Thresholds and the species–area relationship: a synthetic analysis of habitat island datasets.

Aim
The application of island biogeography theory in habitat fragmentation research assumes a simple relationship between species richness and fragment area. However, previous work has suggested that in some cases thresholds can be detected, at which the form of the island species–area relationship (ISAR) changes abruptly. Piecewise regression has been advocated as a suitable statistical technique to model such thresholds. Here we first provide a comparative analysis of piecewise regression models to determine the prevalence and type of thresholds in habitat island ISARs. Second, we evaluate piecewise regression as a method for locating thresholds in the ISAR, with particular emphasis on the implications of data transformation.

Location
World‐wide.

Methods
Seventy‐six habitat island datasets were sourced from the literature. An information theoretic approach was employed to compare linear regression ISAR models with piecewise regression models. The models were applied to untransformed (species–area), semi‐log (species–log area) and log–log (log species–log area) data. Three types of piecewise regression models were evaluated: continuous, discontinuous and zero slope. Model performance was compared using the Akaike information criterion. We also examined the influence on model performance of taxon, number of habitat islands, and area of smallest island.

Results
Linear regression models performed best, although piecewise models were preferred in a number of cases. Cases in which no model was significant were most prevalent in untransformed space relative to the semi‐log and log–log transformations. Piecewise fits were more prevalent in datasets with a larger numbers of islands.

Main conclusions
Data transformation is a key part of model selection and needs to be explicitly considered, especially in terms of drawing inferences from models. Piecewise models, even if selected as the favoured model in our analyses, were often ecologically unintelligible in relation to area alone. When detected, breakpoint values ranged over five orders of magnitude, although with one exception all were under 50 ha. Our findings highlight the limitations of using individual threshold values to inform conservation practice.