The estimation of Vargha and Delaney's A statistic showed that, while the differences between settlement territories and the entire habitable zone were statistically significant, they were often small (Fig. 9.2). The largest effect sizes are found in the central zone settlements' preference for high levees, but even here the A statistic never rises above 0.75. Figure 9.2 displays the A statistics for landforms in each zone and territory size. To ease interpretation, 0.5 has been subtracted from each value, so that landforms that are more prevalent in settlement territories have positive values and those that are less prevalent have negative values. These results demonstrate that levees were consistently favoured and other landforms either ignored or avoided. In the central zone, high levees were most preferred and floodplains avoided, while in the eastern zone, low levees were the most preferred and sandy soil was avoided. The high A statistics for low levees is a result of their relative prevalence in the eastern zone as a whole, where high levees are more common. The average percentage of settlement territories covered by high levees is actually greater than low levees, but many locations in the eastern zone have very high percentages of high levee in their territory, so the settlement locations are less unusual in this regard.

**Fig. 9.2** Graphs showing the Vargha and Delaney A statistics. Note that 0.5 has been subtracted from the A statistic to make the results more easily interpretable

Within this pattern, some diachronic trends can be observed. In the central zone, in 500 m territories, the A statistic decreases for high levees and increases for low levees until the Middle Roman A period, after which they separate again. At the same time, the A statistic for floodplains in 1500 m territories rises until the Middle Roman A period before falling again. This mirrors the results of the cluster analysis

performed by Verhagen et al. (2016) on all rural settlements in the Lower Rhine. They identified clusters of sites whose 500 m territory was dominated by one landform and found that the proportion of sites in the "floodplain" cluster peaked in the Middle Roman A period at the expense of the "high levee" cluster.

In the eastern zone, there is a distinct jump in the A statistic for high levees in both 500 m and 1500 m territories, which is accompanied by a drop in the A statistic for sands and fluvial terraces, in the Early Roman A period. The gap narrows slightly in the Early Roman B period and then remains stable until the Late Roman B period when the A statistics diverge further.

## *9.4.2 Multivariate Analysis*

The baseline logistic regression models were only moderately successful at distinguishing settlements from non-sites on the basis of the landforms in their territories. Nevertheless, some diachronic trends emerge. RMSEs fall in the eastern zone between the Late Iron Age and the Early Roman A period. In both zones, they rise until the Mid-Roman periods before falling in in the Late Roman A and beginning to rise again in the Late Roman B (Fig. 9.3). This is the same trend as observed in settlement numbers suggesting that as population increased, settlement extended into more marginal areas that resemble non-sites in their territory profiles. Alternatively, factors other than the landforms present in settlement territories could have been influencing settlement location.

The addition of MP variables improved model performance little – never more than 3% – but their contribution was often statistically significant. The results are presented in tabular form in the appendix. Beyond the percentage of improvement, three pieces of information are encoded in these tables: which MP variable improved model performance the most within each settlement/non-site dataset, the statistical significance of the MP variable (*p* < 0.1 or *p* < 0.05), and the sign of the coefficient.

The Late Iron Age, with no forts, had only one MP variable. In the eastern zone, it was significant for 4/5 datasets with 500 m territories and 3/5 datasets with 1500 m territories (*p* < 0.05). Proximity to larger centres, then, seems to have been attractive in the late Iron Age, at least in the eastern zone.

In the Early Roman A period in the central zone, no MP variable consistently improves model performance more than the other nor were any of the variables significant. In the eastern zone, the MP variable without forts consistently improves model performance most with both 500 m and 1500 m settlement territories, but it was significant (*p* < 0.1) in only two of the datasets with 500 m territories. Maximizing access to markets might have mattered somewhat to some people at this early period, but the impact was small. If marketing did matter, however, the market system was centred on the civilian settlements, not the forts.

In the Early Roman B period, in the central zone, the civilian MP variable always outperformed the variable that included forts when examining 1500 m territories.

**Fig. 9.3** Root mean square errors. Each point represents one dataset combining settlements and non-sites

This variable was significant in 3/5 datasets, and the coefficient was consistently negative. This makes the role of forts difficult to understand. Rural settlements seem to favour areas far from markets, but the effect is less pronounced when forts are included. The eastern zone settlements show a slight tendency to favour civilian centres over forts, but significant MP variables are almost entirely confined to a single dataset. As in the previous period, evidence that proximity to markets shaped settlement location trends is weak, but there is no evidence at all that forts attracted settlements.

The Middle Roman A period shows more consistent results. In the eastern zone, civilian MP variables consistently outperform civilian and military MP variables at both sizes of territory. The variable that assigns a weight of 37.5 to the *canabae* around the legionary *castra* performs better than the variable in which the *canabae* has a weight of 75. The former variable is significant in three out of five datasets,

while the latter is significant only once. Therefore, despite the great size of this settlement, it did not completely dominate the rural market.

The Middle Roman B period shows inconsistent results in terms of improvement. Significant variables are confined to the eastern zone where three datasets produced at least one. These improvements were also the largest of any in the analysis: 2.69% in the eastern zone using 1500 m territories and the civilian MP variable. However, both variables performed well: the civilian MP variable performed best three times with 500 m territories and four times with 1500 m territories. It seems that proximity to market centres was more attractive at this time than any other, but the evidence that forts acted as market centres is ambiguous.

The Late Roman A period was also highly inconsistent and produced very few significant variables.

The Late Roman B period produced more significant MP variables than any other. In the central zone, using 1500 m territories, both MP variables are significant (*p* < 0.01) in every dataset except one, where the *p* value is less than 0.101. The civilian and military MP variable improves model performance the most four out of five times with 1500 m territories and every time using 500 m territories. As in previous periods, the coefficient is always negative.

In the eastern zone, the civilian MP variable is significant in every dataset with both territory sizes, and the civilian and military MP variable is significant in four out of five datasets at both sizes of territory. Which variable improves model performance the most is ambiguous, though. As in the Middle Roman period, proximity to market centres was clearly attractive, but the role of forts remains murky.

## **9.5 Discussion**

## *9.5.1 Modelling Results*

While much remains obscure, one conclusion is certain: the MP variable that includes forts consistently improves model performance more than the variable that excludes them in only one time and place, the central zone in the Late Roman B period, and in that case it has a negative coefficient. When the results are consistent in other contexts, the MP variable that includes only civil settlements improves model performance more. At the same time, the fact that MP variables had negative coefficients in the central zone complicates the matter.

To understand why MP variables so often had negative coefficients in the central zone and the relative improvements of the MP variables, it is helpful to visually compare the distribution of settlements and non-sites relative to each MP variable (Fig. 9.4). Using the civilian MP variable, there are five high MP areas, and the heart of each is devoid of rural settlements but contains several non-sites. Their unusually high MP score allowed the model to successfully identify these locations as belonging to the category of non-sites rather than sites, which explains why the MP vari-

**Fig. 9.4** Early Roman B settlements and the second set of non-sites overlaid on the civilian (**a**) and civilian and military (**b**) MP variables. MP variables were most significant and produced the largest improvements over the baseline model with this combination of settlements and non-sites

able has a negative coefficient. Using the civilian and military MP variable, a sixth high MP area emerges in the extreme northwest of the central zone. Unlike the others, this area contains a cluster of settlements. Using this variable, high MP values were found among both settlements and non-sites, confusing the model. This cluster suggests that the fort at De Meern might have attracted rural settlement, but in this it was unusual.

## *9.5.2 Historical Implications*

The shift in location preferences identified in the eastern zone in the early Roman A period supports the idea that there was a shift in agricultural practice already in the earliest phase of Roman occupation to supply the new population. Maaike Groot has recently shown that livestock production changed in the early Roman period with an increased emphasis on sheep and a focus on meat production in cattle (Groot 2016, 211–215). Laura Kooistra has emphasized the presence of cereals in Nijmegen and Vechten from this period that could have been locally grown and pointed out the possibility that grain was grown around Meinerswijk and that spelt might have been grown at the behest of the army (Kooistra 2009, 223–226). Groot further argues that, with the exception of the initial conquest, rural producers had a fair degree of freedom in how they responded to the increase in demand (Groot 2016, 213). If the rural settlements did indeed favour proximity to civilian centres, this would support the notion of a mutually beneficial relationship between occupiers and rural producers. At the same time, the fact that the civilian MP variable outperformed the civilian and military MP variable suggests that the new forts themselves did not attract many settlers. Farmers are more likely to have sold their products in civilian markets.

Changes in land use in the central zone are identifiable in the Middle Roman A period, when more settlements have territories that contain larger areas of floodplain and low levees rather than high levees. This coincides with the peak in the RMSEs of the baseline models. With no significant MP variables and negative MP coefficients, there is no indication that the inhabitants of the area were compromising the quality of their land in order to maximize marketing opportunities. Either population pressure was forcing people to inhabit less desirable locales or a large portion of the rural population preferred floodplains. The first option seems unlikely as the number of sites increased in the Middle Roman B period, but the RMSEs of the baseline models fell. Areas with high water tables would have been unsuitable for arable agriculture but well suited to animal husbandry. On the basis of zoological remains and an increase in the sizes of granaries, Groot has argued that both arable farming and animal husbandry intensified in the Middle Roman period (Groot et al. 2009; Groot 2016, 125–128, 215–218). Horse breeding, in particular, became very important in the Middle Roman B period, but increases in the proportion of horse remains are already visible in the Middle Roman A period (Groot 2016, 87–90). Furthermore, variations in species proportions between sites have led her to suggest that settlements were specializing to some extent in the production of different animals for market. If some settlements were focusing on raising animals while others were focusing on agriculture, this would explain the greater variety in environmental preferences observed in this period. This would also help to explain why, even as production for market increased, proximity to markets was not particularly appealing. Livestock has very low transportation costs. The increase in granary size in this period is also consistent with the settlement preferences identified here. Wouter Vos has argued that these large granaries collected produce from other rural settlements (2009, 256–257). By bulking cargo in the countryside, fewer trips to the places of consumption are necessary. Again, this reduces transportation costs. While surplus production for market occurred in the central zone, it seems unlikely that most smallholders were selling their produce directly to consumers. If the forts and *vici* were acting as local market centres, as Vos has argued (2009, 226–229), this function did not influence settlement locations in the central zone.

In the eastern zone, the situation is different. The significant improvements achieved by adding MP variables show that settlers favoured proximity to market centres, which could also help to explain the increasingly poor performance of the baseline model. The peak in model improvement occurs during the Middle Roman B period, which fits well with Groot's conclusions drawn from archaeozoological analysis (Groot 2016). In contrast to the central zone, it seems that access to market centres influenced settlement location tendencies, which in turn suggests that transportation costs were intentionally minimized. This would be consistent with the sale of perishable fruits and vegetables, an undertaking in which the advantages of large landowners are less pronounced than in the sale of grain (Weaverdyck 2016, 4–5), but other scenarios cannot be ruled out.

The forts might have played a role in this process, but it was not particularly large. The civilian MP variable outperformed the civilian and military MP variable consistently in the Middle Roman A period and in the majority of datasets in the Middle Roman B period. What is more, assigning massive weights to the legionary fortress and *canabae* in the Middle Roman A period did not improve model performance as much as assigning them a more moderate weight. Overemphasizing the role of the military only confused the model. The city of Ulpia Noviomagus and the civilian settlements seem to have been the most important market places.

These results should not be taken to deny the importance of the army in the economy of the region as a whole. Many of the civilian settlements were closely tied to the army, military demand surely played a major role in stimulating production, and the salaries paid to soldiers brought significant quantities of coined money to the region. What this does show is that the forts themselves, with the possible exception of De Meern in the Early Roman B period, were not particularly important market centres. The economic relationship between the army and rural producers was usually mediated through civilian institutions. The role of the city of Ulpia Noviomagus would have been crucial. This conclusion mirrors the result of my previous study in the central Lower Danube (Weaverdyck 2016). There too I found that forts failed to influence rural settlement locations despite the undeniable importance of the military in the regional economy. This means that cities and civilian settlements should be seen as an integrated part of the military supply network. It also means, however, that forts played a distinct role as centres of consumption but not necessarily of exchange.

