Abstract
When we find an archaeological network, how can we explore the necessary versus contingent processes at play in the formation of that archaeological network? Given a set of circumstances or processes, what other possible network shapes could have emerged? This is the problem of equifinality, where many different means could potentially arrive at the same end result: the networks that we observe. This paper outlines how agent-based modelling can be used as a laboratory for exploring different processes of archaeological network formation. We begin by describing our best guess about how the (ancient) world worked, given our target materials (here, the networks of production and patronage surrounding the Roman brick industry in the hinterland of Rome). We then develop an agent-based model of the Roman extractive economy which generates different kinds of networks under various assumptions about how that economy works. The rules of the simulation are built upon the work of Bang (2006; 2008) who describes a model of the Roman economy which he calls the ‘imperial Bazaar’. The agents are allowed to interact, and the investigators compare the kinds of networks this description generates over an entire landscape of economic possibilities. By rigorously exploring this landscape, and comparing the resultant networks with those observed in the archaeological materials, the investigators will be able to employ the principle of equifinality to work out the representativeness of the archaeological network and thus the underlying processes.
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Notes
For the full model code and the details of its routines, please download http://dx.doi.org/10.6084/m9.figshare.92953. Open with Netlogo 5. The code itself is annotated with comments explaining what is happening in each procedure and may be reviewed by clicking on the ‘Code’ button.
References
Agar, M. (2003). My kingdom for a function: modeling misadventures of the innumerate. Journal of Artificial Societies and Social Simulation 6(3) http://jasss.soc.surrey.ac.uk/6/3/8.html. Accessed 19 Sep 2013.
Aubert, J.-J. (1994). Business managers in Ancient Rome. A Social and Economic Study of Institores, 200 BC – AD 250. Columbia Studies in the Classical Tradition 21. New York: E.J. Brill.
Bang, P. (2006). Imperial Bazaar: towards a comparative understanding of markets in the Roman Empire. In P. Bang, M. Ikeguchi, & H. Ziche (Eds.), Ancient economies modern methodologies. Archaeology, comparative history, models and institutions (pp. 51–88). Bari: Edipuglia.
Bang, P. (2008). The Roman Bazaar. A comparative study of trade and markets in a tributary empire. Cambridge: Cambridge University Press.
Bang, P. (2009). The ancient economy and new institutional economics. Journal of Romance Studies, 99, 194–206.
Barabási, A.-L. (2002). Linked: the new science of networks. Cambridge: Perseus.
Bastian, M., S. Heymann, & Jacomy, M. (2009). Gephi: An open source software for exploring and manipulating networks. Third International AAAI Conference on Weblogs and Social Media (ICWSM 2009), San Jose, Ca. 2009. http://www.aaai.org/ocs/index.php/ICWSM/09/paper/view/154 and http://gephi.org.
Bentley, R. A., Lake, M., & Shennan, S. (2005). Specialisation and wealth inequality in a model of a clustered economic network. Journal of Archaeological Science, 32(9), 1346–1356.
Bloch, H. (1959). The Serapeum of Ostia and the brick-stamp of 123. New landmark in the history of Roman architecture. American Journal of Archaeology, 63, 225–240.
Boone, J., & Kessler, K. (1999). More status or more children? Social status, fertility reduction, and long-term fitness. Evolution and Human Behaviour, 20, 257–277.
Box, G., & Draper, N. (1987). Empirical model-building and response surfaces. New York: Wiley.
Brughmans, T. (2010). Connecting the dots: towards archaeological network analysis. Oxford Journal of Archaeology, 29(3), 277–303.
Brughmans, T. (2013a). Thinking through networks: a review of formal network methods in archaeology. Archaeological Method and Theory, 20, 623–662. doi:10.1007/s10816-012-9133-8.
Brughmans, T. (2013b). Review of I. Malkin 2011. A small Greek world. Networks in the Ancient Mediterranean. The Classical Review (New Series), 63(1), 146–148.
Brughmans, T., Keay, S., & Earl, G. P. (2014). Introducing exponential random graph models for visibility networks. Journal of Archaeological Science, 49, 442–454. doi:10.1016/j.jas.2014.05.027.
