Geographic interconnections

In this blog post we continue our quest to develop a method for studying trade routes as they are reflected in the ceramic evidence. It provides an alternative and in some ways parallel to our previous post concerning Beta-skeletons.

A computerised model was developed by Rihll and Wilson (1991) to study the interconnections between sites based solely on their geographical coordinates, while taking size, importance and interactions between sites into account. The only thing one needs to enter into the model are the locations of all sites. Other factors are simulated and develop when running the model thanks to three assumptions:

• Interaction between any two places is proportional to the size of the origin zone and the importance and distance from the origin zone of all other sites in the survey area, which compete as destination zones.
• The importance of a place is proportional to the interaction it attracts from other places.
• The size of a place is proportional to its importance.

Through a number of simulations starting from an initially egalitarian state (equal size and importance for all sites), the most likely pattern of interconnections between sites is determined.

Shawn Graham successfully used this model in his analysis of the brick industry in the Tiber valley. Networks of interconnections between sites in the Tiber valley were created to “explore the effects of geography, stripped of all other considerations” (Graham 2006b: 77; Graham 2009: 678-681).

As the Relative Neighbourhood Graph (RNG) this method uses straight line distances, which will allow us to study the influence of distance in the distribution of table wares. However, as it is a probabilistic model its potential for testing hypotheses is far greater.

We could use this method to create a network of all sites included in the distribution patterns of table wares. The network can be analysed to determine the relative positions of all sites, knowing that distance is a significant factor and taking size and importance into account, but most importantly, exactly knowing the value of all these factors for a given result.

We should stress that the simulated importance represents the importance of a site in the table ware trade, given that distance is a significant factor (this might require a revision of the mathematics underlying the model). Instead of running an egalitarian simulation, we can therefore enter the values for importance into the model as they are present in the ceramic data. When we rerun the model we will be able to analyse a network of a certain distribution in a certain period knowing that distance is influential and being able to calculate this influence. Moreover, we can compare these ceramic networks with multiple stages in the egalitarian simulation.

Again, this is just an idea that might bring us one step closer to understanding the decision made by people involved in the distribution of table wares, but it is by no means without its issues:

• We assume a direct correlation between number of sherds and importance in trade patterns. Should we use the diversity and relative amounts of ceramic forms as an index of importance? As this is a simulation we accept that we enter arbitrary values for something we try to study (the relative position of sites in different ceramic distribution patterns). Still we should beware for circular thought patterns which will eventually tell us that the things we think are significant will turn out to be significant.
• What with the ‘size’ factor? Should we remove it from the model or can it represent another aspect of ceramic trade?
• Is it useful to apply this model to the ceramic evidence, or should we just run the analysis without including the number of sherds, to see how sites relate to one another in space? Such an approach might allow us to compare a distance-based simulation with Beta-skeletons of ceramic distributions?

Relative Neighbourhood graphs and Beta-skeletons

Although our preliminary method indicates that a reconstruction of pottery trade flows involves a lot of complications, we cannot seem to let this research topic go. One reason for this is that most archaeological attempts to study the ancient economy make interpretations about trade routes based on ceramic evidence (e.g. Abadie-Reynal 1989 ; Fulford 1989), yet none have ever attempted a networks approach. In this post we will discuss a geographical network in which distance is a significant parameter, an assumption that is not without its complications.

We believe that relative neighbourhood graphs (RNG) and Beta-skeletons might prove to be useful tools for constructing distance-based networks. Unlike other types of cluster analysis (e.g. nearest neighbour) these methods take the position of all points in account. Jiménez and Chapman (2002); discussed the archaeological application of RNG, and summarize its construction as a graph in which “the link between two points is determined by taking into account not only the proximity between the two points, but also the relative distance of each pair to the remaining points ». Lines are drawn between two neighboring points that have no other points in a region around them. By varying the size (beta) of the region of influence for each pair of points, graphs (called Beta-skeletons) can be created with different levels of connectivity: if the region is small, more relationships will be drawn between the points; if the region is large, the network will start to fall apart in smaller networks (see Fig. 1).

Fig. 1 Beta-skeletons with varying regions of influence, indicating that for a higher value of beta the network will start to fall apart. Taken from Jiménez & Chapman 2002.

