Is There a Universal Fractal Human Population Distribution in River Basins?

Abstract:

Human settlement locations are determined by heterogeneous landscape factors together with varied socio-economic conditions. Among these influencing factors, river networks hold an important historical role in affecting human population distribution. Classic scaling relations, Horton’s laws, have been described for stream order and various river network geomorphological variables (e.g. stream number, stream length, and river basin areas). However, it is still an open question on how human population distribution is related with river network topological structure. In this study, we focus on the human population distribution in the river basins of the USA and test the following hypotheses: 1) Human population distribution shows a scaling law with stream order within river basins; 2) Equivalent-order basins become more attractive for humans as adjacency to higher order streams increases; 3) Such scaling relationships are universal across space. We used 2010 Landscan human population distribution data and extracted river sub-basins from DEMs in the USA. Our results show that: 1) the human population distribution shows a fractal structure, with power-law scaling between human population and stream order. This relationship is robust in sub-regions throughout the USA. However, area also shows a similar power-law scaling so population alone is not sufficiently informative. Because the exponents on the area relationship are consistently greater than for population, population density is negatively associated with stream order. This result is consistent with basin length:width ratios and the observed relationship of human distance to water. Populations in equivalent-order basins show large variation, with higher population density emergent in the basins connected with high-order rivers. Such scaling laws between human population distribution and stream order were found universally among hydrological units above a threshold size. The observed reciprocal coupling between human population density and river basin order may reflect an optimum arrangement for humans to better utilize the water resource, ecological assets, and geographic advantage in river basins. The scaling relationships found here underline the controlling influence of river networks on landscape processes.