Settlement scaling theory

In recent times, there has been a great deal of interest in the effects of the sizes of communities on urban life, leading to the creation of a series of general models for how the diverse attributes of settlements vary, or scale, with their populations.Footnote ⁴ These are based on the observation that there is a set of relationships between the infrastructure and the social and economic outputs of settlements and their populations that not only tend to have the same, or similar, slopes or exponents, but also tend not to be linear.Footnote ⁵ In particular, infrastructure tends to increase a little slower than population, with exponents of either about 5/6 or 2/3, depending on context, while social and economic measures tend to increase a little faster, with exponents of either about 7/6 or 4/3, again depending on context. This has been explained by the fact that settlements concentrate people in space and time, increasing their opportunities to share both resources and information.Footnote ⁶ This has led to the formulation of a series of formal, that is, mathematical, models that predict the values for individual cities surprisingly well. These models are based on the twin ideas that, first, settlements can be conceived of as social networks embedded within the built environment and, second, the inhabitants of cities must balance the benefits of interacting with others with the costs of moving around the built environment. An important aspect of these models, however, is that they are meant to be very general and have not been designed to be tailored to specific conditions. This means that they should be applicable to both urban and rural areas and to both ancient and modern contexts, including the Greek and Roman world.Footnote ⁷ As Ortman and I have shown in a number of papers, this is something that is now very well borne out by the available evidence.Footnote ⁸ In particular, this research has shown that there is a consistent relationship not only between the inhabited areas, densities, and populations of ancient settlements, but also between the sizes and dimensions of public spaces and the street network and the footprints and capacities of some of the most important types of monumental buildings, including basilicas, theaters, amphitheaters, and circuses, while ongoing work by the author and others is examining the remainder.Footnote ⁹

Although the exact logic behind how these models are derived is too complex to review here, it is based on the idea that it is possible to come up with a series of models of the relationships between the infrastructure and social and economic outputs of settlements and their estimated populations by considering how the social networks of settlements change as they increase in size, assuming they are embedded within the built environment.Footnote ¹⁰ This leads to a relatively simple model for the relationship between the numbers of social contacts and the populations of sites, which is as follows: K = k ₀N ^1+δ, where K is the total number of social contacts, N is the population, k ₀ is a constant (i.e., the baseline number of social contacts), and δ is an exponent, which is equal to about either 1/3 or 1/6. It is then possible to express this in terms of the average number of social contacts per person by dividing both sides by the population.Footnote ¹¹ This gives: $k = k_0N^\delta $, where k is the average number of social contacts per person and the other terms are as above. These models suggest that the total numbers of social interactions will increase faster than the population, while the average numbers of social interactions per person will also increase, but at a slower rate.

As Lobo et al. have noted, however, since we would also expect the total social and economic outputs of each settlement, including both the total amount of wealth that they generated and the total amount of traffic that flowed into and out of them, to be proportional to the total number of social interactions that occur within them, it is also possible to suggest a model for the social and economic outputs of each settlement by simply substituting the term for the total numbers of social contacts with one for the total social and economic output of each settlement.Footnote ¹² This gives: Y = y ₀N ^1+δ, where Y is the total social and economic output of each settlement, N is the population, y ₀ is a constant (i.e., the baseline social and economic output), and δ is an exponent, which is equal to about either 1/3 or 1/6. Finally, this model can then be adapted to represent the average social and economic output per person. This gives: $y = y_0N^\delta $, where y is the average social and economic output per person and all the other terms are as above. This model therefore suggests that the total social and economic outputs of settlements will increase faster than their population, while average socio-economic outputs per capita will also increase, but at a slower rate. This, in turn, suggests that the total social and economic outputs of settlements will exhibit increasing returns to scale, since larger settlements will be more productive per capita. This suggests not only that we would expect the population of sites to be the most important factor behind their infrastructure and socio-economic conditions, and for the largest sites both to have had the largest disposable income and to have been the most well connected, but also that we would expect all three of these variables to be strongly related, meaning that the generation of wealth and the creation of external linkages are really two sides of the same coin (and probably mutually reinforcing). This means that we would expect both the total and average wealth associated with settlements and the total and average amount of traffic that flowed into and out of them to have increased at the same rate of approximately 4/3 and 1/3 in each case. We would expect them to be so interrelated as to be theoretically and empirically indistinguishable, so that one could even be used as a proxy for the other.

These theoretical models and empirical results therefore allow us to frame a number of specific hypotheses for how we would expect the sizes and capacities of macella to increase with population. In particular, although we would expect these structures to increase at the same rate, with an exponent of about 1, if they were simply a utility that was available to all, we would expect them to increase a little more slowly, with an exponent of about 2/3, if they were a form of infrastructure, a little more quickly, with an exponent of 4/3, if they were a reflection of the total amount of wealth or traffic associated with settlements, but very slowly, with an exponent of about 1/3, if they were a product of either the average amount of wealth of the inhabitants of settlements or the average amount of traffic flowing into and out of these sites. There is no reason to associate them with the percolation of information from an initial group of witnesses to the rest of the community, though, as has been done with theaters and amphitheaters, given that there is no evidence that they were ever designed to have a similar function to entertainment structures.Footnote ¹³

Finally, this approach also gives us a powerful way of thinking about settlements, since it allows us not only to assess how the various aspects of settlements changed as they increased or decreased in size, but also to examine the extent to which individual sites deviate from the overall relationship (measures known as residuals).Footnote ¹⁴ This might then be taken as a reflection of meaningful differences between the socio-economic conditions of sites once their sizes have been taken into account (known as scale-adjusted metropolitan indicators). In other words, although we would expect the overall relationship to be driven by differences in the sizes of sites, we would also expect there to be a certain amount of variation between sites as a result of local conditions such as resource endowments, agricultural potential, and sea, river, and road connections.

