Cross-scale interactions: Quantifying multi-scaled cause–effect relationships in macrosystems

Ecologists are increasingly discovering that ecological processes are made up of components that are multi-scaled in space and time. Some of the most complex of these processes are cross-scale interactions (CSIs), which occur when components interact across scales. When undetected, such interactions may cause errors in extrapolation from one region to another. CSIs, particularly those that include a regional scaled component, have not been systematically investigated or even reported because of the challenges of acquiring data at sufficiently broad spatial extents. We present an approach for quantifying CSIs and apply it to a case study investigating one such interaction, between local and regional scaled land-use drivers of lake phosphorus. Ultimately, our approach for investigating CSIs can serve as a basis for efforts to understand a wide variety of multi-scaled problems such as climate change, land-use/land-cover change, and invasive species.