The tragedy of the commons

Imagine a field at a north-eastern fringe of your village. Everyone’s allowed to use it as a pasture so you always see a lot of cows there. Some belong to you, some to your neighbours. As an intelligent homo economicus you know that if too many cows pasture on the same strip of land the grass gets depleted quicker than it can regrow and the land becomes useless. Nevertheless, you also know that any benefit of using the pasture for your cows means benefit for you, whereas any damage caused to the pasture is shared equally among all neighbours. The logical conclusion: take as much advantage of the shared land as possible. The tragedy of the commons arrises from the fact that all of your neighbours concluded the same and soon all the grass is gone.

Although this seems like a topical story in the world of climate change, dwindling resources and horror stories of imminent doom, it is easy to notice that, generally, human societies have developed many successful strategies to deal with this problem. You can call them ‘institutions’, be it a socially observed rule, superstition or an actual person whose job it is to catch and punish free riders.

In their new paper “The co-evolution of social institutions, demography and large-scale human cooperation” Powers and Lehmann look at the evolution of such social institutions and ask the question: is social organisation inevitable?

I wanted to share it here as this is a fantastic example of how much you can achieve by formalising a system and running a relatively simple simulation. In just a few equations Powers and Lehmann put together the relationship between populations of social and asocial individuals, the competition and cooperation between them, the interplay between the available resources and the population growth as well as the process of sanctioning free riders. On top of that they made the simulation spatial which turned to be a key factor for understanding the dynamics of the system.

It turns out that in a well mixed population neither the socials nor the asocials can take over forever (i.e. maintain the stable equilibrium). However, if the groups live on a spatial grid (just like us – humans) the situation looks different. The population of social agents cooperate to create strategies, which pushes up the ceiling of the carrying capacity for the group.  This means that the group can grow and expand into the neighbouring areas and once they arrive they are to stay. The fact that their carrying capacity ceiling is higher than that of the asocial individuals means that the population remains stable ad infinitum. Interestingly, the amount of resource spent on sanctioning the potential free riders usually fixate on pretty low numbers (10-20%). Therefore, this simulation shows that cooperation between agents coupled with even a small investment into ‘institutions’ leads to dramatic changes in the structure of the group.  A population of cooperative agents is likely to take over asocial neighbours and turn into a hierarchical society.

Although the model is largely abstract, its findings are particularly applicable, as the authors note, to the shift between hunter-gatherer groups and sedentary agriculturalists. A strong cooperation among members of the latter group is necessary for constructing irrigation systems. These, in turn, increase the group’s carrying capacity leading to a higher population size, at which point, sanctioning of the potential free riders becomes a necessity. And so Ms Administration is born…

On the final note, it’s worth taking a good look at Powers and Lehmann’s paper if you’ve never come across EBM (Equation-based Modelling). First of all, this is a fantastic example of how to formalise a complex system. The equation terms represent simplified reality. A good example of this is the group cooperation. The model assumes that people cooperate to make their work more efficient (i.e. to lift their carrying capacity), it doesn’t go into details of what that means in any particular case – digging a canal together or developing better shovels. It really doesn’t matter. Secondly, the authors did a particularly good job in explaining their model clearly, you really don’t need anything beyond primary school maths to understand the basics of the simulation.

We (archaeologists) have been discussing the rise of complex states with their administration and hierarchy for decades (in not centuries) and the question “why?” is always in the very core of all research: why did people get together in the first place? why did they cooperate? why did the hierarchy emerge? Powers and Lehmann’s model takes us one step closer towards answering some of those questions showing how simple interactions may lead to very complex outcomes.

Urban Scaling, Superlinearity of Knowledge, and New Growth Economics

View of Mumbai, from

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. Sourceéolithique_0001.jpg
Neolithic diversity of tools. Sourceéolithique_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.

SCCS2014 CfP is now open

We have already mentioned the Student Conference on Complexity Science which will be held in Brighton between 19th and 22nd August. They have just released their Call for Papers. This is a fantastic opportunity to check out how other disciplines are playing with complexity science and, a little bird told me, that apart from a strong representation in social sciences and artificial societies they may be a whole archaeology & history session!

