Multiscale codependence analysis: an integrated approach to analyze relationships across scales.

The spatial and temporal organization of ecological processes and features and the scales at which they occur are central topics to landscape ecology and metapopulation dynamics, and increasingly regarded as a cornerstone paradigm for understanding ecological processes. Hence, there is need for computational approaches which allow the identification of the proper spatial or temporal scales of ecological processes and the explicit integration of that information in models. For that purpose, we propose a new method (multiscale codependence analysis, MCA) to test the statistical significance of the correlations between two variables at particular spatial or temporal scales. Validation of the method (using Monte Carlo simulations) included the study of type I error rate, under five statistical significance thresholds, and of type II error rate and statistical power. The method was found to be valid, in terms of type I error rate, and to have sufficient statistical power to be useful in practice. MCA has assumptions that are met in a wide range of circumstances. When applied to model the river habitat of juvenile Atlantic salmon, MCA revealed that variables describing substrate composition of the river bed were the most influential predictors of parr abundance at 0.4-4.1 km scales whereas mean channel depth was more influential at 200-300 m scales. When properly assessed, the spatial structuring observed in nature may be used purposefully to refine our understanding of natural processes and enhance model representativeness.