Luís Bettencourt, Joe Hand, José Lobo

Paper #: 15-06-020

Biological and social systems are often characterized by the emergence of general macroscopic patterns within a structure of local variations. Such variations - whether in an ecosystem or a city - express not only statistical accidents but also a rich history of innovation, selection and resulting local adaptations. For these reasons, it has remained a challenge to analyze the structure of complex systems and characterize how much information they contain at different scales of organization. Here we develop a unifying framework for studying the local heterogeneity of complex systems across scales. We show how methods from evolutionary biology and statistical learning theory can be used to quantify how much information is encoded at local levels and how complexity builds up from coarse-grained simple patterns to rich local structures. To illustrate our approach, we apply these ideas to the neighborhood structure of US cities. We observe a strong pattern of local heterogeneity in household income across over 900 cities and 200,000 neighborhoods within a simple and general statistical pattern at the metropolitan level. In this way, we identify variable strengths of local selection by income and quantify the complexity of explanation needed to account for different neighborhood structures observed across US urban areas.