The effects of small sample size and sample bias on threshold selection and accuracy assessment of species distribution models

Species distribution models are used for a range of ecological and evolutionary questions, but often are constructed from few and/or biased species occurrence records. Recent work has shown that the presence-only model Maxent performs well with small sample sizes. While the apparent accuracy of such models with small samples has been studied, less emphasis has been placed on the effect of small or biased species records on the secondary modeling steps, specifically accuracy assessment and threshold selection, particularly with profile (presence-only) modeling techniques. When testing the effects of small sample sizes on distribution models, accuracy assessment has generally been conducted with complete species occurrence data, rather than similarly limited (e.g. few or biased) test data. Likewise, selection of a probability threshold - a selection of probability that classifies a model into discrete areas of presences and absences -has also generally been conducted with complete data. In this study we subsampled distribution data for an endangered rodent across multiple years to assess the effects of different sample sizes and types of bias on threshold selection, and examine the differences between apparent and actual accuracy of the models. Although some previously recommended threshold selection techniques showed little difference in threshold selection, the most commonly used methods performed poorly. Apparent model accuracy calculated from limited data was much higher than true model accuracy, but the true model accuracy was lower than it could have been with a more optimal threshold. That is, models with thresholds and accuracy calculated from biased and limited data had inflated reported accuracy, but were less accurate than they could have been if better data on species distribution were available and an optimal threshold were used.