SETTLEMENT SCALING IN MIDDLE-RANGE SOCIETIES

Scott G. Ortman and Grant D. Coffey

The contemporary relevance of archaeology would be greatly enhanced if archaeologists could develop theory that frameshuman societies of all scales in the same terms. We present evidence that an approach known as settlement scaling theorycan contribute to such a framework. The theory proposes that a variety of aggregate socioeconomic properties of humannetworks emerge from individuals arranging themselves in space so as to balance the costs of movement with the benefits ofsocial interactions. This balancing leads to settlements that concentrate human interactions and their products in space andtime in an open-ended way. The parameters and processes embedded in settlement scaling models are very basic, and thissuggests that scaling phenomena should be observable in the archaeological record of middle-range societies just as readilyas they have been observed in contemporary first-world nations. In this paper, we show that quantitative scaling relationshipsobserved for modern urban systems, and more recently for early civilizations, are also apparent in settlement data from theCentral Mesa Verde and northern Middle Missouri regions of North America. These findings suggest that settlement scalingtheory may help increase the practical relevance of archaeology for present-day concerns.

La relevancia contemporánea de la arqueología sería mucho mayor si los arqueólogos pudieran desarrollar una teoría queenmarcara las sociedades humanas de todas las escalas en los mismos términos. Presentamos evidencia de que un enfoqueconocido como teoría de escalamiento de asentamientos puede contribuir a este marco. La teoría propone que una variedadde propiedades socioeconómicas agregadas de las redes humanas surgen de la organización de individuos en el espacio conel fin de equilibrar los costos del movimiento con los beneficios de las interacciones sociales. Esta búsqueda de un equilibriolleva a desarrollar asentamientos que concentran las interacciones humanas y sus productos en el espacio y el tiempo deuna manera abierta. Los parámetros y procesos incluidos en los modelos de escalamiento de asentamientos son muy básicosy esto sugiere que los fenómenos de escalamiento deben ser tan fácilmente observables en el registro arqueológico de lassociedades de rango medio como se han observado en las naciones contemporáneas del primer mundo. En este artículo semuestra que las relaciones cuantitativas de escalamiento que han sido observadas para los sistemas urbanos modernos y,más recientemente, para las civilizaciones tempranas, también son evidentes en los datos de asentamientos de las regiones dela Mesa Verde Central y el Missouri Medio, ambas en Norteamérica. Estos hallazgos sugieren que la teoría de escalamientode asentamientos puede ayudar a aumentar la relevancia práctica de la arqueología para cuestiones actuales.

Archaeologists have long argued that theirfield should engage concretely with con-temporary issues, including urbaniza-

tion, markets, standards of living, inequality,demography, resource depletion, climate change,and social transformation (d’Alpoim Guedeset al. 2016; Diamond 2005; Hegmon 2016;Hegmon et al. 2008; Kintigh et al. 2014; Kohlerand Reese 2014; Schwindt et al. 2016; Smithet al. 2014; Smith et al. 2012; Van der Leeuwand Redman 2002). We support these efforts and

Scott G. Ortman University of Colorado, Boulder, 233 UCB, Boulder, CO 80303, USA, Crow Canyon ArchaeologicalCenter, 23390 Road K, Cortez, CO 81321, USA, and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA(scott.ortman@colorado.edu, corresponding author)Grant D. Coffey Crow Canyon Archaeological Center, 23390 Road K, Cortez, CO 81321, USA

here address an issue we believe needs resolutionif archaeology is to achieve this goal.

The issue is that human societies today aremuch larger and more complex than those welearn about through archaeology. There will soonbe more than 10 billion people on earth, and mostlive in cities of millions. Today, only 2% of theUS population produces food, and people spenddecades developing the capacity to do extremelyspecialized work. As a result, we are more inter-dependent today than ever before. A financial

American Antiquity 82(4), 2017, pp. 662–682Copyright © 2017 by the Society for American Archaeology

doi:10.1017/aaq.2017.42

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system moves capital instantly and effortlesslyacross the globe; expanding human knowledgeenables us to create cars, computers, chemother-apy, the Internet, and robots that can drive aroundMars; and human consumption drives changes inearth’s basic geology and ecology. Researchersfrom many fields, including some archaeologists,conclude from this reality that archaeology canhelp us to understand how this world came to be,and to imagine alternative worlds, but it is notvery relevant for the decisions we need to makenow and in the future. If this is true, the prospectsfor a policy-relevant archaeology would seemlimited. So if archaeologists want to change thisconclusion, our first order of business shouldbe to develop a way of thinking about humansocieties that dissolves this boundary betweenpast and present by characterizing the structureand functioning of human societies at any scale,and in a way that allows us to use data from thepast to make predictions about the future.

In this paper, we take some initial steps inthis direction by testing the extent to whichscaling relationships observed in contemporarycities, and in past complex societies, are alsoapparent in archaeological data from village-scale societies. Specifically, we investigate thepossibility that these different scales of settle-ment express the same fundamental process:namely, the concentration of social interactionsand their products in space and time, subject toa variety of constraints. Our results suggest thatallometric scaling analysis as developed here andin other recent publications (Bettencourt 2013,2014; Cesaretti et al. 2016; Ortman et al. 2014;Ortman et al. 2015; Ortman et al. 2016) capturessomething fundamental and generalizable abouthuman societies and may provide the founda-tions of a scale-free approach to archaeologicalresearch on human social dynamics. In our view,this should make our findings not only moreinteresting, but also more useful.

To make these points, we first reviewempirical patterns documented through recentresearch on urban scaling. Then we discussemerging theory that seeks to explain thesepatterns and why we believe that this theoryshould apply to the archaeological recordof middle-range societies as well. We thendemonstrate that predictions of settlement

scaling theory are in fact borne out in data fromtwo village agricultural societies from nativeNorth America. Finally, armed with these results,we consider the implications of settlementscaling theory for our understanding of citiesand for general understandings of human society.

Background

One of the exciting developments in complexsystems research is the discovery of widespreadscaling phenomena in contemporary urban sys-tems. This discovery emanated from significantadvances in data collection by a number ofagencies and institutions, and by the abilityto aggregate data collected at various scalesinto metropolitan statistical areas representinghuman settlements as functional units. Severalkey findings have emerged from these studies.First, there are systematic economies of scalewith respect to infrastructure and the use of space,such that more populous metropolitan areas onaverage encompass less land area and get by withless infrastructure per capita (Bettencourt 2013;Bettencourt and Lobo 2016) than less populousareas. Second, there are systematic returns toscale with respect to a wide range of socio-economic outputs, such that more populousmetropolitan areas generally “produce” more percapita (GDP, patents, R&D employment, butalso crime and infectious disease) in comparisonwith less populous areas (Bettencourt, Lobo, andStrumsky 2007; Bettencourt et al. 2010). Third,individuals in more populous cities tend to havemore social connections than individuals in lesspopulous cities (Schläpfer et al. 2014). Finally,more populous metropolitan areas possess amore extensive division of labor and greaterdegrees of productive specialization on average(Bettencourt 2014; Bettencourt et al. 2014).