For more info have a look at their Call for Papers below.

We are please to announce that the Student Conference on Complexity Science (19-22 August 2014, Brighton, UK) Call for Papers is now open. The deadline for submissions is 14th April at 12 p.m. (UCT).

The Student Conference on Complexity Science (SCCS) is the largest UK conference for early-career researchers working within the interdisciplinary framework of Complex Systems, with a particular focus on computational modelling, simulation and networks analysis. Confirmed keynote speakers include prof. Mark Newman (University of Michigan, USA), prof. Eörs Szathmáry (Eötvös Loránd University, Hungary) and prof. Nigel Gilbert (University of Surrey, UK). This year SCCS will consist of five hands-on workshops as well as parallel sessions. The topics will oscillate around ten general themes listed below. Please note that abstracts not falling directly into one of the general themes may still be considered if they are relevant to a specific session.

Theory of Complexity Science

Self-organization, nonlinear dynamics and chaos, mathematical and simulation methodology

Network Science

Technological networks, spatial networks, infrastructure, ecology, social networks, Internet

Planning and Industry

Critical infrastructures, urban planning, mobility, transport, sustainability

Earth System Complexity

Climate change, ocean, atmosphere, ice and solid earth dynamics

Biological Complexity

Systems biology, ecology, ecosystem services, medicine

Evolution and the Origin of Life

Evolutionary systems, origin of life theory, major evolutionary transitions, generative and developmental systems, artificial life

Artificial Intelligence

Swarm intelligence, embodied cognition, robotics, neuroscience

Social Systems

Linguistics, demography, psychology, health, past societies

Economics and Finance

Markets and stability, trade, public policy, game theory

Engineering and Physical Sciences

Quantum dynamics, statistical mechanics, optimisation, turbulence, computational chemistry, nanotechnology, energy

If your work comes under the umbrella of complexity science, then we want to hear from you! To submit your abstract follow this link:

For more information visit our website, follow us on Twitter @SCCS2014 or Facebook

Stefani’s current project has been featured in the Scientific American blog! If you want even more details check out her blogpost about it, here.

Is the universe a simulation?

A recent NY Times op-ed reintroduces the philosophical concept of the simulation hypothesis: the idea that the universe we live in is an elaborate computer simulation.

This is kind of based on the idea that mathematics has rules that, while expressed in a human-derived conceptual language, exist in a plane unto themselves. This concept has been explored by folks like Eugene Wigner, but the simulation hypothesis is still certifiably fringe from what I can tell. It would hold that these rules are what controls our simulated existence, and that each time we learn something about them, we’re pulling back the curtain just a little more.

The op-ed featured some recent mathematical research into this topic, which is looking for “observable consequences” of being in a simulation (the fringy-ness should be apparent in the opening to the conclusion: “In this work, we have taken seriously the possibility..”). These folks are saying “if the simulation were a simulation like this (in this case, a latticed hypercube of time-space), we should be able to detect how that world was set up using physical assessments of certain known phenomena (in this case, high energy cosmic rays). They conclude that as long as there is some limit to the resources available to the simulators, there must be ways of detecting the spacing within the lattice. Other research has focused on detecting this through changes in gravity around black holes in universes of different dimensions. It is interesting to me that the solutions proposed by these researchers, at least as described here, follow a method similar to that of Grimm et al.’s pattern-oriented modeling.

Working in simulation brings up plenty of epistemological issues regarding scientific representation. I think some of the most important of these for archaeologists are those which deal with relationship between a modelled entity and its real counterpart, and the nature and validity of computational “experiments”. Of course, that all becomes more or less moot if we are only part of a simulation ourselves. But what has me puzzled on this existential level concerns the more general role of simulation. Simulations are usually models, or ways of representing the interacting variables within a more complex system. They’ve been described elsewhere as “tools to think with”, a feature of the upcoming workshop at the CAA. But if our universe is a simulation, in the sense of a model, then what more complex phenomenon is our universe a model of?