## **9.6 Conclusion**

Comparative logistic regression analysis of rural settlement landscapes has proven to be a useful tool in detecting the subtle influence of marketing behaviour among a population that was likely more focused on production than on transporting their goods to market centres. As with any statistical tool, however, its results require careful interpretation. Improvements in model fit, significance of MP variables, and coefficients of MP variables all proved crucial in drawing conclusions from the results of the modelling process. Furthermore, the comparison data, the non-sites, have as much of an impact on the model as the settlements, so it is crucial to construct multiple sets of non-sites to avoid drawing spurious conclusions. One significant improvement would be to analyse biases in the archaeological record to minimize the risk of placing non-sites in locations that contain undiscovered settlements.

As with any approach, the results of comparative modelling are most meaningful when interpreted in light of other evidence. The Lower Rhine region has the advantage of a long history of excellent research on military, urban, and rural sites. Location analysis has reinforced and added nuance to the conclusions drawn by other scholars. The presence of the army spurred agricultural intensification and surplus production for market, but this surplus was exchanged in civilian market centres. If the rural population interacted frequently with military personnel, there is little reason to think these interactions occurred in forts. If the military created a landscape of opportunity on the frontier, peasants seized those opportunities primarily in cities and towns.

**Acknowledgements** I gratefully acknowledge the assistance of the "Finding the Limits of the Limes" project in providing me with the data on which this analysis is based. In particular, I would like to thank Philip Verhagen and Mark Groenhuijzen for their help in understanding the structure and genesis of the data. Verhagen and Groenhuijzen also provided insightful comments on an earlier draft of this paper, as did an anonymous reviewer. Their advice greatly improved my methodology, my interpretations, and my presentation of both. Any errors remain my own.

# **Appendix 9.1**

The improvement in RMSE achieved by the addition of MP variables is presented in the tables below. N-S stands for non-site and indicates which set of non-sites was used in each model. Each column corresponds to a different MP variable. When multiple MP variables were tested, the maximum improvement for each set of nonsites is written in bold. When the coefficient of the MP variable was negative, the improvement figure is printed in italics. A single set of parentheses indicates that the *p* value of the MP variable is less than 0.1, and a double set of parentheses indicates the *p* values is less than 0.05.

"Civ" indicates MP variables that include only cities, civil settlements, and cult sites. "Civ & Mil" indicates MP variables that also include *castella* and *castra*. "Civ & Mil\*" is an MP variable used in the Early Roman A, which contains *castella* but not the *castra*. "Civ\*\*" and "Civ & Mil\*\*" are MP variables used in the Middle Roman A period which assign half weights to the *castra* and legionary *canabae*. The weighting scheme is described above (see Table 9.2).

(continued)

#### Early Roman A

(continued)

# **References**

Methods in Archaeology (CAA), Southampton, 26–29 March 2012. Amsterdam University Press, Amsterdam, pp 379–388. Available at http://arno.uva.nl/cgi/arno/show.cgi?fid=516092. Accessed on 14 May 2018

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# **Chapter 10 A Multi-scalar Approach to Long-Term Dynamics, Spatial Relations and Economic Networks of Roman Secondary Settlements in Italy and the Ombrone Valley System (Southern Tuscany): Towards a Model?**

**Stefano Bertoldi, Gabriele Castiglia, and Angelo Castrorao Barba**

**Abstract** In Roman landscapes, the particular sites defined as secondary settlements (also known as *vici*/villages, minor centres, *agglomérations secondaires* and/or *stationes/mansiones*) have played an 'intermediary' role between the cities and other rural structures (*villae*/farms), linked to medium- and long-distance economic and commercial trajectories. The aim of this paper is to apply a multi-scalar approach to model their long-term spatial relationships and connectivity with the Mediterranean exchange network. On the macro-scale, we have analysed a sample of 219 reviewed sites to understand the diachronic trends and spatial dynamics of attraction/proximity to significant elements of the landscape such as towns, roads, rivers and coastline. The Ombrone Valley (Tuscany, Italy) represents a micro-scale case study of a complex system, in which the imported pottery (*amphorae*, African Red Slip ware, *ingobbiata di rosso*) found in the *vicus/mansio* of Santa Cristina in Caio, the Roman *villa* of La Befa and the town of Siena (*Saena Iulia*) provided diagnostic 'macroeconomic' perspectives. The results show how the secondary settlements occupied a nodal position in the Roman landscape in terms of resilience (long period of occupation until the Early Middle Ages) and spatial organization with a close relationship to natural and anthropic infrastructures and trade functions linked to Mediterranean routes.

**Keywords** Settlement patterns · Diachrony · Roman pottery · Network analysis · Statistics · GIS

S. Bertoldi University of Siena, Siena, Italy

G. Castiglia Pontifical Institute of Christian Archaeology, Rome, Italy

A. Castrorao Barba (\*) University of Palermo, Palermo, Italy e-mail<EMAIL_ADDRESS>
# **10.1 Introduction to the Study of Secondary Settlements: Theory and Method**

Archaeological research into indicators for defining Roman settlements as 'secondary' (*agglomération secondaire*) (Leveau 2012; Garmy 2012), a theoretical intermediate between towns and *villae*, is still emerging (see Crogiez 1990, 391; Chevallier 1997, 284; Mezzolani 1992 113; Corsi 2000, 186; Maggi and Zaccaria 1994, 163–168; Cantino Wataghin et al. 2007, 88; Goffredo et al. 2013) (Fig. 10.1). This interpretation related to settlement hierarchy is also expressed in the definition of these sites as 'minor centres' (Tol et al. 2014). In the archaeological record, however, only a certain number of excavated sites were identified as secondary settlements: they are characterized as places with a specific role in the roads of the *cursus publicus* and/or rural agglomerations of the *vicanico* type (communities living in nucleated villages; Tarpin 2006).

Studying the topic of 'secondary settlements' requires the inclusion of a wide variety of themes, including the role of these sites, their abandonment and reuse, the organization of rural areas, trade, production, Christianization and land and river traffics.

The hypothesis that some of these sites seem to respect certain rules of spatial order oriented our research aimed to determine whether a trend or pattern in the spatial order of secondary settlements can be detected.

**Fig. 10.1** Theoretical dendrogram of rank-size classification of Roman settlements, reworked from Garmy (2002, 31). About the classification of settlement types have been re-elaborated the macro generic groups proposed in Witcher (2012), and the typology of Roman cities has been taken from Nevett and Perkins (2000)

This kind of settlement is closely associated with economic functions: secondary settlements appear to fulfil the role of centres promoting and providing trades and services. The 'amount of services offered by a settlement' is a concept introduced in geography by Christaller (1980), who argues that it could be used as an indicator for defining the importance of an inhabited site with greater accuracy than the population of the site. The approach of the German geographer is crucial for addressing the problem of secondary settlements, the materiality and magnificence of which are insignificant in comparison to the monumental *villae*, but which held strategic importance in the 'State system'.

In this regard, the definition given by M. Corbier concerning the Gallo-Roman *vicus* is extraordinarily effective: 'A village that lives by exploiting a territory but not necessarily only through agriculture' (Corbier 1986, 691). A settlement of this kind often is involved in various productive crafts, such as the procurement of raw materials, leading to the construction of a system in which there are patterns ruling the space (Bischi et al. 2004); however, the outcomes are still influenced by many variables. In this system, even small changes can lead to very different results. Therefore, as in climatology and economics, it is very difficult to predict what may occur in the future. Following this line of reasoning, we can compare archaeology to burning matchsticks. Even with similar initial conditions, the smoke of each matchstick will follow very different trajectories, its path difficult to predict (De Guio 1992). This 'chaos theory' has also been studied in Physics, to explain how an attractor regulates a system governed by deterministic and causal dynamics (Lorenz 1963).

By looking at the settlements' network and its analytical composition, and the transformations and degradation thereof, one can observe a few spatial rules: whatever these rules are, we wonder what the driving forces behind them are.

In our work, the concept of 'cause' that Bloch had identified as 'the misstep of a man walking in the mountains' (Bloch 1998, 138–143) and that Flannery (1968, 67–87) and Plog (1975, 213–216) called the differential or 'kicking' element lost importance. What matters more here is to identify the forces generating these causations in their entirety. We will not aim to predict the past, nor will we deal with overly complex phenomena, thus leaving room for physicists, philosophers and theologians (Citter 2012, 13). We will use geographical and statistical methods only for descriptive analysis.

The theme of 'attractors' and the ability of some elements of the natural and human landscape to attract and/or repel goods, settlements, etc. is certainly not a novelty in archaeology (Wheatley and Gillings 2002, 134–135). The study of the diffusion of finds (in this case imported pottery) in certain types of settlements transforms us into a kind of Hop-o'My-Thumb (Perrault 2012, 42–46), in search of the traces left in the woods, with the goal of returning home. Unlike Hop-o'My-Thumb, however, we cannot tell if we are in front of a white stone or a crumb of bread. The truth of the past is difficult to grasp: not all of the material culture has survived, not all of the material culture can be found, not all the material culture has been excavated, not all the material culture indicates trade. However, studying the relationships and trade flows through pottery imports, and the products they carried, requires investigating 'traces', without aiming for the completeness of the record, but nevertheless using the same methodology as the other branches of archaeology. Ultimately, rules exist in archaeology; however they are very complex.

# **10.2 Quantitative Approaches to the Analysis of Secondary Settlements in Italy in the Long Term**

With a full knowledge of certain physiological problems of interpretation, we have tried to establish a program of cataloguing all of the published contexts in Italy, from both excavations and surface surveys, and interpreted in various ways (*stationes*, *mansiones*, *mutationes*, villages/*vici*, etc.), which may all be categorized as part of the group of 'secondary settlements' (Castrorao Barba 2016).

The compilation of a significant sample of sites formed the basis from which to undertake a quantitative approach to comparing the description of long-term historical trends with the spatial relationships to significant elements, both natural (natural coastlines and rivers) and anthropogenic (towns and roads).

The bibliographic inventory was stored in a database with information on the initial and final phases of the various settlements. The sites included in this study are those with a chronology dating between the first and sixth centuries CE and which have been identified by the excavators/publishers as those that may be defined as secondary settlements.1 A sample of 219 sites (Fig. 10.2a) was collected (Table 10.1): 68.9% of them have been subject to excavation, while 31.1% are known only through field surveys.

For the purpose of 'data mining', descriptive statistics and spatial analysis were undertaken on this sample, in order to answer the following questions:

<sup>1</sup>This database is part of a PhD research project granted by the University of Siena (Castrorao Barba 2013), using the DBMS 'Carta Archeologica' (Fronza 2005) managed by the LIAAM laboratory at the University of Siena, under the direction of Marco Valenti.

**Fig. 10.2** (**a**) Distribution map with the sample of 219 sites used for the spatial and statistical analyses. (**b**) Comparison between *villae* and secondary settlements: percentages of deserted sites, of reoccupied sites and chronology of the reoccupation. (**c**) Frequency histograms of percentages related to distances (one class of 1 km from 0 to 15 km and then a unique class superior to 15 km) between secondary settlements and landscape elements (rivers, roads, coastlines, towns)

**Table 10.1** Proportions of collected sites per region Italian regions

• Were the reoccupations (with or without the presence of a place of worship) oriented towards sites in proximity to one of the four 'potential attractors'?

This statistical approach does not exhaust the knowledge that can be gained from this data source, nor is it its purpose. However, it is a robust tool for describing and quantifying a material reality (spatial relationships between sites and landscape) on a large scale, creating a 'normal' trend to be verified in agreement/disagreement with a different spectrum of variables observed on a micro-scale.

# *10.2.1 Descriptive Statistics on Diachronic Trends in the Roman Period and the Middle Ages*

The quantification of the initial chronologies of secondary settlements shows that traces of human occupation dating from before the third century BCE can be detected in a fairly high percentage of sites (14.2%), while just over half of the sample (51.1%) shows an early stage dating to the first century BCE/first century CE. Following this, we see an accelerating decline in the number of new sites being settled, except for a brief period in the fourth century CE (8.2%).