Researchers have been aware of some of theseallometries for decades (Batty 2008; Glaeserand Gottlieb 2009; Glaeser and Sacerdote 1999;Nordbeck 1971; Samaniego and Moses 2009),but only recently have they appreciated that theserelationships have specific quantitative values.So if the functional form of these relationshipsis Y (N ) = Y0Nβ , with Y0 being a baseline value(a y-intercept) and N being a city population,the exponent β is typically about 5/6 when Y

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is a measure of infrastructure or the division oflabor, and about 7/6 when Y is a measure ofaggregate interaction or socioeconomic output(Bettencourt 2013; Bettencourt et al. 2010).

In the past few years, researchers have devel-oped mathematical models that derive these typ-ical exponents from first principles (Bettencourt2013, 2014; Ortman et al. 2014). The basic ideasembedded in these models are as follows: (1)human settlements are first and foremost con-centrations of human interaction; (2) given a setof energetic constraints imposed by technologyand institutions, people arrange themselves inspace and create infrastructural networks so asto balance the costs of moving around with thebenefits of the resulting interactions; and (3)socio-economic rates are proportional to inter-action rates. The parameters of these models—the cost of moving around, the average energeticbenefit of social interaction, the typical distancetraveled per person and per unit time, a number ofpeople, and a settled area—are very general andare not tailored to the specific technologies andinstitutions of the modern world. Yet, as severalstudies show, they succeed remarkably well inpredicting the aggregate properties of moderncities (Bettencourt 2013; Bettencourt, Lobo, Hel-bing et al. 2007; Bettencourt and Lobo 2016).

These details lead to a surprising possibility:if, in fact, urban scaling models explain observedpatterns in modern cities, and the parameters ofthese models are characteristics of any socialnetwork embedded in space, then it stands to rea-son that settlements of a wide range of societiesshould exhibit the same relative scaling prop-erties. In other words, although urban scalingtheory was initially developed to explain empir-ical regularities in modern cities, the frameworkitself may capture basic properties of humansettlements at any scale, and of any time or place.Anthropologists have long been aware of cross-cultural relationships between community popu-lation size and social complexity (Carneiro 1967,2000; Chick 1997; Feinman 2011; Naroll 1956),so the idea of systematic relationships betweenpopulation and other properties of human settle-ments is not surprising. What may be surprising,however, is the notion that these relationshipsmight have specific, predictable values that areinvariant across contexts.

Previous studies show that several predictionsof settlement scaling theory are in fact borneout by archaeological data from the prehispanicBasin of Mexico (Ortman et al. 2014; Ortmanet al. 2015) and historical data for MedievalEurope (Cesaretti et al. 2016). These resultsprovide an important proof of concept, but theyare not ideal because these societies share a num-ber of properties with modern systems, includ-ing cities, class stratification, markets, and pro-ductive specialization. Stronger evidence comesfrom the Central Andes, where prehispanic soci-eties did not have cities or markets (Ortmanet al. 2016); but the strongest possible test shouldinvolve data from middle-range societies, which,in addition to lacking cities and markets, hadless pronounced social differentiation and onlymodest productive specialization. Here we showthat settlements for two middle-range societiesfrom native North America also exhibit proper-ties predicted by settlement scaling theory.

Settlement Scaling Models

In the following paragraphs, we derive severalsimple models that describe how several aggre-gate properties of human settlements change astheir populations grow (these models are alsopresented elsewhere; interested readers may wishto read these sources for additional backgroundand details [Bettencourt 2013, 2014; Ortmanet al. 2014; Ortman et al. 2015; Ortman et al.2016]).

The models we discuss are mean-field mod-els in that they hypothesize what the averagerelationship between settlement population anda variety of aggregate quantities should be acrossthe settlements of a given social and culturalcontext. They are also reductionist in that theysuggest that this average relationship derivesfrom a small set of factors related to the propertiesof social networks embedded in space. Thereare obviously a wide range of social, cultural,and economic factors that contribute to theunique character of any specific settlement, andin presenting these models we do not mean tosuggest that any of these factors is unimportantor uninteresting. What we do argue, however,is that scientific progress depends on the abstr-action of general properties and relationships

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from the mass of details, and the most rigorousway of doing this is to (1) hypothesize whatthe most important factors are behind a givenphenomenon, (2) turn these into equations spec-ifying how these factors are related, and then(3) test the resulting predictions against newobservations. We do not mean to suggest thatthis is easy. All attempts to formalize aspects ofhuman behavior (neoclassical economics, dualinheritance theory, behavioral ecology, etc.) havetheir weaknesses, and there are many interestingand important aspects of human behavior that wecannot imagine how to formalize at present. Butthis does not mean that formalization should notbe a desired goal, as the right equations providea strong basis for prediction, and this is whatarchaeologists must do if we are to convincediverse and skeptical audiences that the thingswe learn through archaeology are relevant totoday. To the extent that the models developedhere successfully predict average properties ofsettlements across a wide range of societies,we believe they have significant promise for apolicy-relevant archaeology.

The most fundamental assumption of ourapproach is that when people create settlements,they arrange themselves in space so as to balancethe costs of moving around inside the settlementwith the benefits that accrue from the resultingsocial interactions. When settlements are rela-tively small and unstructured spatially, the costc of maintaining a mixing population for theaverage individual within the settlement is givensimply by c = εL, where ε is the energetic costof movement (the metabolic cost of walking andcarrying things) and L is the diameter across the(roughly circular) area. Note that in this circum-stance the diameter is proportional to the squareroot of the area, L ∼ A1/2. Also, the number ofinteractions the average resident will have withothers, assuming people are distributed evenlyacross the settlement, is given by i = a0lN/A,where l is the average length of the path traveledby an individual per unit time (think of dailytravel), a0 is the distance at which interactionoccurs (think of it as the width of a path oflength l), and N/A is the population density of thesettlement (the notion that people are distributedhomogeneously within settlements is obviouslynot true in detail, but it is adequate for a mean

field model of what goes on inside a settlement).These interactions can then be translated intobenefits y, by considering that there is someaverage energetic benefit of an interaction, acrossall types of interactions that can occur, whichwe represent as g, such that y = ga0lN/A. Then,if one assumes that there is an equilibrium,on average, between the costs and benefits ofinteraction, one can set c = y:

εA1/2 = ga0lN/A.

