Moths and butterflies on alien shores: Global biogeography of non‐native Lepidoptera

This paper examines how to obtain species biplots in unconstrained or constrained ordination without resorting to the Euclidean distance [used in principal-component analysis (PCA) and redundancy analysis (RDA)] or the chi-square distance [preserved in correspondence analysis (CA) and canonical correspondence analysis (CCA)] which are not always appropriate for the analysis of community composition data. To achieve this goal, transformations are proposed for species data tables. They allow ecologists to use ordination methods such as PCA and RDA, which are Euclidean-based, for the analysis of community data, while circumventing the problems associated with the Euclidean distance, and avoiding CA and CCA which present problems of their own in some cases. This allows the use of the original (transformed) species data in RDA carried out to test for relationships with explanatory variables (i.e. environmental variables, or factors of a multifactorial analysis-of-variance model); ecologists can then draw biplots displaying the relationships of the species to the explanatory variables. Another application allows the use of species data in other methods of multivariate data analysis which optimize a least-squares loss function; an example is K-means partitioning.

In the last decade, new methods of estimating global species richness have been developed and existing ones improved through the use of more appropriate statistical tools and new data. Taking the mean of most of these new estimates indicates that globally there are approximately 1.5 million, 5.5 million, and 7 million species of beetles, insects, and terrestrial arthropods, respectively. Previous estimates of 30 million species or more based on the host specificity of insects to plants now seem extremely unlikely. With 1 million insect species named, this suggests that 80% remain to be discovered and that a greater focus should be placed on less-studied taxa such as many families of Coleoptera, Diptera, and Hymenoptera and on poorly sampled parts of the world. DNA tools have revealed many new species in taxonomically intractable groups, but unbiased studies of previously well-researched insect faunas indicate that 1-2% of species may be truly cryptic.