A scaling rule for landscape patches and how it applies to conserving soilresources in savannas

Scaling issues are complex, yet understanding issues such as scale dependen cies in ecological patterns and processes is usually critical if we are to make sense of ecological data and if we want to predict how land management options, for example, are constrained by scale. In this article, we develo p the beginnings of a way to approach the complexity of scaling issues. Our approach is rooted in scaling functions, which integrate the scale depende ncy of patterns and processes in landscapes with the ways that organisms sc ale their responses to these patterns and processes. We propose that such f unctions may have sufficient generality that we can develop scaling rules-s tatements that link scale with consequences for certain phenomena in certai n systems. As an example, we propose that in savanna ecosystems, there is a consistent relationship between the size of vegetation patches in the land scape and the degree to which critical resources, such as soil nutrients or water, become concentrated in these patches. In this case, the features of the scaling functions that underlie this rule have to do with physical pro cesses, such as surface water flow and material redistribution, and the way s that patches of plants physically "capture" such runoff and convert it in to plant biomass, thereby concentrating resources and increasing patch size . To be operationally useful, such scaling rules must be expressed in ways that can generate predictions. We developed a scaling equation that can be used to evaluate the potential impacts of different disturbances on vegetat ion patches and on how soils and their nutrients are conserved within Austr alian savanna landscapes. We illustrate that for a 10-km(2) paddock, given an equivalent area of impact, the thinning of large tree islands potentiall y can cause a far greater loss of soil nitrogen (21 metric tons) than grazi ng out small grass clumps (2 metric tons). Although our example is hypothet ical, we believe that addressing scaling problems by first conceptualizing scaling functions, then proposing scaling rules, and then deriving scaling equations is a useful approach. Scaling equations can be used in simulation models, or (as we have done) in simple hypothetical scenarios, to collapse the complexity of scaling issues into a manageable framework.