Testing the ability of species distribution models to infer variable importance

Abstract

Models of species distributions and niches are frequently used to infer the importance of range- and niche-defining variables. However, the degree to which these models can reliably identify important variables and quantify their influence remains unknown. Here we use a series of simulations to explore how well models can 1) discriminate between variables with different influence and 2) calibrate the magnitude of influence relative to an "omniscient" model. To quantify variable importance, we trained generalized additive models (GAMs), Maxent, and boosted regression trees (BRTs) on simulated data and tested their sensitivity to permutations in each predictor. Importance was inferred by calculating the correlation between permuted and unpermuted predictions, and by comparing predictive accuracy of permuted and unpermuted predictions using AUC and the Continuous Boyce Index. In scenarios with one influential and one uninfluential variable, models were unable to discriminate reliably between variables in conditions that are normally challenging for generating accurate predictions: training occurrences <8-64; prevalence >0.5; small spatial extent; environmental data with coarse resolution when spatial autocorrelation is low; and correlation between environmental variables where |r| >0.7. When two variables influenced the distribution equally, importance was underestimated when species had narrow or intermediate niche breadth. Interactions between variables in how they shaped the niche did not affect inferences about their importance. When variables acted unequally, the effect of the stronger variable was overestimated. GAMs and Maxent discriminated between variables more reliably than BRTs, but no algorithm was consistently well-calibrated vis-a-vis the omniscient model. Algorithm-specific measures of importance like Maxents change-in-gain metric were less robust than the permutation test. Overall, high predictive accuracy did not connote robust inferential capacity. As a result, requirements for reliably measuring variable importance are likely more stringent than for creating models with high predictive accuracy.