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The Methodological Problem: The Limits of Visual Rank-Size Heuristics

Archaeological interpretations of settlement systems make use of the Rank-size rule and deviations from it to either predict or interpret human behavior. Numerous explanations for deviations from a lognormal distribution of site sizes have been advanced, ranging from low levels of system integration to core and periphery settlement patterns. Many different explanations have been advanced for the same Rank-size distributions. When evaluating these explanations, it is useful to examine the problem from the standpoint of a known site universe that corresponds to the Rank-size rule.

The Rank-size rule, as normally applied in archaeology (e.g. Crumley 1976; Johnson 1977, 1980), is expressed as: S_n = S₁ / n, that is, the size of any nth rank place is found by dividing the size of the largest place by n (meaning that the rank of a given site times its size equals the size of the largest site. When plotted on logarithmic axes with the exponent q = 1, a fully integrated system approximates a linear log-normal distribution with a slope of −1.0.

In archaeological practice, departures from this distribution were traditionally classified into two structural types:

• Primate Distributions: Characterized by an exceptionally large primary center relative to lower-tier settlements, theoretically indicative of core-periphery exploitation, colonial dominance, or high political centralization.
• Convex Distributions: Characterized by multiple settlements of comparable size at the upper end of the distribution, interpreted as poorly integrated, autonomous, or "balkanized" regional sub-systems.

Despite the theoretical utility of these constructs, early archaeological applications suffered from two fundamental statistical flaws:

• The Absence of Significance Metrics: Standard Kolmogorov-Smirnov (KS) critical value tables were developed for continuous statistical distributions, not for discrete, stepped order statistics derived from regional settlement inventories. Archaeologists frequently interpreted minor departures from log-normality as evidence of state centralization without establishing whether those deviations exceeded random expectation.
• The Sensitivity to Incomplete Recovery (The "Lower Limb Problem"): Regional surveys rarely identify 100% of ancient settlement universes. Small agricultural hamlets, field huts, and seasonal campsites are disproportionately obscured by modern land use, alluvium, or survey intensity boundaries. This systemic loss introduces severe artificial drop-offs in the lower tier of the distribution, distorting the empirical slope and manufacturing false structural interpretations.

The 1991 Term Paper (ranksize.bas)

In a 1991 graduate seminar paper at Arizona State University ("A Monte-Carlo Simulation Study of the Rank-size Rule in Settlement Archaeology"), Savage constructed a simulation engine written in Turbo BASIC. Executing more than 35,000 discrete iterations across controlled site universes (N = 50, 100, 200), the algorithm generated custom Kolmogorov-Smirnov confidence boundaries specifically calibrated for settlement data. To resolve the statistical invalidity of continuous KS tables when applied to stepped Rank-size data, the research developed custom simulation algorithms designed to establish empirical confidence intervals around theoretical log-normal distributions. The Monte-Carlo simulation program evaluated the effects of sample proportions, the number of sites in a given population, and the effects of finding or not finding the largest site in a region. Results indicate that eighty-five percent of the sites must be found, and the largest site known, to consistently achieve accurate results. A confidence interval method of evaluating site distributions allowed some of the problems with sampling error to be overcome.

The primary contribution of this initial study was demonstrating the mathematical vulnerability of Rank-size curves to survey sampling rates:

• The Primacy Artifact: The simulation demonstrated that if a survey correctly identifies the regional primate center but recovers less than 80–85% of the lower-tier settlement universe, the resulting Rank-size plot is mathematically guaranteed to exhibit a false primate profile.
• The 85% Threshold: To reliably differentiate a culturally significant primate or convex pattern from an artifact of archaeological recovery, regional surveys must achieve a minimum recovery rate of approximately 85% of the total site universe, while reliably capturing the absolute maximum settlement size.