One can simplify this equation by recognizingthat in a given sociocultural milieu, g, a0, and lare properties of the average individual and thusare effectively constant. As a result, the productof these three parameters will also be a constant,and this allows one to define G = ga0l . One canthink of G as the attractive force the averageindividual exerts on others as a result of her dailymovements. One can thus replace ga0l with Gand rearrange the relation above, leading to:

A (N ) = (G/ε)2/3 N2/3 . (1)

Equation 1 can be simplified further by defininga = (G/ε)2/3 and α = 2/3, yielding:

A (N ) = aNα. (2)

What Equation 2 says is that, on average, the totalarea taken up by a relatively “amorphous” set-tlement of population N grows proportionatelyto the settlement population raised to the α =2/3 power, such that more populous settlementsbecome progressively denser in an open-endedway. Note also that the coefficient or prefactorof this relationship a = (G/ε)2/3 varies in accor-dance with social attraction and transportationcosts, but is independent of population.

Equations 1 and 2 apply to small and spa-tially unstructured settlements, but as settlementsgrow, the inhabitants must begin to set aside aportion of the settlement area as an access net-work An of roads, paths, and other public spacesso that residents can continue to move around andmix socially. We assume that, on average, the aread set aside per person is done so in accordancewith the current population density, such thatd ∼ (A/N )1/2. One can think of d as the area ofthe path in front of each person’s residence in asettlement, which would necessarily get smaller

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on average as the population density increases.Under this model, the total area of the accessnetwork is:

An ∼ Nd = A1/2N1/2. (3)

From here, one can substitute aN2/3 for A inEq. 3 and simplify, leading to:

An ∼ a1/2N5/6. (4)

Equation 4 argues that, as settlements in a givencontext grow, movement and interaction becomeincreasingly structured by the access network,and as a result the area taken up by “networked”settlements grows with population more rapidlythan in an amorphous settlement, namely, inaccordance with the settlement population tothe α = 5/6 power. So, as settlements grow insize and formality, there is still an economy ofscale, but the exponent of the growth rate ofsettled area with population increases slightly,from α = 2/3 → 5/6.

Finally, we propose that the socioeconomicoutputs Y generated by a settlement are, onaverage, proportional to the total number ofsocial interactions that occur among its inhab-itants per unit time. This notion, that increasingproductivity derives from the concentration andintensification of social interaction, is the basicidea behind economics models of agglomerationeffects (Glaeser et al. 1992; Glaeser et al. 1995;Hausmann and Hidalgo 2011; Jones and Romer2010). Given this, and the assumption that set-tlements support as much mixing as is possiblegiven spatial constraints, we can write:

Y (N ) = GN (N − 1) /A ≈ GN2/A, (5)

where G once again represents the net socialattraction of an individual’s movements andinteractions, and one can compute the expectedscaling of outputs relative to population by sub-stituting aN2/3 for A in the case of amorphoussettlements, and a1/2N5/6 for A in the case ofnetworked settlements. This leads to:

Y (N ) ∝ N2−α, (6)

with 2/3 ≤ α ≤ 5/6. This in turn implies anaverage per capita output of:

y = Y/N = GN/A ∝ Nδ, (7)

with 1/6 ≤ δ ≤ 1/3. This means that, as humansettlements increase in population, their averageper capita socioeconomic outputs grow propor-tionately to population raised to the δ power,and their total aggregate outputs grow propor-tionately to population raised to the 1 + δ power.In other words, there are increasing returns toscale, such that more populous settlements aremore productive per capita.

The models derived in this section are verysimple, and their assumptions are realistic onlyat the level of the overall settlement. Yet theresulting equations represent testable hypothe-ses regarding the average relationship betweenpopulation and a variety of other properties ofhuman settlements and, as mentioned earlier,the relationships predicted by these models havebeen observed in a wide range of societies, pastand present. Below, we show that settlement datafrom middle-range societies are also consistentwith these models. But before doing so, webriefly discuss some of the empirical issuesinvolved in testing settlement scaling modelsusing archaeological data.

Testing Settlement Scaling Theory

Several previous archaeological studies exam-ine allometric relationships between settlementpopulation and area, and these reach varyingconclusions regarding the degree to which therelationship is linear, sublinear, or superlin-ear (Naroll 1962; Schrieber and Kintigh 1996;Whitelaw 1994; Wiessner 1974). We cannotreview these studies here, but we do point outthat previous studies have often been hamperedby shortcomings in the data used. Thus, it isimportant to discuss issues related to the datarequirements for archaeological scaling analysis.

The first and most important requirement isa suitable proxy for settlement population thatcan be applied consistently across a range ofsettlement sizes. In addition, population mustbe estimated in such a way that the populationdensities of settlements can vary. Thus, a com-mon method of estimating population, whichinvolves multiplying site areas by a constantpopulation density (Johnson 1987; Naroll 1962;Wright 2001), will not yield suitable data. Prob-ably the most reliable population proxy is the

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number of houses in settlements, but the useof house counts is complicated when individualhouse occupations were much shorter than set-tlement occupation spans, or when it is diffi-cult to identify individual houses from surfaceremains. For example, in many archaeologicalsites, habitation areas are definable but individualhouses are not due to the sharing of walls,insubstantial construction, or poor preservation.An additional issue is the variable relationshipbetween preserved archaeological remains andthe actual population histories of settlements. Inmost cases, one has no choice but to assumethat the actual population of a settlement atthe time it reached its measured extent was onaverage proportional to the number of observablehouses within this area; but this means the databeing compared may not represent a momentarysnapshot of a society. Fortunately, this is notan issue for scaling analysis because the theoryaddresses patterns in the properties of individualsettlements, not the distribution of populationacross settlements (as in rank-size analysis).

A second requirement is that settlement areasshould be estimated by one or a few investigatorsusing consistent methods, or by a large enoughnumber of investigators that interobserver varia-tion is balanced out. A typical method of estimat-ing the areas encompassed by small settlementsis to measure the length and width of the archae-ological remains and compute the area of anellipse defined by these dimensions. This methodis compatible with settlement scaling models, butthe level of precision of the underlying measure-ments can become an issue. To some extent, thisis a practical response to the variety of tapho-nomic processes that affect the archaeologicalrecord. But when archaeological data for a givensociety have accumulated through the collectiveefforts of many researchers, site area datasets areoften a hodgepodge of data collected in a varietyof ways. One needs to keep this reality in mind.

Third, the data need to encompass the entirerange of settlement sizes. This is a problemmore often than one might think. In studies ofearly civilizations, for example, methods areoften tailored to practical problems related torecording the largest settlements, and, as a result,many smaller settlements are either overlookedor measured at the same level of precision as

the largest settlements (Parsons 1971; Sanderset al. 1979). The latter case can be problematicbecause the parameters of scaling relationsare typically estimated through ordinary least-squares regression of log-transformed data.Since the raw measurements are converted tologarithms as part of the analysis, relativelyimprecise data for the largest settlements makelittle difference in the results, but similarlyimprecise data for the smallest settlements canmake a big difference. Imprecise measurementof small settlements leads to blocky or “fat”lower tails of archaeological data distributionsin log-log scatterplots (for an example, seeFigure 3) and can potentially skew scalingparameter estimates. Precision is not criticalwhen one is working with modern cities becauseaggregate measures for these settlementsvary over many orders of magnitude and theminimal measurements are already quite largenumbers. However, in middle-range societies,measures typically vary over only three orders ofmagnitude at best. As a result, scaling analysis isless robust with respect to errors or imprecisionin measurement of the smallest sites. The bestways to counteract this problem are to recordsmaller sites more precisely or to work with largesamples to cancel out errors and imprecision inmeasurement of small sites. The two case studiesconsidered below exemplify these alternatives.

