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Dossier: Analyse des réseaux sociaux en archéologie

New approaches to Archaic Greek settlement structure

Raymond J. Rivers et Timothy S. Evans
p. 21-27

Résumés

Les développements récents dans la théorie des réseaux ont amené la création de nouveaux modèles pour décrire les interactions spatiales et sociales et réexaminer les modèles existants. Bien qu’ils aient été conçus pour l’étude de la société contemporaine, les archéologues les utilisent de plus en plus pour interpréter les données archéologiques. Il s’ensuit la possibilité, avec un si grand assortiment de modèles, d’en trouver un pour justifier ce que l’on veut, si on s’en donne la peine. Dans cet article, nous abordons ce problème à travers un exemple sur le début de la centralisation des cités-états du continent grec au cours des ixe et viiie siècles av. J.-C. En 1987, Rihll et Wilson ont réalisé un travail pionnier sur la structure du peuplement, en appliquant un modèle de planification urbaine, utilisé à l’origine pour expliquer l’urbanisme du xxe siècle. Nous éclairons les problèmes de modélisation des données archéologiques en opposant ce modèle à un autre plus récent intitulé ariadne, un modèle de coût-bénéfice que nous avons développé, et d’autres modèles plus simples. Nous examinons surtout ce qui génère la robustesse des modèles et la manière dont ils incorporent l’éventualité quand ils décrivent des périodes de changement rapide, deux impératifs pour qui cherche à produire des résultats solides et fiables.

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We thank Prof. Carl Knappett of the University of Toronto for helpful discussions.

Prologue

1Recent developments in network theory have led to the creation of new Spatial Interaction Models (SIMs) and a reappraisal of existing models. Although not directed at the archaeology community, these models generalise the familiar gravitational models and Proximal Point Analysis (PPA) used by archaeologists for many years to help explain the archaeological record. However, a problem arises in archaeology that, with the increasing suite of plausible models that now exist, it is unclear how to choose one model over another. This can lead to the criticism that, if we hunt hard enough, we may be doing no more than finding a model which can be manipulated to conform to our preconceptions.

2In recent articles we have begun to address this criticism (Evans 2014, in press) with particular reference to the maritime networks of the MBA Aegean (Rivers 2014, in press). Different historical periods require different approaches and in this paper we continue this analysis by re-examining the onset of centralisation in mainland Greek city states of the 9th and 8th centuries BCE. Pioneering work on this settlement structure was performed in 1987 by Rihll and Wilson (Rihll & Wilson 1987, 1991), adapting a ‘retail’ model devised originally for urban planning. One alternative approach is given by a recent cost-benefit model termed ariadne, developed by ourselves (Evans et al. 2009; Knappett et al. 2008, 2011), initially designed for Bronze Age maritime networks. A comparison of these models and other simpler SIMs for archaic settlements highlights the problems of modelling archaeological data. In particular, we examine what constitutes model ‘robustness’ and the way in which different models handle ‘contingency’ when describing periods of rapid change.

Modelling archaeology

3We begin more generally. A prerequisite for describing ancient societies is an understanding of ‘exchange’. Much of archaeological practice is concerned with describing ‘exchange’, how ‘stuff’, whether artefacts, people or ideas, moves around. An understanding of exchange is also crucial for a description of contemporary society and the last half century has seen a huge body of work on transport models (e.g. Ortuzar & Willumsen 1994: 139-206), urban planning (Wilson 1970, 2010), economics (e.g. Piermartini & Teh 2005) and more general social network analysis. Although devised for today’s different societies they all describe exchange and there is much that can be usefully adapted to earlier historic processes.