Prior to this work, archaeologists routinely applied Zipf’s Rank-size rule-plotting settlement sizes against their rank on logarithmic axes-to infer political integration, economic pooling, or primate/convex settlement hierarchies. However, these interpretations often suffered from qualitative bias: researchers simply visually inspected the slope and declared a pattern "convex" (suggesting poorly integrated systems) or "primate" (suggesting centralized dominance) without evaluating whether the deviation from a log-normal distribution was statistically significant. The initial paper introduced a Monte Carlo simulation method specifically tailored for archaeological Rank-size distributions. This computational tool generated confidence intervals around expected log-normal curves, enabling archaeologists to statistically test whether an observed settlement system deviated significantly from random expectation or represented genuine socio-political structures.

The results of the Monte-Carlo simulation study presented in the first paper were startling. Unless eighty five percent of the original sites, and the largest site in the region are known, the a Rank-size plotting results are almost certainly attributable to sampling errors. If the largest site is found, but less than eighty five percent of the site population is recovered, the results will indicate a primate situation. Thus, many projects that were conducted in the past may have inferred primate conditions and attributed that primacy to several cultural factors, but the results are probably within the realm of sampling error, be it caused by survey design or site attrition.

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The 1992 Ruppé Prize Expansion

Expanded into an award-winning monograph for the inaugural Reynold J. Ruppé Prize in Archaeology ("A Monte-Carlo Simulation Study of the Rank-Size Rule in Settlement Archaeology: With Application to the Chalcolithic and Bronze Ages of the Southern Levant"), the method was rewritten in Turbo Pascal 6.0 as a compiled executable (RankSize).

While the 1991 paper was a purely predictive, controlled experiment using an artificial, simulated site universe, the 1992 Ruppe Prize-winning version transitioned the code from a theoretical exercise into an empirical analytical tool:

• Application to Regional Trajectories: The Pascal engine was run against multi-period survey inventories from the southern Levant (integrating data from Gophna, Portugali, and contemporary regional surveys), establishing baseline profiles across the Chalcolithic, Early Bronze Age (EBA), and Middle Bronze Age (MBA).
• The Primo-Convex Signature: The paper formalized the intermediate primo-convex profile-a distribution exhibiting a dominant, primate primary center paired with a convex, stepped distribution across secondary and tertiary settlements. It demonstrated that this pattern emerges when an imperial or volatile administrative capital is artificially superimposed over a baseline of resilient, self-sustaining rural networks.
• Predictive Performance Regression: The manuscript introduced a spatial linear regression to calculate the statistical predictability of simulation outcomes, defining Optimal Performance (OPerf): OPerf = −153 + (14.4 · LSite) + (9.26 · SProp), where LSite represents the logarithmic magnitude of the largest site and SProp represents the proportion of the recovered site universe. This equation accounted for 98% of the statistical variance across simulation runs, formally establishing that apparent departures from log-normality are heavily conditioned by the recovery proportion of the sample.



• Solving Zipf’s Complete Equation (Calculating q): The initial graduate paper critiqued the standard archaeological practice of assuming Zipf’s exponent q always equaled exactly 1. The Turbo Pascal edition unlocked the ability to empirically calculate the true value of q using the least-squares regression method across log-log plot distributions. Instead of forcing data into an idealized log-normal line, this capability allowed archaeologists to calculate whether the force of urban unification or rural diversification dominated an ancient society. It provided a direct mathematical metric to evaluate the actual degree of state centralization or systemic balkanization across different eras. And the program let the user set a value for q to alter the slope of the expected Rank-size distribution.
• Defeating the "Lower Limb Problem": A universal frustration in regional surface surveys is that very small archaeological sites (hamlets, field huts, and seasonal campsites) skew Rank-size graphs. Because these tiny spaces drop off rapidly or are under-represented due to survey visibility, they cause the bottom of a plot line to curve aggressively downward. The Turbo Pascal RankSize engine introduced diagnostic algorithms specifically built to handle this lower limb distortion. It allowed users to run Monte Carlo simulations on truncated datasets, isolating and filtering out the minor settlement noise. This functionality ensured that missing or hard-to-detect small hamlets would not artificially corrupt the mathematical calculations of upper-tier political complexity.