It is important to point out, however, that, although we now have good evidence that the infrastructure of ancient sites generally increased at a similar rate to other ancient contexts, such that these relationships can then be used as a proxy for wider social and economic conditions, there is so far very little direct evidence for a relationship between either the network potential or the wealth of sites and their estimated populations. As I have shown elsewhere, this is best exemplified by the fact that the total areas of public spaces, such as fora and agorai, and street networks increased a little more slowly than the estimated populations of cities, at the rate of about 2/3 in both cases, while the total widths of city gates increased even more slowly than these, at the rate of about 1/3.Footnote ¹⁵ Since the latter can be used as a proxy for the average amount of traffic that was flowing in and out of cities, we would expect the total amount of traffic that passed through them to have increased a little faster than the estimated populations of cities, at a rate closer to 4/3. Despite this, however, it is not possible to find an equivalent relationship between the sizes of sites and various basic network measures, such as degree centrality, betweenness centrality, etc., derived from the ORBIS network dataset.Footnote ¹⁶ The most likely explanation is that, although the dataset is sufficiently broad to allow us to estimate the overall costs in terms of distance, time, and energy of moving between different parts of the ancient world, it is not sufficiently detailed to allow us to calculate the network values of more than a handful of the most well-known individual sites.Footnote ¹⁷ Finally, as I have also noted elsewhere, there is only a limited amount of evidence that can be used as a proxy for the wealth of settlements, at least on an imperial scale, and that can be used in a way that is comparable to other contexts, in part because of the ways that ceramic evidence has traditionally been recorded.Footnote ¹⁸

Macella

The structures with which we are concerned here, macella or μάκɛλλοι, are generally regarded as providing permanent, specialized market buildings for the processing and selling of high-status commodities such as fish, meat, etc., given not only their location within the built environment, but also their architectural design and layout, accessibility, the attention that seems to have been paid to hygiene, the equipment related to commercial activities, and the evidence for the control and regulation of the prices, quality, and quantities of the commodities that were sold within them.Footnote ¹⁹ The ultimate reason for building these structures therefore seems to have been that they provided the appropriate conditions for the sale of perishable commodities and made it easier to guarantee their freshness, control their quality and quantities, and regulate their prices by bringing the foodstuffs together into a single, enclosed, space. According to Goodman, these structures should consequently be seen as a form of specialization, given that they also represent a conscious desire to devote a space to a particular kind of economic activity.Footnote ²⁰ The development of these structures should be seen against the wider backdrop of the development of shops and workshops used for the sale or manufacture of specific commodities, such as bars and bakeries.Footnote ²¹ They can therefore be regarded as being closely associated with the wealth of the inhabitants of the settlements they are found within, since they seem to have been devoted to selling highly perishable and, accordingly, more expensive commodities. Although some have been hesitant about drawing any direct parallels between the sizes of these structures and the wealth of settlements, recent work suggests that there is a link between the apparent prosperity of sites, largely based on measures such as their monumentality and domestic architecture, and the incidence of macella.Footnote ²² As Richard has noted, for example, “macella were a popular amenity in many well-to-do urban centers of the Roman world.”Footnote ²³ It is less clear, however, whether we would expect these structures to be a reflection of the total wealth of settlements or the average wealth of their inhabitants (and thus whether they are an aggregate or per capita measure).

Although these structures have come to greater prominence in recent years, they are still understudied, especially compared to other types of buildings such as theaters and amphitheaters. Although the most well-known study of their numbers, locations, dates, and architectural designs and layouts is still De Ruyt's Macellum: marché alimentaire des romains, important work has also been done more recently by Richard and Hoffelinck.Footnote ²⁴ The former's work has mainly concentrated on the issues related to defining and identifying the structures and their architectural forms and amenities, paying particular attention to the East. Meanwhile, although the latter's work has provided an updated version of De Ruyt's catalogue, which is used below, it has also mainly focused on using various methods to investigate the locations of macella in the built environment and, in particular, on understanding how consumers gained access to them and how commodities were transported to them. This has included looking at the relationship between macella and other features such as street networks, city gates, harbors, and public buildings, as well as using space syntax to investigate the links between macella and the streets that were most likely to have carried the greatest traffic. The reasons for the sizes and capacities of structures are therefore still poorly understood.

At the same time, there has also been significant debate about the extent to which macella can be regarded as being part of a consistent typology of buildings, while some scholars have raised doubts about whether the category even exists.Footnote ²⁵ As Richard has noted, there are generally two different approaches to this issue, which relate to the two main categories of evidence available.Footnote ²⁶ The first comprises a small group of structures that are explicitly referred to as a macellum or μάκɛλλον in inscriptions, such as the Macellum Magnum and the structure at Perge, while the second is a much larger group of structures that have the same architectural characteristics and amenities as others that have conventionally been regarded as macella, meaning that they can be identified as macella on purely architectural grounds.Footnote ²⁷ A certain amount of caution is required here, though, because the ancient references to macella may refer to the kinds of activities that took place within these structures, rather than the structures themselves, undermining their value for creating architectural typologies. The most useful approach has therefore been to focus on the architectural design and amenities of structures in the attempt to identify a common type of building, perhaps based on Roman and Italian prototypes, which had the same features and thus probably the same function, although it is obviously important to be aware of the scale of the regional and chronological differences between structures, especially between East and West (Fig. 1).Footnote ²⁸ The most characteristic features are usually regarded as being a central courtyard surrounded by ranges of smaller rooms, accompanied by a central columnar monument, or tholos.Footnote ²⁹ A fuller and more detailed list might include an enclosed, self-contained layout, a central courtyard, suites of equally or nearly equally sized, closable, and either inwards- or outwards-facing rooms, and a tholos that was generally proportional to the overall size of the structure, along with paved surfaces and colonnades, thresholds that restricted access to pedestrians, facilities for the processing of fish and meat, and a method of providing water, creating a relatively specialized, restricted, and hygienic environment.Footnote ³⁰

Fig. 1. Examples of macella (after Richard Reference Richard2014, fig. 1 [based on De Ruyt Reference De Ruyt1983: Plates. III and IV]). Left to right, top to bottom: Morgantina, Alba Fucens, Pompeii, Pozzuoli, Herdonia, Saepinum, Baelo Claudia, Lepcis Magna, Thamugadi, Hippo Regius. The structures are drawn to approximately the same scale.

