Prevalence, thresholds and the performance of presence-absence models

The use of species distribution models to understand and predict species' distributions necessitates tests of fit to empirical data. Numerous performance metrics have been proposed, many of which require continuous occurrence probabilities to be converted to binary present or absent' predictions using threshold transformations. It is widely accepted that both continuous and binary performance metrics should be independent of prevalence (the proportion of locations that are occupied). However, because these metrics have been mostly assessed on a case-specific basis, there are few general guidelines for measuring performance. Here, we develop a conceptual framework for classifying performance metrics, based on whether they are sensitive to prevalence, and whether they require binary predictions. We use this framework to investigate how these performance metric properties influence the predictions made by the models they select. A literature survey reveals that binary metrics are widely employed and that prevalence-independent metrics are used more frequently than prevalence-dependent metrics. However, we show that prevalence-dependent metrics are essential to assess the numerical accuracy of model predictions and are more useful in applications that require occupancy estimates. Furthermore, we demonstrate that in comparison with continuous metrics, binary metrics often select models that have reduced ability to separate presences from absences, make predictions which over- or underestimate occupancy and give misleading estimates of uncertainty. Importantly, models selected using binary metrics will often be of reduced practical use even when applied to ecological problems that require binary decision-making. We suggest that SDM performance should be assessed using prevalence-dependent performance metrics whenever the absolute values of occurrence predictions are important and that continuous metrics should be used instead of binary metrics whenever possible. We thus recommend the wider application of prevalence-dependent continuous metrics, particularly likelihood-based metrics such as Akaike's Information Criterion (AIC), to assess the performance of presence-absence models.