4In general, the archaeology community has been slow to pursue these parallels, partly for reasons of technology and partly for reasons of ideology, although there was always a strain of quantitative spatial modelling in archaeological theory. Early techniques for geometrising social relations through zones of influence based on Dirichlet/Voronoi tessellations of space evolved into further spatial approaches such as Renfrew’s Xtent model (Renfrew 1975: 71-90; Renfrew & Level 1979: 145-167). Similarly, the equally simple geometric modelling of PPA, adopted both by archaeologists (e.g. Terrell 1977, 1986) and anthropologists (e.g. Hage & Harary 1991) replaced the ‘push’ of zones of influence with the ‘pulls’ of links, incorporating the network (graph theory) techniques of the social geographers (e.g. Haggett & Chorley 1969).

5The work on ancient city states that concerns us here was built upon the network-based SIMs of the urban planners, in particular of Wilson himself e.g. see Wilson (1970: 1-165). In its detail the Rihll and Wilson model was the exception to the rule in a period in which a post-processual critique had lead to a shift in emphasis in archaeology from ‘space to place’ (Hirsch 1995). In characterising social interactions there were deeper issues about the reductive nature of quantitative modelling which caused a shying away from mathematical analysis (e.g. Sheppard 2001). See Orton (2004) for a succinct summary of archaeological model-making until the turn of the century.

6However, the onset of cheap computing and the arrival of user-friendly packages for modelling and analysis have led to a revival in quantitative methods, network modelling in particular. Lock & Pouncett (2007) provide an overview and two recent edited volumes give the state of the art (Bevan & Lake 2013; Knappett 2013). The class of SIMs is very large (Evans et al. 2012 ; Evans 2014). At the most simple level it accommodates the models most familiar to archaeologists, the Simple Gravity Model (SGM) and PPA. With increasing sophistication it includes constrained gravity models (e.g. Wilson 1970, 2010; Ortuzar & Willumsen 1994; Barthelemy 2011), which include the Wilson ‘retail’ model. In fact, these are all examples of Alonso models (Alonso 1964), for which we can consider the SGM as the null model. In a different direction the class includes the intervening opportunity models of Stouffer (1940) and Schneider (1959), for which the null model is PPA. In a yet further direction SIMs accommodate ‘cost-benefit’ models such as ours (Evans et al. 2009), which we shall describe later.

7Networks, to which we restrict ourselves, comprise nodes (sites) and links (exchange between sites). Archaeology can be very site-centred and archaeological site data is very rich and multilayered, relating to populations, resources and social organisation, etc. On the other hand the data for describing exchange is relatively impoverished, largely comprising site artefacts, particularly pottery, which have to serve simultaneously as a proxy for trade, innovation and the mobility of people. When we take into account the inevitable incompleteness of the data, with sites missing or only partially excavated, we realise that we cannot ask the same quantitative questions that we would of contemporary society.

8This leads to a problem. If we think of choosing a SIM as akin to choosing a piece of electronic equipment, a ‘black box’ with input settings and dials, but no labels beyond its name, how do we know that it is a good choice for the Iron Age Greek city states of this paper? This approach, of shopping for models which posit ‘universal’ behaviour across different historical periods and different technologies, seems to be taking us back to the world systems approach, from which archaeology extricated itself by emphasising known cultural specificity.

9In fact, specificity makes itself apparent very readily. We have seen elsewhere in a study of the MBA Aegean that the shift in maritime technology from oar to sail requires network modelling that is very sensitive to geography, with the network burgeoning at that moment when maritime technology matches the distances required for the network to form (Rivers 2014, in press). This eliminates more epistemic SIMs, which downplay geography, in favour of stochastic optimal choice models. We shall argue that a similar, but contrary, specificity arises here.

The emergence of the city state in ancient Greece: Generics

10Let us turn to the modelling of Greek city states of the 9th and 8th centuries BCE discussed by Rihll and Wilson in 1978 in their seminal paper (henceforth termed R&W), updated by Wilson in 2012 (Wilson 2012). The 109 sites of their dataset are shown on Fig. 1 and given in Evans 2013. See the original paper for site names, omitted here for clarity. Since the appearance of the original paper we realise that some, like Argive Heraion (98) and Nemea (87), are sanctuaries rather than settlements and some, like Lefkandi (41) and Zygouries (90), date from other periods. For the purpose of exploring robustness this is irrelevant and we stay with the original R&W set, with the slight proviso that site 64, not numbered in Fig. 1 of R&W, was inadvertently omitted from our analysis (but to no consequence). The aim is to model the onset of ‘urbanisation’, by which is meant the emergence of dominant settlements within community territories as a result of a transference of ‘sovereignty’ from villages to create larger associations centred upon these dominant settlements.

