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

© The Ecological Society of America www.frontiersinecology.org M environmental problems cannot be adequately addressed by viewing them through a single lens, be it narrow or broad, because ecological interactions often cross boundaries of scale or levels of organization (Peters et al. 2011). Cross-scale interactions (CSIs) occur when driver and response variables in cause–effect relationships operate at different characteristic spatial and temporal scales, sometimes producing nonlinear patterns and dynamics (Carpenter and Turner 2000; Gunderson and Holling 2002; Peters et al. 2007). Understanding these relationships is necessary to predict likely outcomes of alternative management strategies intended to mitigate complex environmental problems (Miller et al. 2004; Peters et al. 2004; Tranvik et al. 2009). Because practitioners of macrosystems ecology study such multi-scaled interactions (Heffernan et al. 2014), this relatively new subdiscipline of ecology includes the study of CSIs. Macrosystems are made up of biological, geophysical, and sociocultural components that exhibit variation at the scale of regions to continents (Heffernan et al. 2014). For simplicity, we use the term “macrosystems” here to include three dominant spatial “scales” (interpreted as spatial extents, but which can be interchanged with temporal extents), and we depict the potential interactions that make up a macrosystem as arrayed along a gradient of complexity (Figure 1). Unidirectional interactions from a broaderto a finer-scaled driver or explanatory variable (green and orange arrows in Figure 1, a–d) and interactions that are bidirectional between two variables within a scale (black arrows in Figure 1, a–d) are perhaps the two most studied interaction types. There are a growing number of examples in the literature describing the more complex relationships that occur when driver variables interact across scales (blue and red arrows in Figure 1, c and d). The first type of CSI occurs when there is an interaction among driver variables at different spatial scales that influences a focal response variable (Figure 1c; the CSI is depicted as a oneway arrow from the interaction between the driver variables to the focal response variable). For instance, consider a case in which a broad-scale regional driver such as anthropogenic disturbance affects the degree to which a local driver variable influences a focal response variable (eg Peters et al. 2007). Later sections of this paper present a case study documenting this type of CSI between regional agriculture and wetland patches connected to and affecting nutrient concentrations in a downstream MACROSYSTEMS ECOLOGY