The incremental increase in contributing area along a main stem river, called here the incremental area function (IAF), has direct relevance to the spatial heterogeneity of environmental fluxes (water, sediment, nutrients, etc.) entering the stream from hillslopes and side tributaries. It also dictates, to a large extent, possible ecohydrologic discontinuities or transitions resulting from large tributary contributions. Mathematically, the IAF directly reflects the topological and geometrical structure of the river network and maps the two-dimensional landscape organization into a one-dimensional function. In this paper, we use two approaches to investigate the spatial heterogeneity of the IAF...