• Multi-Plot Diachronic Overlays: The new interface enabled researchers to overlay multiple archaeological phases and geographic zones simultaneously, facilitating direct comparative analysis of regional restructuring over time.

The theoretical and computational architecture developed across these two papers was subsequently published in the Journal of Archaeological Science (Savage 1997), providing the international discipline with an accessible, standardized method for evaluating departures from log-normality.

Winning the Ruppe Prize for this expanded methodology served as a catalyst for further work in Near Eastern spatial archaeology:

• Methodological Validation: The academic recognition solidified a trajectory in quantitative methodology--directly informing later postdoctoral research on the Early Bronze Age city-states of the Southern Levant, where these methods were used to demonstrate that Levantine urban networks were localized and fragmented rather than monolithic empires.
• Evolution into Geospatial Infrastructure: The success of coding the analytical software (ranksize.bas) set a pattern--instead of relying solely on commercial software, I developed custom digital architecture where needed, ultimately leading to major spatial humanities projects like the Digital Archaeological Atlas of the Holy Land (DAAHL) and TerraWatchers.

By showing that the traditional Kolmogorov-Smirnov (KS) table thresholds were explicitly mathematically invalid for step-wise Rank-size lines, the 1992 work handed a warning--and a solution--to global settlement archaeology:

• Beyond the Visual "Eyeball" Test: Before this paper, archaeologists routinely published log-log settlement plots and subjectively claimed a culture was integrated or decentralized based on looking at line slopes. The paper provided an empirical path forward: researchers can compute exact maximum absolute deviations and compare them to custom Monte Carlo confidence tables to ensure they are not reading meaning into simple noise.
• The Need for Full-Coverage Survey: The paper showed that if you recover less than 85% of a regional settlement pattern, your data is mathematically guaranteed to generate a false primate or convex profile purely from sampling error. Global scholars (such as those mapping Mesoamerican states, Roman empires, or Mediterranean fields) frequently cite these findings to stress to funding bodies that full-coverage, high-intensity visual surveys are mandatory to avoid analytical/interpretive error.

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Empirical Application and Regional Realities: The Levant (1995–2003)

The utility of any computational method relies on its capacity to clarify ambiguous or contested archaeological records. In collaboration with Steven E. Falconer, Savage deployed these Monte Carlo significance models to evaluate long-standing questions surrounding urbanization, state formation, and rural resilience in the Southern Levant.

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Decoupling Urban Collapse from Rural Continuity (Falconer and Savage 1995)

In "Heartlands and Hinterlands: Alternative Trajectories of Early Urbanization in Mesopotamia and the Southern Levant." American Antiquity 60(1): 37-58, the simulation methodology was applied to the settlement dynamics of two regions. Comparative Rank-size analyses revealed highly variable courses of urbanization in ancient Mesopotamia and the southern Levant during the fourth through early second millennia B.C. While traditional Rank-size methods do not consider the efects of archaeological sampling, the authors used a revised approach based on the 1992 Monte Carlo simulation program, which incorporated site-recovery rates and demonstrates the advantages of "full-coverage" survey. The paper highlights the rapid development of urban primacy in southern Mesopotamia's heartland fAdams 1981) and the more static rural integration of the Diyala hinterland (Adams 1965). In contrast, Bronze Age urbanization in the southern Levant describes a mosaic of urban and rural systems following independent trajectories. The paper called for greater attention to small sites, which often define the shape of Rank-size distributions, and showed that modest cases of urbanizatlon in terms of structure, rather than simply of reduced scale, and avoided a tendency to categorize such cases as derivatlve.

For decades, early cities in the Southern Levant were treated as poorly executed imitations of the massive, highly centralized mega-cities found in southern Mesopotamia. Utilizing Savage's simulation frameworks to correct for uneven surface collection across regional datasets, the authors demonstrated that the Southern Levant followed a fundamentally different trajectory. Instead of developing rigid, vertical, state-level command economies, the Levant featured a "heterarchical" mosaic of towns and rural village networks. This paper has been cited over 300 times, shifting the field away from Eurocentric and Mesopotamian-centric definitions of civilization toward localized models of social complexity.