11Models either use relative distance between sites (e.g. the nearest neighbour, next to nearest neighbour, etc. of PPA) or, for the models of interest to us here, ease of travel between sites, which as in the original R&W model we characterise by geographical separation, ignoring topography and landscape. The first observation for the sites of Figure 1 is that site separation is small. The average distance from one site to its nearest neighbour is 5km. The largest distance between any two sites is about 150km (sites 42 to 93) while the average distance between any one site and all the others lies between 45km and 85km. These distances are small, two to three days travel by foot. With distance important, a key input is the ‘ease of travel function’ or, more commonly, the ‘deterrence function’ f(r/D) which measures the ability of an individual to travel a distance r in a single journey. It depends on a characteristic distance D which sets the scale for individual journeys. We shall discuss specific choices later.

Fig. 1

Fig. 1

The 108 archaic settlements based on figure 1 of R&W and using the same labels. Site 64 was accidently omitted from our analysis (without changing our conclusions). The regions A to H are those in which urbanisation occurs in the R&W analysis with either one or both choices of deterrence function that we describe in the text. Site 25 is Thebes, which only assumes importance with an exponential deterrence function. See the text and Evans 2013 for details and explicit data.

12We also need to quantify ‘exchange’. We label sites by Roman letters i, j,.. which can take values from 1 to 109, (except for 64), the labels chosen by R&W. As with R&W, we flatten exchange between site i and site j to the single variable Tij. Relative values are important; larger T means larger exchange, smaller T smaller exchange, but the absolute values are meaningless. From this pattern of Tijs we can extract many site attributes (Newman 2010: 168-234), centrality and betweenness in particular. However, given the relatively local nature of ‘urbanisation’ we shall eschew these for the simpler site ‘in-strengths’ at sites j, the flows

13 Ij = Σi Tij (1)

14In the context of R&W Ijis a measure of the ‘attractiveness’ of site j. This has the merit that, in a situation in which a few sites dominate, the other sites have little or no in-strength, whereas other ranking schemes are more gently graded.

15Before attempting our specific models there are still some general issues to be explored. In particular, we see this centralisation of power in the Archaic city states as a dynamical process and we would like our models to reflect the temporal evolution from the relatively homogeneous distribution of sites in Figure 1 to a configuration with a few ‘hubs’ which describes how sites concede their individual status to local centres of influence.

16The two main models discussed here are the R&W model itself and the ariadne model of our earlier papers. Taking the models in turn, the R&W model introduces a variable parameter which modifies the ‘attractiveness’ of a site with regard to its neighbours. With site out-strengths fixed and equal, the attractive sites which can become hubs are those for which the in-strengths are large. The equilibrium solution can be construed in several ways, but it is most simple to think of it as the solution that maximises the Shannon entropy of the network,

17 S = Σij Tij(lnTij – 1) (2)

18(or, equivalently, minimises the ‘Hamiltonian’ H = - S) subject to appropriate constraints, in particular that

19 X = Σj Ij(ln Ij – 1) (3)

20be fixed. The ‘attractiveness’ is the Lagrange multiplier to this constraint. [The other Lagrange multiplier is associated with the ‘cost’ of sustaining the network, which can be transmuted into the distance scale D for single journeys, once the deterrence function is chosen.] That is, we have a two-parameter set of solutions: D and ‘attractiveness’. In the original R&W paper, these are effectively β (where D = β-1)and α respectively. If we do not impose the constraint (3) we recover the SGM (e.g. see Jensen-Butler 1972). Since entropy can be understood in terms of the information required for a complete description of the network, this systemic approach can also be construed as one that makes the best of our limited knowledge of the constrained system.