Due to these empirical issues, appropriate datafor scaling analysis either do not exist or arenot available for many past societies. And, inother cases, data may exist but proxy measuresfor population or socioeconomic outputs arecalculated in such a way that they preclude thepossibility of scaling relationships. Fortunately,the archaeological record of some past societiesdoes preserve the raw material for appropriatemeasures, and some of these records have beeninvestigated in such a way that it is possibleto estimate population, settled area, and socio-economic output for the full range of settlementsizes at a reasonable level of precision. Here, wework with data from two such societies.

Materials and Methods

The analysis that follows uses archaeologicalsettlement data from two native North American

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societies. Both were village-level societies witheconomies focused on maize agriculture, a mod-est division of labor beyond the household, andonly informal political integration above thevillage level. Both created settlements that haveclear boundaries, were inhabited for relativelyshort periods, and contain houses that are visi-ble on the modern ground surface. In addition,both societies have been studied intensively overmany decades, resulting in large amounts ofrelatively high-quality data.

The Central Mesa Verde Region

Our first case is the ancestral Pueblo societyof the Central Mesa Verde region in south-west Colorado. The building blocks of settle-ments in this society were highly standardizedhousehold residences that leave robust archae-ological expressions (Figure 1). These “unitpueblo” residences are defined by a central,circular pit structure, an associated, small sur-face room-block, and a trash midden locatedto the south or downslope of the pit structure.The households associated with these residenceswere the basal units of production and repro-duction in this society (Bradley 1993; Caterand Chenault 1988; Kuckelman 2000; Lightfoot1994; Lipe 1989; Ortman 1998; Varien 1999).Most settlements were single-family farmsteads,but villages containing more than 100 housesalso occur.

We focus on the period between AD 1060 and1280 for several reasons. First, most settlementswere constructed of sandstone masonry duringthis period. These stone masonry buildings weremuch more substantial than earlier constructionsof earth and wood, were inhabited for longerperiods, and were rarely razed and built over(Cameron 1990; Lightfoot 1994; Varien andOrtman 2005). Although the sizes of these set-tlements changed over time, in most cases, it isreasonable to assume that the entire architecturalfootprint of a village was inhabited at somepoint. Second, the stone-lined pit structures ofthis period are identifiable today as fairly deepand well-marked depressions, allowing archae-ologists to make accurate house counts andhouse area measurements. Third, these stonesettlements are typically surrounded by relativelydense artifact scatters that are easy to see and

measure. So it is straightforward to measurethe area encompassed by stone masonry and toobtain at least a minimal site area, although thereis interobserver variation in the definition of siteboundaries that is generally more pronounced forsmaller settlements than for larger villages.

Finally, this period in Central Mesa Verdesociety has been studied intensively over manydecades, most recently by the Village Ecody-namics Project (Kohler et al. 2012; Kohler et al.2007; Kohler and Varien 2012). As a result, teamsof researchers have put considerable effort intocompiling data from cultural resource databasesand the extensive local literature to reconstructthe population histories of individual settlementsand the larger region (Ortman et al. 2007; Varienet al. 2007). Recently, we have augmented exist-ing site area, pit structure count, and room-blockarea estimates for all recorded settlements inthis area by digitizing the best available mapof every settlement containing eight or morehouses for which a map exists, including newmaps from VEP field work (Glowacki 2012;Glowacki and Ortman 2012). The resulting mea-surements are incorporated into a settlementpattern reconstruction for the VEP II Coloradostudy area (Schwindt et al. 2016). We use thesettlement database from this project, incorpo-rating information from all settlements associ-ated with three or more houses, settled areaestimates, and total room-block area estimates.We chose a cutoff of three houses because thisseemed to be the smallest possible settlementin which the spacing of houses might capturethe balance of costs and benefits associatedwith interaction between houses. The data forsettlements associated with three to seven housesrepresents a compilation of data from manysources in which significant interobserver varia-tion exists. However, the data for all settlementsassociated with eight or more houses have beenrecorded consistently.

The Middle Missouri Region

The second society we consider is the ances-tral Mandan and Hidatsa society of the MiddleMissouri region, primarily in North Dakota. Wefocus on the period between AD 1200 and1886, which corresponds to the agricultural vil-lage tradition of the northern Middle Missouri.

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Figure 1. Sand Canyon Pueblo, a thirteenth-century Central Mesa Verde village, illustrating surface stone rubble areas, pit structure (kiva) depressions, and a sample of excavatedhouses. Map courtesy of Crow Canyon Archaeological Center.

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Figure 2. Larson Village, a Middle Missouri village, illustrating surface features. The houses within the innermostfortification date from the eighteenth century; the entire settlement was inhabited during the sixteenth century;portions have eroded into the Missouri River floodplain. Map courtesy of Mark Mitchell.

The building blocks of villages in this societywere earth lodges—partly subterranean timber-framed or post-and-beam structures with packed-earth walls (Figure 2). These lodges left clearrings and depressions on the modern groundsurface, as well as subsurface traces that canbe picked up through geophysical survey when

surface preservation is poor (Kvamme and Ahler2007; Mitchell 2008). Continuity with ethno-graphic descriptions of Mandan and Hidatsacommunities demonstrates that earth lodges weredomestic residences (Bowers 1950, 1965). Thus,for many settlements, the total number of lodges,and therefore households, is known. Lodge sizes

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vary somewhat, and due to the long historyof excavation and remote sensing, the floorareas of individual houses are available formany villages.

Settlements were constructed on terracesabove and outside the Missouri River floodplainand were often defined by ditches or other forti-fications. These are often visible on the modernground surface or are identifiable through remotesensing (Kvamme and Ahler 2007). As a result,it is relatively straightforward to define villageboundaries and to count the houses within them.Settlements range from a few to more than 100earth lodges. The occupation spans of thesevillages vary, and some were rebuilt and reoccu-pied multiple times (Johnson 2007). Fortunately,when this occurred, houses were often rebuilton the foundations of old ones (Fenn 2014),and it is often possible to distinguish distinctoccupations (Kvamme and Ahler 2007). Recentstudies of the economies of these communitiesshow an emphasis on domestic production, withevidence of part-time community specializationand increasing household productivity duringperiods of larger community sizes (Mitchell2013).

