The statistical power to detect cross-scale interactions at macroscales

Macroscale studies of ecological phenomena are increasingly common because stressors such as climate and land-use change operate at large spatial and temporal scales. Cross-scale interactions (CSIs), where ecological processes operating at one spatial or temporal scale interact with processes operating at another scale, have been documented in a variety of ecosystems and contribute to complex system dynamics. However, studies investigating CSIs are often dependent on compiling multiple data sets from different sources to create multithematic, multiscaled data sets, which results in structurally complex, and sometimes incomplete data sets. The statistical power to detect CSIs needs to be evaluated because of their importance and the challenge of quantifying CSIs using data sets with complex structures and missing observations. We studied this problem using a spatially hierarchical model that measures CSIs between regional agriculture and its effects on the relationship between lake nutrients and lake productivity. We used an existing large multithematic, multiscaled database, LAke multiscaled GeOSpatial, and temporal database (LAGOS), to parameterize the power analysis simulations. We found that the power to detect CSIs was more strongly related to the number of regions in the study rather than the number of lakes nested within each region. CSI power analyses will not only help ecologists design large-scale studies aimed at detecting CSIs, but will also focus attention on CSI effect sizes and the degree to which they are ecologically relevant and detectable with large data sets.