21The equilibrium network is the solution to non-linear equations, which are most simply solved iteratively. The relaxation time (or machine-time for the simulations) should be distinguished from chronological time, the historic time (in years) over which the city state network evolves and which is used to parameterise the variable attractiveness of the model. This two-time modelling, with independent machine time and real time, is well understood in stochastic physics (Rivers 1987: 145-58). As for the reasons why the physical parameters vary in time, this is a result of social pressures or external forces, which need to be displayed if possible.

22Our second model is ariadne, a cost-benefit model that we developed (Evans et al. 2009) for the maritime networks of the MBA Aegean. In its simplest form that we present here the benefits arise from exchange between sites, for which we assume homophily, larger sites getting most benefit from exchanging with larger sites. [See Jackson 2008: 77-184 for similar models.] These non-linear benefits are offset against the cost of sustaining the network, assumed linear in the total network activity. Specifically, we minimise the ‘Hamiltonian’

23 H = -E + µC (4)

24where E and C (both positive) correspond to the exchange and resource benefits and network ‘costs’ respectively, of the form

25 E = Σij Tij νj f(dij /D); C = Σij Tij(5)

26In (5) the νi, which scale the Tij, are proxies for the populations at sites i. Like R&W, in the first instance we take the distances between sites labelled i and j to be the map distances. Minimising H determines the νi as well as the exchanges Tij. The coefficient µ measures the relative importance of these terms. In particular increasing µ diminishes overall activity, while reducing it increases activity.

27The temporal evolution of urban hub formation is due to the explicit temporal variation in the model parameters which measure the importance of exchange and local resource exploitation, dependent on the overall activity level that we deem appropriate.

More generics: Contingency and robustness

28What can we expect? With the R&W model and ariadne both 2-parameter models it is clear that we can only provide a very broad-brush description of the behaviour of 109 sites. Even worse, our null PPA and SGM have only one parameter, the number of nearest neighbours with whom to interact, a Dunbar number for settlement-settlement interactions (Dunbar 1992), or the distance scale D respectively. Indeed, there is no way that a detailed comparison to data could be made if such data existed. In fact, it is the converse situation. Our goal is only to identify suitable sites to become hubs or terminals within the resultant settlement networks and to compare these to the known centres of influence from the archaeological record as it stands. R&W put it well, in that we use our general expectations of the settlement network prior to urbanisation to calibrate the model, and then use finer detail to describe the emergence of central sites.

29Both the R&W model and ariadne are optimisation models, minimising the model’s Hamiltonian, but they do this in different ways. We have already seen that, for a given set of initial conditions, the R&W model progresses to a single solution. On the other hand the ariadne model, while looking for the optimal network, is willing to accept networks that are ‘good enough’. This ‘satisficing’ strategy (Simon 1957), also known as ‘bounded rationality’ means that ariadne outputs have to be interpreted in a (Bayesian) statistical sense. Specifically, is interpreted as a ‘social potential’ (Butts 2007) which defines a network ‘landscape’. Each point in this landscape is a network whose elevation is the numerical value of H. Our aim is to find the lowest point we can in this landscape and identify its network. The Monte Carlo Metropolis algorithm which we adopt can be thought of as throwing a ‘ball’ into the landscape and shaking the landscape many times until we can get the ball to roll no further downhill. With more than 100 sites this landscape has more than 10,000 dimensions and not all valleys lead to the unique site of lowest elevation. However, as long as we shake sufficiently hard the lowest that the ball goes is acceptable, and we read off the network corresponding to its position of rest. We appreciate that throwing the ball in again and shaking will, in general, give a different network.

