Véronique Boucher-Lalonde

Many studies correlate geographic variation of biotic variables (e.g., species ranges, species richness, etc.) with variation in environmental variables (climate, topography, history). Often, the resulting correlations are interpreted as evidence of causal links. However, both the dependent and independent variables in these analyses are strongly spatially structured. Several studies have suggested that spatially structured variables may be significantly correlated with one another despite the absence of a causal link between them. In this study we ask: if two variables are spatially structured, but causally unrelated, how strong is the expected correlation between them? As a specific example, we consider the correlations between broad-scale variation in gamma species richness and climatic variables. Are these correlations likely to be statistical artefacts? To answer these questions, we randomly generated pseudo-climatic variables that have the same range and spatial autocorrelation as temperature and precipitation in the Americas. We related mammal and bird species richness both to the real and the pseudo-climatic variables. We also observed the correlations among pseudo-climate simulations. Correlations among randomly generated, spatially unstructured, variables are very small. In contrast, the median correlations between spatially structured variables are near r2=0.1 – 0.3, and the 95% confidence limits extend to r2=0.6 – 0.7. Viewing this as a null expectation, given spatially structured variables, it is worth nothing that published richness–climate correlations are typically marginally stronger than these values. However, many other published richness–environment correlations would fail this test. Tests of the “predictive ability” of a correlation cannot reliably distinguish correlations due to spatial structure from causal relationships. Our results suggest a three-part update of Tobler’s “First Law of Geography”: #1) Everything in geography that is spatially structured will be collinear. #2) Near things are more related than distant things. #3) The more strongly spatially structured two variables are, the stronger the collinearity between them will be.

Species’ geographic ranges could primarily be physiological tolerances drawn in space. Alternatively, geographic ranges could be only broadly constrained by physiological climatic tolerances: there could generally be much more proximate constraints on species’ ranges (dispersal limitation, biotic interactions, etc.) such that species often occupy a small and unpredictable subset of tolerable climates. In the literature, species’ climatic tolerances are typically estimated from the set of conditions observed within their geographic range. Using this method, studies have concluded that broader climatic niches permit larger ranges. Similarly, other studies have investigated the biological causes of incomplete range filling. But, when climatic constraints are measured directly from species’ ranges, are correlations between species’ range size and climate necessarily consistent with a causal link? We evaluated the extent to which variation in range size among 3277 bird and 1659 mammal species occurring in the Americas is statistically related to characteristics of species’ realized climatic niches. We then compared how these relationships differed from the ones expected in the absence of a causal link. We used a null model that randomizes the predictor variables (climate), while retaining their broad spatial autocorrelation structure, thereby removing any causal relationship between range size and climate. We found that, although range size is strongly positively related to climatic niche breadth, range filling and, to a lesser extent, niche position in nature, the observed relationships are not always stronger than expected from spatial autocorrelation alone. Thus, we conclude that equally strong relationships between range size and climate would result from any processes causing ranges to be highly spatially autocorrelated.