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| Urban population dynamics |
in PLOS-one (
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| 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.
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| 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.
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| 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.
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| 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.
15 comments:
Thanks for this introduction to the PlosONE paper!
I am curious about the application of urban scaling in situations where/when population is not increasing but rather decreasing.
@Stefano - Population growth or decline is not specifically part of the scaling models. They describe a system of cities of varying sizes, and not changes through time. Our language, however, often uses phrases for temporal change to describe changes within a system at a given time.
So is the implication of this work that there really isn't a qualitative difference between how cities work and how villages work? That seems to be one of the conclusions of the paper ("all human settlements function in essentially the same way"). That's very interesting!
@DNak - Well, the implication would be that there are SOME aspects of social dynamics that are comparable in settlements of different types and sizes. But the EXTENT of such similarities will be an interesting research question.
Perhaps I should spend a week in Santa Fe, because after the Bettencourt (2013) paper it felt to me like any other mathematic model. Sure we can prove or disprove variables follow a model, but what does that make us understand? Even after your enthusiasm here, which makes my reading of Ortman et al. (2014) more pertinent, I still don't really see what the importance really is. I would say that at the very least theoretically there has never truly been a question about certain processes in settlements necessarily having to work in similar ways. That is an inevitable effect of the human condition. So what does scaling add, but a way of showing that certain aspects narrowly correlate with size? And if size is population and area, how reliable is our data and what is assumed about the borders of the 'system'? I don't mean to criticise so much as to say that the contribution of scaling still isn't clear to me and therefore how would it revolutionise understanding of social interaction? Mind you, that is before reading Ortman et al. (2014), which might yet sway me, if not, perhaps a Santa Fe tour should become part of archaeologists' curricula!
@Benjamin - Yes, scaling is, as you say, "a way of showing that certain aspects narrowly correlate with size." But there are several things about this that are interesting. First, these quantitative associations have a strong degree of regularity that can be captured mathematically. Each city is unique, and each operates in its own way. Yet the aggregate result, for particular relationships among variables, is quite regular. For me, that stands out as something quite amazing. This may not be remarkable to the complex systems theory people, but I find it startling and fascinating.
Second, there are three different, yet each very regular, patterns. (1) First is the way city area varies with population size. This is the topic of the new paper by Ortman et al. Of the three patterns, this is one I am most dubious about. But the proof is in the pudding, and perhaps the data will show that some of my preconceptions are incorrect. (2) Infrastructure. These two patterns scale in a sub-linear fashion. (3) social outputs. These are the patterns that scale super-linearly, and express the amplifying aspects of city life.
The second thing I find very interesting is that some of the scaling patterns (and perhaps many of them) also work for premodern cities. And, the Ortman study suggests that they work for non-urban settlements as well. Thus they cannot be the result of capitalist agglomeration economies, and the explanation must be found at a more basic level. Bettencourt's quantitative model points to human interactions with a delimited space as the cause of the scaling regularities. So this work has the potential to bridge all kinds of human settlements, focusing on the nature and intensity of the social interactions that take place. I see the need for more research on the on-the-ground human social patterns that ultimately generate the scaling regularities. Just how do urban economies grow? How do people move into cities and towns? Do people interact differently in formal spaces (like plazas) than in other kinds of spaces? Etc.
Urban scaling laws don't explain everything about cities, but they seem to explain several kinds of things in cities, to a level of precision uncommon in social science.
As for the problem of boundaries (not surprising that you should raise this, since it is a major theme of your research!), I know it is an issue that the scaling scholars are concerned with and try to refine as much as they can. For contemporary cities, the problem is that the "city" is a political or administrative entity, but the relevant economic spatial unit, the MSA (metropolitan statistical area) is larger and more difficult to bound and to gather data on. For premodern cities, boundaries are a huge problem, which is one reason your work is important. I see this not as an objection to scaling research, but as a methodological obstacle that requires our attention.
Perhaps surprisingly, I do agree with most of what you say. But I feel that most of these aspects of urban life needed addressing even before scaling indicated there might be a mathematically commensurate model for their occurrence. That, in itself, I still doubt is of actual importance.
In addition, the boundary (I'd rather say border here as not to confuse myself with my own work) to the city (as well as the reliability of population estimates)) question should indeed not deter, but it is important to know what is being assumed, otherwise it seems to me that any suggested conclusion on the basis of 'demonstrating' scaling laws is rather spurious. As you indicated yourself, the sublinear infrastructure occurrence was obvious without scaling. Similarly, and actually I do find this somewhat problematic, if it is so that social output is superlinear according to scaling, this hypothesis again seems somewhat devoid of new insights. By attempting to define cities in different ways for decades, scholars have in essence always suggested there is output in urban life that differs from other situations. But indeed, as you suggest, how people move/use space or how space affords social interaction, to me seems an approach that will remain more insightful than adding a mathematical model to it.
