Y can represent categories such as social activity, wealth, pollution, patents, or material resources like energy. $latex Y_0$ is a constant, and β is the scaling exponent. Bettencourt et al. (2007, 2010) found that some factors defining cities such as income and innovation, change in a consistently super-linear manner (with exponent β ~1.15) in response to growth showing increasing returns, while others, like infrastructure, respond sub-linearly (β ~ 0.85), suggesting economies of scale. They hypothesize that this symmetrical divergence from 1 by +/- 0.15 to be related to the underlying rules governing cities’ increase in social interactions (Bettencourt 2013, Schläpfer et al. 2014).

While this previous research has primarily focused on indicators of economic innovation and provision of infrastructure, we will expand the study of urban scaling laws to investigate two aspects: (1) socio-ecological innovation, and (2) patterns of urbanization.

Socio-ecological innovation

We define socio-ecological innovation as the capacity to create social and ecological capital including new technologies, infrastructures, strategies, concepts, ideas, institutions, and organizations that enhance ecosystem function (Olsson and Galaz 2012). We focus on elements for which there is emerging evidence of enabling systemic transformations towards resilience and sustainability.

The research will focus on the selection of a number of indicators of socio-ecological function in cities using publicly available data from US metropolitan areas. Indicators range widely from ecosystem function, environmental quality and carbon emissions, to energy and water efficiency, and from diversity and equity to novel financial mechanisms and governance experiments. We will pilot test these functional socio-ecological indicators and investigate the fruitfulness of the proposed approach using multiple simulations.

Patterns of urbanization

We hypothesize that patterns of urbanization might play a critical role in socio-ecological interactions. A number of scholars have suggested that factors associated with urban heterogeneity might explain the variability observed across cities of the same size (Pan et al 2013, Sim et al 2015). Among these factors may be urban density and/or city structure as well as the spatial and temporal dynamics of urban development. It is currently not known how spatial heterogeneity may influence the response of cities to growth. Nor do we know if these proposed scaling laws and effects apply to other aspects of the urban ecological system. Furthermore, other scholars have pointed out that the area boundary definition may have a non-trivial effect on the results (e.g. Modifiable areal unit problem, MAUP, Cottineau et al. 2015).

To test the sensitivity of scaling relationships to urban structure and heterogeneity we propose to create a synthetic data set and use simulation methods (e.g. Markov Chain Monte Carlo, Geyer 2014) for a set of socio-ecological indicators for which we have disaggregated data. We will apply a synthetic approach using a hybrid data structure combining grid and a network data and explore a variety of statistical methods for alternative design (Kolaczyk 2009, Mark and Giles 2010).

The presence of time series for remote-sensing and population data also allows for the possibility of investigating the consistency of the proposed relationships over time, using identical analytical techniques. These disaggregated synthetic data will be used to create random samples for multiple scale geographical areas and may also allow for the testing of scale and boundary effects.

Research Questions

1. Do urban socio-ecological functions (e.g. ecological indicators) and innovation (e.g. green infrastructure) scale non-linearly with city size (measured via population/population density)?
2. How do scaling relationships vary with patterns of urbanization and cities’ spatial heterogeneity?