By looking at the distribution of the frequency of sites in the individual centuries (Fig. 10.3a) between the third century BCE and the thirteenth century CE, a peak is observed in the fourth century CE (83.6%) and in the first century CE (81.7%) with

**Fig. 10.3** (**a**) Diachronic trend of secondary settlements in Italy: start and continuity of occupation. (**b**) Frequency histogram with the secondary settlements' centuries of life

the period between the first and the fourth centuries CE containing an average 80.6% of the sample. In the following period, between the fifth and the seventh centuries CE, we see a progressive reduction of occupied sites with a growing decline: −16.4% between the fourth and the fifth centuries CE, −28.1% between the fifth and sixth centuries, and − 60% between the sixth and seventh centuries. After a stabilization between the seventh and ninth centuries CE (average − 3.4%), there were slight increases in the eleventh to twelfth century CE compared to the tenth century CE, + 18.1% and + 15.9% respectively, and a further decline in the thirteenth century CE (−13.5%). However, this last trend should be interpreted with caution as it often refers to the presence of religious buildings constructed in the High Middle Ages, which arose in those Roman secondary settlements for which we do not have reliable data on the different phases of continuity or discontinuity between Late Antiquity and the Early Middle Ages.

A frequency histogram (Fig. 10.3b) regarding the number of centuries during which a site was in use indicates a maximum peak for the class '5 centuries' (18.8%) and a maximum concentration (57.5%) in the classes from the third to seventh century inclusive (5 classes of 19). We can consider those sites occupied for the first century, or between the sixteenth and nineteenth centuries as abnormal exceptions, as each class holds a value of less than 1%, thus excluding these 'extreme' values. An average value (sum of the number centuries/occurrences sites/total sites) was calculated as 6.5, which indicates roughly the average number of centuries during which the secondary settlements remained active.

Regarding the phenomenon of post-Roman reuses, only the excavated sites have been taken into account, by comparing them with the Roman *villae*, 151 secondary settlements and 768 *villae* in total (for statistics about Roman *villae* and reuses, see Castrorao Barba 2014a, b). The comparison between the cases with traces of reuses and the definitively deserted sites reveals a clear difference between the two groups, with secondary settlements most likely to be reused (59.6%), compared to the villae (49.2%) (Fig. 10.2b).

Curves relating to the history of the initial phases of reuse showed similar trends: the fifth to sixth century CE is the period with the highest number of reuses both in secondary settlements and in *villae* (50% and 56.2% respectively). A similar peak can be seen during the sixth century CE, although more pronounced in the group of *villae* (32.8% vs. 26%). From the seventh century CE, the number of new cases of reuse begins to decrease, with the rates of reuse slightly higher in secondary settlements compared to *villae*, as well as in the eighth century CE (5.8% vs. 4% respectively), the ninth century CE (4.8% vs. 3.7%) and the tenth century CE (4.8% vs. 1.5%). The slight increase recorded for the period eleventh to thirteenth century CE (8.7% vs. 5.8%) is likely to refer to contexts in which reuse phases prior to the construction (or perhaps reconstruction) of churches in Roman sites have not been recognized.

Further data concerns the presence of Christian places of worship built on preexisting Roman sites: the presence of a church is documented in 44.2% of cases of reuse of secondary settlements, with a lower proportion of reuses of *villae* (34.6%). In absolute terms, the number of *villae* in which a church has been identified is higher, but this figure is highly biased by the higher total number of Roman *villae* and the greater spread of their territory. The high percentage for the secondary settlements indicates that this type of site was more attractive for the construction of churches, while *villae* had proportionally higher rates of other types of reuses (housing units or groups of tombs).

# *10.2.2 Spatial Statistics for the 'Attractive Force' of the Landscape's Significant Elements on Secondary Settlements*

Assessing the relationship between settlement choices and landscape elements on a large scale, whether natural (rivers and coast lines) or anthropogenic (roads and towns), required an extensive amount of data processing.

To quantify the concept of 'attraction', it was necessary to connect it to the idea of 'distance': the closer site *x* is to place *y*, the greatest the attractiveness of *y* on *x*. Through a further effort of abstraction, the Earth's surface was considered flat and smooth, eliminating all geomorphological roughness, as if it were a two-dimensional Cartesian plane (Euclidean space). GIS-based spatial analysis made it possible to calculate all distances in meters between the individual sites and the four potential attractors: rivers, coastlines, roads and towns. The goal was to understand the distribution of the sample in various intervals of linear distances in relation to the attractors, in order to numerically verify the different levels of proximity.

A statistical indicator was used to summarize the relative percentage frequency of the values of the site/attractor distances within 15 size classes. This operation expresses the number of times (as a percentage of the total) in which a distance value is included in a class (Coccarda 2011, 64). The definition of the number and amplitude of the classes included only the sites' attractors within a 15 km limit, beyond which the relationship between the entities is practically irrelevant.

The reading of the frequency histograms allows us to make some observations. In general, the majority of sites are located within 1 km of a river (22.4%) or a road (32.9%), with the terrestrial communication routes representing the main attractor. A much lower proportion of sites are located within 1 km of the coastline (13.2%), while those in close proximity to urban settlements (0–1 km) represent only 0.5% of sites. The low combined force exerted by coasts and cities can be also observed in the high number of inhabited centres located over 15 km away: 63% and 67.1% for coastal and urban areas, respectively, while only 11 0.9% and 11% are positioned that far from rivers and roads (Fig. 10.2c).

The data on the first quartile for the four attractors, i.e. the value falling in the first 25% of the distances sorted in ascending order, mirror the patterns seen in the frequencies. The roads show the lowest values, an indicator of the higher proximity of sites to roads, followed by rivers and then by coasts and cities, where 75% of sites are at a distance that exceeds at least 4 km from the attractor.

A different spatial analysis allowed us to identify the 'unique element' closest to rivers, roads, coasts and cities for each settlement: also in this case, the proximity to roads constitutes the most attractive element with 46.6%, followed by rivers (41.1%), coastlines (11.4%) and towns (0.9%).

In order to evaluate the impact of the different surface occupied by the buffer zones of 1 km around rivers, cities, coastlines and roads, the statistics are weighed. The percentage of the sites inside this proximity area was subtracted from the total area covered by the single buffer zones in the entire surface of Italy. The results show – also in comparison with the villas – the stronger relationship between the secondary settlements and the roads, the coastlines and the rivers.

These percentages are a numerical representation of the close spatial link between secondary settlements and communication systems (major roads and rivers), a characteristic that demonstrates the importance of the inclusion of these populations within a complex system of interactions and flows of people, ideas and goods. In contrast, towns appear to exercise a centrifugal and bumping force, creating an area of 'respect' related to the authority of the town, which is not seen around 'secondary rank' settlement types. This 'hegemonic' role of the cities characterized by its surroundings empty of large sites, such as secondary settlements, is well explained in the classic geographical theories of central places (Christaller 1980) and rank-size law (Zipf 1949). Secondary settlements appear to have an alternative role and perhaps competition compared to cities.

The same pattern (proximity to rivers and roads and distance from towns) is also found in sites that were reoccupied for an extended period, with new functions between the Late Antiquity and the Middle Ages (fourth to thirteenth century CE), 47.5% of the total sample. Fifty per cent of the reused settlements were located at a short distance from a road compared to the other landscape elements (39.4% from a river, 9.6% from the coast, 1% from towns). Furthermore, the relative frequency percentages indicate the same trend outlined for secondary settlements: a maximum peak in the sites located 0–1 km from roads (34%) and rivers (27.9%) and a minimum for coasts (12.5%) and cities (0%). If we compare the histograms of the total with those of the reused sites, we notice an increase in the incidence of proximity to rivers in the reused sites (+5.5%) and a sharp decline in reused complexes in the vicinity of a city (& gt;15 km 73.1%, +6% compared to all sites).

Within the reused contexts, there were 46 cases (44.2%) in which the presence of a Christian place of worship can be identified. The places chosen for reuse for the construction of a church were those in proximity to a road (50%) or river (37%) and further from the coast line (13%); 39.1% of the sites were located within 2 km of a road, 30.4% within 2 km of a river and 13% within 2 km of the coastline.

## **10.3 From Global to Local: The 'Ombrone System'**

The objective of the data presented thus far is the definition of an economic landscape that we have defined as the 'Ombrone System' (Fig. 10.4). The strength of our analysis comes from the fact that this system was not conceived a priori but was

**Fig. 10.4** Map of central and southern Tuscany (Arno and Ombrone valleys) with the sites mentioned in the text

based on analysis made in previous research (Bertoldi and Castiglia 2015; Bertoldi et al. 2015) which embraced landscape studies, spatial analysis and the study of material culture and settlements, which have gradually come to define the economic landscape. Research based primarily on the analysis of the secondary settlement of Santa Cristina in Caio (Bertoldi and Valenti 2016) gradually led to the framing of a much wider network, made up of roads, towns, commodities, rivers and people. From a positivist point of view, a base of quantitative data allows us to understand how countryside, urbanization and commercial trade (in different hierarchies) can interact with each other, despite some significant differences. The rigorous analysis of the origin of *amphorae* was undoubtedly one of the indicators with the greatest impact in this respect. This is not the place to dwell into the details of individual *amphora* types observed in the different contexts we have considered, as it would serve only to repeat a precise assessment already made in another study (Bertoldi and Castiglia 2015), but rather we want to dwell on a range of selected indicators, fundamental to the definition of the 'Ombrone system'. One of the most striking points in the comparison between the town and countryside is dictated by the presence/absence of the so-called '*amphora* of Forlimpopoli'. These were produced in the Adriatic side of Italy (in different types: see Aldini 1978; Aldini 1999; Panella 1989; Panella 2001) predominantly between the first century BCE and the third century CE. It is common in Santa Cristina in Caio, present in smaller quantities at La Befa, but is completely absent in Siena. In order to discuss this phenomenon, we must first consider this important fact: Santa Cristina and La Befa, despite being settlements occupying different hierarchic levels, form part of the same economic 'system' (albeit with different roles). They were in dialogue with each other but also with entities at both the hinterland and the coast (via Ombrone), a 'block' that is both different and complementary to towns such as Siena.

This dichotomy is well readable also in the proportional values of African Red Slip (ARS) ware and *ingobbiata di rosso* (local red slipware produced as imitation of ARS, see Fontana 1998), which allows us to develop a hypothesis regarding the development of relationships within a network of settlements which, even on a heterogeneous hierarchical scale, seems to consist of a solid network of commercial/ productive exchanges. Introducing the Roman *villa* of Aiano-Torraccia di Chiusi (within the territory of Siena) into these comparisons, we can see that the *ingobbiata di rosso* coming from this site (quite plausibly produced in situ, as indicated by the presence of a kiln; see Cavalieri 2008) is not comparable either with the area of Lucca or with that of Florence, Pisa or Empoli and only minimally so with Fiesole. The only stratigraphic basin with which there are actual and demonstrable affinities is that of Siena (Fumo 2010, 33). The same trend can be detected in the *ingobbiata di rosso* coming from Santa Cristina in Caio and the Chianti region, sites with which there are also striking comparisons for coarse ware, especially regarding the *ollae* (cooking wares). An important aspect of these three contexts is also the fact that they are, respectively, to the north, south and east of the city of Siena, with a practically equidistant mileage from the city centre. It is therefore plausible to think about this complex of settlements as a deeply interconnected economic system, in which each vector acts as both an origin and a destination for certain types of pottery.

Based on the fact that a kiln has been identified in Torraccia di Chiusi and on production waste from the Chianti region, the presence of *ingobbiata di rosso* manufacturing workshops has been hypothesized (Valenti 1995). This leads us to believe that the town of Siena was the primary destination of a production chain originating in rural areas. Furthermore, the interdependence of Siena with rural settlements seems well demonstrated by its relationship with the third region, namely, Santa Cristina in Caio. In fact, remarkable similarities between the artefacts can be recognized here too, so on the one hand, Siena could be the starting point of what was produced in the other two settlements/distribution areas but at the same time also the destination of the goods passing by Santa Cristina. In this regard, in fact, in a recent and already quoted article (Bertoldi and Castiglia 2015), we have shown (or at least have proposed an interpretive key worthy of further consideration) that the Ombrone river, on the banks of which Santa Cristina was located, represented a constant artery in the period between the first and seventh centuries CE, ensuring supplies to the hinterland of Siena to a greater degree than the roads. This, therefore, explains the arrival of *amphorae* to the city from overseas during the seventh century CE (Cantini 2005, 197), right through the *vicus/mansio* of Santa Cristina in Caio.