Key Impact and Conceptual Contributions:

• Rejection of "Core-Periphery" Bias: Historically, Levantine settlements were often dismissed as peripheral, "watered-down" versions of massive Mesopotamian cities. Savage and Falconer argued that the Southern Levant possessed a unique, locally adapted form of urbanization defined by a mosaic of town-village networks rather than mega-cities.
• Statistical and Methodological Innovation: The authors pioneered the use of rigorous, simulated sampling (like Monte Carlo simulations) to ensure that archaeological surveys account for uneven surface coverage and the inherent biases of missing small, rural sites.
• Heterarchical Organization: The paper popularized the idea that societies could be politically and economically integrated "horizontally," allowing for resilient regional development without rigid, state-level vertical control.

How Researchers Use the Paper:

• Studies of the "Canaanite City": Researchers such as archaeologists Alexander Fantalkin, Oren Tal, and Aren Maeve have leveraged the Heartlands and Hinterlands framework to redefine Canaanite urbanization. They utilize the paper’s principles to argue that the Middle Bronze Age and Iron Age city-states in the Levant functioned as localized "domesticating apparatuses"--highly tied to their rural hinterlands--rather than mere imitations of Mesopotamian or Egyptian empires.
• Spatial Analysis and Settlement Scaling: Urban archaeologists and geographers (e.g., Fulminante, Blanton, Fargher) have widely adopted the paper's statistical approach to settlement hierarchy and Rank-size distribution. The paper's models of primate vs. convex (primate vs. highly centralized) settlement distribution allow scholars to compare ancient Levantine urbanization with global models of state-level societies, ranging from Highland Mesoamerica to the Etruscan city-states of Italy.
• Comparative Settlement and Territoriality: Specialists in the Near Eastern Bronze Age rely on Falconer and Savage's framework to differentiate localized regional integration from massive urban cores. Scholars like Timothy Harrison apply this paradigm to understand how the diverse ecology of the Mediterranean and Jordan River Valley supported distinct agricultural intensification that necessitated flexible, independent economic and political networks.

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Delving Deeper: An in-depth discussion and application of the 1992 simulation to the southern Levant (Savage 1997)

While the 1995 publication presented the archaeological results of their calculations, the strict page limits of American Antiquity prevented a full breakdown of the software, leading instead to the 1997 solo publication, "Assessing Departures from Log-normality in the Rank-Size Rule" (Journal of Archaeological Science 24: 233-244). This paper served as the explicit methodological manual for the custom Monte Carlo algorithm, detailing how the software generated an ideal, log-normal

population of settlements, took thousands of empirical random samples to mimic imperfect archaeological exploration, and calculated true critical values. Applying the completed program to a dataset of Chalcolithic through Middle Bronze Age sites on the Levantine coastal plain (Gophna, & Portugali, 1987), the paper successfully separated real historical changes from background statistical noise, demonstrating that underneath highly cyclical urban elite collapses lay an incredibly resilient, structurally stable rural network.

The 1997 paper outlined a custom Monte Carlo simulation algorithm designed to empirically establish a true baseline of statistical significance:

• Defining the Ideal Population: The program begins by generating a theoretical, perfectly log-normal population of settlements based on a specified maximum site size and a baseline exponent, assuming Ziph's q = 1.
• Empirical Random Drawing: The software simulates archaeological reality by repeatedly drawing random samples from this ideal population. It mimics factors like incomplete regional surveys or missing smaller rural sites.
• Calculating Empirical Critical Values: For every single random iteration (often run 1,000+ times), the program measures the maximum deviation from log-normality. By compiling thousands of these simulated deviations, the software calculates maps a customized probability distribution.
• Assessing True Significance: The program compares the actual, observed archaeological data against this simulated distribution. It calculates the exact probability that the observed curve's deviation could simply happen by random chance or sampling bias.
• Simulation v. Significance Tables: The simulations indicated that the threshold values for K- in standard statistics tables are far lower than those which result empirically. Their use results in rejecting the null hypothesis of no significant difference between observed and expected distributions far more often than required.

