Living in a network of scaling cities and finite resources

TitleLiving in a network of scaling cities and finite resources
Publication TypeJournal Article
Year of Publication2014
AuthorsQubbaj MR, Shutters ST, Muneepeerakul R
JournalBulletin of Mathematical Biology
Volume77
Issue2
Pagination390-407
ISBN Number0092-8240
Keywordspopulation-resource dynamics, scaling, sustainability, urban networks
Abstract

Many urban phenomena exhibit remarkable regularity in the form of non- linear scaling behaviors, but their implications on a system of networked cities has never been investigated. Such knowledge is crucial for our ability to harness the com- plexity of urban processes to further sustainability science. In this paper,we develop a dynamical modeling framework that embeds population–resource dynamics—a generalized Lotka–Volterra system with modifications to incorporate the urban scaling behaviors—in complex networks in which cities may be linked to the resources of other cities and people may migrate in pursuit of higher welfare. We find that iso- lated cities (i.e., no migration) are susceptible to collapse if they do not have access to adequate resources. Links to other cities may help cities that would otherwise col- lapse due to insufficient resources. The effects of inter-city links, however, can vary due to the interplay between the nonlinear scaling behaviors and network structure. The long-term population level of a city is, in many settings, largely a function of the city’s access to resources over which the city has little or no competition. Nonethe- less, careful investigation of dynamics is required to gain mechanistic understanding of a particular city–resource network because cities and resources may collapse and the scaling behaviors may influence the effects of inter-city links, thereby distorting what topological metrics really measure.

URLhttp://link.springer.com/10.1007/s11538-014-9949-3
DOI10.1007/s11538-014-9949-3
Source DocumentAccessible with appropriate permission
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Living in a network of scaling cities and finite resources

Case
This is a placeholder case for the model of the same name. A quantitative model of a multiple consumer-resource system with multiple consumer-consumer and consumer-resource couplings. Consumers are "cities" that display non-linear scaling behaviors and inter-city migration. 
30 Sep 2016

Living in a network of scaling cities and finite resources

Model
A modified Lotka-Volterra system in which multiple consumers and resource systems are connected by both consumer-consumer and consumer-resource links. Consumers represent cities, and thus exhibit nonlinear scaling behaviors as population increases w.r.t. harvest rate and harvest conversion efficiency. Populations can also migrate between cities along a welfare-dependent gradient.Analysis of the model for a simple dyadic network reveals that the basic Lotka-Volterra formulation can lead to...
30 Sep 2016