The River Ombrone was navigable for at least part of its course; Plinius describes it as *navigiorum capax* (Naturalis Historia, III, 51) and Rutilius Namatianus as *non ignobile flumen* (De Reditu Suo, I, 337). The Ombrone's navigability is controversial. Some argue that the river, at most, was passable until Istia d'Ombrone (a few kilometres north-east of Rusellae) (Cardarelli 1971, 15), while others more recently have denied its navigability (Arnoldus-Huyzendveld 2011, 41).

However, addressing the problem from a wider standpoint, its navigability becomes a 'non-issue': the importance of a river is not determined only in terms of its use for aquatic transport. It is no coincidence that in Italy the systems of the Po and Arno rivers have been thoroughly studied. In order to understand the role of a river network, it is sufficient to look at the permeability (north-south) and convenience (east-west) of the Danube in Roman times, apparently used only as a natural border.

Returning to our subject, we know that there must have been a road that connected Siena with Populonia; at first, it was assumed that this road accessed not only the area of Siena but also the whole countryside south of the city.

Noting, however, the distribution of the extra Italic pottery findings, there is a clear 'penetration line' stretching from the coastlines to the hinterland, independent of the previously mentioned line of access, which connected Populonia and Siena. In this system, Roselle becomes a point of departure/sorting of products coming from ports along the coastline (as previously supposed for the town of Siena and the *ingobbiata di rosso*). From here, the goods traced the course of the Ombrone until the current town of Civitella Paganico, home to a site identified as a Roman *villa*, called Pietratonda (Barbieri 2004: the author thinks actually of a *vicus* or of a *mansio*, due to the thermal baths for public use). This site would act as a junction, with the goods that had been travelling north-east and then crossing the Ombrone at the confluence of the river Orcia and bypassing the hill of Montalcino in the south. This route guaranteed faster communication between the coastal area and the valleys of the Orcia and Arbia and the site of Santa Cristina in Caio. This settlement was the terminal of the trade network and a market place for a large area, south of the city of Siena. A similar settlement is likely to have existed in Val d'Orcia (likely in the south-east), although the current state of knowledge is insufficient for estimating its location.

# *10.3.1 Pottery Imports in the Sites of Siena, Santa Cristina in Caio and La Befa*

As already noted in other papers (e.g. Bertoldi and Castiglia 2015), the definition of relational systems between settlements and other forms of secondary agglomerates, at different hierarchical levels, must be accompanied by a systematic analysis of the pottery finds, in order to identify commercial relations at various distances. *Amphorae* should be considered a key part of the economic system and, therefore, an indication of contact between human settlements. This approach should be complemented with the fundamental study of ARS ware and its imitations. This brief introduction is essential, as this methodological approach is useful not only for purely 'descriptive' goals but also for an understanding of what will be defined as

the 'Ombrone system'. In this context, it was decided to enrich previous research (Bertoldi and Castiglia 2015) with the analysis of a little-known and previously overlooked site, the Roman villa of La Befa. Located only a few kilometres away from Santa Cristina in Caio, it was partially investigated archaeologically during the 1970s. It is not necessary here to describe the entire stratigraphy and structural evolution of the complex (for that, see the integral edition of the excavation in Dobbins 1980). It is sufficient to point out how the structures, at least in the investigated area, were abandoned at the end of the fourth century CE and that traces of later settling are not recorded. What aim to outline here is the assemblage of the identified pottery types, which will be integrated with the assessment of the Santa Cristina in Caio archaeological record, in order to later compare them with the data related to the urban context of Siena.

It must be stressed from the start that *amphorae*, and in particular the ARS ware, are not found in large quantities in La Befa, although qualitative analysis can be used to draw significant conclusions. The chronological frame of interest was divided into two main macro-blocks, one from the first century CE to the first half of the third century and the other from the second half of the third century CE to the end of the sixth century. It can be noted that in the earlier centuries, imports coming from the coastlines formed greater than 78% of the total, while the goods coming from inland areas make up the remaining to 22%. In the second chronological period, the disparity increases further, with a coastline/hinterland relationship of 98%/2%. With regard to the ARS ware, only five fragments of this typology were identified throughout the stratigraphic sequence, with only two having a reliable chronology, dating back to the half of the third century CE (Dobbins 1980, 143). In the period between the first century CE and the first half of the third century, 63% of the amphorae originated from the coastline, while 37% was from inland areas; between the second half of the third century CE and the end of the sixth century, these values diverge further, with 74% of the goods travelling from the coast and 26% originating inland. Using the same kind of analysis on Siena shows that in the first period there is a prevalence of coastline-sourced (and therefore maritime) items comprising 91% compared to 9%. In the second period, this trend remains almost unchanged, with a ratio of 89–11% (for Siena, see Cantini 2005; Castiglia 2014, 2015).

These analyses reflect very clear trends: La Befa and Santa Cristina, while playing different roles in the landscape and having heterogeneous 'settlement hierarchies' (being in the first place a *villa* and secondly a *vicus/mansio*, probably acting in the role of 'central place'), reflect the same tendency towards trade related to coastal environments (and, therefore, in close relationship with the Ombrone river, as we shall see in the following paragraphs). The town of Siena itself displays the same trend, reflecting the inclusion of the urban centre in the same system. It does not seem to be accidental that the fraction reflected in the two chronological macrogroups corresponds to a very specific economic phenomenon that swept much of the Mediterranean from the third century CE. In all three analysed settlements, we witness, in the Early Imperial Age, a majority of goods coming mainly from the Iberian Peninsula (primarily from Baetica but partly also from Tarraconensis, especially *garum* and oil), as well as high-quality *amphorae* coming from Italy, associated with the transport of wine. From the third century CE, a sharp decline in both Hispanic and Italian products is documented, corresponding to the explosion of goods from North African markets, which become a characteristic feature in the archaeological record.

This evidence is derived exclusively from *amphorae*, as the ARS ware is present in very low quantities, in some cases close to zero, although higher quantities are seen in towns. In this sense, it is very important to consider the role of local products imitating the ARS such as the *ingobbiata di rosso*. These are characterized by almost slavish reproductions of the original North African pottery, although are of lower quality, especially in the coatings (consisting of reddish or brownish engobe), and peak chronologically in Tuscia between the late fourth and the sixth to early seventh centuries CE (Valenti 1991, 1995, 1996; Cantini 2015; Vaccaro 2015). This class is widely seen in both Siena and Santa Cristina, revealing a desire to imitate forms that no longer reached inland markets and, a need to fill the gaps to which the available supply could not respond. This indicates that a demand for ARS ware still existed, so the lack of certain types of ARS ware reflects a decline in trade routes. At the same time, the need to imitate, and therefore produce, these morphologically similar types ties to Roman tradition, mirror of the presence of still configured (although resized) needs and requirements that cannot yet plausibly be read as a reflection of a real crisis, which instead will accrue and be completed only in later centuries (Valenti 1999, 85). The absence of this pottery class in La Befa, however, could simply be due to the fact that, following the disintegration and subsequent abandonment of the facilities of the villa at the end of the fourth century CE, it has not been possible to record anthropogenic activities for those centuries in which the *ingobbiata di rosso* was a 'guide fossil'.

Since we have completed all the 'descriptive' and quantitative assessment, in the following section dedicated to the definition of the so-called Ombrone system, we will trace the implications of the material culture on the 'settlement hierarchies' and how we believe that these implications can be read.

# **10.4 Approaching Network Analysis: The Case of the Ombrone Valley**

Trade relations in archaeology, especially for products for which we know the origin, contribute to the understanding of the complex interchange systems, especially within the Roman globalized world (Pitts and Versluys 2015).

In archaeology, the concept of networks is not a novelty: commercial exchanges, ideas, artisans and road networks are studied, but generally the term is used in a very generic way, or as a synonym of connectivity (Leidwanger et al. 2014). Like many other disciplines, such as statistics and geography, the network analysis had already been intuited by the New Archaeologists (see Clarke 1998), long before the development of software able to help us in the application of such methodologies. With the development of post-processual theories, during the 1980s and 1990s, an antinetwork thought was affirmed, which criticized the excessive rigidity of the system, technique and analysis (Knappett 2013; Collar et al. 2015).

We used the software Cytoscape (version 3.4), which is created for the visualization of molecular interaction in bioinformatics.2

We have selected the sites where a specific ARS form has been identified (e.g. Hayes 61), to create series of relationships and then linking the sites with the GIS least-cost path algorithm, for example, from the Salebrum harbour to the city of Roselle, from Roselle to Santa Cristina in Caio, and from Santa Cristina in Caio to the La Befa *villa*.

Fundamental statistics in network analysis are those linked to the concept of centrality: the calculation of the degree of centrality for each vertex and the degree of centralization of the network in general (Freeman 1978).

Besides the graphic representation, it is interesting to analyse some values that the network analysis generates: in particular, the betweenness centrality, which corresponds to the sum of the length of the shortest paths between each node and all the others to which it is directly connected and the edge betweenness, that is defined as the number of the shortest paths that go through an edge in a graph or network (Girvan and Newman 2002; Fig. 10.5).

Between the second and the third centuries, the chronological period chosen for network analysis, we identify three major commercial flows: the Mediterranean imports (arriving in the Tuscan hinterland from the Tyrrhenian ports), the Empoli *amphorae* and the Adriatic productions.

Santa Cristina is a central place in the commercial network of Roman Tuscany and in particular in the subnetwork of the southern part of the region. In particular, the settlement was a node of the three commercial routes described. The Mediterranean imports arrived in Santa Cristina from the Ombrone valley and were sold in the valleys of the Arbia and Orcia (and perhaps up to Chiusi). The Adriatic productions came from the valleys of Chiana and Orcia and are sold in nearby areas (such as the La Befa villa). The amphora of Empoli came to Santa Cristina from Siena and then in Roselle via the Ombrone river.

During the second century, Santa Cristina in Caio was the third site for betweenness centrality: the settlement had a role of distribution of Mediterranean products coming from the coast, towards Pienza, La Befa and Podere Caselle, and the Adriatic products coming from the Chiana valley towards Roselle, La Befa, Siena and then Volterra. The other nine sites on the top ten list are Pisa, Vada Volaterrana, Portus Scabris, Lucca, Roselle, Pistoia, San Genesio, Firenze and Portus Pisanus.

During the third century, among the top ten settlements with higher betweenness centrality, there are four cities (Pisa, Firenze, Arezzo and Lucca), four ports (Vada Volaterrana, Portus Pisanus, Portus Scabris and Spolverino) and two inland secondary settlements (San Genesio and Santa Cristina), connected to Roman roads and

<sup>2</sup>This software was developed in Seattle by the Institute for Systems Biology in 2002, then released under an Open license and currently maintained by a group of developers.

**Fig. 10.5** (**a**) Network analysis of Tuscan settlements with ARS ware. The size of the sites is based on the factor named betweenness centrality, and the size of the edge is based on the edge betweenness. (**b**) GIS spatial representation of network analysis

important rivers (Arno and Ombrone). This type of sites was connected to commercial function. Secondary settlements were central places for the surrounding economic landscape and also to exchange goods with distant market places. It is not a coincidence that in these sites there were also productive activities, like pottery, iron and bricks (for Santa Cristina in Caio, see Bertoldi et al. 2017).

In conclusion, using this type of analysis, the principal network of Tuscany during the Roman period was the Arno system in the north of the region (Portus Pisanus-Pisa-San Genesio-Firenze-Arezzo). The second commercial network was located in the Ombrone valley (Salebrum-Spolverino-Roselle-Santa Cristina in Caio-Siena/Chiusi), and Santa Cristina in Caio was the principal node of the system.

## **10.5 Concluding Remarks: First Steps Towards a Model?**

In order to define secondary settlements in their specificity throughout the transformations of landscapes between Roman times and the Middle Ages, we have chosen two different perspectives. Firstly, a macro-scale was used with the aim of understanding general trends by using 'data mining' methods (descriptive statistics), described by Richard Hodges (1989) as a 'parachutist's job' equipped with calculator. Secondly, we used a micro- or semimicro-scale (being 'cyclists' rather than truffle hunters) in order to study an economic system, the Ombrone valley, in which we can grasp the significance of the role of secondary settlements such as Santa Cristina in Caio, within a complex net of relationships between the hierarchy of settlements and commercial routes.

