Accounting for the causal basis of collinearity when measuring the effects of habitat loss versus habitat fragmentation

Collinearity among metrics of habitat loss and habitat fragmentation is typically treated as a nuisance in landscape ecology, and it is the norm to use statistical approaches that remove collinear information prior to estimating model parameters. However, collinearity may arise from causal relationships among landscape metrics and may therefore signal the occurrence of indirect effects (where one model predictor influences the response variable by driving changes in another influential predictor). Here we suggest that, far from being merely a statistical nuisance, collinearity may be crucial for accurately quantifying the effects of habitat loss versus habitat fragmentation. We use simulation modelling to create datasets of collinear landscape metrics in which collinearity arose from causal relationships, then test the ability of two statistical approaches to estimate the effects of these metrics on a simulated response variable: 1) multiple regression, which statistically removes collinearity, and was identified in a recent study as the best approach for estimating the effects of collinear landscape metrics (although this study did not account for any indirect effects implied by collinearity among metrics); and 2) path analysis, which accounts for the causal basis of collinearity. In agreement with this previous study, we found that multiple regression gave unbiased estimates of direct effects (effects not mediated by other model predictors). However, it gave biased estimates of total (direct. indirect) effects when indirect effects occurred. In contrast, path analysis reliably identified the causal basis of collinearity and gave unbiased estimates of direct, indirect, and total effects. We suggest that effective research on the impacts of habitat loss versus fragmentation will often require tools that can empirically test whether collinear landscape metrics are causally related, and if so, account for the indirect effects that these causal relationships imply. Path analysis, but not multiple regression, provides such a tool.