To Fit or Not to Fit? A Poorly Fitting Procedure Produces Inconsistent Results When the Species–Area Relationship is used to Locate Hotspots

Abstract

Ulrich and Buszko (2005, Biodivers Conserv 14:1977-1988 have recently applied the species-area relationship (SAR) to find butterfly hotspots in Europe using the linearized power function. They found that, with this method, despite the fact that the larger southern European countries and the Asian part of Turkey belong to the group of ecological hotspots defined by Myers et al. (2000, Nature 403:853-858), the SAR was unable to separate these countries from others. However, this result was a consequence of a poor fit. When different fitting models are compared, there is no obvious reason to prefer the linearized power function model, while a curvilinear fit to the power function should be selected as a best fit for this data set. Using this fit, two large southern European countries (Italy and Greece) and the Asian part of Turkey are identified as hotspots by the SAR. This simple exercise illustrates how an inappropriate choice of the fitting equation for the SAR may lead to inconsistent results.

Shapes and functions of species–area curves (II): a review of new models and parameterizations

“…Multiple regressions assessing the effect of two or more independent variables (transformed or not) on species numbers are also very common (e.g. Dodson, 1992;Adler & Lauenroth, 2003;Triantis et al, 2003;Adler et al, 2005;Storch et al, 2005;Kalmar & Currie, 2006, 2007Ulrich, 2006;Evans et al, 2007).…”

“…Fattorini & Fowles (2005) applied 10 different models to SARs of beetle species on Greek islands and have reported that the power model and the Weibull distribution produced the best fits. Fattorini (2007), who applied five models plus a linearized power model to the distribution of butterflies in Europe, reports the linearized power function and the Archibald logistic (which he calls the 'He-Legendre model') produces the best fit. Stiles & Scheiner (2007) have applied 15 models to SARs of Sonoran Desert plants in remnant habitat patches.…”

Taxonomic and regional uncertainty in species-area relationships and the identification of richness hotspots

“…This includes convex, sigmoid, asymptotic, and nonasymptotic functions, thus encompassing the various shapes attributed to SARs in the literature. The linearized forms (via logarithmic transformations) of the power and exponential models were not included in the set because of nonequivalence in the study of the variation in a variable and in its transformation (23,53) and bias of back-transformed results obtained on a logarithmic scale (54). Furthermore, the nonlinear form of the power equation leads to a more realistic detection of biodiversity hotspots than does the log-linearized power equation (54).…”

“…The linearized forms (via logarithmic transformations) of the power and exponential models were not included in the set because of nonequivalence in the study of the variation in a variable and in its transformation (23,53) and bias of back-transformed results obtained on a logarithmic scale (54). Furthermore, the nonlinear form of the power equation leads to a more realistic detection of biodiversity hotspots than does the log-linearized power equation (54). AIC and other model selection criteria that estimate Kullback-Leibler information (see SI Materials and Methods) are used widely in the ecological literature, but other criteria such as the Bayesian Information Criterion (BIC) are also commonly used to carry out model selection (42,50).…”

Small-scale area effect on species richness and nesting occupancy of cavity-nesting bees and wasps

“…They have also been applied in the context of conservation biogeography for identifying hotspots for species richness (e.g. Fattorini 2007), for systematic conservation planning (e.g. Desmet & Cowling 2004), for predicting species loss after habitat destruction (e.g.…”