Data from a series of Chalcolithic through Middle Bronze IIB/C sites in the Levantine coastal plain were examined with the simulation. The results indicated that, except for the Early Bronze III period, all of the periods examined present significant departures from the Rank-size rule. Rank-size plots of the verified distributions indicate the possible existence of a relatively constant rural component in the coastal plain, which exhibits a central-place like distribution. Superimposed on this low-level rural component is a higher level urban distribution, which can be seen to develop, collapse, and redevelop during the periods in question, providing exciting new insights into the nature of Bronze Age urbanism in the Levant.

How Researchers Use the Paper:

• Altaweel, Mark, and Andrea Squitieri (2018) cite the 1997 paper in Chapter 3 ("Methodologies for Measuring Universalism"). The authors use the 1997 work strictly as a technical reference within their discussion on archaeological survey methodologies and measuring settlement structures. When analyzing ancient population distributions across the Near East, archaeologists use the "Rank-size rule" to see if a region is dominated by a single massive capital city (primate distribution) or a balanced network of medium towns (log-normal distribution). Savage (1997) introduced a specific mathematical method to measure exactly how much a real-world archaeological dataset "departs" from that perfect log-normal curve. Altaweel and Squitieri cite the paper to justify the specific statistical limits and mathematical formulas they use when modeling settlement systems later in the book.
• In Archaeological Survey, Banning, Edward Bruce (2002) cites the 1997 publication as a methodological reference for conducting Rank-size analyses and identifying urban settlement hierarchies. The text utilizes Savage's work to illustrate how ancient settlement systems relate to Zipf’s Law and regional population distributions.
• In Francesca Fulminante’s 2014 book, The Urbanisation of Rome and Latium Vetus, the author relies on the 1997 publication in Chapter 4 to establish theoretical rules regarding Rank-size and lognormal settlement distribution graphs. In subsequent comparative research such as Patterns of Etruscan Urbanism, Fulminante utilizes Stephen H. Savage’s 1997 paper ("Assessing departures from log-normality in the Rank-size rule") to apply mathematical formulas calculating the trajectory of ancient urban systems. These formulas help interpret how stabilizing systems naturally trend toward a lognormal layout over time.

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Multi-Scalar Clustering and the Amarna Letters (Savage and Falconer 2003)

In "Spatial and Statistical Inference of Late Bronze Age Polities in the Southern Levant" (Bulletin of the American Schools of Oriental Research (BASOR)), the analytical framework was expanded by pairing Monte Carlo Rank-size testing with K-means Cluster Analysis Here, Savage and Falconer use the methods developed by Savage to create a statistically based model of the Late Bronze Age in the southern Levant, and compare it to polities drawn by reference to the Amarna Letters and large sites. The 2003 paper fundamentally changed how historians and archaeologists map ancient political landscapes. The paper has been cited approximately 60 to 80 times. It remains a foundational text because it solved a classic problem: how to prove whether historical texts (like the Egyptian Amarna Letters) match actual ground-level archaeology.

The Core Methodology: Savage and Falconer used K-means spatial clustering and geographic data from thousands of documented archaeological sites. Instead of just drawing arbitrary circles around famous capital cities mentioned in texts, their computer models grouped actual town and village data to let the borders form naturally. Their findings mathematically demonstrated that the Late Bronze Age Levant was "balkanized"--divided into dozens of tiny, highly competitive, and structurally diverse city-states. Rather than treating the southern Levant as an undifferentiated regional whole, the K-means algorithm mathematically partitioned hundreds of Late Bronze Age (LBA) settlement locations into 24 distinct spatial clusters. Once these territorial boundaries were delineated, rank-size simulations were executed within each discrete polity.

This model provided an independent, site inventory-based validation of the Amarna Letters (14th century BCE cuneiform correspondence between Levantine vassal rulers and the Egyptian New Kingdom). After assembling an extensive list of Late Bronze Age settlements from published sources and the files at the Israel Antiquities Authority, we conducted a K-means cluster analysis on their locations, and overlaid the best cluster solution on a digitized map--Figure 6 from Shlomo Bunimovitz's (1995) publication of Theissen polygons based on the "city-states" identified in the Amarna Letters.