I guess, I don't find the elegance and precision of it that convincing on an interpretive scientific level. However, before I say more, I should study more! If this research serves to say that we should put greater effort in studying how ancient cities function, I'm all for it!
Another interesting phenomenon to contrast things with is the idea of agro-urban settlements. After all, while delimited, the degree of delimitation in space and its structure differs dramatically in such cases. This makes me realise that in my own 'working definition' of the city as urban life, I'm suggesting something of similar explanatory character, i.e. that 'urban' means that large proportions of the inhabitants can conduct their lives without the necessity to leave the confines of the city. If that presupposition is true, it leans on a delimited space in which an intensification of social interaction takes place. My 'boundaries' are the focal points of transitions in interactional opportunities and could therefore help disentangle the way urban built complexity could be conducive to this. Still, I'm not sure if scaling is going to help me in explicating or understanding this.
Michael, I would like to ask two (related) questions about this:
1. How would this work for low-density urbanism, such as in the Maya area, where rural densities are higher?
2. It seemed to me, after reading a paper by Hirth's on urbanism in central Mexico (in Joyce Marcus' book on comparative urbanism) that Lockhart's altepetl idea was really useful for understanding Mesoamerican cities. How would a cellular-modular form of urban organisation mesh with a model focused on agglomeration?
@Marus. First, the question about low-density cities is a very good one. That was a topic of conversation when I was at the Santa Fe Institute last year, and it is something that a number of us are thinking about. I don't have any insights now, though. Does is require a different approach to scaling models? That is far from clear yet.
As for the "altepetl model," let me just say that this is a very problematic model. First, Lockhart's model is based on idealized structuralist preconceptions, and not on data. The archaeological data (as well as central Mexican native historical data), in fact, contradict much of what Lockhart says about modular organization and the spatial expression of the altepetl. See my book Aztec City-State Capitals for some discussion of this.
Second, Hirth's application of the "altepetl model" to central Mexico misses a feature that, to me, is perhaps the most interesting and important thing about the altepetl: they exist in groups, not as isolated polities. Their group dynamics are crucial for understanding both individual polities and the regional system. These were city-states, and Hansen's model of "city-state culture" captures much of what is important about the altepetl, much more than the so-called "altepetl model."
Check out the Time.com piece about the new PLOS-One article:
http://science.time.com/2014/02/25/ancient-aztecs-modern-new-yorkers/
"What ancient Aztecs shared with modern New Yorkers."
It's really interesting to see these initial results of the application of scaling theory to ancient cities. I think this is an important contribution in simply demonstrating that one aspect of scaling theory works for preindustrial urban centers.
However, I see this paper as more of a 'proof of concept' as opposed to an important contribution to what we know about ancient cities. Its exciting, but at the same time, the relationship between settlement area and population is (to me, at least) among the least interesting aspects of the theory. In that sense, this paper is just scratching the surface. Its important, but the real significance lies more in the types of research that could extend the use of this theory to other areas of urban life.
This touches a bit of Benjamin's comments, but I see the real potential contribution of urban scaling theory in understanding the various social interactions that conform to superlinear scaling, particularly those relating to invention and innovation. Urban scaling provides quantitative backing for a pattern people have talked about for a long time: how places of concentrated human interaction function as factories for new ideas and innovation.
In an intro class I'm teaching right now, we've been talking about V. Gordon Childe's concepts of the Neolithic and Urban Revolutions, and more generally about how the pace of human technological advancement has been advancing on a more or less exponentially over the past 5-10K years, in sharp contrast to the preceding ~250K years in which modern humans have existed on earth. I wonder how much of this very general pattern is rooted in the rise of nucleated settlements and cities, and if we should view urban life as not just a symptom of general process, but something that actually drives long-term social change.
In this area, I think archaeology could contribute a long-term perspective to research focusing on the role of cities in human societies. This isn't just a topic for understanding the initial rise of cities, but has potential significance in the future given the steadily increasing numbers of people living in cities globally.
Maybe I'm getting ahead of myself. But for me, the relationship between settlement area and pop. isn't all that profound. But this paper is exciting because it suggest that the more interesting things that happen in modern cities might also apply in ancient cities. After reading that paper, I started thinking about how we could frame research questions to study different social dynamics that demonstrate superlinear scaling from archaeological data. It will likely be more difficult than this pilot study, but certainly not impossible.