These structures are natural candidates for the scaling analysis advocated in this article and provide an excellent opportunity to test theoretical models against empirical data and explore their potential for understanding structures. As we will see below, although it is necessary to expend some effort on collecting evidence for the dimensions of macella and measuring their other architectural characteristics from maps and plans, there is usually only one macellum per settlement. This matters for this study, as it means that we generally do not have to confront the same kinds of sampling issues as we do with other kinds of structures, such as temples, of which the numbers of extant and measurable examples vary, leading to concerns about the representativeness of the samples used. At the same time, these models should allow us to shed new light on macella, since they enable us not only to explore the relationships between the sizes of the structures themselves and the estimated populations and network potential of sites, but also to distinguish between the sites that simply have larger macella because of their greater size and the sites that have larger macella than we would expect based on their size as a result of more favorable local conditions or external linkages. Finally, this approach might also enable us to test how usual or unusual a given structure is (and thus whether it has been correctly identified and interpreted) by assessing the extent to which it conforms to the overall relationship. Consequently, this approach can be used to identify whether structures conformed to a single type in the first place, given that we would not expect a random selection of heterogenous structures to vary, or “scale,” with population, and to identify any anomalous structures that should not be included in this group. The next section will therefore focus on the evidence for the Macellum Magnum and four other important, but potentially problematic, cases.

There are two qualifications that need to be made before proceeding. First, these structures were not the only places where high-end commodities could be sold: others include the forum or agora and perhaps the tabernae. Having said this, we would expect a good proportion, if not all, of the high-end commodities that were available in each settlement to have been sold in macella, given the facilities they offered for controlling and regulating prices and quality, and the logic behind grouping specialist activities into one location. Second, we must also be careful not to remove these structures from their wider social, cultural, political, and economic contexts, or to regard them as an exclusively commercial phenomenon. As some scholars have argued, they might also have had a religious function, given their regular proximity to temples and possible role in the distribution of meat from sacrifices, at least in Italy and the West (this is based on the idea that the parts of the carcasses that were not offered to the gods were prepared for consumption and displayed on selling tables).Footnote ³¹ This should not make that much difference to the results below, however, given that such distributions can also be seen as a form of conspicuous consumption and therefore as a reflection of the overall amount of disposable income that was available in each settlement.

The Macellum Magnum

Although it is possible that earlier cases existed in Rome, the first evidence we have for a structure resembling the kind of market building with which we are concerned here comes from the statement in ancient sources that two markets for fish and meat in Rome were grouped into a single complex, which was referred to as a macellum.Footnote ³² This complex seems to have been located near the Forum Romanum and to have been built sometime during the 3rd c. BCE.Footnote ³³ Although there is some uncertainty about what exactly happened to this structure and why it was replaced, reflecting some confusion in ancient sources, the modern consensus is that it was superseded by two structures.Footnote ³⁴ The first, the Macellum Liviae, seems to have been built by Augustus and located on the Esquiline, while the second, the Macellum Magnum, which is our focus here, seems to have been built by Nero, dedicated around 59 CE, and located on the Caelian.Footnote ³⁵ This structure then seems to have been restored after the fire of 64 CE and continued to operate for at least a hundred, if not several hundred, years.Footnote ³⁶

Although there has been much speculation about the exact location and the architectural design of the Macellum Magnum, there are no extant remains of the structure, meaning that our only significant evidence comes from a combination of near-contemporary and later references in textual sources, the representation of the façade of the building on contemporary coinage, its inclusion on the later marble plan of the capital, some epigraphic evidence, and comparison with other structures. The textual material comprises an apparent reference to the building by Dio, who describes the construction of a “provision market called the Macellum” in Rome around 59 CE, and a direct reference to the building in the 4th-c. CE Regionary Catalogues the Curiosum and the Notitia, which locate it in Regio II, the Caelimontium, and list it between the Temple of the Deified Claudius (Claudium) and the neighboring brothels (lupanarios).Footnote ³⁷ The structure is also shown on various contemporary or near-contemporary dupondii, most of which bear the inscription MAC. AUG. S. C. (mac(ellum) Aug(usti)) and show a simplified view of the building, and it appears on three fragments (157a,b,c) of the marble plan of Rome installed in the Temple of Peace under the Severans, the Forma Urbis Romae, which show it in plan (Figs. 2 and 3).Footnote ³⁸ These fragments also clearly include the word “MACELLUM” and, although this label could, in principle, refer to another structure on the missing parts of the slab, its placement is most likely consistent with that of other labels on the Forma Urbis Romae, which are generally below the structure to which they pertain.Footnote ³⁹ This structure is therefore normally interpreted as being the Macellum Magnum.Footnote ⁴⁰ Finally, it is also worth mentioning the funerary stele of one L. Calpurnius Daphnus, given that it explicitly refers to him as an argentarius working in the Macellum Magnum and depicts him alongside two freedmen carrying baskets of fish.Footnote ⁴¹

Fig. 2. One of the dupondii of Nero showing the Macellum Magnum (now in the British Museum; asset no. 637159001). © The Trustees of the British Museum. Used under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) license. No changes were made to the image.

Fig. 3. Drawing of the fragments of the Forma Urbis Romae showing the Macellum Magnum; the inset number refers to the slab, while the letters refer to fragments (after Rodriguez Almeida Reference Rodriguez Almeida1981, pl. 40). The original figure has been cropped.

There have been several attempts to locate the structure.Footnote ⁴² Although earlier scholars assumed that it was situated under the church of San Stefano Rotondo, largely on the basis of the round plan of the basilica, this idea was dispelled by the discovery of the remains of the Castra Peregrina on the same site.Footnote ⁴³ Meanwhile, although both Rainbird et al. and De Ruyt have suggested new locations, in the grounds of the Villa Fonseca (for complicated reasons that involve reinterpreting earlier descriptions and linking them to known remains) and to the northeast of the Temple of the Deified Claudius (on the basis of the relative locations of the known fragments of the Forma Urbis Romae) respectively, both possibilities have been ruled out by more recent excavations, largely on the grounds of the absence of sufficient space for such a large structure.Footnote ⁴⁴ The exact location of the structure therefore remains unknown. Having said this, given the likelihood that the structure was at least partially designed to accommodate the sale of fish and related products, and the importance of supplying fresh water for filling and cleaning fish tanks, it might be productive to focus on the available free space along the line of contemporary aqueducts. This proposition also raises the intriguing possibility that at least part of the reason for Nero's construction of the new branch of the earlier aqueduct, the Celimontano Aqueduct, at some point between 54 CE and his death in 68 CE might have been to feed the Macellum Magnum rather than just the Domus Aurea, as has traditionally been suggested.