The first data coming from the sample of reviewed sites show some trends:

general, for Lazio, see also the fundamental Fiocchi Nicolai 1994). The position of secondary settlements in the landscape, favourable both for the interaction of man and environment and for its proximity to the crucial areas of the economic framework (roads, rivers and the sea), may have played an important role in the choice of secondary settlements as ideal places for the construction of rural churches, in a view of 'a precise plan of territorial occupation by the diocesan authority' (Cantino Wataghin et al. 2007, 105; Castiglia 2018).

Under this general framework, however, lies a greater complexity in which certain factors and variables play a key role in our understanding of the historical processes.

The analysis of the 'Ombrone system' allowed us to compare the data of different kinds of sites (town-secondary settlement-villa) in the context of relations between sea and land along communication routes. In this framework, using the pottery analysis (*amphorae*, ARS and *ingobbiata di rosso*) as an indicator of economic flows has enabled us to better delineate connections between sites and between sites and the wider economic system.

Moreover, the detailed analysis of pottery held diagnostic 'macro-economic' perspectives, revealing how towns, secondary settlements and *villae* within this system, although playing different roles, managed to silently communicate. The city seems to be both the point of arrival and departure of certain types of goods, especially the *ingobbiata di rosso* produced in rural areas. The urban context, therefore, seems to remain an important point of reference in the hierarchy of commercial exchanges, despite the context of deep structural and topographic reconfigurations, such as the transition between Late Antiquity and Middle Ages. Nevertheless, the actual production needs to take place in rural areas and in the infrastructure connected to them, with workshops now constructed *extra urbem*, aiming to satisfy needs no longer tied to a large economic system such as that of the Empire but still anchored in the requirements of a market still influenced by it. The real turning point will take place only in the fully Early Medieval period, from the seventh century onwards. If we look at the nearby regional case of Lazio, the Tiber Valley Project, carried by the British School at Rome (Patterson 2010), represents a significant and interesting comparison. In this case, from the third century onwards, there is a marked drop of settlements, with just an ephemeral reprise in the fourth and fifth centuries, with the secondary settlements going through a deep crisis: in the Tiber valley, only some *villae* and those sites that were reused for the building of churches ensured some tendencies of continuity (see Fiocchi Nicolai 1994; Patterson 2010, 145). But if we look at the material culture, mainly pottery, the trends are similar to those we identified in the Ombrone valley: from the fifth century onwards, in fact – quite analogously to what happens in our research area – the markets' needs were satisfied mainly thanks to local production that somehow guaranteed 'standardized good quality products' (Patterson 2010, 146).

Another interesting comparison is the Arno river: there were some secondary settlements that alternated with the cities in the valley. These minor settlements had a strong commercial vocation, as evidenced by the findings of imported ceramics (Cantini et al. 2009).

The Ombrone river is then a complex socio-economic system that favours longterm trade from the coastlines to the hinterland, through a 'winning' settlement type, the *vicus*. Santa Cristina in Caio and perhaps Pietratonda are the nodes of the system, living mainly on trade and crafts.

In conclusion, to define the economic and commercial role of secondary settlements in greater detail in the long term, two main things are needed: an increase in stratigraphic investigations of these contexts and an intensification of comparative analysis between the different provinces of the Empire and the individual systems, where rivers, roads and secondary settlements formed a segment of the economic history of the countryside between Roman times and the Early Middle Ages.

## **Authorship per Section**

## **References**

Aldini T (1978) Anfore foropopilensi. Archeologia Classica 30:230–245

Aldini T (1999) Anfore foropopiliensi in Italia, Forlimpopoli. Documenti e studi 10:23–56

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# **Part III Transport and Movement**

# **Chapter 11 Modelling of Pathways and Movement Networks in Archaeology: An Overview of Current Approaches**

#### **Philip Verhagen, Laure Nuninger, and Mark R. Groenhuijzen**

**Abstract** This chapter presents and discusses current approaches and trends in computer-based modelling of pathways and movement networks in archaeology. After an introduction to the theoretical concepts involved, we present a state of the art of methodologies applied for reconstructing pathways and movement in ancient landscapes and discuss the various difficulties in using these methods as well as the most important technical hurdles involved. The problems of integrating optimal pathfinding algorithms with 'softer' socio-cultural variables are highlighted, as well as the limitations of modelling connections between places using least-cost path techniques. Network analysis reconstruction and analysis approaches are then reviewed as tools to better understand the overall structure of movement and communication in ancient landscapes. It is concluded that, while the potential of current approaches for understanding ancient movement is considerable, improvement is still needed in three main areas: the integration of approaches, sensitivity analysis and validation, and the theoretical underpinning of models of ancient movement.

**Keywords** Movement · Pathways · Landscape archaeology · Least-cost paths · Network analysis

# **11.1 Introduction**

In this chapter, we provide an overview of the current approaches to computer modelling of pathways and movement networks in archaeology. The subject has been of interest to archaeologists since the early 1990s, when the first studies were published that tried to reconstruct ancient pathways using GIS (e.g. Van Leusen 1993; Verhagen et al. 1995). Since then, a considerable amount of research has focused on

L. Nuninger

P. Verhagen (\*) · M. R. Groenhuijzen

Faculty of Humanities, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands e-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>
Chrono-Environnement UMR 6249/MSHE C.N. Ledoux USR 3124, Besançon, France e-mail<EMAIL_ADDRESS>
P. Verhagen et al. (eds.), *Finding the Limits of the Limes*, Computational Social Sciences, https://doi.org/10.1007/978-3-030-04576-0\_11

the modelling process itself, by trying to find ways to incorporate the factors that influence movement into the models as realistically as possible in order to arrive at good reconstructions of ancient routes and movement patterns. While clear successes can be observed in this respect, some major questions remain. These are centred around the possibilities of accurately modelling human movement and navigation practices on the basis of archaeological and experimental data, the validation of the models, and the relationship between the modelled routes, communication and transport networks and settlement patterns.

The purpose of this chapter is to summarize the main issues in the debate and put them into a larger theoretical and methodological perspective, since such a comprehensive overview is currently lacking. However, we refrain from discussing the results of individual modelling projects in terms of their archaeological interpretation. The chapters that follow (Chaps. 12, Groenhuijzen; 13, De Soto; 14, Parcero-Oubiña et al.; and 15, Crawford) provide a number of case studies in which this aspect is addressed.

## **11.2 What is Movement, and How Do People Move?**

## *11.2.1 Affordances and Movement Potential*

When discussing modelling of movement and pathways, it is useful to think in terms of *affordances* (Gibson 1977, 1979; Ingold 1992; Llobera 1996; Murrieta-Flores 2010). The concept of affordances was formulated by the psychologist James Gibson in 1977, and the term is a neologism based on the verb 'to afford'. Thus, the affordance of an environment corresponds to what it can offer to an individual (in the broad sense of the term including humans and non-humans), for better or for worse. It implies an interdependency between the individual and the environment. It is not only the set of abstract physical properties of the environment that can be measured in standard units, scales, etc. but a set of properties that are relative to the individual considered. Affordance could thus be defined as the potential offered by the environment in relation to an individual's properties and abilities to act in that environment (to move, obtain food, etc.): it is a set of environmental properties related to individual behaviour. According to Gibson (1979), the affordance of an environment is not the sum of its qualities but is more related to what the individual will normally pay attention to when doing something, like moving for example. Gaver (1991) supplemented the definition of affordance as the properties of the environment that make certain actions possible for an individual who is equipped for this purpose. In addition, he distinguished three types of affordances:

When moving, the affordance thus is the potential offered to an individual within a specific environment to move from one place to another, even when the individual is unaware of this or is not able to take advantage. It is only by considering the reciprocal influence of the environment (geographical, cultural) and the *movement capability* (technical, social) of individuals that we will arrive at identifying a set of movement affordances.

The basic premise of modelling of pathways and movement in archaeology is that we can use the affordance properties of the environment for movement in order to compute the *past movement potential* for a set of locations, using a GIS, for example (Llobera 2000).

Closely related to movement potential is the concept of *accessibility*. While movement potential is origin-oriented, accessibility considers movement from the perspective of the destination. In a completely isotropic environment, accessibility is the reciprocal of movement potential. In reality, the affordances can vary according to the direction of movement. For example, a site located on a hilltop can have a large movement potential, but not be very accessible.

Movement potential and accessibility are, however, only a set of possible, as-yet unfulfilled movement patterns. Modelling the actual movement of people and the pathways they have taken requires us to understand not only the affordances associated with movement but also the goals of movement and the cognitive and social processes that guide movement and structure the development of pathways that may eventually take on a permanent nature, and thereby change the affordances.

How to model movement, accessibility, and pathways has therefore been the subject of a substantial and lively debate characterized by a large number of experimental studies that heavily rely on GIS-based data and techniques. Underlying these are a number of assumptions about (ancient) movement that we will shortly discuss in the following sections. The main elements to consider are the movement capability of individuals, the definition of movement potential and accessibility by means of cost surfaces, and the use of least-cost paths as a technique based on optimal path-finding routines.

## *11.2.2 Movement Capability*

#### **<IP_ADDRESS> Energy or Speed?**

It is common practice in path modelling studies to measure movement capability in either *energy expenditure* or *movement speed*. Both are innate to the individual considered: humans walk slower than horses and spend less calories per time unit of movement. However, we have to take into account that modelling of movement capability is usually determined on the basis of averages for healthy individuals. Furthermore, individuals will not always maintain an average speed but can decide to go slower or faster.

The calculation of energy expenditure is often preferred because it is a direct measure of the effort that humans or animals will have to make in order to go somewhere while maintaining a certain speed. Ultimately, energy will run out and will need to be replenished with food and/or fuel and rest. It therefore poses a limit to the amount of time that can be spent on movement and thus on the distance covered.

Movement speed is more relevant for dealing with types of movement that prioritize speed, such as the deployment of troops, the trade in perishable goods, or the transfer of messages. It is also easier to understand when interpreting and comparing modelled pathways. Movement speed and energy expenditure are of course related, and there are even conversion formulae available (e.g. Groenhuijzen and Verhagen 2015).

#### **<IP_ADDRESS> Transport Modes**

The human capability for movement differs depending on the mode of transport used, which is in turn dependent on the transport medium (land or water). Almost all studies on modelling land-based movement up to date have focused on walking as the primary mode of transport. This has been studied in sufficient detail to allow for realistic modelling of movement capability, including the effects of carrying a load (see Sect. <IP_ADDRESS>).

For other modes of transport, there is much less reliable data available. Riding animals, in particular horses, can obtain much higher speeds than humans and will have been used when longer distances needed to be covered quickly. While average speeds and maximum distances per day covered on horseback or by riding other animals are known from historical sources, good data on the energy expenditure of riding animals are scarce. Some comparisons were made between human and donkey by Yousef et al. (1972), and the effect of loads on the movement speed of horses were studied by Wickler et al. (2001).

For carrying heavy loads, pack animals and wheeled transport will have been preferred, although these were not available to all ancient societies. In all probability, the use of pack animals (mostly mules, donkeys, and horses, but also camels, llamas, and elephants) will not have greatly influenced the speed of movement and the distance covered, since there would always be humans accompanying the transport animals. However, in the case of llamas, it seems that they could not travel for more than two days consecutively and would only cover distances of up to 20 km per day (D'Altroy 2015).

In the case of wheeled transport, there is only very general information available on the types of carts used, the number and type of traction animals employed to draw them, the maximum loads carried, and the accompanying movement speeds and distances (Bachrach 1993; Roth 1998; Kolb 2000; Yeo 1946; Laurence 1999; Raepsaet 2002; Adams 2007).

Water-based transport is another often overlooked transport mode in the modelling of movement, even though rivers in many areas form natural corridors of movement from the hinterland to the sea (Laurence 1999; see also Chap. 10, Bertoldi, Castiglia and Castrorao Barba). Water transport is also capable of transporting much heavier loads than land transport. Relatively little research has been done on the quantification of ancient movement over water. The speed or energy expenditure is dependent on various factors, including the ship type, manner of propulsion (floating, paddling, rowing, sailing, towing, and/or using a push pole), the direction of travel, and the flow of the river. Some information is available on long-distance movement, for example using prams on the Rhine in the Roman period (Jansma and Morel 2007). However, most local transport over water probably made use of dugouts (also known as dugout canoes or logboats), a type of watercraft that has been used at least since the Mesolithic. McGrail (1978) and Gregory (1997) provide an overview of dugouts from the UK and Ireland, including some quantification on speed and load capacity. Ancient sea transport, while having been studied in considerable detail (e.g. Casson 1994; Pomey 1997; Arnaud 2005), is even more challenging to model given the lack of (historical) data on how ships responded to weather and water conditions.