Photo credit:  Sergey Galyonkin via Wikimedia Commons

This Year we all Go to Barcelona

In the tough world of Academia there is nothing better than a conference in a city boasting with vibrant research community and a beach. For archaeologists working with computational modelling Barcelona fits the bill nicely and this year no excuses are needed to visit this absolutely fantastic city. After the success of the ECCS2013 last September Barcelona seems to become the world capital for modelling social complexity with at least three major conferences scheduled for 2014.

European Social Simulation Association Meeting

The European Social Simulation Association  will hold its annual meeting  at the Universitat Autònoma de Barcelona between 1-5 September, 2014.  You can find more information about the conference here.

But more importantly, our colleagues from the SimulPast project are organising a satellite event Simulating the past to understand human history. Although the conference is aimed at showcasing the achievements of the SimulPast project, the wide range of topics indicated by the organisers shows that we can expect a good set of interesting papers dealing with different aspects of modelling and complexity science applications in archaeology.

Finally, the conference is worth a trip even if only for the keynote speakers.  Timothy A. Kohler (Washington State University) is known from his Village Ecodynamics Project and, probably by all students thanks to his classic paper “Complex Systems and Archaeology” in Ian Hodder’s Archaeological Theory Today.  And we can only hope that someone will ask  Joshua M. Epstein (Johns Hopkins University) – the second keynote speaker  – his trademark question ‘Why model?

The Call for Papers closes this Thursday ( 28th, February, 2014).  According to the CfP the organisers look for a wide range of papers diverse in both archaeological but also methodological scope: Applications are welcomed on all subjects (from Anthropology, Archaeology, Geography and History) using different approaches to social simulation and presenting case studies from any region of the world and any prehistoric or historic period. Theoretical aspects of social and cultural evolution are also encouraged.

Coincidentally, at the same time (1-7 September) Burgos will be hosting the XVII Congress of the International Union of the Prehistoric and Protohistoric Sciences (UISPP). You can find the list of session here.

European Conference on Social Networks

The second complexity science conference held this year in Barcelona is the 1st European Conference on Social Networks between 1-4, July, 2014. They haven’t opened their CfP yet so only preliminary information are available on their website but it looks as if it was going to have a strong archaeological twist.

SocInfo 2014

Finally, the 6th International Conference on Social Informatics, although focused more on present rather than past human societies, may also be of interest to many, especially in light of the conference mission statement: This year’s special purpose of the conference is to to bridge the gap between the social sciences and computer science. We see the challenges of this as at least twofold. (..)  emphasis on the methodology needed in the field of computational social science to reach long-term research objectives. We envision SocInfo as a venue that attracts open minded researchers who relax the methodological boundaries between informatics and social sciences so to identify common tools, research questions, and goals. SocInfo will be  held in Barcelona between 10-13 November 2014.

Review: Simulating Social and Economic Specialization in Small-Scale Agricultural Societies

Photo of adze head, Mesa Verde National Park. Author’s hands in picture for scale.

Humans are really good at doing multiple different things. If you look at Homo sapiens we have a vast amount of different types of jobs—we hunt, we gather, we farm, we raise animals, we make objects, we learn. Some individuals might be good at one job, and some individuals might be better at another. This is okay, though, because by specializing in what each individual does well we can have a well-rounded society.

But where do we get a switch from generalist to specialist behavior? In small-scale societies, where is the switch from every household making ceramics, to one household making ceramics for the whole village? Specialization only works when there is enough exchange among the individual nodes of the group, so that each specialist can provide their products to the others.

Cockburn et al. in a recent paper for the Journal of Artificial Societies and Social Simulation (JASSS) explore the effects of specialization via agent-based modeling. While the degree to which agents specialize is in some instances unrealistic (Ancestral Puebloans were not able to store 10-years of grain—it would have rotted; also nobody probably specialized in gathering water), Cockburn et al. are aware of this, and state that by using “unrealistic assumptions, we hope to, as Epstein (2008: 3-4) says, “illuminate core dynamics” of the systems of barter and exchange and capture “behaviors of overarching interest” within the American Southwest.”