The archaeology of the Middle Missouriregion is not as well-known or as intensivelystudied as that of the Central Mesa Verde region,but due to long-term efforts by a group ofdedicated researchers and a large volume ofsalvage archaeology related to reservoir con-struction, the local literature contains manyuseful data for these settlements. A recentsynthesis and evaluation of the archaeologi-cal information by Mitchell (2013) providesa suitable dataset for this analysis. We haveaugmented Mitchell’s dataset with additionalestimates from archaeological and documentaryevidence (Table 1). Although small, the datasetis of generally high quality and contains, for themost part, data that derive from consistent meth-ods, often involving excavation and geophysicalsurvey.

Expectations

The settlements of both societies we examinedwere relatively small, and only the very largestvillages from the Central Mesa Verde containevidence of formalized paths that facilitated

within-settlement movement. In addition, theareas of most settlements in both regions aredefined as elliptical circumscribing areas on thebasis of artifact scatters or boundary features(walls, banks, ditches). Thus, one would expectthe amorphous settlement model (Eq. 1–2) toapply to settlements from these societies. Inaddition, the best population proxy in both casesis the number of houses, and thus households,in a settlement. Although these settlements wereinhabited for varying lengths of time, we thinkit reasonable to assume that the actual numberof households living within measured settlementareas was, on average, proportional to the numberof observable houses within these areas, suchthat errors in actual household estimates areeffectively random. If these assumptions are rea-sonable, and if it is appropriate to measure pop-ulation in terms of households, then one wouldexpect the average relationship between housecount N and settlement area A to be A = aNα ,with α ≈ 2/3 and a reflecting the area takenup by an individual household in the smallestsettlements.

In addition, settlement scaling theory hypoth-esizes that the productivity of an economic unitis proportional to the number of interactionsthat unit has with others per unit time. Thus,households in larger settlements should be moreproductive on average. Household productivityshould in turn be reflected in the total roofedspace under which household members lived andunder which they stored and consumed their pos-sessions. The basis for this conclusion is that, inpast societies, most of a household’s wealth wasmaterial—taking the form of food, manufacturedgoods, or valuables—and these took up space andthus needed to be stored in the house. This view issupported by studies of house area distributionsfrom a variety of past societies (Abul-Megd2002; Blanton 1994; Bodley 2003; Hirth 1993;Maschner and Bentley 2003; Morris 2004), andevidence from the Middle Missouri region alsosuggests that changes in house size over timereflect changes in productivity as opposed tohousehold composition (Mitchell 2013). Giventhis, one would expect average house area toincrease with settlement house count accordingto y = y0Nδ (Eq. 7), with 1/6 ≤ δ ≤ 1/3 andy0 reflecting the average area of a house in the

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Table 1. Middle Missouri Settlement Data.

Site Dates (CE) CompleteaArea(ha)

TotalHouses

Exc.Houses

Mean housearea (m2) Ditchb Plazac

Jake White Bull 1200–1300 N 1.6 11 YKetchen 1200–1300 Y 1.4 12 2 87.5 N YPaul Brave 1200–1300 Y 1.5 14 3 120.4 N NClark’s Creek 1200–1300 Y 2 14 N YMcKensey 1200–1300 Y 0.8 7 1 98.5 N YVanderbilt 1200–1300 Y 3.5 22 N YBendish 1200–1300 Y 6.2 45 2 109.2 N YTony Glas 1200–1300 Y 5.2 46 2 152.8 Y YHavens 1200–1300 Y 5.9 56 4 109.6 N NThomas Riggs 1200–1400 Y 3.4 22 6 132.4 Y YCross Ranch 1300–1400 N 1.3 9 2 68.1 NHelb 1300–1400 N 1.3 15 2 75.6 YDurkin 1300–1400 Y 2.1 15 3 118.9 N YSouth Cannonball 1300–1400 Y 6.5 35 6 109.6 N YMandan Lake 1400–1500 Y 3.5 97Bagnell (Late) 1400–1500 Y 3.9 97 YHuff 1400–1500 Y 4.4 103 10 122.8 Y YLarson 1500–1550 Y 5.1 115d Y YDouble Ditch 1500–1550 Y 8.9 160e Y YSmith Farm 1500–1600 Y 1.8 27 YLower Sanger 1500–1600 Y 1.6 34 YHensler 1500–1600 Y 4 125Larson 1700–1785 N 0.6 15f Y YDouble Ditch 1700–1785 Y 1.7 33 Y YSlant Villageg 1700–1785 Y 3.4 85 Y YBoleyh 1500–1600 N 4.5g 102g 1 84.4 YMotsiffg,h 1500–1600 Y 6.5 142 Y YAmahami 1785–1830 N 1.3 21 Y YRock 1785–1830 N 1.3 35 13 85.2 Y YGreenshield 1785–1830 Y 1.5 40 Y YSakakawea 1785–1830 N 2.2 41 1 147.3 Y YBig Hidatsa 1785–1830 Y 4.7 86 Y NStar Village 1830–1886 Y 5.8 85 5 137.2 Y YFort Clarki 1830–1886 Y 7.2 86 Y YLike-a-Fishhook 1830–1886 Y 11.9 175j 14 198.8 Y Y

Note: All data are from Mitchell (2013) unless otherwise noted.a“N” indicates that an unknown portion of the village has eroded away. For these cases, we assume patterns in the preservedportions are representative of patterns in the whole.b“Y” indicates the presence of fortification ditches and banks surrounding all or a portion of the settlement.c“Y” indicates the presence of a plaza within the site area.dEstimated from the enclosed area based on the mean house density of other large villages in the region (Mitchell 2008:77).eEstimated from the mean house density of other large villages in the region (Swenson 2007).fFeatures labeled “house” or “house?” in Figure 2 (Mitchell 2008).gData derived from historic maps by Swenson (2007).hThe total site footprint is assumed to correspond to the sixteenth-century occupation, with contraction during historic timesbased on patterns observed at Double Ditch and Larson.iAlso known as Mih-tutta-hang-kusch.jMcChesney’s 1872 tabulation of inhabited houses (Smith 1972:25-30).

smallest settlements. In turn, one would expectthe total productivity, as proxied by the totalarea encompassed by houses in a settlement,to vary with house count according to Y =Y0N1+δ , where Y0 reflects the average house area

in the smallest settlements (note that this is asomewhat different quantity than the area takenup by a household in the smallest settlements,a, as the latter includes extramural use areasas well).

Ortman and Coffey] 673SETTLEMENT SCALING IN MIDDLE-RANGE SOCIETIES

Finally, given that per capita (household)productivity y = GN/A (also after Eq. 7), andG = ga0l is a combination of several factorsthat are independent of population, estimates ofsocial attraction, G, for individual settlementsshould vary independently of house count. Gcan be estimated for individual settlements asGi = yiAi/Ni, and although one would expectit to vary across settlements for a variety ofreasons, theory suggests that this variation shouldbe independent of N . Thus, the exponent γ ofthe scaling relation between G and N , G(N ) =G0Nγ , should be approximately zero, and thecorrelation between these two variables shouldalso be approximately zero.