Although there are small variations between the coins, they are consistent in showing a two-storied building with a central tholos that rests on a high podium, has a short flight of steps, is surmounted by a domed roof, and is surrounded by porticoes on both sides.Footnote ⁴⁵ The tholos also contains a life-size statue of a deity, probably Neptune, while garlands are strung between the columns of the tholos and porticoes.Footnote ⁴⁶ Meanwhile, the relevant fragments of the Forma Urbis Romae show an L-shaped building that seems to consist of an entrance, a central courtyard containing a circular colonnade on a podium reached by steps, a rectangular portico, several ranges of small rooms that run along at least three sides of the courtyard and face both inwards and outwards, and at least one exedra.Footnote ⁴⁷ It is important to bear in mind, however, that the Forma Urbis Romae reflects slightly later conditions and, therefore, might also include some evidence for later rebuilding in either the 1st or the 2nd c. CE.

This evidence has been used to suggest various reconstructions of the building that are based on the assumptions that the imagery shown on the coins is relatively reliable but simplified and that the building shown on the marble plan was more or less symmetrical.Footnote ⁴⁸ Although there are some differences between these reconstructions, they largely agree that the building took the form of a square structure with three or four entrances that led onto a central courtyard with a tholos, on a podium, that could be accessed by one of four staircases, was comprised of 16 columns, and probably contained an over-life-size statue. This courtyard was surrounded by at least four ranges of shops, while the exterior of the building was also articulated by a portico, with additional shops that opened onto the street. These were accompanied by at least one and probably two exedrae, which have been interpreted variously as fountains or niches for statuary by other scholars but as latrines by Carandini and Carafa, and up to four triangular fish tanks.Footnote ⁴⁹ The main differences between the rival reconstructions have therefore revolved around the exact number and function of the exedrae, although Carandini and Carafa have also raised the interesting possibility of a bridge connecting the tholos with the second floor of the portico.Footnote ⁵⁰ Meanwhile, although earlier reconstructions, such as Tameanko's, have now largely been dismissed by scholars, they are still valuable in reminding us of the potential existence of other features, such as shrines.Footnote ⁵¹

I have followed Carandini and Carafa's reconstruction, using it to estimate the total footprint and explore the other architectural features of the structure referred to above, because it is the most up-to-date and the most in keeping with what we know of the wider architecture of Rome under Nero (Fig. 4).Footnote ⁵² This suggests that the building was just under 95 m long by just under 80 m wide, covering a total footprint of about 7,600 m² (the exact figure is 7,573 m²), and included four blocks of eight rooms (four facing outwards and four inwards), two ranges of 12 (seven outwards and five inwards), four further blocks of three rooms, and four more miscellaneous rooms, coming to a final total of 72. It is worth pointing out, however, that we would expect any slight variations in the reconstruction to have only a minor effect on the results, especially when examined using logarithmic scales.

Fig. 4. A comparison of the known fragments of the Forma Urbis Romae showing the Macellum Magnum and Carandini and Carafa's reconstruction of the same structure (based on Rodriguez Almeida 1981, pl. 40, and Carandini and Carafa 2017, pl. 138). The scales and orientations are approximate.

Other problematic cases

Aside from the Macellum Magnum, there is a small number of other problematic cases. It is important also to discuss these briefly, since there has been some uncertainty as to whether they should be classified as smaller public spaces or large commercial markets (i.e., macella).

As Richard has noted, although there has been significant debate about it, recent work on the “Lukasgrab” at Ephesus has shown that it should probably also be regarded as a macellum, on the basis of the circular structure that was found in its middle; therefore, it has been included in the set of data used below.Footnote ⁵³ As Hoffelinck has shown, this tholos was probably added later, perhaps dating to some point in the third quarter of the 2nd c. CE, while the portico itself is a little earlier, probably dating to the first half of the 1st c. CE.Footnote ⁵⁴ As we will see below, this structure is also the fourth largest in the catalogue, measuring about 63 by about 81 m, on the basis of recent geophysical survey and excavation, giving a total footprint of about 5,103 m² and placing it on a par with other public, rather than commercial, spaces. This means that it is interesting to assess how well this structure compares with the other structures discussed below.

Two other important cases are the structures at Perge and Side, given that these have also been described by scholars both as commercial agorai and as macella (despite the fact that the former is explicitly referred to as a μάκɛλλον in inscriptions).Footnote ⁵⁵ These structures both comprised a large square containing a central circular columnar structure (i.e., tholos), lined on all sides with porticoes and with either inwards- or outwards-facing shops (35 at Perge and two sets of 30 and 13 at Side), accompanied by latrines (at least at Side) (Fig. 5).Footnote ⁵⁶ These structures are unusual given not only their relatively large sizes, about 5,776 m² (76 by 76 m) and 8,554 m² (91 by 94 m) respectively, but also the fact that the central structures within them are less in proportion to the overall footprint than elsewhere, and the one at Side is notably off-center.Footnote ⁵⁷ As Richard has noted, “in the case of the gigantic complexes at Perge and Side … we could instead be dealing with agorai which happened to include a tholos-like (cult?) building.”Footnote ⁵⁸ It is for this reason that I have assumed that they were public spaces in earlier work.Footnote ⁵⁹ Finally, as we will see below, there seem to be similar issues with the structure at Pompeiopolis, largely known through geophysical prospection, again because of its enormous size: it covered roughly 65 by 120 m, giving a total footprint of 7,800 m².Footnote ⁶⁰ These structures have therefore been set aside for the moment, although the extent to which they conform to the wider relationship, and to the wider typology, is also explored below.

Fig. 5. The macella at Perge (left) and Side (right) (after Richard Reference Richard2014, figs. 3 and 4). The original figures have been combined.

Data and methods

Given the uncertainties about both the definition and the identification of macella, and the issues with the quality and quantity of the data, I have begun by deriving a basic list of structures from Hoffelinck's work, which largely supersedes earlier work such as Cristilli's, since it includes nearly double the number of structures.Footnote ⁶¹ This not only provides us with a list of known or suspected macella throughout the Roman world in the Imperial period, but also includes details about their exact locations and their dates of construction, along with some figures for their lengths and widths (although there is no attempt to estimate their total footprints or to explore how the sizes and proportions of structures varied between sites).Footnote ⁶²

As Hoffelinck has shown, these structures are much more abundant in Italy, parts of North Africa, and (to a slightly lesser extent) the East than in the northwest and the Balkans, although this might be more a result of the relative density of cities, which is also highest in these regions, than anything else.Footnote ⁶³ Meanwhile, although the evidence for the construction of these structures peaks twice, during the Julio-Claudian dynasty and the Nervan/Antonine dynasty, they are relatively common throughout the Imperial period as a whole.Footnote ⁶⁴ This generally matches what is known of construction rates throughout the empire. It is important to remember that large numbers of these structures are of unknown date, but there is no reason to suspect that being able to specify these would dramatically affect the overall picture. This means that these structures are a relatively discrete phenomenon.