So, what are these behaviors of overarching interest? Well, for one, specialization and barter lead to increasing returns to scale, allowing for denser and larger groups as well as higher populations than when individuals do not specialize. Also, the networks that formed in this analysis were highly compartmentalized, suggesting that certain individuals were key to the flow of goods, and thus the survival of many people. Cockburn et al. suggest that the heterogeneity of the networks may have helped individuals be more robust to critical transitions, as Scheffer et al. (2012) suggest that modular and heterogeneous systems are more resilient.

This paper should be of interest to our readers, as it combines both agent-based modeling and network analysis, trying to shed light on how Ancestral Puebloans lived. One key drawback to this article is its lack of comparison (in goodness-of-fit measures) to the archaeological record, leaving the reader wondering how well the systems described would fit with archaeological output. Kohler and Varien, in their book on some of the early Village Ecodynamics Project work, develop various goodness-of-fit measures to test the model against archaeology. Perhaps Cockburn et al. intend to use their work with some of these goodness-of-fit measures in the future.

However, despite this drawback, the article does help illustrate highly debated questions of specialization vs. generalization in the archaeological record. Could people have specialized? Yes. Does specialization confer a benefit to individuals? Yes. Taking this article in tandem with debates on specialization may help us to come to a consensus on how specialized people were in the past.

Please read the open access article here:


–Stefani Crabtree

Connected Past in Paris

For all you network analysis fanatics out there, a quick reminder that the Connected Past Conference is happening for the second time this April. Since the  beginnings as a TAG (Theoretical Archaeology Group Conference) session in 2011 in Birmingham the Connected Past team has been bringing together researchers working on network analysis and successfully promoting this core complexity science technique among archaeologists.

Looking at the conference programme there is a good mix of applications typical to archaeology such as modelling ancient trade  (Eivind Heldaas SelandFrancisco Apellaniz) or interpreting the distribution of archaeological finds (Henrik Gerding and Per ÖstbornHabiba, Jan C. Athenstädt and Ulrik Brandes), but also quite a lot of historical case studies ranging from ancient writers (Thibault Clérice and Anthony Glaise) to early modern financial networks (Ana Sofia Ribeiro) to modern academic networks (Marion Beetschen).

Thanks to a leak from one of the organisers  we know that there are literally only a few places left so book asap to avoid disappointment:

Flocking: watching complexity in a murmuration of starlings

My father is a bird watcher. One of my earliest memories is watching a giant flock of wild geese in ponds in eastern Oregon. The way the individual birds would react and interact to form what seemed like an organism was breathtaking. I bet my dad didn’t realize that this formative viewing of a flock of waterfowl would influence the way I study science.

This is a video shot by Liberty Smith and Sophie Windsor Clive from islands and rivers that shows, in exquisite beauty, how individual decisions can have cascading effects on the system. By each bird trying to optimize its distance to the bird in front and on the sides, these birds form a flock of birds. Flocking behavior, shoaling behavior in fish, and swarming behavior in insects all have similarities.  Mammals, too, exhibit this behavior when they herd.

Craig Reynolds first simulated this in his “Boids” simulation (1986). The agents (the boids themselves) want to remain aligned with the other agents around them, want to retain separation from the other agents around them, and will steer their heading toward a perceived average of the headings of the other agents around them. These three simple rules produce the complexity of the flock.

Who can forget the iconic scene of the herding wildebeest in the Lion King? My understanding is that this was one of the first uses of computer graphics in an animated film, and the animation followed similar rules to Reynolds’ simulation.

While my father would likely be appalled that I would promote starlings (their negative effects on biodiversity in the Americas is well documented) this video shows flocking behavior perfectly. Enjoy the beauty of complexity.

(And thanks Joshua Garland and Brandon Hildebrand for pointing me toward this video!)

–Stefani Crabtree

From the world of Complex Systems Simulation in Humanities