Christakis, N., & Fowler, M. (2009). Connected: the surprising power of our social networks and how they shape our lives. New York: Little, Brown, and Company.
Cilliers, P. (1998). Complexity and postmodernism: understanding complex systems. London: Routledge.
Coward, F. (2010). Small worlds, material culture and Near Eastern social networks. Proceedings of the British Academy, 158, 449–479. http://www.fcoward.co.uk/Cowardsmallworlds.pdf.
Dibble, C. (2006). Computational laboratories for spatial agent-based models. In L. Tesfatsion & K. Judd (Eds.), Handbook of Computational Economics, Vol. 2: Agent-Based Computational Economics (pp. 1511–1550). Amsterdam: Elsevier.
Drummond, A. (1989). Early Roman clientes. In A. Wallace-Hadrill (Ed.), Patronage in ancient society (pp. 89–116). London: Routledge.
Frier, B., & Kehoe, D. (2007). Law and economic institutions. In W. Scheidel, I. Morris, & R. Saller (Eds.), The Cambridge economic history of the Greco-Roman world (pp. 113–143). Cambridge: Cambridge University Press.
Garnsey, P., & Woolf, G. (1989). Patronage of the rural poor in the Roman world. In A. Wallace-Hadrill (Ed.), Patronage in ancient society (pp. 153–170). London: Routledge.
Gilbert, N., & Troitzsch, K. (2005). Simulation for the social scientist (2nd ed.). Milton Keynes: Open University Press.
Graham, S. (2005). Of lumberjacks and brick stamps: working with the Tiber as infrastructure. In A. MacMahon & J. Price (Eds.), Roman urban living (pp. 106–124). Oxford: Oxbow.
Graham, S. (2006a). Ex Figlinis: The Network Dynamics of the Tiber Valley Brick Industry in the Hinterland of Rome. BAR International Series 1468. Oxford: John Hedges.
Graham, S. (2006b). Networks, agent-based models and the Antonine itineraries: implications for Roman archaeology. Journal of Mediterranean Archaeology, 19(1), 45–64.
Graham, S. (2006c). Who’s in charge? Studying social networks in the roman brick industry in Central Italy. In C. Mattusch & A. Donohue (Eds.), Proceedings of the XVIth International Congress of Classical Archaeology (pp. 359–362). Oxford: Oxbow.
Graham, S. (2009a). The space between: The Geography of Social Networks in the Tiber Valley. In Coarelli, F. and H. Patterson (eds.) Mercator Placidissimus: the Tiber Valley in Antiquity. New research in the upper and middle river valley. Proceedings of the Conference held at the British School at Rome, 27-28 Feb. 2004. (pp.671-686) Rome: British School at Rome – Edizioni QVASAR.
Graham, S. (2009b). Behaviour space: Simulating Roman social life and civil violence. Digital Studies / Le Champ Numérique, 1(2). http://www.digitalstudies.org/ojs/index.php/digital_studies/article/view/172/214. Accessed 18 Sep 2013.
Graham, S., & Ruffini, G. (2007). Network analysis and Greco-Roman prosopography. In K.S.B. Keats-Rohan, (ed.) Prosopography Approaches and Applications. A Handbook. Occasional Publications of the Unit for Prosopographical Research (pp. 325–336). Oxford: Linacre College.
Graham, S., & Steiner, J. (2008). Travellersim: growing settlement structures and territories with agent-based modelling. In J. Clark & E. Hagemeister (Eds.), Digital discovery: exploring new frontiers in human heritage. CAA 2006. Computer Applications and Quantitative Methods in Archaeology. Proceedings of the 34th Conference, Fargo, United States, April 2006 (pp. 57–67). Budapest: Archaeolinga.
Grimm, V., Berger, U., Bastiansen, F., Eliassen, S., Ginot, V., Giske, J., Goss-Custard, J., Grand, T., Heinz, S. K., Huse, G., Huth, A., Jepsen, J. U., Jørgensen, C., Mooij, W. M., Müller, B., Pe'err, G., Piou, C., Railsback, S. F., Robbins, A. M., Robbins, M. M., Rossmanith, E., Rüger, N., Strand, E., Souissi, S., Stillman, R. A., Vabø, R., Visser, U., & DeAngelis, D. L. (2006). A standard protocol for describing individual-based and agent-based models. Ecological Modelling, 198(1-2), 115–126.