As noted above, architecturally, macella are usually enclosed, self-contained entities and are normally made up of a central courtyard, surrounded by ranges of smaller rooms, with a circular structure known as a tholos in the middle.Footnote ⁶⁵ They are either square or rectangular, with entrances on all four sides, although they can have a slightly irregular shape. They occasionally have upper stories, but not always. The rooms are usually of a uniform size, with wide, closable thresholds, so that they are normally interpreted as shops, while the tholos generally consists of a few steps, a ring of columns, and a domed roof. Although we do not know the exact function of the tholos, the most likely options are that it was where fish was sold, where weights and measures (and other equipment) were held, where small rituals were performed, or where auctions took place. Tholoi are therefore often described as multi-functional kiosks, which could be used to accommodate a number of different things, from basins or fountains to statues or shrines devoted to the gods associated with commercial activities. Finally, as Hoffelinck has shown, macella are also usually located in or near accessible locations, such as in the heart of the urban center, near the forum or agora, on main streets, by the gates, or on the outskirts of a settlement near harbors, rivers, or roads (although they are usually found within settlements, they are also occasionally found immediately outside them), given the obvious need for access by both producers and consumers.Footnote ⁶⁶

I have used Hoffelinck's figures for the lengths and widths of structures to estimate their rough area: given that the majority of these structures are either square or rectangular, this should be a close approximation of their total footprints.Footnote ⁶⁷ However, I have not included any of the structures where either the length or width is unknown, where there is some uncertainty about one of these measurements, or where we only know a limited amount about aspects of them, such as the radii or diameters of their tholoi.

In total, this provides us with useable figures for 49 structures, which are associated with about the same number of sites and which represent about a third of the 145 structures (and 135 sites, because some sites have more than one structure) recorded in Hoffelinck's catalogue, illustrating the relatively limited amount of information that we have about this type of structure (these data are detailed in the Supplementary Materials). The catalogue includes a series of new figures for the sizes of the structures, of which the most notable for the purposes of this article are the “Lukasgrab” at Ephesus and the macellum at Pompeiopolis, where the measurements are based on recent geophysical surveys and/or new excavations. The Macellum Magnum itself, however, was never included in Hoffelinck's catalogue, and has therefore been added, bringing the grand total to 50 structures and about the same number of sites.

It is important to make three observations about these data. In the first place, as Richard has noted, one of the challenges of looking at these structures is that, although a large number of them have been documented, only a few have been comprehensively excavated, recorded, and published.Footnote ⁶⁸ This means that we generally have better evidence for the West than the East (in fact, we only have evidence for a handful of structures in Asia Minor and the Levant), the exception to this being Greece. Therefore, our evidence is a little biased. Second, as noted above, although there is usually only evidence for one macellum per settlement, there are a limited number of examples with evidence for more than one. In those cases, I have simply taken the largest structure. The most important example of this is at Thamugadi (Timgad), where I have taken the value for the early 1st-c. CE Market of Sertius, rather than for both that and the late 2nd- or early 3rd-c. CE Central Market.Footnote ⁶⁹ The differences in scale between them are slight, however (38 by 26 m, as opposed to 29 by 22 m), and including both makes hardly any difference to the results. Finally, it is also worth noting that the measurements do not include upper floors, given the uncertainties about how much of the footprint these occupied and what the space was used for (in particular, whether it was given over to more shops or used for other things, such as storage). Since this condition has been applied to all the sites dealt with here, it should not make that much difference to the results given below.

Next, I have also taken the opportunity to use a combination of ArcGIS and existing maps and plans to measure the sizes of the structures’ courtyards, using the same approach as in earlier work, but only focusing on the structures with the clearest, most detailed, and most complete maps and plans, meaning that the size of this sample is a little smaller.Footnote ⁷⁰ This makes it possible to either measure or estimate the total area that was given over to shops within most of these structures, to count the total number of units within these areas, and then to divide the former by the latter to calculate the average sizes of the shops within each structure.

I have then used the same evidence for the estimated inhabited areas, densities, and populations of sites as I did elsewhere (originally published in this journal).Footnote ⁷¹ This is based on a calibration dataset of all the sites where it is possible to measure both the inhabited area of the site and the number of residential units in a specific zone within it, meaning that it is then possible to estimate the population densities of each site, assuming an average of five people per household. This approach can be used to explore the overall relationship between estimated inhabited areas, densities, and populations, and to provide a method for estimating any site's population based on its inhabited area. The figures have been rounded to the nearest thousand in the results and discussion below to reflect their likely reliability, but not in the underlying analysis, where it is best to use the original estimates to assess the statistical significance of the relationship, examine the amount of variation between sites, and assess the residuals of the relationship with a view to understanding sources of error and accounting for other, secondary effects. As in earlier work, I have assumed that most of these structures coincide with the maximum expansion of each settlement or are at least close enough to it to have no marked effect on the results.Footnote ⁷²

I have then assessed the relationship between the footprints and other architectural features of these structures and the estimated populations of the sites using a common form of regression known as ordinary least squares regression (Table 1). As has been noted elsewhere, this is feasible because y = bx ^m and log y = mlog x + log b are equivalent expressions.Footnote ⁷³ Therefore, we can estimate the exponent and pre-factor of the power function by estimating the y-intercept and slope of the best fit linear function, so long as it is based on log-transformed values, as well as measuring the extent to which each side deviates from it.

Table 1. The results of regressing the total footprints, courtyard areas (both in m²), number of shops, and average sizes of shops (again in m²) of macella against the estimated populations of sites. All regressions are done using ordinary least squares regression on log-transformed values.