30If we compare different sequences leading to equally acceptable final networks, the divergences of the sequences can be thought of as a result of different choices of comparable merit having been made. A priori, this contingency built into ariadne is a reflection of real life decision making and a virtue of the model. Whether we get useful results or not depends on the nature of our ‘landscape’. If it is one of ‘Swiss valleys’ in which there are only a limited number of channels that the ball can follow, we shall get roughly consistent results from which we can draw sensible conclusions. If, on the other hand, our ‘landscape’ is more that of the ‘American mid-west’, largely flat and featureless, we shall find it very difficult to draw conclusions, since there are no penalties (of having to climb over hills) in moving from network to network on it. A certain level of insensitivity to contingency is a necessary robustness that we ask of our model.

31Although the R&W model and PPA and gravity models evade this particular statistical uncertainty by fiat all face ambiguity of another kind. All but PPA require a choice of the deterrence function f(x) (and PPA requires the number of interacting neighbours). There are two extreme idealisations of f(r/D). The first, adopted in R&W, assumes exponential falloff with r/D, f(x) = exp (-x). In transport modelling this corresponds to journeys having a ‘cost’ proportional to distance. The other extreme is to make all journeys of distance r < D equally easy to accomplish, but to forbid all journeys of distance r > D in a single stage i.e. f(x) = 1 for 0 < x < 1, zero otherwise. We would argue that the latter is closer to how walkers behave, and we assume that walking is the most common means for implementing ‘exchange’ between these communities, given the relatively short distances involved. In practice, we take a smoothed-off version of this, a compromise allowing some latitude for journeys with r > D,

32 f(x) = 1/(1 + x4) (6)

33We note that the x-4 falloff in (6)is much stronger than the x-2 falloff of the conventional gravity model (Wilson 2007; Lambiotte et al. 2008) but less than the exponential falloff of R&W.

34If our models are to be taken seriously we would not want the results to depend sensitively on the form of f(x). This additional component of robustness complements the robustness due to the limited nature of contingency that we discussed earlier.

The emergence of the city state in ancient Greece: Specifics

35The R&W model, with its imposition of fixed site outflows, puts its emphasis on ranking neighbours rather than their geographical position, whereas ariadne puts geographical position first. Before going into these more sophisticated models it is useful to see to what extent geography and proximity might be all we need by briefly considering our null models, Directed PPA (DPPA) and a Simple Gravity Model (SGM) (see Evans 2014).

36In the DPPA we connect each site to its k nearest neighbours and these (unweighted) directional links determine the site in-strengths. As in the original R&W paper, in the first instance the sites essentially split into three regions. On varying k from 3 to 6 we find that the appearance of dominant centres occurs in the regions labelled A to H in Figure 1. What follows should be taken with circumspection since changes in k give rise to a reshuffling of site ranking and we identify just the gross features. Site ranking by DPPA in-strength has a long tail but within Attica Athens (E, 70) is always significant, as are Meranda (F, 58) and Kalyvia (F, 59). [The first label in the bracket is the region, the second the site number in Fig. 1.] In the land neck Korinth (G, 82), Kromnia (G, 78) and Lekhaion (G, 80) are dominant and further south Mykenai (H, 95) and Prosymna (H, 97) lead. In the north Haliartos (C, 19) and Askra (C, 20) are important, as is Itonion (D, 21).

37For the SGM it is more difficult to identify key sites since the tail is much longer and the dominant sites less dominant. Roughly, the sites in G are the key sites for that area, as are the sites in A for the north-east. In addition Akraiphnion (B, 7) and Argos (H, 101) become important (at D 8km). In particular, for neither model did we manage to promote Thebes to be a significant centre! Nonetheless, we see that geography and proximity obviously play a significant role in determining which sites are important. However, from the very long tails present in the rankings it is clear that neither of these models is describing urbanisation in which the emergence of just a few dominant sites from a large number of roughly homogeneous settlements (i.e. very short tails) can be understood as a transition between one type of settlement structure and another (Wilson & Dearden 2011).