Of particular interest for our study is a Beta-skeleton of sites in the Eastern Mediterranean at the stage just before it starts to fall apart, so without any unconnected sub-networks (similar to the network for ‘Beta=2’ in Fig. 1). This Beta-skeleton can be analysed as a network, which will allow us to define the relative position of every site for the hypothesis “what if straight-line distance were a determining factor in the distribution of table wares?”

Such a network obviously avoids all complications but is invaluable in testing a distance-based hypothesis. For every ware in every period the number of sherds being transported from centre of production to centre of consumption can be plotted on such a Beta-skeleton (only including those sites in which the ceramics in question were found). We can easily compare the relative positions of sites in these transportation networks, as we know the influence of our basic ‘distance’ network.

To test our hypothesis that proximity is an important parameter in the distribution of table wares, we have to analyse our ceramic networks and compare them to our basic networks. If the relative position of sites weighted by the ceramic evidence is similar to sites in a ‘distance network’, we can conclude that distance played an important role in determining trade relations and thus trade routes. If there is a significant difference between ceramic and distance networks, we can conclude that distribution was influenced by other parameters, e.g. personal contacts of traders and land owners. Testing the hypothesis for 15-year periods will allow us to identify periods in which distance was more likely to be a determining factor than others.

Some of the numerous issues with this method should be listed:

• although RNG is a formidable method for cluster analysis, it still does not take into account any of the complexities that determine trade routes. Could this method be combined with a cost-surface analysis to paint a more accurate picture of regional overland trade?

• Will the ceramic evidence influence the distance network to such a degree that its basic connectivity can be altered?

• Using a Beta-skeleton as the basis for testing our hypothesis might lead us to find exactly what we were looking for (distance = significant) because it is inherent in the network. Should the Beta-skeleton be compared with a more neutral network of ceramic distribution through space?

Co-presence of forms and wares

Our previous post mentioned the issues concerning the definition of non-geographical networks. In this blog post we will give an example of such networks, and how it might lead to interesting insights about pottery distributions.

The production centres of major eastern table wares range from a limited number of cities (e.g. Eastern Sigillata C (ESC)) to a more widespread regional production (e.g. African Red Slip Ware (ARSW)). Each centre produces fine wares with a specific fabric, making it possible to differentiate their distribution patterns. Such distributions might be visualised as networks in which sites are the individual nodes and the relationships between sites represent the number of wares (not sherds) that are present at both sites at the same time-period. This would provide a series of very simple but rather informative networks representing the sites involved in the distribution of a specific table ware, which can be compared and added up with the networks of all other wares and analysed through time in 15-year periods.

These networks might provide useful insights on the relationships between cities and most importantly people, who were involved in inter-regional ceramic trade.

Another approach focuses on the individual forms which, in contrast to the general distinctions between producing centres, presents us with a different type of information going back to the individuals producing the pots and the people for whom they are made. In addition, a single form can be produced in several centres and in different table ware fabrics, allowing for the rise and fall in popularity and the diffusion of pottery forms to be analysed. A network of pottery forms represents sites related to each other on the basis of the number of forms they have in common in a specific period.

Such networks allow the study of the distribution of individual pottery forms, to group sites based on the simmilarity or difference of their pottery assemblages, and to see the evolution of these disstribution patterns in 15-year periods.

The two non-geographical networks described above might form the basis for discussions around the following topics: are the distribution patterns of individual forms dependant on/similar to the existing inter-regional socio-economical networks of major fine ware distribution? Do forms that are produced in multiple table ware fabrics circulate in networks that are similar to one or more of these wares? Are form/ware networks linked to social networks of potters, traders, land owners and how can we distinguish between the actors in pottery trade?

An important issue we need to raise, however, is that in the above networks we only used the number of co-present wares/forms rather than the number of co-present sherds. Although we might avoid the bias of archaeological research interests and emphases in this way, we might also miss a chance of having an indicator of the intensity of distribution as represented in the sheer volume of sherds.

The above networks can be tested on their validity by confronting them with their socio-economic and political framework (Bes 2007). We have not yet figured out a way to test these hypotheses quantitatively.

Any comments on these networks, the questions they might answer or the very nature of this approach are more than welcome!