Tag Archives: population dynamics

Urban Scaling, Superlinearity of Knowledge, and New Growth Economics

View of Mumbai, from http://www.worldpopulationstatistics.com

How far did they fly? …not very far at all, because they rose from one great city, fell to another. The distance between cities is always small; a villager, traveling a hundred miles to town, traverses emptier, darker, more terrifying space.” (Salman Rushdie The Satanic Verses p. 41)

Compelling recent work from folks at the Santa Fe Institute suggests that both modern and ancient cities follow similar growth patterns. As cities grow, and if they are regular in layout, it becomes easier to add roads, add parks, add public buildings. You no longer need to invest large amounts to build the infrastructure. It’s easier to add length on to existing roads than it is to create a new road altogether. This phenomenon is knows as increasing economies of scale. Bettencourt found that in modern cities, infrastructure and public spaces both scale to the population at an exponent of between 2/3 and 5/6. Ortman et al. found that the same exponent works to explain population growth and infrastructure in the prehispanic Valley of Mexico.

Okay, what does this mean? Ortman suggests that principals of human habitation are highly general, and that there may be an inherent process to settlement. What’s remarkable in this study is how parallel the growth processes are between ancient and modern cities. Would a modern Saladin Chamcha feel as at home not only in modern Mumbai and London, but also in medieval London or classic Teotihuacan? Is the distance between cities truly small, as Rushdie (via Chamcha’s character) suggests?

Maybe so. Cities, both teams argue, are social reactors. Cities amplify social interaction opportunities. We may expect that things like the number of patents awarded for new inventions would scale linearly with growth, but this isn’t so. It turns out that the number of patents scales superlinearly as do other measures of modern output. With more density comes more creativity.

Infrastructure scales sublinearly, and output scales superlinearly. The larger the city, the less has to be spent to create more infrastructure. The larger the city, the more we can expect to have more intellectual output, like increasing quantities patents.

And, to say it again, this is not true just of modern cities, but prehistoric ones as well.

This brings us to the question of GDP and new growth economics. It turns out that just measuring labor and output does not calculate GDP, but there is an additional, unknown factor, which economists call the A factor. That factor is knowledge. This superlinearity of output in cities, of things like invention and patents, is this that extra A-factor and do we see it rise superlinearly due to the density of networks in cities? And can we truly see prehistory and moderninty working in similar ways? It turns out it’s really difficult to measure the A-factor (economists have been trying for a while), but maybe we’re seeing the effects here.

Ortman et al. argue:

“all human settlements function in essentially the same way by manifesting strongly-interacting social networks in space, and that relative economies and returns to scale (elasticities in the language of economics) emerge from interactions among individuals within settlements as opposed to specific technological, political or economic factors” (Ortman et al. 2014, p. 7).

While Saladin Chamcha might not have been able to communicate with inhabitants in Teotihuacan, he would have felt at home. The city would have held similar structures to 1980s London—he could find a center, a market, a worship space, and those things would have scaled to the size of the population. As humans we build things in similar ways. Bettencourt and Ortman’s work is compelling and causes us to think about how our brains function, how we establish social networks, and what common processes there might be across humanity, both spatially and temporally.

To read Ortman et al.’s work, see this link in PLoS ONE

To see Bettencourt’s work, see this link in Science

A new recipe for cultural complexity

In their new paper Carolin Vegvari and Robert A. Foley (both at University of Cambridge) look at necessary ingredients for the rise of cultural complexity and innovation in their recent paper in PloS One.

The question of cultural complexity is an anthropological mine field.

Neolithic diversity of tools. Source http://en.wikipedia.org/wiki/File:Néolithique_0001.jpg
Neolithic diversity of tools. Source http://en.wikipedia.org/wiki/File:Néolithique_0001.jpg

To start with,  the definition of ‘cultural complexity’ is controversial and difficult to quantify even if we concentrate solely on material culture. Should we count the number of tools people use? But that would be unfair towards more mobile societies who, understandably, don’t like carrying tons of gear. So maybe we should look at how complex the tools themselves are? After all, a smartphone contains more elements, combined in a very intricate way and performs more functions than, say, a hammer. It doesn’t work well in a nail-and-wall situation though. In fact, the differences in the amount and complexity of material culture among contemporary hunter-gatherers is: “one of the most dramatic dimensions of variation among foragers (…). Some foragers manage to survive quite well with a limited set of simple tools, whereas others, such as the Inuit or sedentary foragers, need a variety of often complex tools.” (Kelly 2013, 135).

