How perilous are broad-scale correlations with environmental variables?

David J Currie,Véronique Boucher-Lalonde,Cloé Pétrin

doi:10.21425/f5fbg44842

Abstract

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.

Highlights

The most basic questions in ecology and biogeography are: why do some places on Earth have more species, or higher productivity, or greater densities of individuals, or more herbivory, etc., than other places (Wallace 1876; Rosenzweig 1995; Adams 2009)? A first step toward answering these questions is to ask which characteristics of the environment are most strongly correlated with variation in the biotic variable of interest (Currie 2019)
We focus on correlations between broad-scale variation in species richness and environmental variables
We focused on temperature and precipitation because the strongest richness–environment correlations reported in the literature often involve those two variables (Wright et al 1993)

Summary

Introduction

The most basic questions in ecology and biogeography are: why do some places on Earth have more species, or higher productivity, or greater densities of individuals, or more herbivory, etc., than other places (Wallace 1876; Rosenzweig 1995; Adams 2009)? A first step toward answering these questions is to ask which characteristics of the environment are most strongly correlated with variation in the biotic variable of interest (Currie 2019). We focus on correlations between broad-scale variation in species richness and environmental variables. Randomization studies have shown that species’ ranges sometimes correlate strongly with randomly generated, spatially structured independent variables (Chapman 2010; Bahn and McGill 2013; Fourcade et al 2018) This led Beale et al (2008) to conclude dramatically that “opening the climate envelope reveals no macroscale association with climate in European birds”. To answer whether broad-scale variation in species richness and environmental variables are stronger than predicted from induced spatial dependence alone, we used a randomization study, as advocated by Lennon (2000). We carried out the same process for precipitation, and we repeated the simulations 1000 times

Methods

Results

Discussion