed by traditional techniques that assume linear response curves.