The expected range of δ requires further com-ment. Under the amorphous settlement model,we assume that houses are sufficiently dis-persed and unorganized that interaction betweenhouseholds is accomplished through travel alongstraight paths such that the distance L needed totraverse the settlement is simply its transversedimension, L ∼ A1/2. These conditions lead toan expected exponent of α = 2/3 for the rela-tionship between population and settled area,and thus a per-household productivity of y =GN/A = GN/aN2/3 ∝ N1/3. However, even inamorphous villages, movement becomes con-strained by the distribution of houses, and onewould expect this constraint to increase asthe size and density of the village increases.Under these conditions, paths across the set-tlement become progressively longer than thetransverse dimension. Thus, in compact villagesone might expect the morphology of typicalpaths to approach that found in “networked”cities organized around transportation infrastruc-ture, in which α = 5/6 and thus y = GN/A =GN/aN5/6 ∝ N1/6. As a result, one might expectthe value of δ to range between 1/6 and 1/3, evenif the value of α remains close to 2/3 in thesedata.

To evaluate these expectations, we esti-mate a, α, y0, Y0, and δ through ordinaryleast-squares regression of log-transformed data.This is feasible because y = bxm and log y =m log x + log b are equivalent. We also providea measure of Gi for individual settlements bymultiplying the mean house area by the settledarea, and then dividing by the house count.

Results

General Results

The results of our analyses, presented in Table 2,show that the expectations described above aremet for the most part. First, in both societies, the95% confidence intervals for α do not include1, and the point estimates are very close to 2/3.Thus, the relationship between population (housecount) and area is almost certainly sublinear andexhibits an economy of scale, with α ≈ 2/3, aspredicted by the amorphous settlement model.Second, in both societies, the rate of increasein mean house area with population is δ ≈ 1/6,and the 95% confidence interval for δ excludeszero (or one in the case of 1 + δ). This meansthat the relationship between population andeconomic output is almost certainly superlinearand exhibits increasing returns to scale at a levelconsistent with theory. Note that, in the CentralMesa Verde case, we estimated 1 + δ, whereas inthe Middle Missouri case we estimated δ directly,because in the former case we have only the totalhouse area for each settlement, whereas in thelatter we have only house areas for a subsampleof excavated houses. We assume that the meanhouse area in the subsample is a reasonableapproximation of the mean house area acrossall houses in each settlement. We do not knowthe degree to which this is true for any singlesite, but the results suggest that any errors in ourestimates for mean house area across settlementsare unstructured relative to the house count.

We also note that the exponent δ, which relateshousehold productivity to settlement population,is much closer to 1/6 than to 1/3. This is notsurprising given the density of houses in villagesfrom both societies. This would have requiredpeople to take more circuitous paths to interactwith village-mates, and thus a scaling of interac-tion with area that is closer to that observed innetworked settlements.

Finally, our measure of social attraction, G, isclearly independent of N for the Middle Missouridata, and is most likely independent of N forthe Central Mesa Verde data. In both cases, theR2 value of the relationship is practically zero,and the confidence interval for the exponentincorporates or very nearly incorporates zero.

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Table 2. Scaling Results for the Central Mesa Verde and Middle Missouri Regions.

Sample Exponent PrefactorSystema Dependent Variableb size (95% C.I.) (95% C.I.) R2 Signif.

Central Mesa Verde Settled Area A (ha) 278 α = 0.662 a = 0.213 0.216 0.000(AD 1060–1280) (0.513–0.812) (0.160–0.285)Middle Missouri Settled Area A (ha) 35 α = 0.643 a = 0.269 0.654 0.000(AD 1200–1886) (0.483–0.802) (0.147–0.493)Central Mesa Verde Total House Area Y (m2) 130 1 + δ = 1.167 Y0 = 56.14 0.735 0.000(AD 1060–1280) (1.044–1.289) (43.58–72.31)Middle Missouri Mean House Area y (m2) 17 δ = 0.163 y0 = 63.05 0.305 0.022(AD 1200–1886) (0.038–0.287) (40.30–98.64)Central Mesa Verde G 121 γ = −0.248 G0 = 10.96 0.040 0.029(AD 1060–1280)c (−0.470–0.026) (6.86–17.52)Middle Missouri G 17 γ = −0.132 G0 = 16.04 0.050 0.387(AD 1200–1886)c (−0.423–0.158) (5.64–45.63)

aPopulation ranges: Central Mesa Verde, 3–192 houses; Middle Missouri, 4–175 houses.bIn all cases, the independent variable is population (house count).cGi for each settlement is estimated by Gi = yiAi/Ni, where yi is the mean house area, Ai is the settled area, and Ni is thehouse count.

The p-value of the Central Mesa Verde relation-ship suggests that G may be slightly negativelycorrelated with N in this case, but in light ofthe low R2 and confidence interval, we interpretthis result as due to overgenerous site areaestimates for some small settlements derivingfrom use of a low artifact density threshold todefine site boundaries. This would have resultedin inflated G values for those sites relative tolarger ones and increased the negative slope ofthe relationship. So, overall, our results suggestthat the “social attraction” exerted by individualsin both societies was independent of settlementpopulation, as predicted.

These results indicate that both economies ofscale with respect to settled area, and increasingreturns to scale with respect to house area,are apparent in the settlement data from thesetwo societies. Further, the magnitudes of theseeconomies and returns are consistent with mod-els that predict their observed values in modernurban systems. These results thus suggest that theallometric properties observed for these village-level societies derive from the same social net-working processes that lead to scaling phenom-ena in modern cities.

It is also remarkable to note that the prefactors(coefficients) of the average scaling relationsare quite similar for these two societies: theestimated average area taken up by a household(both the house itself and adjacent extramural

areas) in the smallest settlements was 0.21 hain the Central Mesa Verde and 0.27 ha in theMiddle Missouri, and the average house areain single-household settlements is estimated at56 m2 in the Central Mesa Verde and 63 m2 inthe Middle Missouri (this is because the meanhouse area equals the total house area, y0 = Y0,when N = 1). These similar values are strikinggiven the different data collection methods usedto generate these data. In the Central Mesa Verde,for example, settled area is most often definedby the extent of the surrounding artifact scatter,whereas in the Middle Missouri, it is most oftendefined by fortifications or house distributionscombined with terrace edges. Likewise, in theCentral Mesa Verde, archaeologists recordedonly the total house area across all householdsusing surface evidence, whereas in the MiddleMissouri, they estimated mean house areas fromexcavated houses in various sites. Yet Figure 3shows that, if one multiplies these mean houseareas by the number of houses for the MiddleMissouri data and then plots the results on thesame axes as the Central Mesa Verde data fortotal house area, the scaling relationship is nearlyidentical.