• Balkanized Political Landscape: The computational clustering confirmed that Late Bronze Canaan was not governed by unified regional states, but was fragmented into competitive, localized peer polities ("petty kingdoms") with restricted territorial reach.
• Geographic Structural Divergence: Polities situated on the Coastal Plain exhibited primate distributions, reflecting centralized administrative control over agrarian hinterlands. Conversely, polities in the Central Hills and the Jordan Valley exhibited convex or log-normal distributions, confirming the fragmented, decentralized, and contested administrative authority explicitly described by local rulers such as Biridiya of Megiddo and Labayu of Shechem.

The 2003 paper, Spatial and Statistical Inference of Late Bronze Age Polities in the Southern Levant, is actually highly self-contained. It is a dense, deeply specialized computational paper. The 2003 paper did exactly what spatial archaeology is supposed to do: it provided an empirical, bottom-up check on top-down textual histories. Before their work, historians looked at the Amarna Letters, saw the names of major city-states (like Megiddo, Jerusalem, or Shechem), and just assumed those capitals smoothly controlled everything around them. We threw actual archaeological site distributions into an algorithm to see if those political borders made sense on the ground. They showed that the Levant was deeply "balkanized"—showing that geography (the Coastal Plain vs. the Central Hills vs. the Jordan Rift) fundamentally dictated how these polities were structured. Because it bridges the gap between raw data and political history, the 60+ citations of the paper (from Google Scholar and ResearchGate) generally come from three very real groups of scholars:

• Regional Survey Projects: Archaeologists completing sweeping regional surveys in Israel, Jordan, and Palestine use it to contextualize their own localized findings within the broader macro-regional landscape Savage and Falconer modeled.
• Scholars of the Amarna Age: Historians and text-based scholars writing about Egyptian New Kingdom hegemony over Canaan use it to understand the actual demographic and geographic limits of the "kings" who were writing those letters.
• Iron Age Transition Studies: Researchers tracking the collapse of the Late Bronze Age cite it as the baseline map for what Canaan looked like before the systemic social re-organization of the early Iron Age.

When researchers cite the 2003 article, they are usually doing so for three reasons:

1. To justify using K-means clustering: Researchers use it as a precedent to prove that an algorithm can successfully group ancient sites together without relying entirely on biased ancient texts (like the Amarna Letters). Eva Kaptijn and Lucas P. Petit note that "These texts, primarily correspondence from petty Canaanite rulers to the pharaohs Amenophis III and Amenophis IV (Akhenaten), allude to a checkerboard of small polities across the Levantine landscape, each maneuvering for the favors of the Egyptian crown (Moran 1992). A series of critical studies infer 20-30 such polities and K-means cluster analysis concurs with the locations of most of these polities by suggesting 24 settlement clusters or potential polities during the Late Bronze Age (Savage and Falconer 2003)." Kaptijn, Eva & Petit, L.P.. (2009). A timeless vale. Archaeological and related essays on the Jordan Valley in honour of Gerrit van der Kooij on the occasion of his sixty-fifth birthday. Leiden, Leiden University Press.
2. To reference the "Balkanization" map: Scholars cite it simply to reference Savage and Falconer's specific calculation that the Late Bronze Age Southern Levant was split into roughly 24 fragmented micro-regions. An example is Nava Panitz-Cohen's, in "The Southern Levant (Cisjordan) during the Late Bronze Age" (2013) In The Oxford Handbook of the Archaeology of the Levant (c. 8000-332 BCE) (pp.535-554) Chapter: 36 . Oxford University Press. Editors: M.L. Steiner and A.E. Killebrew. Panitz-Cohen cites the 2003 study to demonstrate that Late Bronze political-territorial organization represented a more diverse and less integrated [i.e. Balkanized] system than in the Middle Bronze.
3. To compare their balkanized settlement system to regions beyond the Levant: Bevan contrasts the political geography of Palatial Crete with the more closely packed kingdoms of the south--central Levant[Bevan, Andrew. (2010). Political Geography and Palatial Crete. Journal of Mediterranean Archaeology. 23. 27-54. 10.1558/jmea.v23i1.27.]