Next, I investigated whether the best-connected and best-integrated sites had the largest macella by exploring the relationship between the sizes of these structures and their network potential. To do this, I used ORBIS: The Stanford Geospatial Network Model of the Roman World (henceforth ORBIS), which offers a simplified dataset of cities and sea, river, and road networks in the Greek and Roman world, roughly reflecting conditions around 200 CE (Fig. 6).Footnote ⁷⁴ Although this dataset only includes a limited selection of settlements, 678 in total, it does allow us to calculate the distance, time duration, and financial expense associated with different types of travel between different locations for most of the sites that we are interested in here. I therefore began by cross-referencing these data with the catalogue of cities referred to above. I then used standard techniques to identify the most significant nodes in the network. The measures we are concerned with are degree centrality (the number of edges to a node), betweenness centrality (the number of times a node acts as a bridge along the shortest path between two other nodes), and Eigenvector centrality (the likelihood of a node being connected to other well-connected nodes in the network).Footnote ⁷⁵ The last of these assigns a score to each node that is based on the idea that a node will be more important if it is linked to other important nodes in the network. The network was then analyzed in Gephi, assuming that all the edges are undirected, but using the cost of moving along these edges in terms of distance (in km), time (in days), and expense (in sestertii) as their weights (I have disregarded the season, though, since this is not relevant at this scale). In total, it is possible to estimate the network values of 341 sites from throughout the Roman world in the Imperial period (this number is simply a product of the number of sites that are included in the ORBIS model).

Fig. 6. The ORBIS model, which offers a simplified dataset of cities and sea, river, and road networks in the Greek and Roman world, roughly reflecting conditions around 200 CE (after Hanson Reference Hanson2020, fig. 3). The black circles represent cities, the blue lines represent the sea and river network, and the purple lines represent the road network. The data are derived from https://purl.stanford.edu/mn425tz9757 (accessed January 18, 2019). No changes have been made to the underlying data.

Finally, I have examined the relationship between the extent to which each site deviates either positively or negatively from the overall relationship discussed below (a value that is known as a residual) and measures of the numbers of calories that could be derived from agriculture (this is known as a total calorific suitability index), the distances between sites and the nearest harbors, and the same network measures discussed above, using the same data as in previous work.Footnote ⁷⁶ This can be used to assess whether any of the extra capacity that is contained within some structures can be explained by the presence of either slightly more or slightly less favorable agricultural and commercial circumstances.

Results and discussion

In total, it is possible to estimate the footprints of 50 structures (including the Macellum Magnum), which are associated with the same number of sites. They vary widely in size, ranging from as little as 196 m² (Genava) to as much as 7,573 m² (Rome), but with an average of about 1,265 m². This is interesting in its own right, as it suggests that most structures were substantial buildings, with an average size about five times larger than the average domestic unit in Pompeii and Herculaneum.Footnote ⁷⁷

The results of regressing these data reveal that there is a strong relationship between the footprints of these structures and the estimated populations of sites (Table 1 and Fig. 7). At the most basic level, this confirms that it is legitimate to regard these structures as belonging to the same basic type of building, although, as we will see below, this does not necessarily mean that all of the structures that have been dealt with should be included within this category. Another feature of these results is that the exponent of the relationship is very close to, if not exactly the same as, the expected value of 1/3, while the confidence intervals include this figure comfortably, meaning that it is consistent with the theoretical and empirical work discussed above. The overall relationship is also statistically significant at the 0.00001 level (the p-value is <0.00001). This is remarkable, given that the datasets used are completely independent (i.e., they are derived from separate published sources). Although the R² of the relationship is relatively low overall, reflecting a reasonably large amount of unexplained variation in the relationship, it is nonetheless relatively high for historical and archaeological data and is more or less comparable with both earlier and ongoing work on other types of structures (for example, the R² for macella is 0.42, while for basilicas and theaters and amphitheaters it is 0.39, 0.38, and 0.35 respectively).Footnote ⁷⁸ The reasons for this variation will be returned to below. It is also worth noting that including or excluding the Macellum Magnum makes little difference to the results, simply decreasing the exponent of the relationship from about 0.41 to 0.40 and increasing the pre-factor from about 22 m² to about 25 m² (marginal differences). Although it also has the effect of reducing the R², this is probably to be expected, given that removing this structure also has the effect of lowering the numbers of orders of magnitude being dealt with in each case. The Macellum Magnum has therefore been retained within the data below. The relationship is also extremely sublinear, meaning that, although the largest communities do tend to have the largest macella, the sizes of these structures tend to increase much more slowly than the estimated populations of sites (or, in other words, doubling the size of a settlement does not lead to a macellum that is twice as large). This means that these structures increase at a rate that is broadly comparable to that of theaters, amphitheaters, and city gates, but markedly different from fora/agorai and street networks.Footnote ⁷⁹ This has interesting implications for our understanding of macella, as it suggests that there is an increasingly small ratio between the size of the population and the size of macella, meaning that there is a decreasing amount of space per person as cities increase in size (i.e., there is a decreasing amount of space per capita).

Fig. 7. The relationship between the total footprints of macella (in m²) and the estimated populations of sites (in persons). Both scales are logarithmic. The lighter grey line indicates a linear relationship, which is provided for reference. The Macellum Magnum, which is included in the dataset here, is marked with an open square. For the effects of including or excluding it, see Table 1.

One of the most striking aspects of this relationship for the purposes of this article, however, is that the slope, or exponent, of the relationship is closest to the value of 1/3, rather than 2/3, 1, or 4/3, as we might have expected. At first glance, this is surprising, given that we might have expected a relationship similar to that associated with buildings that function like a form of infrastructure; this usually scales in a sublinear fashion, but with a slope, or exponent, of 2/3. Alternatively, we might have expected the relationship to be similar to the social and economic outputs of settlements, which generally scales in a superlinear manner, with a value of 4/3. These results, however, suggest that the sizes of macella should be interpreted as a reflection of both an increasing average amount of wealth and a greater amount of traffic per person, in both cases as the sizes of settlements increase.Footnote ⁸⁰ The reason for this is that, as noted above, although we would expect the total amount of wealth and traffic generated by a settlement to have increased at a rate of 4/3, we would only expect the average amount of both of these measures per capita to have increased at the rate of 1/3. Finally, it is also interesting to consider the pre-factor, or y-intercept, of these relationships, since this can be used as an index of the baseline size of structures.Footnote ⁸¹ This is about 22 m², indicating that these structures were relatively modest in comparison with other kinds of buildings (such as theaters and amphitheaters, which have a pre-factor for their seating capacities of 292 and 630 persons respectively, equating to very roughly 82 m² and 176 m² each).Footnote ⁸²