The close similarity of the scaling parametersfor these two societies may seem surprising inlight of the many differences between them. Forexample, in the Central Mesa Verde, walking wasthe only means of traveling between settlements;

Ortman and Coffey] 675SETTLEMENT SCALING IN MIDDLE-RANGE SOCIETIES

Figure 3. Relationship between settlement population (house count) and total productivity. For the Central Mesa Verdesystem, Y is the total roofed area; for the Middle Missouri system, Y = yN, where y is the mean area of excavatedhouses and N is total house count. The nearly identical relationship in the two datasets implies that changes in averagehousehold productivity through time were due to changes in community scale as opposed to agricultural productionor technology.

however, Middle Missouri people used bull boatsor canoes to transport goods and people along theriver, dogs and travois to transport goods overland, and horses to move both goods and peopleafter AD 1750. Also, the baseline productivity ofagricultural land varied substantially in the twosocieties. Studies of agricultural yields suggestthat traditional Mandan fields produced at least1,200 kg/ha on average (Mitchell 2013), whereasCentral Mesa Verde fields produced only 250–400 kg/ha (Varien et al. 2007). One would expectthese dramatic differences in between-settlementtransport technologies and agricultural produc-tivity to have enabled higher regional popula-tion densities in the Middle Missouri, but thesedifferences appear to have had little effect onsettlement densities or the baseline productivityof households. The insensitivity of our analysesto between-settlement transportation technologyand agricultural productivity is consistent withour theory because these factors are not incorpo-rated in the models that derive settlement scalingrelationships. However, within-settlement trans-port costs are incorporated into these models, andin both societies the only way of moving peopleand goods within settlements was on foot. Given

this, similarities in the observed results makemore sense than they may appear to at first.

Context-Specific Results

An important aspect to consider with regard tothe Middle Missouri data is the long period oftime represented, as there is no a priori reason topresume that the relationships between popula-tion, settled area, and socioeconomic rates shouldhave been stable over a period of more thansix centuries. Indeed, recent studies suggest thatmean house areas, storage pit count and density,internal settlement densities, and the intensityof craft production all increased through time(see Mitchell 2013). To investigate this issue,Figure 4 illustrates the relationship between pop-ulation (house count) and settlement area forthe Middle Missouri data, with groups of siteslabeled by time period. Each interval, of about200 years, is roughly equivalent to the entire timespan encompassed by the Central Mesa Verdedata. There are visual suggestions in Figure 4that the internal densities of Middle Missourisettlements changed through time, but the figurealso suggests that the average population ofsettlements increased. This raises the question

676 [Vol. 82, No. 4, 2017AMERICAN ANTIQUITY

Table 3. Chronological Analysis of Northern Middle Missouri Settlements.

Time PeriodPopulation-AreaExponent

Population-AreaPrefactor (ha)

Settlement Population(House Count)

Settlement Area(ha)

AD 1200–1400 α = 1.020 a = 0.1219 Mean = 23.1 Mean = 3.05(N = 14) S.E . = 0.0899 S.E . = 1.3098 S.E . = 9.51 S.E . = 0.690AD 1400–1600 α = 0.829 a = 0.0960 Mean = 100.2 Mean = 4.42(N = 10) S.E . = 0.1073 S.E . = 1.6236 S.E . = 11.25 S.E . = 0.817AD 1700–1886 α = 1.19 a = 0.0254 Mean = 63.8 Mean = 3.78(N = 11) S.E . = 0.1104 S.E . = 1.5528 S.E . = 10.73 S.E . = 0.779ANOVA F = 2.7669 F = 0.0001 F = 13.9259 F = 0.8354

P = 0.3005 P = 0.9999 P < 0.0001 P = 0.4429

Figure 4. Relationship between settlement population (house count) and settled area, Middle Missouri region. Symbolsreflect the time period of each settlement; the power-law fit is for all settlements. Although visual patterns suggestchanges in the underlying relationship through time, this cannot be shown statistically (see Table 3).

of whether changes in settlement density weredue to increases in their baseline density or toincreases in their average population. Based onthe chronological analysis presented in Table 3,it appears that an increase in average settlementsize is the more likely culprit because the differ-ences in scaling exponents and prefactors calcu-lated by chronological period are not statisticallysignificant, whereas changes in average settle-ment population (house count) through time are.Also, note that settlement populations changed toa much greater extent than settlement areas overtime, and this implies that the average populationdensity of settlements changed as well. Theseresults suggest that increases in the average

density of northern Middle Missouri settlementsthrough time were due primarily to increases inthe scale of community organization as opposedto technological progress or increases in regionalpopulation density per se. This result mirrors thatfound in other studies of nonindustrial societies(Ortman et al. 2015; Ortman et al. 2016) and itsuggests that socioeconomic development priorto the Industrial Revolution was driven largelyby factors that promote increases in the scaleof strongly interacting social networks. This isa fascinating prospect for future research, andpotentially for policy.

There is another area where scaling analysisreveals differences between the Middle Missouri

Ortman and Coffey] 677SETTLEMENT SCALING IN MIDDLE-RANGE SOCIETIES

and Central Mesa Verde systems. Although thereis no clear relationship between G and N ineither society, the value of G0 is somewhathigher for the Middle Missouri system than itis for the Central Mesa Verde system. SinceG = ga0l , and both l and a0 are defined by humanbiology and are thus effectively constant, thelarger mean value of G for the Middle Missouriimplies that the average energetic benefit ofeach social interaction, g, was greater in thatsociety. Why this should have been the case isan interesting question. One possibility is thatthe Middle Missouri floodplain was more pro-ductive than the Mesa Verde loess, so the highervalue of G in the Middle Missouri may reflectthe fact that there were more calories availablefor exchange in that society. Another possibilityis that the social institutions of Middle Missourisociety lubricated the flow of goods and servicesto a greater extent than those of Central MesaVerde society. Ethnohistoric literature indicatesthat the Middle Missouri was a well-knowntrade center and that the Mandan and Hidatsapeople inhabiting this region were skilled tradenegotiators (Fenn 2014). In addition, native soci-eties throughout the Great Plains used a set ofceremonies known as the calumet to forge tradepartnerships that greatly facilitated intertribalexchange (Blakeslee 1975, 1981). In contrast,very little evidence of external trade or of inter-tribal ceremonies has been found in CentralMesa Verde sites (Lipe 1992, 2002). If thesedifferences in between-group interaction weremirrored at the settlement level, social interactionmay also have been more productive on anenergetic level in the Middle Missouri than inthe Central Mesa Verde.

