Determining the underlying structure of insular isolation measures

Aim Island isolation is measured in many ways. We seek to determine what the underlying latent factors characterizing these measures are, in order to understand how they mechanistically drive island biogeographical patterns and in order to recommend the most parsimonious measures. We then test the discriminatory power of the identified components against hypotheses generated from the biogeographical patterns of invasive rats. Location The 890 offshore islands (>= 1 hectare area) of the New Zealand archipelago (latitude: 34.1-47.3 degrees S, longitude: 166.2-178.4 degrees E). Taxon Mammals. Methods We identified 16 measures that have been frequently used to characterize isolation in the past, including Euclidean-based distance metrics, landscape connectivity metrics derived from least-cost and circuit theory modelling, landscape buffers, stepping stones and insular area. We used principal components analysis (PCA) to synthesize the underlying structure of insular isolation with respect to terrestrial mammal dispersal. Finally, we tested the discriminatory power of retained principal components (PCs) using permutational multivariate analyses of variance (PERMANOVA). Tests include comparison of historical rat distributions, islands targeted for rat eradication and islands reinvaded by rats. Results The underlying structure of island isolation as characterized in the 16 metrics was described by three independent PCA components. Variable clustering suggests that PC1 captured distance from the mainland source to the focal island (PC1 Distance), PC2 described stepping stones available along the dispersal pathway (PC2 Stepping Stones) and PC3 described the focal island's position in the landscape (PC3 Insular Network). Each discriminatory test affirmed its respective biogeographical pattern hypothesis. Main conclusions The three underlying components we identify form the basis of a robust description of insular isolation that is of broad importance to understanding island biogeography dynamics. Moreover, these components can be applied across taxa without extensive structural or functional assumptions because the highest loading variables are not biologically informed.