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

An increasing number of studies have focused on identifying thresholds in the species–area relationship (SAR). The most common approach in such studies is to use piecewise regression models. While a few software packages are available for fitting piecewise models, these resources are general regression packages (i.e., they are not specifically designed for the analysis of SAR data) and tend to only provide functions for fitting a subset of the piecewise models proposed in the SAR literature. Given the large number of SAR studies now fitting piecewise models, there is a need for a software package that provides functions for fitting a range of piecewise models, including continuous, left-horizontal and discontinuous models in addition to supplementary functions for analysing model fits, in the context of SAR data. To this end, we provide a set of functions for fitting six piecewise regression models to SAR data, calculating confidence intervals around the breakpoint estimates (for certain models), comparing the models using various information criteria, and plotting the resultant model fits. Here, we present these functions and illustrate them using a selection of empirical datasets. These functions are implemented in the freely available and open-source R package ‘sars.’