Shapes and functions of species-area curves: a review of possible models

Aim This paper reviews possible candidate models that may be used in theoretical modelling and empirical studies of species-area relationships (SARs). The SAR is an important and well-proven tool in ecology. The power and the exponential functions are by far the models that are best known and most frequently applied to species-area data, but they might not be the most appropriate. Recent work indicates that the shape of species-area curves in arithmetic space is often not convex but sigmoid and also has an upper asymptote. Methods Characteristics of six convex and eight sigmoid models are discussed and interpretations of different parameters summarized. The convex models include the power, exponential, Monod, negative exponential, asymptotic regression and rational functions, and the sigmoid models include the logistic, Gompertz, extreme value, Morgan-Mercer-Flodin, Hill, Michaelis-Menten, Lomolino and Chapman-Richards functions plus the cumulative Weibull and beta-P distributions. Conclusions There are two main types of species-area curves: sample curves that are inherently convex and isolate curves, which are sigmoid. Both types may have an upper asymptote. A few have attempted to fit convex asymptotic and/or sigmoid models to species-area data instead of the power or exponential models. Some of these or other models reviewed in this paper should be useful, especially if species-area models are to be based more on biological processes and patterns in nature than mere curve fitting. The negative exponential function is an example of a convex model and the cumulative Weibull distribution an example of a sigmoid model that should prove useful. A location parameter may be added to these two and some of the other models to simulate absolute minimum area requirements.