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Communication Dans Un Congrès Année : 2021

Stable results from spatial interaction models: was this settlement really popular?

Résumé

Over a short period between the fourth and the first century BC, an unprecedented process of urbanisation developed in non-Mediterranean Europe. By focusing on trade interactions, we question the links between the observed hierarchy of grouped settlements and long-distance economic flows over the territory. The aim is to assess the extent to which long-distance trade networks and the economic flows they involve may have had an influence on the emergence, the prosperity and the hierarchy of grouped settlements identified in central-eastern Gaul. To address these types of questions despite the partial nature of archaeological data (Rhill and Wilson, 1987) proposed to use the Harris and Wilson (HW) urban retailer model. This simple dynamic interaction model estimates ‘flows’ between ‘centres’ from their geographical positions and can be used to predict the development of large agglomerations favoured by their location in long-distance traffic flows. Since this seminal work, the HW model has been applied successfully in numerous archaeological studies. For instance in (Bevan and Wilson, 2012), it is used to study the hierarchy of towns in Bronze Age Crete. Interaction models are useful in particular to test hypotheses such as the influence of a given settlement over their global hierarchy, the effects of travelling costs of interaction flows, etc. We study in this communication the sensitivity of the Harris and Wilson interaction model to its inputs (geographical aspects) and to its parameters, in the context of a large-scale experimental exploration of the urbanisation processes of central-eastern Gaul between the fourth to the first century BCE (309 identified grouped settlements). By sensitivity we mean the tendency of the model to produce quite different results when applied to close configurations. In the Harris and Wilson (HW) model, the flows between settlements are computed using as input the travel costs between those settlements. A simple approach consists in using straight line geographical distances as travel costs, but this disregards the actual landscape. A more realistic solution consists in computing shortest (least cost) paths between settlements, using a terrain related cost model (Bevan & Wilson, 2012). Sensitivity of the model to the position of the settlements or to their existence is a desirable feature that can be leveraged to test simple archaeological hypotheses. However least cost paths calculation involves parameters that can be difficult to set based on evidence. Then sensitivity to the variations in the paths induced by changing their calculation can be more problematic. The HW model uses two numerical parameters. The first parameter alpha represents the importance of dominant settlements: it is well known for the HW model that increasing the value of alpha will decrease the number of dominant settlements (and vice versa), with a phase transition in alpha=1. The second parameter beta controls the effect of the travel costs on the flows: a small value of beta enables long distance exchanges while a large one reduces those opportunities. Apart from those general considerations, theoretical results on the effect of the parameters on the outcome of the model are scarce. Practitioners generally use trials and errors to compare several configurations, using visual representations of the flows and some associated aggregated values (such as the number of terminals, which are settlements that receive more incoming flow than settlements to which they send some flow). We propose to use a more systematic approach for exploring the results of the HW model when both inputs and parameters are varied over a large collection of possible values. Our approach is based on the use of additional aggregated values computed on the outcomes of the HW model and on the search of stable results. For instance, we enhance the terminal based analysis used in e.g. (Bevan and Wilson, 2012). For a given geographical input (travel costs), the subset of the settlements identified as terminals depends on the numerical parameters. We extract the most frequent subsets over the parameter space and consider them as stable results for the given travel costs. In addition, we associate to each settlement its “popularity” among stable configurations: for a fixed number of terminals, the popularity of a settlement is its frequency among the sets of terminals of the given size. Using those tools, rather than considering all outcomes with say 10 terminal settlements as identical, we can distinguish between a true dominant situation with only a single 10 terminal subsets and a more complex situation with numerous comparable but distinct 10 terminal configurations. In the latter case we can identify “super” terminals: settlements that appear in all of the possible 10 terminal configurations. Using the proposed methods we study the sensitivity of the model with respect to its parameters but also with respect to its inputs. We use bimodal least cost paths to compute travel costs between settlements, integrating both terrestrial movements and fluvial ones. We compare results obtained with and without the fluvial mode, as well as the effects of the parameters of the least cost path calculation themselves (for instance the cost of embarking on a river). Our experiments confirm the sensitivity of the model, in particular regarding the variability of the terminal subsets even for a fixed number of terminals (see e.g. Evans and Wilson, 2013). They also show important effects of variations in the input. As expected, including fluvial transport changes significantly the least cost paths and as a consequence the results of the HW model. More subtle modifications, such as changing the ratio between the downstream fluvial cost and terrestrial costs can also have large effects on the results. Interestingly, most of those effects do not manifest on simple aggregated metrics such as the number of terminals, but are only visible when we focus on stable terminal configurations. Our work confirms the need for a systematic exploration of the parameter space of the Harris and Wilson model (and of related models) beyond simple diagnostics based on aggregated values. We show also that travel cost models can have a strong effect on the results. A systematic exploration of the parameter space of those travel cost models is therefore also needed. Bevan, A., and Wilson, A. 2013. “Models of settlement hierarchy based on partial evidence.” Journal of Archaeological Science, 40(5), 2415-2427. Evans, T. S., and Rivers, R. J. 2017. “Was Thebes Necessary? Contingency in Spatial Modeling.“ Frontiers in Digital Humanities, 4, 8. Rihll, T. E., and Wilson, A. G. 1987. “Spatial interaction and structural models in historical analysis: some possibilities and an example.” Histoire & Mesure, 5-32.
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hal-03911358 , version 1 (22-12-2022)

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  • HAL Id : hal-03911358 , version 1

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Fabrice Rossi, Clara Filet. Stable results from spatial interaction models: was this settlement really popular?. CAA 2021 “Digital Crossroads”, Computer Applications and Quantitative Methods in Archaeology, Jun 2021, Limassol, Cyprus. ⟨hal-03911358⟩
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