Finally, it is important to emphasize that,although previous studies of settlement scaling incontemporary and archaeological contexts haveused individuals as the units of population, thisstudy obtains the same results when householdsare the population unit. This is good news forarchaeologists because in many societies it isfar easier to count houses than to determine thenumber of residents of each house. But this mayalso seem surprising given that household com-position varies across households in individualsettlements (Wilk 1984), within societies (Wilkand Netting 1984), and across societies (Blanton

1994). There must have been similar variation inthe households considered here, but this seems tohave had little effect on overall scaling relations.We can think of several factors that may underliethe insensitivity of scaling analysis to householdcomposition. First, in middle-range societies,households are productive units and the divisionof labor is strong within households but repli-cated between them for the most part (Sahlins1972). Thus, even if each individual in a house-hold has interactions with others in their com-munity, these interactions are generally comple-mentary rather than overlapping with regard tooverall household needs. Second, social relationswithin households are typically characterized bygeneralized reciprocity, and economic decisionsare generally made to benefit the householdoverall. Settlement scaling theory, in contrast,describes the dynamics of balanced reciprocity,and this realm is more characteristic of overallrelations between households than to relationsbetween each individual, even in modern soci-eties. So it may be that households are the mostappropriate unit of “mass” for scaling analysis,even in contemporary societies, and total popu-lation is merely a good proxy that is proportionalto household count in most settings. Finally,in agricultural villages the primary impedimentto movement and interaction is created by thedistribution of houses and households, not peopleper se. Thus, one would expect the connectivityand intensity of interaction between people fromdifferent households to be influenced primarilyby the physical arrangement of houses them-selves.

Conclusions

The cities that most humans live in today arecomplex places with pronounced divisions oflabor, intensive interaction across specializa-tions, and massive flows of people and materialthroughout dense infrastructure networks. Agri-cultural villages, in contrast, appear to be muchsimpler places where the division of labor waslimited above the household level, interactionwas structured primarily by kinship, and the builtenvironment was relatively unorganized. Suchcomparisons lead many researchers to view a cityas a fundamentally different kind of thing than

678 [Vol. 82, No. 4, 2017AMERICAN ANTIQUITY

an agricultural village. From this perspective, theappearance of cities in history represents a water-shed moment, and the remarkable economiesand returns to scale noted in contemporarycities are seen as a product of urbanization—a process that did not occur in smaller-scalesocieties.

Our results cast doubt on this view and suggestthat one should instead view contemporary citiesas lying on a continuum with smaller forms ofhuman settlement. Indeed, the results presentedhere are consistent with the idea that the pro-ductivity and division of labor that characterizepresent-day urban systems are actually propertiesof human social networks that expand exponen-tially and in an open-ended way with scale. Thisleads to the appearance of qualitatively differentsocial processes in contemporary cities, whenin fact these are just quantitative differences inexpressions of the same processes. Since theproperties of social networks are nonlinear, theylead to exponential changes in the use of space,productivity, knowledge, and the division oflabor as the nodes in a social network grow—butthe processes that generate these changes appearto have been part of human societies for as long aspeople have been creating permanent settlementsthat promote “organic solidarity” (Durkheim1984 [1893]) and expand the “extent of themarket” (Smith 2007 [1776]). Thus, from a scal-ing perspective, cities are simply bigger villageswhere the division of labor, levels of productivity,and rates of change are more pronounced dueto the opportunities created by scale itself. Forexample, in Middle Missouri society, the archae-ological record suggests a trend toward part-timespecialization that correlates with agglomeration(Mitchell 2013), but, given the small scale ofthese settlements, the effects were sufficientlymodest that they affected household task mixesmore than economic specialization of the kindwe are familiar with from contemporary cities(also see Bettencourt 2014).

Our results, which demonstrate that scalingpatterns observed in present-day urban systemsare equally apparent in middle-range societies,suggest that settlement scaling theory capturesbasic and widespread aspects of human societiesas social networks, at a level of abstractionwhere their effects are well-behaved and partly

predictable, but not obvious or trivial. Social sci-entists make many generalizations about humansocial behavior, but few of these have beenformalized in ways that yield specific, integrated,and novel predictions that are borne out by newdata and that produce results that also makesense in light of contextual details. There aremany important areas of human behavior thatmay never be amenable to this explicit, physical-science approach—but, given the accomplish-ments of the physical sciences in other fields,it seems important for archaeologists to takeadvantage of those domains where this type ofreasoning is productive. Based on accumulat-ing results like these, settlement scaling theoryappears to be one such domain.

Finally, our results suggest something impor-tant about the potential of the archaeologicalrecord for expanding knowledge of human soci-ety. The archaeological record will always bepartial, distorted, and contextually unique whenviewed in detail. Nevertheless, this record cap-tures information on the full sweep of humanexperience and can provide insights into the fun-damental nature of human societies that cannotbe gleaned from any other data source. Onemight question whether all of the assumptionsembedded in our analysis are reasonable, but thevery fact that they lead to results consistent withtheory provides support for both our assumptionsand the models we tested. In short, it is highlyunlikely that the data could have been biasedin unacknowledged ways and still yield resultsthat are consistent with settlement scaling theory.Given that dominant signals overpower noisydata at large spatial and chronological scales, andthat human behavior appears more regular at suchscales, it seems to us that archaeological evidencehas a significant role to play in building a generaltheory of human societies as complex systems.The archaeological record has undeniable powerdue to the fact that it preserves traces of socialdynamics in utterly different kinds of societiesthan the ones most people live in today, andwe can know that the people who created thisrecord were not aware of the theories we bringto interpreting it, or that one day we would tryto measure their behavior. Thus, finding thatspecific predictions of settlement scaling theoryare borne out by data from societies organized at

Ortman and Coffey] 679SETTLEMENT SCALING IN MIDDLE-RANGE SOCIETIES

a variety of scales has theoretical significance farin excess of the data.

In addition, archaeological data do more thanprovide novel tests of an existing theory—theyalso expand it by clarifying the underlying con-cepts, as this study has done by noting the roleof households, the effects of agglomeration forinteraction intensity in the absence of infrastruc-ture, and the identification of institutional factorsthat may have impacted the average productivityof social interaction. For these reasons, we sus-pect that continued use of archaeological data inscaling research will prove critical for a deeperunderstanding of human societies as complexsystems, and that the overall endeavor shouldincrease the practical relevance of archaeology.

Acknowledgments. Portions of this work were supported bythe National Science Foundation (CNH-0816400), the JohnTempleton Foundation, the James S. McDonnell Foundation(#220020438), and the Santa Fe Institute Omidyar Fellow-ship program. We thank Luís Bettencourt, José Lobo, RobertKelly, Michael Smith, Tim Kohler, Mark Varien and MarkMitchell for discussions, and four anonymous reviewers fortheir many helpful comments and suggestions. We also thankPayson Sheets for translating the abstract into Spanish.

Data Availability Statement. All data analyzed in this paperare available through the Digital Archaeological Repositoryat www.tdar.org.

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Submitted January 5, 2017; Revised April 5, 2017;Accepted April 5, 2017