Next, it is interesting to note that the lengths and widths of these structures increase with estimated population at almost identical rates, in keeping with the assumption that they were mostly square structures. Meanwhile, although the number of observations is a little lower, given the smaller amount of available information, it is also striking that there is a series of relationships between the estimated populations of sites and the architectural features of the structures found within them (Table 1). These results suggest that the sizes of the courtyards within macella generally increase much more slowly than the estimated populations of sites. Although the exponent of the relationship does not match any of the theoretical expectations discussed above, the confidence intervals do include the value of 1/3 (the relationship also has a relatively high R² and is significant at the <0.00001 level), suggesting that it might be profitable to measure the total amount of space available for moving and interacting with others within a larger range of types of structures in the future. Perhaps more importantly, these results also suggest that both the numbers and the average sizes of the shops that are found within these structures also increase much more slowly than population and at broadly similar rates, especially if one considers the full range of values included within the confidence intervals (both of these relationships also have a relatively high R² and both are significant at the <0.005 level, although the p-value for the former is a little lower than for the latter). This suggests that roughly half of the gains of increasing the sizes of cities were put into building larger shops and roughly half into building more of them (allowing for a little margin for error in both relationships). This echoes recent work on the widths of gates, which has also suggested that about half the gains that were made by larger settlements went into building more gates and about half into making wider ones.Footnote ⁸³

Although we obviously have to be cautious about assigning any specific functions to these rooms without more detailed excavation (and most importantly without more detailed ethnobotanical and archaeozoological studies), these results nonetheless strongly suggest that the larger macella that were associated with larger sites could have provided both a greater volume and a greater range of commodities, assuming the number of rooms is an index of diversity and their sizes are an index of capacity. These results might have wider implications for our understanding of food supply, since they suggest that the inhabitants of larger cities might have had access to not only more foodstuffs, but also a greater range of them, meaning that they might have had a more varied diet (and a greater amount of choice), with obvious implications for our understanding of supply and demand. These results also reveal, for the first time, that it is possible to extend the basic approach behind settlement scaling theory to the numbers of rooms within structures, moving far beyond earlier work, which has simply focused on the total footprints or overall dimensions of structures. This is a result that could have significant implications for future research.

Given everything that has been noted above about the interrelated nature of wealth and traffic, it is also not surprising that there is a series of broad relationships both between the populations of the sample of sites used here and the network measures discussed above (and vice versa), and between the footprints of macella and the same network measures (and vice versa) (Table 2).Footnote ⁸⁴ This effectively means that the largest structures are found not only in the sites with the largest numbers of immediate neighbors (degree centrality), but also in those with the greatest likelihood of being passed by traffic moving along the network (betweenness centrality) and the greatest overall influence over the rest of the network (Eigenvector centrality), supporting the suggestion that was made above that we would expect the largest macella to be found within the most well-connected and integrated sites. None of these relationships, however, match the expectations discussed above very closely, perhaps because none of them is a direct equivalent for the volume of traffic itself. Finally, although we need to be careful about overinterpreting these values, it is notable that the figures for the R² of the first and last sets of relationships are the largest. This is important, as it suggests that the numbers of immediate neighbors and the overall influence over the rest of the network are the most important of the three factors discussed here. These results therefore have significant implications for our understanding of the ancient world, since they suggest not only that the sizes and capacities of market buildings, the estimated populations of cities, and their overall levels of connectivity and integration are all related, but also that increasing population is associated with both increasing urban demand and increasing ability to supply that demand through external linkages.

Table 2. The results of regressing the total footprints of macella and the network potential and estimated populations of sites. All regressions are done using ordinary least squares regression on log-transformed values. The number of observations is 29 in all cases.

More generally, these results have important consequences for our understanding of the different kinds of food that were supplied to cities and the facilities that were built to support this. In turn, there are implications for our understanding not only of the nature of wider retail, but also of the diets of the inhabitants of settlements and the overall standard of living and quality of life within urban contexts. In the first place, these results demonstrate the importance of large, specialized market buildings for the supply of food to cities, as well as raising the possibility that the residents of larger cities might have had access to a more plentiful and wider diet than their counterparts in smaller cities. This echoes recent ethnobotanical and archaeozoological work in other contexts, such as Rome, Pompeii and Herculaneum, and Silchester, that has been used to suggest that there was a significant widening of tastes throughout the Roman world in the Imperial period.Footnote ⁸⁵ Secondly, these results suggest that these structures can be seen as a reflection not only of a significant amount of economic development, but also of the development of middle-income groups with a certain amount of disposable income. Thirdly, these results are in line with the increasingly widely held view that ancient cities were extremely highly integrated and connected with the rest of the Roman world, and the related suggestion that they induced a significant amount of professional specialization, including in relation to food. As shown elsewhere, although we do not have much information about the numbers of occupations in ancient cities, we do have evidence for the numbers of professional associations, such as collegia. These can be used as a proxy for the range of activities that occurred in settlements, suggesting an expansion of both specialization and diversification with city size.Footnote ⁸⁶ In addition, as Kaše et al. have shown, drawing on epigraphic material, there is evidence for a much larger number of occupational categories in general and a much larger number of occupational categories related specifically to food production in large cities compared to both medium-sized and small ones.Footnote ⁸⁷ Meanwhile, although there is evidence for at least 200 different crafts or trades in the capital, of which about 35 are related to the importation, preparation, or sale of food, there is very little or no comparable evidence for most other sites.Footnote ⁸⁸ In the capital, at least, there were also a number of structures that seem to have been named after specific commodities (or the traders of them), implying that they also specialized in certain kinds of merchandise.Footnote ⁸⁹ Finally, these results also have implications for our understanding of urban munificence, given that most market buildings seem to have been funded by local citizens, acting either as private benefactors or within the framework of political offices or religious appointments, according to the associated inscriptions mentioning individuals.Footnote ⁹⁰ It could therefore be instructive to extend the approach here to other structures associated with commerce, including tabernae.Footnote ⁹¹

At the same time, although there is much less variation in the extent to which each site deviates from the relationship than for other structures discussed elsewhere, there is still a certain amount of variance that needs to be explained.Footnote ⁹² As noted above, although we would expect these deviations, which are known as residuals, to be the result of errors both in how the sizes and densities (and therefore populations) of sites have been estimated and in how the footprints of these structures have been measured (especially given that the latter have been calculated by multiplying their lengths and widths, rather than measuring them from maps and plans), not to mention mismatches in date, they can also be taken as a reflection of meaningful differences between sites, including differences in their social and economic conditions.Footnote ⁹³ The residuals of the relationship between the total footprints of these structures and the estimated populations of sites are shown in Figure 8.

