A Procedure for Making Optimal Selection of Input Variables for Multivariate Environmental Classifications

Abstract

Multivariate classifications of environmental factors are used as frameworks for conservation management. Although classification performance is likely to be sensitive to choice of input variables, these choices have been subjective in most previous studies. We used the Mantel test on a limited set of sites for which biological data were available to iteratively seek a definition of environmental space (i.e., intersite distances calculated with a set of appropriately transformed and weighted environmental variables) that had maximal correlation with the same sites described in a biological space. The procedure was used to select input variables for a classification of New Zealand's rivers that discriminates variation in fish communities for biodiversity management. The classification performed (i.e., discriminated biological variation) better than classifications with subjectively chosen variables. The inherently linear measures of environmental distance that underlie multivariate environmental classifications mean that they will perform best if they are defined based on variables for which there is a linear variation in the biological community throughout the entire range of the variable. Classification performance will therefore be improved when variables that have nonlinear relationships with biological variation are transformed to make their relationship with biological turnover more linear and when the contributions of environmental factors that have particularly strong relationships with biological variation are increased by weighting. Our results indicate that attention to the manner in which environmental space is defined improves the efficacy of multivariate classification and other techniques in which the environment is used as a surrogate for biological variation.