On piecewise models and species–area patterns

Abstract

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.

Thresholds and the species–area relationship: a set of functions for fitting, evaluating and plotting a range of commonly used piecewise models in R

“…The six piecewise models included here ( Fig. 1) are a selection of 6 models out of the 14 listed by Gao et al (2019) and comprise the continuous one-threshold (Eq. 1, Fig.…”

“…6, Fig. 1f) models (see Gao et al 2019 for further information). The equations of these six models are:…”

“…An increasing number of studies have focused on identifying thresholds in the ISAR, including studies i) focused on identifying the small island effect (i.e., a different relationship between island area and species richness on smaller compared to larger islands ; SIE; Lomolino and Weiser 2001, Gao and Perry 2016, Wang et al 2018, ii) determining whether the ISAR has an upper asymptote (Lomolino 2000), iii) looking for signals of speciation in the ISAR (Losos and Schluter 2000), and iv) identifying thresholds in habitat ISARs, which are often systems of conservation concern (Fahrig 2001, Matthews et al 2014. The most common approach in such studies is to use piecewise regression (e.g., Lomolino and Weiser 2001, Toms and Lesperance 2003, Gentile and Argano 2005, Matthews et al 2014, Gao et al 2019.…”

“…A wide range of piecewise models have been fitted to ISAR data, with Gao et al (2019) providing functions for 14 different models. These can be broadly grouped into continuous models, where the slope of the line changes at a breakpoint (Fig.…”

“…The slope of the line to the right of a breakpoint (in all piecewise models) can be steeper or shallower than the slope of the line to the left, leading to what have been termed shallow-steep and steepshallow relationships, respectively (Matthews et al 2014, Gao et al 2019. Most work to date has focused on one-threshold (i.e., single breakpoint) piecewise models, but it has recently been suggested that the number of thresholds in the ISAR often increases with the range in island area analysed (Gao et al 2019). For example, it has been argued that the ISAR exhibits both a SIE and a change in slope at large island areas where in situ speciation becomes a dominant assembly process (Losos andSchluter 2000, Lomolino andWeiser 2001).…”