Helen, T. (1975). Organization of roman brick production in the first and second centuries A. D.: an interpretation of Roman Brick stamps. Helsinki: Suomalainen Tiedeakatemia.
Hirt, A. (2010). Imperial Mines and Quarries in the Roman World. Organizational Aspects 27 BC–AD 235. Oxford: Oxford University Press.
Holleran, C. (2010). The Roman Economy (P.F.) Bang The Roman Bazaar: a comparative study of trade and markets in a tributary empire. The Classical Review (New Series), 60(2), 529–531.
Horden, P., & Purcell, N. (2000). The corrupting sea: a study of Mediterranean history. Oxford: Blackwell.
Katsari, C. (2010). P. Bang, The Roman Bazaar: a comparative study of trade and markets in a tributary empire. The Journal of Romance Studies, 100, 260–261.
Kiiskinen, H. (2009). Review of: The Roman Bazaar: A Comparative Study of Trade and Markets in a Tributary Empire. Cambridge Classical Studies (51 2009). Bryn Mawr Classical Review 2009.06.51 http://bmcr.brynmawr.edu/2009/2009-06-51.html. Accessed 20 Nov 2013.
Knappett, C. (2011). An archaeology of interaction. Network perspectives on material culture and society. Oxford: Oxford University Press.
Kohler, T., Gumerman, G., & Reynolds, R. (2005). Simulating ancient societies. Scientific American, 293(1), 77–84.
Kowarik, K., Reschreiter, H., & Wurzer, G. (2012). Modelling Prehistoric Mining. In F. Breitenecker, I. Troch, (eds.) Mathmod Vienna 2012, full paper preprint volume. http://seth.asc.tuwien.ac.at/proc12/full_paper/Contribution468.pdf Accessed 18 Sep 2013.
Kuchar, J. (2011). Social network analysis plugin for Gephi. http://gephi.org/plugins/social-network-analysis/ Accessed 18 Sep 2013.
Lo Cascio, E. (2006). The role of the state in the Roman economy: making use of the New Institutional Economics. In P. Bang, M. Ikeguchi, & H. Ziche (Eds.), Ancient economies modern methodologies. Archaeology, comparative history, models and institutions (pp. 215–236). Bari: Edipuglia.
Macal, C., & North, M. (2010). Tutorial on agent-based modelling and simulation. Journal of Simulation, 4(3), 151–162.
Malkin, I. (2011). A Small Greek World: Networks in the Ancient Mediterranean. Greeks Overseas. Oxford: Oxford University Press.
Malkin, I., Constantakopoulou, C., & Panagopoulou, K. (2007). Preface: networks in the ancient Mediterranean. Mediterranean Historical Review, 22(1), 1–9.
Manning, J. (2010). Networks, hierarchies, and markets in the Ptolemaic economy. In J. Archibald, J. Davies, & V. Gabrielsen (Eds.), The economies of Hellenistic societies, third to first centuries BC (pp. 296–323). Oxford: Oxford University Press.
Manning, J., & Morris, I. (2005). The ancient economy: evidence and models. Stanford: Stanford University Press.
Meiggs, R. (1982). Trees and timber in the ancient Mediterranean world. Oxford: Clarendon.
Mitchell, M. (2009). Complexity: a guided tour. Oxford: Oxford University Press.
Morley, N. (2010). Peter Fibiger Bang. The Roman Bazaar: a comparative study of trade and markets in a tributary empire. The American Historical Review, 115(1), 267–268.
North, D. (1990). Institutions, institutional change and economic performance. Cambridge: Cambridge University Press.
Premo, L. S. (2006). Agent-based models as behavioral laboratories for evolutionary anthropological research. Arizona Anthropologist, 17, 91–113.
Ruffini, G. (2008). Social networks in byzantine Egypt. Cambridge: Cambridge University Press.
Ruffini, G. (2012). Irad Malkin. A small Greek World: networks in the ancient Mediterranean. The American Historical Review, 117(5), 1643–1644.
