On piecewise models and species–area patterns

AIM: Area thresholds, at which the form of the species–area relationship (SAR) changes abruptly, have played an important role in the theoretical framework of conservation biogeography and biodiversity research. The application of piecewise regressions has been advocated as a rigorous statistical technique to identify such thresholds within SARs, but a large variety of piecewise models remains untested. We explore the prevalence and number of thresholds in SARs and examine whether the currently widely used method for detecting the small island effect (SIE) is robust. LOCATION: Global. TAXON: We consider all multicellular taxa based on the criteria of datasets selection. METHODS: We apply 15 regression models, including linear regression and piecewise regressions with two and three segments to 68 global island datasets that are sourced from the literature. RESULTS: The number of area thresholds in SARs varied among groups and correlated positively with area range of a studied system. Under the AIC or AIC(c) criterion, three‐segment piecewise models were more prevalent, whereas under the BIC criterion, two‐segment piecewise models were more prevalent. From the results of Aegean Sea isopods, West Indies herpetofauna, and Australian Islands mammals, we found evidence that the traditional criteria for detection of SIEs are not robust. MAIN CONCLUSIONS: Our study demonstrates that (a) to detect an SIE, the comparison should use as many models as possible, including not only variants with and without a left‐horizontal part, but also those with two and more segments; (b) naive use of the traditional two‐segment piecewise regressions may cause poor estimations of both slope and breakpoint values; (c) the number of thresholds increases with the area range of a studied system; (d) conservation biologists and applied ecologists should determine the number of area thresholds when estimating the precise species–area patterns and making management strategies in fragmented landscapes.