Very exciting!
I just wanted to thank Mike for the post and everyone for their comments.
I've been a fly on the wall so to speak, but wanted to totally agree with Jerry Ek's latest comment:
While it was essential for us to test for the relationship between settlement area and population the real interesting questions are to probe the social capacities for organization and innovation in these societies using quantitative archeological data and this sort of theoretical perspective, to really test hypothesis against measurements.
Without spoiling the surprise, Scott and I have been working on doing just that and have some very interesting preliminary results.
I also want to emphasize that this is not just another passive application of modern urban theory to archeology: there is fundamental archeological theory to be done here, as we tried to explain in the paper.
That is really exciting to us and, we hope, to most of you as you really are the ones positioned to do it, as we have been discussing with Mike.
More soon!
Luis Bettencourt
@Jerry and Luis - I agree with most of your remarks. Jerry, I, too, find the population/city area relationship the least interesting kind of scaling pattern. And for the dataset I am working with, I am estimating population based on site area, so I can't work with that relationship at all!
Apologies in advance for this slow, long and split post reaction, but I hope I'm working towards a better understanding here.
Thanks to Jerry Ek for offering his comment, which did bring some of the potential relevance of using scaling laws home to me. Somehow this argument seems to become lost in the modelling technicalities reported on. If interaction in delimited spaces is conducive to innovation, could it be suggested that the lower density of Maya cities may have caused them to be unable to ‘invent’ adaptive solutions to their city growth? If so, I find it even more interesting that over the course of two millennia their building patterns are socially resilient, that is, they keep recurring in new cities. Something therefore must be functioning for them and/or they fail to see or agree with ways they could adapt. But is spatial dispersal the cause? At the same time we see a densification and social change in Post-Classic cities, which in turn suggests innovation is reached. Also, urbanity seems an essential part of their way of life, regardless of occasions of collapse, so at least some of the functional benefits must still be achieved in lower-density settings. So this begs the question, if there are similar beneficial aspects of ‘superlinear scaling’ at play in Maya cities, why is it that current scaling propositions struggle with it?
From what I understand, scaling laws merely seem to be another way of expressing (and within some assumptions: measuring) that we understand (indeed there was never really any doubt about that, was there?) that settlements and cities increase diversity and frequency of interaction. This provides the supportive basis for other social traits and characteristics to emerge, as well as in that process increasingly create support for spatial efficiency (i.e. leading to potential for greater density). The benefits of these social traits and efficiency causes people to adopt and accept the related lifestyle. Power relations of various kinds (political, economic, etc.) may sometimes go against the densification grain. Some current Asian city dwelling shows that densification without power can achieve startling effects (people living in concrete boxes, which I’d be interested to compare to Victorian large families in small terraced housing).
I suppose what is largely unclear to me is exactly what is being measured (which information) and why and on what basis (theory and/or assumption/hypothesis). While in general I have little issue with the suggestion that in delimited spaces social interaction can attain particular causal characteristics, there must be many ways to do this and therefore many ways of building cities that would be conducive to this. In other words, rather than measuring whether cases follow the brackets or narrow ranges of the power law, in order to understand this we must investigate how city life can take place within the urban spaces created as well as (insofar we are not archaeologists) indeed how it does take place.
While it seems only logical that groups have other causal powers than individuals and that large agglomerations of individuals (whether that is capitalist economics or not) can support a greater variety of groups with diverse abilities, it seems to me that it much depends on everyday urban life whether or not, as well as how this groups with causal powers emerge. I may simply lack the modelling knowledge to truly judge and understand whether the scaling laws can cope with this, but the suggestion that low-density cities would still be a challenge rather suggests that cities are currently being measured against a model or ideal type that is considered normative or average and for which assumptions about what is happening and how and why that functions are being made.
I guess what I’d like to know more about is, when Mike says: “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”, then how are scaling laws relevant and helpful or informative. I believe that if this link is explicitly grounded I could perhaps be swayed. While indeed it could be fascinating if most cities conform to a certain mathematical regularity, I first wonder how many crucial variables of relatively spatially independent activities are concealed and therefore assumed to occur or function one way or another. Secondly, I wonder exactly what it helps us understand, since it doesn’t seem to explain how or why it occurs. Being able to translate aspects of observations into mathematical regularity remains unable to interpret ancient urban life or influence current urban life. Is it not much more important to enable the interpretation of observations that let certain causal powers and amplifications emerge, regardless of whether this conforms to a mathematical expression? Or am I again missing something essential?
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