38As it stands the R&W model is very successful. In identifying Hyria (A, 13) or Khalkis (A, 40), Akraiphnion (B, 7), Medeon (C, 17), Koroneia (D, 23), Thebes (25) as the key northern urbanisation centres it reflects the archaeological record well. [Sites are labelled alphabetically.] This is also true for Attica where the dominant centres are Athens (E, 70), Kalyvia (F, 59) and perhaps Meranda (F, 58) and for the Southwest where the dominant sites are Korinth (G, 82) and Kromnia (G, 78), Argive Heraion (H, 98) and Argos (H, 101). See Rihll & Wilson (1987) for details.

39In fact, this agreement with the record looks too good to be true and it is important to see how robust these conclusions are. As we shall now show, they are not as robust as we would hope, with details sensitive to the choice of the deterrence function f(x). The R&W paper uses f(x) = exp(-x) and we compare their simulations to identical calculations using f(x) of (6), over a wide range of values of D and varying attractiveness, spanning the values of the original R&W paper and beyond. It is not straightforward to summarise the effect of changing the deterrence function but essentially, while the generic behaviour remains the same, the differences are significant. Yet again we find the appearance of dominant centres in the regions labelled A to H in Figure 1. However, the choice of site within the regions is often different. The dominant northern centres are now more typically (in alphabetical order by region) Aulis (A, 14), Ay. Marina (B, 4) or Akraiphnion (B, 7) (typically the former), Medeon (C, 17) or Onchestos (C, 18), and Alalkomenai (D, 22). Yet again, in no case did Thebes arise as a significant centre or, in many cases, even a visible presence! In Attica the situation is better where we again find Athens (E, 70), Meranda (F, 58) and Kalyvia (F, 59) to be the dominant settlements (showing that our omission of site 64 had no effect). The situation was more mixed in the Southwest where the dominant centres are more typically Argos (H, 101) and/or Mykenai (H, 95) and/or not, both Kromnia (G, 78) and Lekhaion (G, 80). In no case did Korinth itself become a centre although G was a dominant region.

40In summary, taking the R&W model as it stands, the authors were surprisingly successful with their choice of deterrence function. Our choice, which to us seems equally or more likely, leads to results less in accord with the archaeological record. Although it does not change the general positions of the emergent urban systems, it often gets the positions of the dominant sites within them wrong. Nonetheless, despite that the model remains a qualified success since, with two parameters it could hardly be expected to provide a close fit to a process that it characterises well qualitatively. It could be that the situation is improved (e.g. Thebes becomes significant) on taking topography into account (Wilson 2012) but that was not the point of the exercise, which was to look for robustness within the simplified model of R&W which ignored topography.

41However, if the robustness of the R&W model leaves something to be desired, the contingency arising from our adoption of bounded rationality in ariadne is so great as to make it ariadne a totally ineffectual model to describe the emergence of centres. This contingency is a consequence of large fluctuations in the vicinity of transitional behaviour, common to many systems in the presence of rapid change. Interpreting the Tij as a discrete ‘field’ the R&W model is a deterministic theory which ignores the problem by averaging out the effect of fluctuations (see Leung & Yan 1997) whereas ariadne demands that we examine their effects. In the language of our earlier simile, do we have a Hamiltonian ‘landscape’ that is heavily valleyed in which these fluctuations are channelled, or one that is largely featureless? Unfortunately, it turns out to be the latter.

42To be specific, we take f(x) of (6) in (4). As µ increases we see the anticipated site coalescence into increasingly few local centres in this transitional regime. However, re-running the simulation for identical initial conditions gives dramatically different outcomes for consecutive runs as we show in Table 1 below in which we have given two examples. We could have given many more with the same effect. Such fluctuations totally swamp any ambiguity over the choice of deterrence function.

