Short Communication Environmental Correlation Structure and Ecological Niche Model Projections

The environmental causation of species' distributions depends on three general, interacting types of factors: the abiotic (or physical) environment, the biotic environment, and accessibility of areas across complex landscapes (Pulliam 2000; Soberón and Peterson 2005; Soberón 2007). Indirect variables, such as elevation, are those associated with the presence of species owing to correlation with the actual variables that directly and causally affect the fitness of the species, such as temperature or precipitation (Austin 2002). Put another way, variables can be arranged along a gradient of proximal to distal, regarding the immediacy of causality regarding the fitness of the species: indirect variables are always distal variables (Austin 2002). Contrary to proximal variables, distal variables are often easy measurable, and thus available in georeferenced databases (Fig. 1). Many researchers now attempt to reconstruct these environmental dimensions as ecological niche models (also termed " bioclimatic envelopes, " " environmental niche models, " or even " species distribution models "), using a variety of inferential approaches. Niche models have been used to predict geographic distributions of species (Guisan et al. 2006), anticipate distributions of unknown species (Raxworthy et al. 2003), estimate the invasive potential of species (Peterson 2003; Thuiller et al. 2005), and forecast climate change effects on species' distributions (Araújo et al. 2005). The predictive capacity of these approaches makes them particularly useful in applications involving " transferring " the niche model to make predictions regarding other landscapes or time periods (Araújo and Pearson 2005; Peterson et al. 2007). Such transferability applications, however, depend critically on the assumption that environmental variables relevant on one landscape or at one time will be relevant on another. Niche models are probably never based directly on genuinely proximate variables, but rather rely on more easily measurable variables that are inevitably less directly related to the population biology of the species in question. As such, the correlation structure among environmental variables becomes key (Morin and Lechowicz 2008): if correlation structures are stable and consistent across different landscapes and time periods, then niche models may be transferable to those other situations; if, on the other hand, correlation structures are not consistent among situations, then models may not be transferable, or at least not as fully or as readily. As correlation methods, niche modeling techniques simply select the set of variables that is best to explain the largest part of the variation in the dependent variable. Transferability exercises require the …