## *11.2.3 External Factors Influencing Movement Capability*

#### **<IP_ADDRESS> The Natural Environment**

The human capability for movement is influenced by external factors that are out of control of the individual, in particular terrain conditions – although atmospheric conditions can play a role as well. Topography, and in particular slope, is the most frequently used environmental factor considered. Steep slopes hinder movement for all modes of land-based transport, up to the point where zones may become impassable. The effect of slope on energy expenditure for walkers has been studied in detail (see Sect. <IP_ADDRESS>). For other modes of land transport, however, the effects of slope are less well defined.

A number of other environmental constraints can influence movement capability. One of the most important is the presence of muddy and boggy terrain that can considerably slow down movement or even impede it. Unlike topography, hydrological conditions can change relatively quickly and may have a distinct seasonal component. In tidal zones, conditions will even change within hours. In colder regions, the presence of snow and ice in winter is a factor to consider as well. Movement potential in winter may be quite different from summer, when wet areas will be frozen over that are difficult to negotiate in summer. Vegetation, especially high brush, can also reduce movement capability.

There is some experimental evidence available that relates different terrain conditions to the energy expenditure of walkers (Soule and Goldman 1972; Pandolf et al. 1976, 1977; De Gruchy et al. 2017). This evidence is rather limited, and similar data for other modes of transport are not available. Pack animals, however, seem to have no difficulties in keeping up with humans in any form of terrain, although for steep slopes mules and donkeys were usually preferred over horses, since they

are better at negotiating this type of terrain. For wheeled transport, critical slopes are clearly lower than for walking (Herzog 2013a), and in difficult terrain, wagons and carts will experience more difficulties than humans and pack animals (Haisman and Goldman 1974).

The effects of river crossings on movement capability across land have also been considered in a number of path modelling studies (see e.g. Van Leusen 2002; Fiz and Orengo 2008; Whitley et al. 2010). The procedure followed is usually to consider rivers (and other water bodies) as if they are zones that hinder movement in the same way as very steep slopes. Whitley et al. (2010) instead took the energy expenditure of wading and swimming as input for their models and this would seem to be the most realistic approach to estimate movement capability of walkers in wet terrain. Again, no similar data is available for other forms of land-based transport. We also have to keep in mind that getting one's feet or body wet comes with additional disadvantages, so the use of water-based transport will quickly become attractive even when the total distance to be covered over water is not very large.

For water-based transport, however, much less data is available on the effects of the natural environment on movement, even when some research has been done into modelling the effects of winds and currents on sea transport (see for example the ORBIS project http://orbis.stanford.edu).

#### **<IP_ADDRESS> Infrastructure**

Human intervention in the landscape can improve movement conditions considerably. Whether humans tried to overcome or reduce the effects of terrain conditions on movement will have depended on the importance attached to moving with little effort from one place to the next and on the technical abilities of ancient societies. Relatively simple measures include clearing the ground to make the going easier in the case of dense vegetation or boulders, the use of stepping stones to negotiate small rivers, and using switchbacks, steps, and stairs to climb steep slopes. More complex solutions are the construction of bridges to cross wider rivers and ravines, paving of roads in the case of wet terrain, and even cutting tunnels to pass steep rock faces.

In order to travel larger distances, people and animals also need places to stock up on food and water and find shelter to safely spend the night (Murrieta-Flores 2010). Locations where these facilities are found can be both natural and anthropogenic. Also, places where people could shift between modes of transport, like harbours and horse stables, will have been important logistical facilities. In the Roman period, for example, an empire-wide infrastructure of *mansiones*, *mutatione*s, and *stationes* was maintained to provide food, rest, and, if needed, fresh horses. The stageposts along the Inka road system known as *tampus* also provide a very good example of such an infrastructure. Hyslop (1984) estimates there were around 2000 of them along the ca. 40,000 km of the road network.

An important effect of infrastructural improvement is that it will concentrate movement in specific locations, and thereby also increase the possibilities for

control of travel and transport (see Sect. <IP_ADDRESS>). Modelling the effects of infrastructural improvement on movement patterns has however not been explored in depth.

#### **<IP_ADDRESS> Safety**

The factors considered so far are primarily concerned with energy efficiency and maximizing the speed of movement, i.e., they have direct effects on the movement capability of individuals. Many factors that influence movement, however, do not just have an effect on movement capability but also or even predominantly on the perceived affordances of the environment.

Unsafe areas in particular will have been avoided by travellers unless they were sufficiently prepared to deal with any dangers on the road. Knowing where enemy groups or wild animals lived – not to mention the residential areas of evil spirits or grumpy ancestors – will thus have been a very important consideration when choosing a route. Many ancient routes will therefore have been determined by the ability to avoid potential dangers, or if this could not be done, to equip them with protective infrastructure, such as forts and watchtowers.

Other aspects of safety have to do with weather conditions: a route could become unsafe or even inaccessible because of rainfall, snow or drought, and may have had specific infrastructure to deal with the effects of excessive water, cold or aridity.

Modelling safety of movement is highly complex since we usually don't have much evidence on where hostile groups of humans or animals, or even malicious spirits could be found (see Whitley 2000 for an exception). Visibility must have been an important aspect for this, and in some contexts it is therefore possible to analyse if routes are safer or more unsafe than others on the basis of being hidden from sight (Lock et al. 2014). However, we should not underestimate the role of sound and smell either. Estimating the effects of extreme weather conditions would seem more feasible, but as far as we know there are no studies around that have specifically addressed these questions from a route modelling perspective.

#### **<IP_ADDRESS> Control**

Control of routes was important for guaranteeing the safety of travellers, but many societies also used roads and other infrastructure to impose political and economic control on their own or hostile populations. Roads and waterways facilitate the movement of troops and can be used to regulate the access of travellers and goods by means of tolls. Travellers could also be forced to pay for the use of infrastructure and logistic facilities. Obviously, this kind of control system may also have led people to take different, non-controlled routes to escape paying the taxes.

A different type of control is supposed to have played a role in the positioning of the Inka imperial road system (Lynch and Parcero-Oubiña 2017). The Inka placed great importance on the symbolic appropriation of spiritual landmarks, in particular

the snow-capped mountaintops of the Andes. It is suggested that the positioning of the imperial roads can at least partly be explained by the wish to keep the mountain tops within view over a long stretch of road, and in this way assert the empire's power over places of spiritual importance.

#### **<IP_ADDRESS> Navigation**

Various authors have pointed out that navigation is inherent to movement (e.g. Lock and Pouncett 2010; Murrieta-Flores 2010), and thus the ease of navigation constitutes one of the major factors determining the affordances for movement on both land and water. Humans rely on sequential and mostly visual cues to find their way in the landscape. Cognition plays a vital role in the human ability to navigate, and the more local knowledge the traveller has, the easier it will become to find one's way. When travelling in unfamiliar terrain, however, navigational markers are necessary to help travellers arrive at their destination as they allow to provide oral or written instructions for wayfinding, like the famous indigenous Australian songlines. This latter aspect of creating a 'mental map' rather than using distance calculations was also relevant for maritime navigation in the Pacific (Turnbull 2000, 136). Permanent roads and water courses will even better guide movement, but even then markers will help the traveller to decide where to go, for example when arriving at a junction.

Navigational markers can be both natural and anthropogenic. The most important natural ones are terrain morphology (e.g. peaks, valleys, slope breaks, caves, horizon profiles), hydrology, vegetation, and geology (rock outcrops, boulders). They can be related to both short-distance and long-distance travel. A mountain top or river, or in the absence of such a landmark, the position of the sun or the stars, may provide the general orientation of travel. For navigation over short distances, and especially in circumstances of reduced visibility, local markers are more important. We should also be aware that markers can change their appearance over the seasons: ground can be covered in snow, trees will lose their leaves and water courses may flood or disappear in the dry season.

In the absence of suitable natural markers, humans have for a long time created their own ones, for example by erecting standing stones, cairns and milestones or by planting trees. Lighthouses were already in use in Antiquity to aid maritime navigation. Markers can also be used to emphasize the visibility of natural features, for example by placing cairns on hilltops, or by creating rock art (Fairén-Jiménez 2007). However, there will have been myriads of other anthropogenic markers available to travellers, since paths and routes express their character in a number of ways, for example because of their mode of construction, their trajectory including curves and crossings, and the presence of related infrastructure and other human activity in the vicinity of the path.

Understanding the role of navigation and markers in movement is a complex exercise, as is demonstrated in the studies by Murrieta-Flores (2014) and Llobera (2015). Researchers have therefore also focused on more general indicators to model the influence of navigation on path location, such as the general direction of movement (Zakšek et al. 2008; Lock and Pouncett 2010) and overall visibility (Lock and Pouncett 2010). Visibility, while being the sense that still provides 'most information on the structure of space to the brain compared to the rest' (Llobera 2007, 52), is however only one aspect of how people navigate; smell, sound, and even the touch of the feet on the ground also provide clues on the position of the traveller and will change according to the season.

## **11.3 Modelling Approaches to Ancient Movement**

The interest in modelling ancient movement was initially triggered by site catchment analysis studies in the 1970s (Vita-Finzi and Higgs 1970; Higgs and Vita-Finzi 1972). This approach can be characterized as establishing the affordances of a settlement's environment for agriculture or hunting-gathering, for which movement potential was considered to be the major factor. The area that could be reached within a certain amount of time from the settlement was considered to be the extent of its territory (see e.g. Ericson and Goldstein 1980). Since this analysis involved actually walking the areas around archaeological sites to map the extent of the territories, the utility of creating cost surfaces to quickly calculate and analyse the movement potential around settlements was therefore already clear when GIS arrived on the scene (see e.g. Gaffney and Stančič 1991; Verhagen et al. 1995).

However, the possibility to calculate least-cost paths (LCPs) in order to reconstruct ancient movement patterns and pathways was a new addition to the quantitative archaeological toolbox (Van Leusen 1993) and attracted much interest from the mid-1990s onwards. Least-cost path modelling is a method to find the optimal path between two or more locations. First, a cost surface is defined that determines the costs of crossing one grid cell, usually specified in time or energy units spent. A cumulative cost surface is then created from a starting point which will provide the cost distance from the starting point to every grid cell in the study area. Finally, we can then determine the least-cost path between the starting location and any other location, giving us some idea on where transport and movement may have taken place. The cumulative cost surface can also be used to find the area that can be reached within a certain amount of time (or by spending a maximum amount of energy).

Applications of path modelling are not just found in archaeology but also in economic and human geography (see Rodrigue et al. 2017) and to a lesser extent in ecology (see Cushman et al. 2013). In these disciplines path modelling is used to understand and predict movement patterns of traffic, goods and people (in geography) and animals (in ecology) within a constrained environment. These constraints are either natural, or created by human intervention. In contrast to archaeology, however, the movement processes modelled in geography and ecology can still be observed today.

Archaeologists and historians, on the other hand, are confronted with the fact that factors influencing movement patterns and transport networks have changed considerably in the recent past. Both the capacity of humans to intervene in the landscape and create new possibilities for movement, as well as the modes of transportation are completely different from those in prehistory, or even from a period as recent as the nineteenth century (see e.g. Lawton 2004). Analogies from modern day transportation are therefore not very suitable for archaeological applications. However, reliable information on how people dealt with these issues in the past is limited. Researchers therefore have to rely on modern-day data, such as physiological research into the speed of movement of humans in different environments, and use the scant historical evidence, for example by applying data from historical military sources to situations that did not involve the movement of troops.

Furthermore, the underlying premise of GIS-based modelling of movement and pathways is the calculation of optimal, least-cost or least-effort paths. This is an assumption that is very restrictive when investigating past movement (see e.g. Ingold 2011), and many studies in archaeological path modelling over the past decade have tried to come to grip with this. The main issues to be considered have been summarized in various papers (e.g. Murrieta-Flores 2010; Herzog 2014), but it is useful to provide a condensed overview here.

