The effect of scaling and connection on the sustainability of a socio-economic resource system

Policy makers dealing with complex systems oftentimes rely on “linear thinking.” This is understandable due to the ease and convenience offered by the simplicity of such conceptualization. Although this line of thinking may help facilitate decision making processes, it is only as defensible as the degree at which the system under consideration behaves linearly. Recent work shows that diverse properties of cities exhibit power-law relationships with population size. Such relationships may invalidate the reliance on linear thinking. Furthermore, in the era of globalization, resources and people move virtually freely through bounds of any confines used to define a system. We incorporate into a simple resource-population model the power-law scaling behavior and the influence of import and immigration, and investigate their effects on sustainable growth of communities. We explore through bifurcation analysis the different scenarios of how an unsustainable system could be sustained. Import can be effective if: the import exceeds a critical level and a critical mass of people populates the system. In contrast, increasing immigration alone can rescue the intrinsically unsustainable system, both directly through people entering the system and indirectly by increasing its harvesting ability, although critical values exist that cause the population to sharply rise or shrink.