New methods for measuring ENM breadth and overlap in environmental space

Environmental niche models (ENM) and species distribution models (SDM) are used to estimate species’ environmental niches and the distribution of suitable habitat. ENMs are used to aid conservation decisions and to study niche evolution. Investigators use metrics of niche breadth (Levins 1968, Mandle et al. 2010) to quantify the estimated geographic distribution of projected habitat suitability, or overlap to measure similarity between ENMs (Warren et al. 2008, 2010, Rödder and Engler 2011).

Breadth and overlap metrics are calculated based on habitat suitability in geographic space. While focussing on geographic space may be ideal for applications that aim to quantify the distribution of suitable habitat, breadth and overlap metrics are often treated as estimates of species’ physiological responses. Given this interpretation, calculating metrics in geographic space may be misleading because the measurements will be filtered through the available combinations of environments in the study region. If the available environment represents a biased subset of potential environments, measures of breadth and overlap may also be biased (e.g. Fig. 1).

Figure 1

Similarity between GAM (A, C) and Bioclim (B, D) models for Anolis allogus in geographic and environmental space. In (A–D), brighter colors represent combinations of environments that are predicted to be of high suitability, while darker colors represent less favorable environments. In (E), colors represent the relative availability of different environmental combinations in the training region, with brighter colors representing more common environmental combinations. Geographic predictions of habitat suitability for the GAM and Bioclim models are quite similar (A, B), with high overlap and correlation values (table, bottom left). When similarities are measured in environmental space, however, it becomes clear that models are more different than their spatial projections would suggest. This difference is largely driven by the fact that environmental combinations predicted suitable by the GAM (C) and Bioclim (D) model are common (E). Additionally, the difference in breadth of the two models in environmental space is considerably greater than the differences in geographic space (table, bottom right).

Hence, ENM breadth and overlap measurements in geographic space are best interpreted in a geographic context. For biological questions regarding the fundamental niche or methodological questions regarding the structure of models in environmental space, it may be more appropriate to calculate metrics within the continuous space of environmental variables. While these calculations can be performed analytically for ENMs or niche estimates with simple structures (Graham et al. 2004, Blonder et al. 2014, Swanson et al. 2015), no general purpose method exists for calculating breadth and overlap in environmental space on ENMs.

Many ENM algorithms produce continuously‐varying n‐dimensional models with highly malleable functional shapes. This presents complications for calculating metrics in environmental space. Niche breadth and overlap are calculated using predicted suitability across a range of environmental variable combinations. In geographic space, these combinations are determined by the values for each predictor in the grid cells representing the study region. In environmental space, however, there are no discrete units such as grid cells for predictor variables, nor predetermined limits to the maximum and minimum values each predictor variable may take. While one can divide predictors into bins (Mandle et al. 2010, Carmona et al. 2016), the number of combinations of bins increases exponentially with the number of predictors, rapidly becoming computationally unwieldy even when the number of bins per predictor is low.

Here we demonstrate efficient methods based on Monte Carlo integration for approximating breadth and overlap in environmental space using continuous predictions. These methods are currently implemented for models built with most ENM algorithms available in ‘dismo’ (Hijmans et al. 2017) as well as Poisson point process and ‘rf.ranger’ models (Renner 2015, Renner et al. 2015, Wright and Ziegler 2015). Our approach allows measurements to be estimated in n dimensions to a user‐defined level of precision, with metrics widely used in the literature (e.g. D, I, and Spearman's ρ for overlap, B2 for breadth – see Supplementary material Appendix 1 for the calculation of these metrics). We provide an implementation in R (R Development Core Team) as the ‘env.breadth’ and ‘env.overlap’ functions in the package ‘ENMTools’ (< http://github.com/danlwarren/ENMTools >). This package replaces the standalone ENMTools package, one of the most popular platforms for conducting comparative studies using ENMs (Warren et al. 2010).

In many studies, ENMs are treated as niche estimates, but phenomena are measured in geographic space (Warren et al. 2008, Rödder and Engler 2011), which may result in misleading inferences when the availability of environments is strongly biased. For instance, a species with a narrow fundamental niche that occupies environmental conditions common in a particular region will have a high breadth when models are projected to that geographic space, but a low breadth in environmental space. Measures of niche breadth and overlap are also used in methodological studies to compare ENMs obtained from different approaches. For many of these studies, the metrics provided here are more relevant than those based on geographic space, as models may project very similar spatial predictions yet make wildly different niche estimates (Fig. 1). Measuring breadth and overlap in environmental space will highlight differences between modeling approaches that would otherwise remain invisible to investigators, often in cases where these differences can have significant effects on biological inferences and model transferability.

Funding – Funding received from the Australian Research Council (DE140101675).

Supplementary material (Appendix ECOG‐03900 at < www.ecography.org/appendix/ecog‐03900 >). Appendix 1.