The effects of species' range sizes on the accuracy of distribution models: ecological phenomenon or statistical artefact?

1. Conservation scientists and resource managers increasingly employ empirical distribution models to aid decision-making. However, such models are not equally reliable for all species, and range size can affect their performance. We examined to what extent this effect reflects statistical artefacts arising from the influence of range size on the sample size and sampling prevalence (proportion of samples representing species presence) of data used to train and test models. 2. Our analyses used both simulated data and empirical distribution models for 32 bird species endemic to South Africa, Lesotho and Swaziland. Models were built with either logistic regression or non-linear discriminant analysis, and assessed with four measures of model accuracy: sensitivity, specificity, Cohen's kappa and the area under the curve (AUC) of receiver-operating characteristic (ROC) plots. Environmental indices derived from Fourier-processed satellite imagery served as predictors. 3. We first followed conventional modelling practice to illustrate how range size might influence model performance, when sampling prevalence reflects species' natural prevalences. We then demonstrated that this influence is primarily artefactual. Statistical artefacts can arise during model assessment, because Cohen's kappa responds systematically to changes in prevalence. AUC, in contrast, is largely unaffected, and thus a more reliable measure of model performance. Statistical artefacts also arise during model fitting. Both logistic regression and discriminant analysis are sensitive to the sample size and sampling prevalence of training data. Both perform best when sample size is large and prevalence intermediate. 4. Synthesis and applications. Species' ecological characteristics may influence the performance of distribution models. Statistical artefacts, however, can confound results in comparative studies seeking to identify these characteristics. To mitigate artefactual effects, we recommend careful reporting of sampling prevalence, AUC as the measure of accuracy, and fixed, intermediate levels of sampling prevalence in comparative studies.