## *11.3.1 Cost Surfaces and Cost Definitions*

#### **<IP_ADDRESS> Defining Movement Capability**

Most modelling studies in archaeology have been explicitly interested in movement on foot and assume that slope was the main constraint to movement. While slope clearly is a major factor influencing movement capability, we already listed a number of other factors that can be considered. The popularity of slope as the primary cost factor is therefore not just related to its (perceived) archaeological importance, but also to the fact that elevation data is relatively easy to obtain, and can usually be considered a reasonable approximation of the topography in the past, since it is the most stable and enduring geographical factor. Also, walking on slope is the only type of movement for which there is reasonably detailed experimental evidence (Margaria 1938; Imhof 1950; Givoni and Goldman 1971; Pandolf et al. 1977; Ericson and Goldstein 1980; Minetti et al. 2002; Langmuir 2004; Kondo and Seino 2010).

Herzog (2013a) provides an overview of the different cost (or 'hiking') functions that have been used to estimate the effect of slope on walking speed and energy expenditure. She compares these functions to the data collected by Minetti et al. (2002) when walking on a slope and presents a 6th order polynomial function that best approximates the experimental data. The alternative equation developed by Llobera and Sluckin (2007), however, seems to better match the empirical data. Since these equations only provide values for energy expenditure, they cannot be

directly converted to time units, which are easier to understand and compare. By far the most popular hiking function in archaeology has therefore been the one attributed to Tobler (1993).

Similar functions for riding or pack animals and wheeled transport are not available because of a lack of experimental data. It has been noted (Llobera and Sluckin 2007; Herzog 2013a) that there is a critical upward slope for vehicles beyond which movement is not possible. As far as we can tell, however, the only equation that directly connects slope, and to some extent terrain friction, to movement of carts is given by Raepsaet (2002).

When calculating LCPs using slope-based hiking functions, it is important to keep in mind that upslope movement will lead to different paths than downslope movement, and therefore 'isotropic' cost distance calculations are unsuitable to estimate the optimal paths. A further problem with slope-based cost surfaces is that slope in GIS is always calculated as the average of slope from a grid cell to its 8 neighbouring cells. However, in order to find the optimal path, we need to know the slope in the direction of movement, or effective slope. Solutions to this problem have been implemented in various GIS packages (IDRISI, SAGA, ArcGIS), but Herzog (2013d) showed that the existing tools are either not implemented correctly or lack sufficient documentation to judge their performance. Alternative approaches, taking into account the general direction of movement, have been presented by Zakšek et al. (2008) and Lock and Pouncett (2010), but in practice there does not seem to be agreement on the best way to proceed.

#### **<IP_ADDRESS> The Role of DEMs**

Herzog (2014) also discusses the problems associated with creating LCPs from digital elevation model (DEMs). Most available DEMs are not well suited to create cost surfaces and least-cost paths for archaeological research questions. LiDARbased elevation models are very popular with archaeologists nowadays because of the level of detail they provide. However, their high resolution is also a drawback for path modelling since many modern-day, anthropogenic landscape features are present in the models as well, and filtering techniques to easily suppress these are not sufficiently developed yet. The vertical and horizontal accuracy and/or precision of the popular and free Aster and SRTM products on the other hand is often not sufficient for a realistic calculation of the accumulated cost surfaces. Also, interpolation techniques used to create DEMs from digitized contour lines and irregularly spaced point elevations can greatly influence the results. A well-known effect is the creation of artificial elevation 'steps' in relatively flat terrain because of very widely spaced contour lines. Ideally, DEMs used for LCP modelling should be based on corrected and sufficiently detailed height information that ignores recent anthropogenic features, and takes into account recent natural changes in topography as well. This often still implies correcting the DEMs manually, for example by consulting and (partly) digitizing historical elevation maps.

Lock and Pouncett (2010) and Lock et al. (2014) point out that scale is also an important factor influencing the results of slope-based path modelling. The horizontal resolution of a DEM will have a marked effect on the end results, as is for example shown by Verhagen et al. (2014). A DEM at a resolution that is too coarse may obscure difficult passages, especially the occurrence of cliffs, since these have a very limited horizontal extent (width). A cliff with only a few meters height difference is in practice impassable, but an elevation difference of 5 m will not seem very important when the cell size is large enough. The slope at 5 × 5 m resolution will be 100%, but at 50 × 50 m only 10%. DEM resolution also influences the results of path modelling when introducing linear features like rivers and cliffs as barriers or zones of difficult access, because of the effect of diagonal crossing (Van Leusen 2002).

#### **<IP_ADDRESS> Modelling Other Terrain Costs**

Other terrain factors directly influencing movement capability, in particular vegetation and soil type, would seem easier to model since their effects are isotropic, but in practice they are more difficult to estimate. Experimental data on energy expenditure when walking through various types of terrain were published by Soule and Goldman (1972) and Pandolf et al. (1976) and converted to terrain coefficients reflecting the difficulty of movement (summarized by Herzog 2014). A recent study by De Gruchy et al. (2017), however, indicates that these coefficients cannot be translated directly to movement speeds. For movement of vehicles, it is even more difficult to obtain reliable estimates. Groenhuijzen and Verhagen (2015) therefore combined the terrain coefficients obtained for handcarts by Haisman and Goldman (1974) with data on average movement speeds of vehicles reported from historical sources (Roth 1998).

Water-based transport has to take into account the direction of movement (upstream of downstream, which can be included through artificial slope; Groenhuijzen 2018), the flow of the river and the costs of moving between land and water. Wheatley and Gillings (2002, 156–157) suggest to model waterways as part of multimodal pathways as low-cost corridors which can be accessed through a barrier of high costs. Whitley et al. (2010) included portage of canoes as a cost factor as well. As mentioned in Sect. <IP_ADDRESS>, some experimental and historical information is available on sailing speeds for different types of vessels, but in practice it is very challenging to model all aspects influencing movement capability on water.

#### **<IP_ADDRESS> Visibility as a Movement Cost**

Possibly the most frequently considered non-terrain-based cost factor in pathway modelling is visibility, because of its close relationship to navigation, safety, and road construction practices but also because it can be relatively easily modelled on the basis of DEMs. The interest in visibility as an aspect of strategic placement of settlements, military infrastructure and monuments has a long history, and has been extensively explored in archaeological GIS studies (e.g. Gaffney and Stančič 1991; Wheatley 1995; Ruggles and Medyckyj-Scott 1997; Loots et al. 1999; Lake and Woodman 2003; Llobera 2003; Trifković 2006; Gillings 2009).

The inclusion of visibility as a cost factor for movement is usually approached through the calculation of *total viewsheds* (Llobera 2003) within the region of interest, and then adding the relative visibility of each grid cell as an additional cost. The drawback of this approach is the heavy computational load associated with total viewshed calculations. For this reason, Verhagen and Jeneson (2012) used openness (Yokoyama et al. 2002) as a proxy for visibility.

Recent studies (Bourgeois 2013, 105–158; Čučković 2015) have drawn attention to the fact that networks of intervisibility of archaeological sites and prominent landscape features can be successfully modelled and analysed, and may be of interest for understanding navigation and movement as well.

#### **<IP_ADDRESS> Modelling Socio-cultural Costs**

Herzog (2013a) discusses how to use parameters not related to movement speed in path modelling, like visibility or the presence of particular features attracting or repelling travel. 'Socio-cultural' costs are not based on expenditure of energy, and the resulting models will therefore not necessarily result in 'optimal' paths. Since the costs cannot be expressed in units of time and energy they need to be translated into a different 'currency', using some form of subjective weighting. This can produce confusing end results, since the costs then calculated are no longer real costs but 'pseudo-costs'.

The basic procedures for combining factors that are not intrinsically comparable are covered by the literature on multi-criteria analysis (MCA; Saaty 1980; Nijkamp et al. 1990; Malczewski 1999), a technique that is quite commonly applied in archaeological predictive modelling (Dalla Bona 1994; Verhagen 2006) and which has also been used for path modelling (Howey 2007). Importantly, the weighting of factors can take place at two levels: the attribute level (e.g. where it concerns the importance of visibility with increasing distance) and the criterion level (e.g. whether visibility is a more or less important factor to consider than slope). Normally, the weightings in MCA are based on expert judgement, preferably obtained by consulting a number of experts who then express their weight preferences using a procedure known as pair-wise comparison (Saaty 1980; Verhagen 2006). However, there is no objection to using different weighting methods or to include 'fuzzy' weights.

## *11.3.2 Calculating Routes and Movement Potential*

#### **<IP_ADDRESS> LCPs and Corridors**

Many published case studies in archaeology concerned with the reconstruction or prediction of ancient movement are modelling linear connections between two or more locations. This is mostly because the LCP toolboxes in GIS packages only calculate a single optimal route between start- and endpoints. The shortest path algorithms used in GIS are based on the work of Dijkstra (1959) and other computer scientists (Hart et al. 1968) who wanted to find efficient solutions to the problem of finding the shortest path in a graph consisting of multiple, unevenly spaced nodes. Movement in a grid is a special case of this, since all the nodes (grid cells) are evenly spaced. It is only by attaching differential costs to moving from one grid cell to the next that we can apply shortest path algorithms in a raster-GIS environment.

The assumption of a linear route is true for single travels, but the paths taken for multiple travels may shift in location, especially if these are continued over long periods of time, and when the routes are not consolidated by means of infrastructural amenities. Therefore, archaeologists have also explored the possibility of defining corridors of movement on the basis of cost surfaces, as a more fuzzy and possibly more realistic approach to reconstructing and predicting ancient movement patterns (e.g. Howey 2011; Murrieta-Flores 2012; Van Lanen et al. 2015a; Howey and Brouwer Burg 2017).

Some attempts have also been made to model potential movement patterns via agent-based modelling (ABM; Herzog 2016). The advantage of this approach is that the modelled paths are not deterministic: the agents can react to stimuli of the environment, and they can interact with other agents moving in the landscape. These models can also be used to simulate the spatio-temporal development of movement patterns. Simulation models are very well suited to investigate all kinds of sociocultural processes, but they are often based on highly abstracted representations of environmental and archaeological settings involved, whereas GIS-based studies often aim for more realistic representations. Furthermore, the few ABM studies around (e.g. Lake 2001; Wren et al. 2014) have mostly focused on dispersal, for example in the context of foragers looking for food or hominids moving out of Africa, rather than on the goal-oriented movement that is more commonly modelled in GIS. An exception to this is the study into army movement by Murgatroyd et al. (2012), who used computer-intensive ABM to model the logistics and most probable marching route of Byzantine troops on their way to the lost battle of Manzikert.

#### **<IP_ADDRESS> Movement Potential**

LCPs and corridors assume travel between fixed start- and endpoints, an assumption that is not necessarily valid when studying movement in the past. Non-agricultural societies, for example, can be highly mobile, so routes and pathways will be highly variable as well, depending on the availability of mobile or seasonal resources. Furthermore, the archaeological data sets we use are incomplete and do not provide us with all the clues we need to model ancient routes. Methods to predict *potential* routes can therefore be very useful.

A first step in this direction can be to model the movement potential for a set of locations (see Herzog 2013c for an in-depth overview). As indicated earlier, movement potential is closely related to accessibility but not its exact reciprocal. Llobera (2000) introduced the concept of 'total path costs' as a proxy for movement potential. By calculating for each grid cell the average costs of moving to every other grid cell within a predefined radius it can be analysed at various scales (local, middle range, global). Mlekuž (2013, 2014) developed a similar method of calculating 'potential path fields', which proceeds by summing accumulated cost surfaces ('site catchments') for every single grid cell. This method can also be used to analyse movement potential at multiple scales. Herzog and Yépez (2013), lastly, introduced 'least-cost kernel density estimation' to obtain movement potential maps, giving a higher weight to the areas closer to the point of departure. All these methods are computationally intensive on larger grids. It has to be emphasized that all published examples are based on the calculation of terrain costs influencing walking speed, in particular slope.

A map of movement potential based on least effort is not yet an indicator of probable movement patterns. Whitley and Hicks (2003) therefore experimented with creating multiple LCPs crossing a region from edge to edge, maintaining a regular distance between the start- and endpoints, and then cumulated the results. This idea was also applied by Zakšek et al. (2008) and Fovet and Zakšek (2014), using multiple LCPs connecting known settlements, and was further explored by Murrieta-Flores (2012). Using this approach, the LCPs will concentrate in specific locations, and their density can then be used as a proxy for the probability of movement.