The rise of cultural complexity and especially the factors that contribute to it and the conditions that need to be met are therefore a big unknown in anthropology and  archaeology alike. Similarly to all scientists we like big unknowns so a number of models have been developed to investigate various recipes for cultural complexity quite often involving radically different ingredients.

Since early 2000s (I suspect Shennan 2001 was the seed for this trend) one of the favourite ingredients in the cultural complexity mix was the demography and the population size in particular. In very simple terms, the hypothesis goes that only large groups, which can sustain a pool of experts from whom one can learn a given skill, will exhibit higher cultural complexity.

The Movius Line

And this was actually applied to archaeological case studies, for example by Lycett and Norton (2010). They argued that the notorious Movius Line slashing through the Lower Palaeolithic world is a reflection of lower population density in the south-east, central and north Asia causing the groups to drop the fancy Acheulean handaxes and to revert to the simpler Oldowan core-and-flake technology.

Vegvari and Foley’s paper is a new stab at the issue. Their simple yet elegant Agent-based model consists of a grid world on which agent groups forage on depletable resource according to their skill level represented as a list of generic cultural traits. These traits can be improved to achieve higher efficiency in extracting the resources and new traits can be invented.  Vegvari and Foley tested a number of scenarios in which they varied group size, selection pressure (really interestingly constructed as a factor lowering the efficiency of resource extraction from the environment), different costs of learning and the ability to interact with the neighbouring groups.

The results of the simulation are really interesting. Vegvari and Foley identified the good old natural selection and its friend population pressure as the main drivers behind the increase in cultural complexity. Although, they work hand in hand with the demographic factors, the population size is a bit of a covariant. Lower population size means less competition over the resource, i.e. lower population pressure. It will, therefore, correlate with the cultural complexity but mostly because it is linked to the selection pressure.

Interestingly, the learning cost came as another important stimulant for groups under high selection pressure and those who could interact with their neighbours as it increase the population pressure even further. Finally, Vegvari and Foley recognised a familiar pattern of the sequential phases of logistic growth.

The logistic curve of population growth.
The logistic curve of population growth.

It starts with the population climbing towards their relative carrying capacity (= the maximum of resource they can extract from a given environment), when they reach the plateau they undergo a strong selection pressure, which leads to innovation. A new cultural trait allows them to bump up the carrying capacity ceiling and so the population  explodes into the logistic growth and the cycle repeats.

Vegvari and Foley created a simple yet very robust model which tackles all of the usual suspects – demographic factors, natural selection and the cost of cultural transmission. It shows that the internal fluctuations of a population arising from simple social processes can induce complex population dynamics without any need for external factors such as environmental fluctuations.  And this is a fantastic opening for a long and fruitful discussion in our discipline.


Kelly, Robert L. 2013. The Lifeways of Hunter-Gatherers. The Foraging Spectrum. 2nd editio. Cambridge: Cambridge University Press.

Lycett, Stephen J., and Christopher J. Norton. 2010. “A Demographic Model for Palaeolithic Technological Evolution : The Case of East Asia and the Movius Line.” Quaternary International 211 (1-2): 55–65. doi:10.1016/j.quaint.2008.12.001.

Shennan, Stephen. 2001. “Demography and Cultural Innovation: A Model and Its Implications for the Emergence of Modern Human Culture.” Cambridge Archaeological Journal 11 (1): 5–16. doi:10.1017/S0959774301000014.

Vegvari, Carolin, and Robert A. Foley. 2014. “High Selection Pressure Promotes Increase in Cumulative Adaptive Culture.” PloS One 9 (1): e86406. doi:10.1371/journal.pone.0086406.