Accounting for the Influence of Geographic Location and Spatial Autocorrelation in Environmental Models: A Comparative Analysis Using North American Songbirds

Abstract

Environmental models are a critical tool for identifying where organisms occur by estimating the relationship among species occurrence and important environmental factors. To date, the overwhelming majority of predictive occurrence models disregard both the impact of spatial autocorrelation (interaction between neighbouring points) as well as the possibility that model relation- ships may vary depending on geographic location. To address this gap, we measured their impact on five bird species observed during seven years of the North American Breeding Bird Survey. We first built traditional occurrence models (of varying functional complex- ity) using logistic regressions and generalized additive models (GAMs). We then compared model accuracy and goodness-of-fit to those incorporating spatial autocorrelation (ALOG) and spatial dependence (via geographically weighted regression, GWR). Environmental variables included aspects of land cover, climate, and topography. A residual analysis indicated that spatial autocorrelation persisted within even the most complex traditional models. In contrast, not only did ALOG models incorporate this effect (as indicated by a lack of residual autocorrelation), but also offered better predictive power for some species (+0.118 in the case of the American Crow, relative to the best GAM model). From an information-theoretic perspective, ALOG models were consistent improvements over traditional models. Adoption of GWR models also improved predictive accuracy (ranging from +0.078 for the American Crow and +0.008 for the Purple Finch). However, comparison of their evidence ratios with ALOG models indicated that ALOG models were generally superior. While we were unable to determine why geographic location influenced species’ responses to environmental conditions, evi- dence from generalized estimating equations (GEEs) revealed significant within-route correlation (Ï = 0.54 ±0.26 SE), and implicated an observer effect. A combination of broad-scale and fine-scale factors were important for predicting occurrence, but we demonstrate that the incorporation of spatial factors offers the potential to measure the spatially explicit outcomes of intra-specific interactions, and regional differences in resource usage. We recommend that these methods be considered, particularly when evidence points to spatially autocorrelated errors or when there are a priori reasons to suspect geographic variability in resource selection.

Keywords: modeling, species distribution, spatial autocorrelation, autologistic regression, non-stationarity, geographically weighted regression, generalized estimating equation, predictive accuracy, birds