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Multiple Parallel Ordinations: the Importance of Choice of Ordination Method and Weighting of Species Abundance Data

Abstract Most species-abundance matrices subjected to ordination are analysed by applying one ordination method to one single weighting (transformation) of the raw abundance values. We argue that such an approach is sub-optimal for identification of species-environment relationships. In order to capture the full range of qualitative and quantitative components of variation unique to each species-abundance matrix, data sets covering the full range of abundance weights from presence/absence to raw abundance data should be subjected to ordination. Furthermore, two or more ordination methods should be used in parallel to enhance detection of artifacts in the results. We describe and exemplify a multiple parallel ordination (MPO) procedure, which ensures that both qualitative and quantitative properties of the data set are revealed. This procedure implies that different ordination methods are applied in parallel, each with different weightings of elements in the species-abundance matrix. Two species-abundance matrices are used to exemplify the MPO procedure, one of individual counts from a marine benthic study of mollusc and echinoderm species and one of percent cover of vascular plants, bryophytes and lichens from a study of boreal forest understory vegetation. Striking differences between point configurations obtained by different ordination methods and strong dependence of ordination results on the weights given to abundance are demonstrated. Properties of species and data sets that may explain the observed variation in ordination results are analyzed and discussed. We show that the widely held belief that changes in ordination structure with changes of weighting function are brought about only by highly abundant and frequent species is an over-simplification. We conclude that the MPO procedure - applying more than one ordination method and more than one weighting function is likely to enhance the user’s insight into the multivariate structure of species-abundance matrices resulting from ordination analyses.