Urban scaling arrives in archaeology

Urban population dynamics

The first application of the methods of urban scaling to archaeological data was published last week (Ortman et al. 2014). This should be the first of a series of archaeological applications of urban scaling research, a trend that has the potential to revolutionize scholarly understanding of the basic processes of urbanization. While some of the discussion is pretty technical, the basic results and their implications are clear. The population sizes and areas of a large sample of ancient settlements conform to the expectations of urban scaling power laws as identified for contemporary cities. Yes, I said settlements. Not just cities, but smaller settlements as well, all conform to the scaling model. I discussed the scaling research on modern cities in Wide Urban World last fall, based mainly on Bettencourt (2013).
in PLOS-one (

Superlinear scaling (Bettencourt 2013)

To summarize briefly, the relationships between the sizes of contemporary cities, and various social, economic, and spatial phenomena, conform two two basic power law patterns called superlinear scaling and sublinear scaling. Superlinear scaling has been found for diverse social outputs, from economic productivity to crime. It means that as the population of cities increases, the level or frequency of these traits (per capita) increases faster than the rate of increase of the population. Sublinear scaling means that the level or frequency of other traits increases more slowly than the population does. This has been found for two types of urban phemonema: infrastructure, and the area or footprint of the city. The infrastructure pattern is pretty obvious: if you have twice as many people, you don't need twice the length of roads or cables (per capita). As for area, the pattern indicates that larger cities have a higher density than smaller cities. What is fascinating and important about these patterns is that the rates of increase (measured by the slope when plotted on a log-log graph) conform to a narrow range of values. In other words, these processes follow trajectories with similar quantitative parameters.

Sublinear scaling (Bettencourt 2013)

The new paper focuses on this latter factor. The authors ask whether the area of Prehispanic settlements in the Basin of Mexico increase at the equivalent rate as in modern cities; do the data conform to the same power laws? The answer is yes. The authors analyzed a mass of settlement pattern data from the surveys of William Sanders, Jeffrey Parsons, and others. Not only do larger settlements have a higher density than smaller settlements, but the increase in density occurs at a predictable rate. Why is this so revolutionary? Because it suggests that not only do ancient cities follow the same quantitative laws of growth and change as modern cities, but non-urban settlements conform to these patterns as well.

As my students are probably tired of hearing, I think urban scaling is a really important topic of study for archaeology right now. I am in the process of measuring a bunch of Mesoamerican urban maps, and before long I'll be able to test whether they exhibit super-linear scaling. Actually, I should say that I have a talented undergraduate, Alexandra Norwood, measuring the maps! And I know Scott Ortman is working on other data, as are a few other colleagues.

I approach this topic as a convert, and they say that converts are the biggest fanatics. When physicists Geoffrey West and Luis Bettencourt announced that finding power laws of urban scaling meant that they had found "a unified theory of urban living (Bettencourt and West 2010), and could point for the first time to a "science of cities," I was highly skeptical. My skepticism came more from these grandiose claims than from the content of the scaling research (which I didn't understand at the time). If there is to be a science of cities, it will have to be considerably broader than finding a few power laws.

Then I was invited to spend a week at the Santa Fe Institute to discuss ancient cities: In what ways were they similar or different from contemporary cities? Can we expect scaling laws to work for ancient cities? How could archaeologists test these models? In preparation for my visit, I read a bunch of literature in economic geography and urban economics. It seemed clear the the processes of urban growth are at the heart of the scaling relationships, and urban growth is the major theme of these disciplines today. I found that the key processes identified for contemporary cities center on agglomeration effects. The spatial concentration of labor, firms, and information in cities is synergistic, and creates economies of scale and increasing returns, and many authors suggested that these are responsible for regularities like the scaling effects. But premodern cities did not have capitalist economies, and agglomeration effects either did not exist, or else existed at a much smaller scale than in contemporary cities. Urban growth in the past was a quite different phenomenon than urban growth today.

So when I arrived in Santa Fe I had two propositions in mind:

• IF agglomeration economies are the cause of scaling laws today, then ancient cities should not exhibit similar scaling patterns, because they lacked agglomeration economies.
• If ancient cities DO exhibit scaling laws like contemporary cities, then the causes must lie at a more fundamental level than agglomeration economies.

After only a day of discussion with Luis Bettencourt, Geoffrey West, José Lobo, and Scott Ortman, it became clear that the processes that generate scaling regularities in fact lie in the basic realm of social interactions among people within a delimited space. This is the basis of Luis's model of contemporary urban scaling (Bettencourt 2013), although I was too obtuse to pick up on it until I got to Santa Fe.

Urban dynamics ???

If it is indeed the case that social interaction generates scaling effects, this opens up new avenues of research. Scaling should work not only for premodern and ancient cities, but also for non-urban settlements as well. Processes of rural-to-urban migration, and settlement nucleation become central to these dynamics. I wrote a paper on these processes, now under review at World Archaeology. One of the conclusions is that in premodern societies, spatial movement (within and among regions) was quite common, including nucleation and urbanization. There were few barriers to people moving into settlements, and thus there were few barriers to settlement growth. One implication is that urbanization and nucleation dynamics in the past could generate interactions and growth comparable to the agglomeration economies of the modern world.

Jeff Parsons

I think research in urban scaling has the potential to illuminate basic human processes of social interaction and their effects on society. Those effects include urbanization, economic change, and a host of other social phenomena. Ancient cities were different from modern cities, and the specific urbanization processes were different, yet several kinds of end result (such as the amount of infrastructure, or the level of social outputs) were quite similar. This situation is nothing new to those who work with complexity theory, but it is something that the rest of us need to learn. And for me, the important implications lie not in the abstract realm of scaling parameters and network structure, but in the on-the-ground realm of human behavior and social processes. I wonder if Jeff Parsons ever thought his survey data would be analyzed and discussed by physicists.

When is the last time scholars from other disciplines came knocking on your door, saying they need archaeological data in order to answer fundamental scientific questions?

Bettencourt, Luís M. A.  (2013)  The Origins of Scaling in Cities. Science 340:1438-1441.

Bettencourt, Luís M. A. and Geoffrey B. West  (2010)  A Unified Theory of Urban Living. Nature 467:912-913.

Ortman, Scott G., Andrew H.F. Cabaniss, Jennie O. Sturm and Luís M. A. Bettencourt  (2014)  The Pre-History of Urban Scaling. PLOS-one 9(2):e87902.