Incorporating sampling bias into permutation tests for niche and distribution models
Randomization tests are often used with species niche and distribution models to estimate model performance, test hypotheses, and measure methodological biases. Many of these tests involve building null models representing the hypothesis that there is no association between the species occurrences and the environmental predictors, then comparing the empirical model to null distributions built from these models. These null models are commonly based on points randomly selected with a uniform probability from the study area. However, spatial sampling bias, a near-universal feature of the occurrence data used to build niche and distribution models, results in a non-uniform probability of observing species in different areas even when species occurrences are unrelated to environmental predictors. Failing to account for this bias in randomization tests results in null distributions that do not accurately represent the null hypothesis, potentially leading to incorrect conclusions. In this study, we use simulations to demonstrate that uniform sampling in randomization tests can lead to unacceptable rates of type I error and poor estimates of methodological bias when spatial sampling bias is present in the occurrence data. We present a new method that incorporates a bias estimate into replicate simulations for these randomization tests, and show that this adjustment can reduce type I error rates to an acceptable level.