This concept was taken further by creating LCPs from regularly placed departure points in a region, running either to the edges of the study region or to a number of terminus points within a predefined radius of movement. This approach was independently developed by White and Barber (2012), who named it 'From Everywhere To Everywhere' or FETE modelling and by Verhagen (2013) who referred to it as 'cumulative cost path' or CCP modelling. Llobera (2015) created similar patterns by calculating LCPs between random locations at varying distances. Herzog (2013c) notes that this approach has drawbacks in application: the concentration of paths is not dependent on the absolute costs involved, so even in areas where movement costs are generally high there still will be many paths.

A different approach to the problem of modelling potential routes is presented by Llobera et al. (2011), who used hydrological flow accumulation algorithms on accumulated cost surfaces, first experimented with by Fábrega Álvarez (2006), to create a 'focal mobility network'. A similar procedure was published in the same year by Frachetti (2006). It results in the creation of multiple, converging paths from the edge of the accumulated cost surface to the point of departure (see also Chap. 14, Parcero-Oubiña et al.). The locations where the paths converge can be considered as nodes in a network, and a 'mobility basin' is then defined as the number of cells 'draining' into a node.

## *11.3.3 Sensitivity Analysis and Validation*

While substantial debate has thus been directed towards the definition of cost parameters and the best ways to calculate movement potential and pathways, sensitivity analysis and validation of the models has been of less concern (see also Kantner 2012). Sensitivity analysis will reveal the effects of changing the

parameters that are entered into the model, and it has a solid tradition in computational modelling outside archaeology (Brouwer Burg et al. 2016).

Since path modelling is based on three different steps (cost definition, creation of accumulated cost surfaces, and least-cost path calculation), we can make comparisons and perform sensitivity analyses in all three stages. Of these, the comparison of cost definitions is the easiest, since we know the equations and/or weighted costs involved, and GIS offers good tools to compare these by making overlays and obtaining spatial statistics. It therefore may come as a surprise that such simple analyses are never presented (the authors of this paper plead guilty as well). Comparing accumulated cost surfaces is more complicated, since we will have to compare them for each and every starting point (and maximum distance, if applicable). This is an exercise that has never been published either, as far as we are aware.

Comparison of individual LCPs or movement corridors is a more common procedure (e.g. Howey 2007; Gietl et al. 2008; Verhagen and Jeneson 2012; Kantner 2012; Herzog 2013a, d; Verhagen et al. 2014). In most cases this is only done visually. Aspects like path length, deviation, sinuosity (Mueller 1968) and path travel time, however, are relatively easy to calculate, and can be used to assess the relative efficiency of the routes. Also, the characteristics of the paths can be quickly analysed by overlaying them on one or more of the cost factors used or on other environmental characteristics, for example to see where the paths are crossing difficult terrain. However, this becomes computationally expensive when doing this for a large number of paths.

Validation of path models is very comparable to sensitivity analysis, the only difference being that it compares the model outcomes to empirical data such as field observations, indigenous knowledge or ethnographic accounts and/or historical documents (e.g. Howey 2007; Becker and Altschul 2008; Fiz and Orengo 2008; Polla 2009; Fovet 2010; Murrieta-Flores 2014; Verhagen et al. 2014; Güimil-Fariña and Parcero-Oubiña 2015; van Lanen et al. 2015b; Supernant 2017; Fonte et al. 2017). Most work so far has been concerned with establishing the accuracy of the reconstructed routes in comparison to the available evidence. This is because a correct prediction is desirable from a heritage management perspective, but also because the interpretation of the functioning of the path or road system can only give meaningful results if it departs from a correct reconstruction. The chances of successfully predicting a stretch of road will obviously increase with the number of available independent sources for testing the model.

There currently seem to be no standard methods for judging the reliability of the predictions of pathways, even when methods for assessing predictive model performance are well established (Kvamme 1988; Verhagen 2008; Verhagen and Whitley 2012). The most commonly applied approach is to analyse the distance of the modelled paths to the archaeological and historical evidence (e.g. Bell and Lock 2000; Ejstrud 2005; Fovet 2010; Güimil-Fariña and Parcero-Oubiña 2015; Van Lanen et al. 2015b; Fonte et al. 2017): the more traces of roads and other evidence that are found close to or aligned with the modelled pathways, the better the model is thought to perform. However, some of these studies do not provide a statistical assessment of the reliability of the modelling results.

In terms of computational efficiency, the comparison of large numbers of path models can only be profitably approached through statistical simulation modelling techniques. These have not been applied extensively to questions of path modelling yet (in contrast to visibility analysis; see Lake and Ortega 2013), and this is almost certainly due to the use of GIS as the exclusive toolbox for path modelling. While GIS has many virtues, efficient statistical computing is not one of them, whereas standard statistical simulation techniques such as Monte Carlo-analysis and bootstrapping are not primarily intended for use with spatial data. A middle ground between the two is not available at the moment, so performing sensitivity analysis and validation of path models still requires combining different software solutions and programming.

## **11.4 Movement, Pathways, and Networks**

Pathways are always part of a network. They are connected to other paths that can be combined into routes that can be travelled in any order, not just the shortest or most efficient one. The network perspective changes the way in which we analyse movement: whereas cost surfaces consider the totality of the space that can be travelled, a network of paths represents a linear set of affordances for movement that limits travel to the network's structure. While this has some disadvantages from a theoretical point of view because it neglects the possibility of movement outside the path network, it also has strong analytical advantages since the properties of the network can be used to better understand the structure and development of (reconstructed) networks (see e.g. Gorenflo and Bell 1991; Brughmans 2010; Collar et al. 2015).

Social network analysis was developed in sociology in the 1970s and was initially only concerned with non-spatial relationships. Over the past decade, network analysis has become a major field of archaeological and historical investigation as well (see Knappett 2013a; Brughmans et al. 2016) with studies focusing on (supra-) regional trade and communication networks (e.g. Earl and Keay 2007; Sindbæk 2007, 2015; Knappett et al. 2008; Knappett et al. 2011; Carreras and De Soto 2013) and the possible development of social networks on the basis of observed finds (e.g. Mills et al. 2013; Coward 2013; Golitko and Feinman 2015). Archaeologists, however, have been keen to include geographical aspects in their studies as well (e.g. Carreras 1994; Isaksen 2007; Brughmans 2010; Coward 2013).

From a network analysis perspective, LCPs are graphs connecting two or more nodes via (weighted) edges. The only real difference with 'standard' network models is that the 'edges' have an irregularly shaped spatial extent. The shape of the pathways is not essential for performing network analysis, but the cost-distance between nodes is. Using relative distances instead of Euclidean ones can potentially lead to different configurations and thus interpretations of the networks. Several authors (Kaddouri 2004; Llobera et al. 2011; Herzog 2013b; Verhagen et al. 2013; Verhagen et al. 2014; Groenhuijzen and Verhagen 2015, 2016; Orengo and Livarda 2016) have explored the potential of using network analysis techniques with path modelling. Moving from LCPs to network analysis however implies that we first need to reconstruct the full network of possible connections.

## *11.4.1 What to Connect?*

Network analysis can only be undertaken when we know which places to connect. In the majority of case studies, the places where movement starts and ends are taken from settlement data, and to a lesser extent from places of symbolic or strategic interest, or where resources could be obtained. The existence of these connections is mostly inferred from theoretical considerations and from material evidence of exchange of goods and people. The nature of movement, its frequency and the distances covered, however, are more difficult to establish, which is where LCP modelling comes in.

Connections can be modelled most easily when we only consider direct links between the two nearest points (see e.g. Van Lanen et al. 2015b). This conceptually simple model is however problematic for two reasons. First of all, direct connections to places further away may have existed as well. And secondly, the archaeological record will not always tell us where the nearest connected place was. Both chronological inaccuracy and incompleteness of survey data sets will complicate the reconstruction of all existing connections.

Apart from the supposed start- and endpoints of movement, waypoints should be considered as well. Waypoints can be defined as locations that provide navigational aid and/or logistical support during travel. Certain waypoints will strongly concentrate movement because they provide easy access through difficult terrain, like fords, bridges and stairs. Many waypoints, however, are of a more ephemeral nature than settlements, and are therefore difficult to include in path models. There is also a reciprocal relationship between the two: paths may be chosen because of the presence of natural features that support travel, but since humans adapt the landscape, human-made waypoints may become an integral part of the path system as well. From a technical point of view we can either treat them as additional nodes to be connected, or add them as attractors to the cost surfaces using a distance decay function, so that the modelled paths will have a higher probability of passing through the waypoints.

## *11.4.2 Network (Re)construction Techniques*

Path modelling routines in GIS are not very efficient for network (re)construction since they do not allow for simultaneously connecting multiple nodes on the basis of standardized criteria. Commonly used and effective network construction techniques limit the number of allowed connections on the basis of distance and/or the number of closest neighbours (see Gorenflo and Bell 1991; Jiménez Badillo 2004; Rivers et al. 2013; Groenhuijzen and Verhagen 2017; Fulminante et al. 2017). This limitation is necessary in order to prevent the creation of spurious connections, since direct links from everywhere to everywhere are not realistic. Note that this approach does not exclude the existence of long-distance connections, it only constrains the number and length of *direct* connections.

A common approach to define the thresholds for direct connections between places is to use gravity models derived from economic theory and urban geography (see Hodder and Orton 1976, 187–195 for an introduction). These are based on the assumption of a decrease in interaction potential with increasing (cost) distance. Gravity models can be created by simply calculating accumulated cost surfaces around sites. Instead of assuming a linear decrease in interaction potential with increasing travel time or energy expenditure, an exponential decrease is then specified in a *deterrence* (Evans and Rivers 2017) or distance decay function (Nuninger et al. 2006). This assumption is based on the consideration that interactions are much more probable over short distances.

The functions can further be weighted according to the (hypothesized) importance of nodes in the network. Archaeologists who explored the utility of gravity models in the 1970s (e.g. Plog 1976; Crumley 1979) often used settlement size as a weighting factor, but other factors were included as well (e.g. Hodder 1974; Jochim 1976). Nuninger et al. (2006), for example, considered distance, hierarchical categorization of settlements and visual control to estimate the strength of interaction between nodes.

A network can then be set up by creating direct connections between places that fall within a predefined maximum weighted (cost) distance threshold. A further refinement can be introduced by limiting the number of allowed connections, using some form of nearest neighbour analysis (e.g. Broodbank 2000).

However, depending on the approach chosen, these techniques can result in the creation of unconnected network clusters, and the various methods will inevitably result in different configurations. Furthermore, creating optimal connections between pairs of points is not necessarily optimal for the network as a whole. So-called Steiner points (extra nodes to be used as junctions) can be inserted in order to optimize the connectivity of the whole network, but applying this principle to cost surfaces is very challenging (Frommer and Golden 2007; Verhagen et al. 2014). Sensitivity analysis and validation of the resulting networks would therefore seem an important issue, but best practices for assessing the realism of (re)constructed networks are still largely lacking (Knappett 2013b; Groenhuijzen and Verhagen 2017).

The realism of the (re)constructed networks is also influenced by the completeness of the dataset of places to connect. Lack of information on presence and dating of sites is a common feature in archaeology and may influence not just the network configuration, but also all resulting analyses. Bevan and Wilson (2013) and Paliou and Bevan (2016) approached this by adding simulated settlements in the modelled network, based on a prediction of suitable site locations. By repeating this procedure a large number of times, it could be assessed whether the resulting networks' characteristics were stable or not. Davies et al. (2014) and Groenhuijzen and Verhagen (2016) used a similar approach. In their case the site dataset was assumed to be relatively complete but lacking in chronological precision, making it difficult to interpret the evolution of the network through time. By repeatedly taking subsamples of the dataset and creating networks from them, the robustness of the observed patterns could be established.

## *11.4.3 Network Analysis Techniques*

Network analysis metrics come in two flavours, global and local (Wasserman and Faust 1994; Collar et al. 2015). Global descriptors, such as average shortest path length and clustering coefficient, give insight into the level of integration of the network: are all places well connected to each other, or is the network fragmented? Local descriptors are primarily used to understand the position of individual nodes in the network through the concept of centrality: which nodes are most advantageously positioned in the network? These local metrics, such as degree and betweenness centrality, are well suited to study the hierarchical structure of the network.