Scheidel, W. (2012). The Cambridge companion to the roman economy. Cambridge: Cambridge UP.
Scheidel, W., & Meeks, E. (2012). ORBIS The Stanford Geospatial Network Model of the Roman World. Stanford. http://orbis.stanford.edu Accessed 18 Sep 2013.
Setälä, P. (1977). Private Domini in Roman brick stamps of the empire: a historical and prosopographical study of landowners in the district of Rome. Helsinki: Suomalainen tiedeakatemia.
Shennan, S. (2002). Genes, memes and human history: Darwinian archaeology and cultural evolution. London: Thames and Hudson.
Silver, M. (2009). Historical otherness, the Roman bazaar, and primitivism: P.F. Bang on the Roman economy. Journal of Romance Archaeology, 22(2), 421–443.
Skydsgaard, J. (1976).The Disintegration of the Roman Labour Market and the Clientela Theory. Studia Romana in honorem Petri Krarup Septuagenari (pp. 44–48). Odense: Odense University Press.
Steinby, E. M. (1993).L’Organizzazione produttiva dei laterizi: un modello interpretativo per l’instrumen in genere? In W. Harris (Ed.), The inscribed economy : production and distribution in the Roman empire in the light of instrumentum domesticum : the proceedings of a conference held at the American Academy in Rome on 10-11 January, Journal of Roman Archaeology Supplementary Series 6 (pp. 139-144). Portsmouth, Rhode Island.
Tesfatsion, L. (2013). Growing Economies from the Bottom Up. Agent-Based Computational Economics (ACE) http://www2.econ.iastate.edu/tesfatsi/ace.htm Accessed 2 Sep 2013.
Verboven, K. (2002). The economy of friends. Economic aspects of Amicitia and Patronage in the Late Republic. Bruxelles: Latomus.
Wallace-Hadrill, A. (Ed.). (1989a). Patronage in ancient society. London: Routledge.
Wallace-Hadrill, A. (1989b). Patronage in Roman society: from Republic to Empire. In A. Wallace-Hadrill (Ed.), Patronage in ancient society (pp. 63–87). London: Routledge.
Watts, D. (1999). Small Worlds: The Dynamics of Networks between Order and Randomness. Princeton Studies in Complexity, Princeton: Princeton University Press.
Weingart, S. (2011) Demystifying Networks, Parts I & II. Journal of Digital Humanities 1.1. http://journalofdigitalhumanities.org/1-1/demystifying-networks-by-scott-weingart/ Accessed 20 Nov 2013.
Wilensky, U. (1998). NetLogo Wealth Distribution model http://ccl.northwestern.edu/netlogo/models/WealthDistribution. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
Wilensky, U. (1999) NetLogo. http://ccl.northwestern.edu/netlogo/ . Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.
Wilkinson, T. J., Gibson, M., Christiansen, J., Widell, M., Schloen, D., Kouchoukos, N., Woods, C., Sanders, J., Simunich, K.-L., Altaweel, M., Ur, J. A., Hritz, C., Lauinger, J., & Tenney, J. (2007). Modeling settlement systems in a dynamic environment: case studies from Mesopotamia. In T. Kohler & S. Van der Leuw (Eds.), The model-based archaeology of socionatural systems (pp. 175–208). Santa Fe: School for Advanced Research Press.
Acknowledgments
An early exploration of this model was presented at the Land and Natural Resources in the Roman World conference in Brussels, May 2011. A subsequent elaboration was presented at SAA2013 in Honolulu at the Connected Past session. We would like to thank Paul Erdkamp, Koen Verboven and Tom Brughmans for inviting us to participate in those conferences, and also the participants for their insight and criticism of these ideas. Thanks also to Fiona Coward, Anna Collar and Barbara Mills for their feedback and support for this special issue. Various drafts have been seen by various people at various stages, and we thank them for their comments and patience, especially Mark Lawall. We are especially grateful for the thoughtful and generous comments of the anonymous peer reviewers. Errors of logic or understanding are of course our own.
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Appendix
Appendix
The Model
This model description follows the ODD protocol developed by Grimm et al., (2006). The model may be downloaded at http://dx.doi.org/10.6084/m9.figshare.92953. Open with Netlogo 5. It is an elaboration of Wilensky’s Wealth Distribution model (1998), built using the Netlogo platform (Wilensky 1999).