Fig. 8. The residuals of the relationship between the total footprints of macella (in m²) and the estimated populations of sites (in persons). Note that the values are logarithmic. The sites that are less than one 1 km away from a useable harbor are marked in orange.

This reveals a somewhat mixed picture, since, although there is a small number of sites that have larger macella than we would expect, based purely on their size, and are clearly associated with major ports, such as at Ephesus, Ostia, and Puteoli (which have the large, positive residuals of 0.37, 0.30, and 0.48 respectively), there is very little overall relationship between the sizes of these residuals and the distances between each site and the nearest useable harbor. This is particularly apparent in Figure 8, where the sites that are less than 1 km away from a useable harbor are marked in orange. In addition, many of the sites with the largest positive residuals are relatively far from the coast, as illustrated by Aquincum (with a residual of 0.30). Somewhat disappointingly, there is also very little evidence for any relationship between the sizes of these residuals and the total calorific suitability indices and the network measures discussed above, although it is worth noting that the sites with the largest positive residuals do tend to have the largest Eigenvector centrality. This result echoes recent work, on subjects such as the relationship between the seating capacities of theaters and amphitheaters and the sizes of sites, that also shows that there is very little or no relationship between the residuals of these relationships and the network measures derived from the ORBIS model.Footnote ⁹⁴ These results therefore suggest that it is not possible to explain the additional capacity of specific structures with reference to these conditions, at least based on current evidence.

Next, our results illustrate the potential of using settlement scaling theory to address some of the uncertainties about the structures within particular sites by assessing how well they conform to our expectations. In the first place, as noted above, this relationship can be used to assess how plausible the current estimates for the size of the Macellum Magnum are, given that it allows us to make a simple prediction about how large a structure would be appropriate to a settlement of the capital's size that can then be compared against existing reconstructions. Although we would expect the capital to have had a macellum with a footprint of about 5,842 m², based on an estimated population of just under one million for the site and the overall relationship discussed above, Carandini and Carafa's reconstruction, which is the most widely accepted, indicates that it would have covered about 7,600 m².Footnote ⁹⁵ This suggests that, although the figures that have been given for the dimensions of the Macellum Magnum provide us with an estimate for the size of this structure that is about 30% larger than we might have expected, this is not unreasonable and is well within the range of variation that is incorporated into the rest of the relationship. This means that it is almost certainly legitimate to regard the estimate as being relatively reliable, despite the notes of caution that were raised above about the reconstructions of the structure. It also perhaps allows us to be slightly more optimistic about the utility of the Forma Urbis Romae and coinage as evidence for missing structures than we have generally been. It is also worth noting that the Macellum Magnum is only a modest positive outlier if it is included within the relationship, with a residual of just 0.08, placing it in the middle of the pack (23rd out of 50). This also supports previous work, which suggested that, although Rome often has by far the largest example of any particular type of building, these structures are also often almost exactly the size or capacity that one would expect once we have taken account of the city's (comparatively) enormous size.Footnote ⁹⁶ This, in turn, suggests that the capital was much more normal that we might have expected. These results are akin to the modern situation in the USA, where New York City is ranked only 88th out of the 363 Metropolitan Statistical Areas (MSAs) studied for their total income, which makes it seem more normal than abnormal, again once its size has been taken into account.Footnote ⁹⁷

Second, these results support the idea that the “Lukasgrab” at Ephesus should be regarded as a macellum, given that, although it is the fourth largest structure in the catalogue, with a total footprint of 5,103 m², this is not particularly large once the size of the site has been taken into account, and it falls well within the expected range for the size of the structure associated with it, again based on the overall relationship between the footprints of macella and the estimated populations of sites discussed above.

In contrast, both Perge and Side would be major outliers from the overall relationship if included, given that the former is nearly six times larger than we would expect, based on the size of the population of the site, while the latter is over 11 times larger. This is because, as noted above, although the macella at Perge and Side have total footprints of about 5,776 and 8,554 m² respectively, we would only expect them to have total footprints of about 1,001 and 758 m² apiece based on the overall relationship described above and the estimated populations suggested previously.Footnote ⁹⁸ These results therefore surely support the idea that these structures had a different function from the other sites discussed above and that would be better interpreted as commercial agorai than as macella. Interestingly, these results reveal that Pompeiopolis is also an extreme outlier from the overall relationship, for similar reasons, with a structure that is again over 10 times larger than we would expect, at least on the basis of the current estimates for its population and the size of its macellum (in this case, while the macellum has a total footprint of 7,800 m², the line of best fit predicts a structure of only 750 m²). This suggests that it was also correct to exclude it. There are several possible explanations. The first, of course, is that the current estimates for the population of the site, which are based on its wall circuit, are too low, while the second is that the current estimates for the size of the macellum itself are much too high. This is perfectly plausible, given that the latter are mainly based on GPR and magnetometer survey, combined with limited excavations, while it is also striking that the current estimate is the second largest in Hoffelinck's entire dataset, after Side. It is also intriguing, however, that this structure is very similar in both length and width (and therefore in overall size) to the Macellum Magnum, as well as sharing many of the same architectural features. This raises the possibility that the structure was inspired by, or intended to be in direct competition with, the one at the capital. Given that all three sites, Side, Perge, and Pompeiopolis, are located in modern Türkiye and date to either the 2nd or 3rd c. CE (and specifically to the 2nd c. CE, middle or second half of the 2nd c. CE, and 2nd or 3rd c. CE respectively), this raises the question of whether these structures should be regarded as being part of a unique regional and chronological phenomenon, possibly led by direct competition between them.Footnote ⁹⁹

Finally, although it is not possible to comment on all the sites that are included in the dataset at any length here, it is worth noting that both Lepcis Magna and Thamugadi lie almost exactly on the best fit line, with residuals of effectively 0 and 0.05 respectively, while Pompeii, Gerasa, and Aquincum lie somewhat above it (0.22, 0.32, and 0.30) and Corinth lies somewhat below it (-0.24), reflecting earlier results for other kinds of structures, such as theaters and amphitheaters, to different extents. An obvious avenue for future research will therefore be not only to discuss these specific deviations in more detail, but also to compare and contrast the values for different kinds of structures across different sites, allowing us to come up with a much more nuanced understanding of fluctuations within and between sites.