Table 1

Run number

Dominant centres listed numerically

1

     22 25 26  32 38    41            81 83      106

2

 18   24     27       40 41 49      77    89    98

3

                     54 55  70 71        

Run number

Dominant centres listed numerically

1

 07    12   20 25         70 77  83 89    98

2

 06 08       27 28  58  69             96 97   106

3

 04    12 17      57  60 68  71 77       97

The upper table describes three consecutive runs of ariadne for the Hamiltonian (4) and (5) for µ =2.5 and D = 6. The lower table describes three consecutive runs for µ = 2.5 and D = 8. In each case the dominant centres are listed numerically. In the third run of the upper table only sites in Attica survived.

43There is another reason why ariadne fails for these sites. This is because of their relative homogeneity and because of their small separation in comparison to the distance scales we adopt (we have taken 5 D 30). This means that it is not difficult to find another site at comparable separation to switch to without incurring any penalties. This is equally true of the more general ariadne model of Evans et al. 2009, with additional resource benefits and population costs.

Conclusions

44We have used the example of the urbanisation of archaic Greek settlements as the basis for an improved understanding of the role of robustness and contingence in dynamical networks. Such periods of rapid change take us from one phase of social organisation to another and require explanation through models which can accommodate such transitions. For models to be robust outcomes must not be sensitive to details of the model which we have to make, but for which we have no compelling choice. We have found the R&W model to be tolerably robust to the choice of deterrence function, showing how dominant sites arise, but with sufficient latitude as to which they may be to make a detailed comparison to the archaeological record problematic. Of course, we could try to use the archaeological data (with its flaws) to determine the deterrence function, but we lose any postdictive power unless we find comparable data to test with this function, the existing set not being large enough to split.

45The R&W model averages over the fluctuations that we would interpret as contingency within the bounded rationality of our ariadne model. For the level of contingency to be acceptable, fluctuations must be controlled. We are not saying that fluctuations in the two models are identical but when fluctuations are large, as happens with ariadne here, averaging is unhelpful (e.g. think of averaging Tables 1). The outcome is that we can draw no conclusions whatsoever from ariadne in this geopolitical context, unlike for the MBA Aegean, where the distance of travel to permit a thriving network just matches that of the sailing technology of the time (Rivers et al. 2013 ; Rivers 2014, in press).

46The implications for dynamical network modelling are mixed. Firstly, we need to be careful when modelling rapid change lest the fluctuations be too large. Secondly, if site separation is small in comparison to manageable travel distances and there are many sites to choose between we anticipate both large fluctuations and sensitivity to model morphology with corresponding lack of robustness. We stress that we are not discussing ‘black swan’ events (Taleb 2010: 305-437), like the eruption of Thera, to which ariadne has been applied successfully (Knappett et al. 2011) since that is a change in boundary conditions rather than model parameters.

47For these reasons our next test of these models will be for the maritime networks of the LBA E. Mediterranean where sites are inhomogeneous and distances large.

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Table des illustrations

Titre Fig. 1
Légende The 108 archaic settlements based on figure 1 of R&W and using the same labels. Site 64 was accidently omitted from our analysis (without changing our conclusions). The regions A to H are those in which urbanisation occurs in the R&W analysis with either one or both choices of deterrence function that we describe in the text. Site 25 is Thebes, which only assumes importance with an exponential deterrence function. See the text and Evans 2013 for details and explicit data.
URL http://nda.revues.org/docannexe/image/2316/img-1.jpg
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Raymond J. Rivers et Timothy S. Evans, « New approaches to Archaic Greek settlement structure », Les nouvelles de l'archéologie, 135 | 2014, 21-27.

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Raymond J. Rivers et Timothy S. Evans, « New approaches to Archaic Greek settlement structure », Les nouvelles de l'archéologie [En ligne], 135 | 2014, mis en ligne le 01 janvier 2016, consulté le 24 juillet 2017. URL : http://nda.revues.org/2316 ; DOI : 10.4000/nda.2316

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Auteurs

Raymond J. Rivers

Department of Physics, Imperial College London (Grande-Bretagne),
R.Rivers@imperial.ac.uk

Timothy S. Evans

Department of Physics, Imperial College London (Grande-Bretagne),
T.Evans@imperial.ac.uk)

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