Purpose
The purpose of this model is to explore network formation under the conditions described by Bang’s formulation of what he calls ‘the Roman Bazaar’. It focuses on the emergence of networks generated by Roman patronage (as understood in Bang’s model) under different economic conditions (concerning natural resources).
State Variables and Scales
In this simplified world, there is one kind of resource available for extraction and consumption at a time (forest, coppiced woodland, mines and clay). Each individual agent represents the head of a single family who exploits this world. Each agent has a ‘metabolism’, the maximum value of which is set by the user. Every agent will have a random metabolism up to that maximum. This metabolism is a value indicating how much of the resource is consumed at each time step. The other variable is ‘vision’, and it is set the same way. Thus, the population as a whole has normally distributed values for these two variables, but the particular combination for a particular agent is distinct from every other agent. These two variables represent in a larger sense the agent’s ability to move in the world—its transport economics, if you will—and the agent’s ability to know about the world, to find other agents who can help it, or to find other resources. Similarly, a random life span is set between a globally determined minimum and maximum.
Each patch in the world has a chance of holding a certain amount of whatever resource is being simulated. Each resource regenerates after a set amount of time (forest; coppiced woodland). Mines and clay pits do not regenerate. Each patch in the world can hold a maximum amount of resource, and a certain amount is allowed to regenerate on each tick. The combination of these four variables (growth interval; amount grown; maximum allowed; percent best land) is preset to represent the four kinds of resource.
Forest takes twice as long as coppiced wood to regenerate. Coppiced wood is more productive (and has more uses) than forest wood. Both wild and coppiced wood cover the same density of patches, with the highest concentrations occurring on 4 % of patches (and surrounding patches containing diffused amounts).
Mines hold an order of magnitude more resources than clay pits, but mines are set to be very rare (1 % of the patches) while clay pits are somewhat more common (3 %). These resources do not diffuse but are constrained to a single patch.
Finally, each patch keeps track of how often it has been ‘harvested’, allowing for exhaustion or depletion of the resource and thus taking it out of play.
Process Overview and Scheduling
Resource Growth
Each patch checks to see how much resource is allowed and examines how much it currently contains. If it is less than the maximum, it regenerates the allowed amount to grow.
Harvest
Each agent examines its local neighbourhood and heads towards the local maximum amount of the resource (if the patch is exhausted, it moves on). If the amount of resource is above the mean for the world, the agent notes the number of other agents on the patch, and they divide the resource between them. If the amount is less than the mean for the world, the agent examines whether or not it is embedded in social networks. If it is embedded, it will not harvest, but rather rely on help from its social network to obtain resource. If it is not embedded, it will go ahead and harvest anyway.
Move-Eat-Age-Die
Each agent consumes some of its resource that it is holding, and ages +1. If an agent has less resources than its metabolism value, or if its age has now reached beyond its life span, the agent ‘dies’ and a new agent takes its place, thus, representing a generational change-over.
The agent, however, is aware that it may be in peril. If the agent has now consumed all of its resources, it may ask for help (and thus stave off ‘death’).
Patronage (Ask-For-Help)
When an agent asks for help, it examines its local neighbourhood (within its range of vision, that is knowledge-of-the-world) for a possible patron. A possible patron is one whose prestige is equal to or greater than its own (initially, all agents have the same prestige value). If a potential patron can be found, and the potential patron accepts the other agent as client (determined by a roll of the die), then the patron gives the client some of its resource. This gift increases the patron’s prestige and puts the client in its debt.
Set-Initial-Variables
Should an agent be unable to find help, or its age exceeds its life span, the agent ‘regenerates’. Its generation is set +1, and its metabolism is reset randomly. Some of the prestige of the previous generation carries onwards. Since vision can be thought of as representing an agent’s knowledge of the world, there is an ‘educational’ function in that the richer agents are able to impart a greater degree of their knowledge to succeeding generations. The poorest have their vision set at random within the limits of the user-set maximum vision.
Euergetism
Patrons invest in their local area. Patrons who are in the top half of the population by prestige build ‘super-improvements’ which magnify the resource by 50 %. All other patrons improve the productivity by 10 %.
