Residuals cannot distinguish between ecological effects of habitat amount and fragmentation: implications for the debate

Habitat amount and fragmentation usually covary in natural and simulated landscapes. A common way of distinguishing between their effects is to take the residuals of the fragmentation index or indices regressed on habitat amount, as the index of habitat fragmentation. We used data on prairie songbird relative abundances from southern Alberta, Canada to compare this approach with the reverse: taking the residuals of habitat amount regressed on habitat fragmentation as the index of habitat amount. We used generalized additive models (GAMs) to derive residuals, and modeled relative abundances using linear mixed-effects models. The modeling approach used strongly influenced the statistical results. Using residuals as an index of fragmentation resulted in an apparently stronger effect of habitat amount relative to habitat fragmentation. In contrast, habitat fragmentation appeared more influential than habitat amount when residuals were used as an index of habitat amount. Regression of residuals may eliminate statistical collinearity, but cannot distinguish between the ecological effects of habitat amount and fragmentation. Habitat fragmentation may therefore have a larger effect on species than previously studies have shown, but experimental manipulations of underlying mechanisms are ultimately required to address this debate.