Games of Patronage (Compete, Patron-Compete, Calculate-Clients-Worth, Extract-Wealth-From-Clients)
At the end of each cycle, the agents compare their resource amount both locally and globally. They set their colour to reflect their local status into top, middle and bottom thirds. They do the same comparison at the global level. Each patron (an agent with at least two other agents in its debt) selects another patron to compete against; the decision is made based on colour, i.e. wealth (thus, local elites compete against other local elites; the middling sort compete against the middling sort). Elites compare both the quality and number of their followers against each other. A patron with a few wealthy clients might beat a patron with several poor ones. Winning the game increases prestige; losing reduces prestige. The winner then calls on its clients to support it through gifts of resources.
Exhaustion (Grow-Settlement)
Every 25 cycles, the patches examine how many times they’ve been harvested, and if they are in the top 1 %, they become ‘exhausted’ and can no longer be harvested.
Design Concepts
Emergence
The simulation is allowed to run until the population as a whole has reached an average of 50 generations. How quickly that end state is reached depends on not just the resource being modelled but also on the interplay between the average movement costs (metabolism) in the world and the average ability of the agents to know the world (vision).
As we sweep through the various combinations of the two variables, there are three distinct peaks and troughs in terms of social stability (that is long-lived generations and thus the amount of resource they have in any given moment (whether obtained through direct harvest or through gift giving) is sufficient to keep them going.
The rate with which social networks emerge also depends on the resource being extracted, with forest growing linearly, while coppiced woodland and clay grow almost exponentially very quickly and then plateau for the duration, and mines show an initial linear growth and then slowly plateau.
The tripartite breakdown of ‘wealth’ in the model is different when measured locally versus globally. While, locally, there can be a great deal of equality (measured as each agent reports its own wealth in comparison to those in its range of vision), when every agent is compared against every other, different structures emerge. These are dependent not just on the resource and its distribution in the world but also on the interplay of metabolism and vision.
Adaptation
Individuals will move to a new site with greater resources than the one where they are currently located. Individual patrons can improve a location and distort the ‘natural’ patterns of resource growth.
Sensing
Agents know how much resource is available anywhere within their range of vision. They know the relative wealth of others within their vision. They know also the relative prestige of others within their vision. Patches know how many times they’ve been harvested and whether or not they are still productive.
Interaction
Agents interact when they are in danger of using up all of their resources; patrons require support from their clients when the patron is competing for prestige against other patrons. Agents also act indirectly through the competition for resources at a particular location and the carrying capacity of that location.
Stochasticity
All processes are modelled as probabilities.
Collectives
Each agent, at the end of the model run, reports its patrons and its clients. These can then be knit together into a social network, whose characteristics can be explored statistically. Patrons call on their clients for support at certain times, drawing on the entire wealth of the group (and thus slowing down the patron’s generational turnover.) Individuals who are not part of a group exhibit selfish behaviour when harvesting, as they will not leave resource for others if the resource is in danger of being depleted.
Initialization
The world is torus-shaped. The environment is set to represent one of the four resources. Agents are distributed randomly across the world. Each agent is given a random life span within the minimum and maximum amounts. Each agent is given a random metabolism within the maximum amount. Vision is similarly set. Each agent is initially given a random amount of resources around the maximum metabolism (so that they survive longer than the initial model cycle). Prestige and generation are set to 1.
Output
At the end of the model run, each agent writes its patrons and clients into a single file for network analysis. The network analysis is performed using the Gephi network analysis programme.
Data on the state of the model at each time step is written to a spreadsheet, counting the number of agents who are patrons, clients, their degree of prestige and their classification into high-middle-low status both locally and globally.
During the run itself, a Gini index of inequality and Lorenz Curve are calculated and displayed (a legacy of the original Wealth Distribution model).
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Graham, S., Weingart, S. The Equifinality of Archaeological Networks: an Agent-Based Exploratory Lab Approach. J Archaeol Method Theory 22, 248–274 (2015). https://doi.org/10.1007/s10816-014-9230-y
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DOI: https://doi.org/10.1007/s10816-014-9230-y