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Updating RankSize

The culmination of the analytical engine was realized in the transition of the codebase to a 32-bit standalone application: RankSize v3 (Visual Basic Edition). The RankSize v2 program, described earlier, was written with the final DOS version of Turbo Pascal 7.0, released on October 27, 1992. By the time we began working on the 2003 article--the research was done in 2001-2002--a much better Windows-based environment dominated the PC market, and I wrote RankSize v3 in 2002 using Visual Basic 5.0 Control Creation Edition. Major upgrades to the program included a much smoother user interface and the curve plotting ability, which required me to write a custom log-log line plotting control, hence the use of the Control Creation Edition of the Visual BASIC IDE.

By releasing the software freely to the archaeological community, the program provided a unified graphical interface that automated the mathematical corrections developed since 1991:

• Direct Calculation of Zipf’s Exponent (q): Rather than assuming an idealized q = 1.0, the software utilized least-squares linear regressions across log-log arrays to calculate the true empirical value of q, providing an objective measure of system-wide centralization.
• Correction for the Lower-Limb Problem: The application integrated automated truncation functions, allowing researchers to model the effect of missing smaller settlement tiers and generate corrected simulation envelopes that isolated upper-tier political structure from lower-tier recovery bias.
• Multi-Plot Diachronic Overlays: The interface enabled researchers to overlay multiple archaeological phases and geographic zones simultaneously, facilitating direct comparative analysis of regional restructuring over time.

The Multiplot Tab on the RankSize Program screen opens the Multiplot form. For the sake of convenience, I've already filled in parameters for the plots, to illustrate how a multiplot appears. Note that this form lets the user create multiple line Rank-size plots, but it does not alolow things like set the value of Q or the lower limit for a plot. There is no simulation function; the program simply plots lines, so up to four different data sets can be compared. The Plot Curves button causes the program to plot all the curves that have been set up so far. It can be pressed after each set of input data is designated, or wait until all the desired plot lines are set up. It doesn't matter. When this button is pressed, the program looks through all the data sets designated and finds the largest and smallest site sizes, and the largest number of sites. It uses these values to recalculate the multiplot x- and y-axis, so all the data from all the plots are displayed.

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Macro-Regional Synthesis and the Deconstruction of "City-States" (2007–2009)

The subsequent maturation of this research trajectory integrated spatial simulation into macro-regional comparative syntheses, challenging classic evolutionary taxonomies that had categorized Early Bronze Age societies as standardized "city-states."

Overturning the Early Bronze Age City-State Paradigm (2007)

Meredith Chesson and Raphael Greenberg wrote foundational papers in the late 1990s and early 2000s arguing that Levantine towns were corporate and lacked stark social hierarchies. Savage, Falconer, and Harrison (2007) used a massive database to provide statistical GIS backing to those ideas, coining the phrase that these settlements were "neither cities nor states.

Savage, Falconer, and Harrison's 2007 paper, "The Early Bronze Age City States of the Southern Levant: Neither Cities Nor States" aggregated regional survey datasets from the southern Levant and Jordan to argue that Early Bronze Age fortified sites the region were not true urban city-states, but rather heterarchically organized, collaborative corporate communities. By combining the mathematical modeling of Rank-size and K-means analyses with massive spatial datasets, the authors delivered a direct challenge to the conventional terminology of Near Eastern archaeology. The work serves as a foundational critique of Levantine urbanization models, widely cited by scholars to support "rural complexity" models, while simultaneously being contrasted by other researchers who uphold the evidence for centralized city-states in the Western Levant. The paper has become a cornerstone text for scholars debating the exact nature of complex societies in the ancient world.

How the 2007 Paper Directly Relates to the Earlier Publications: This paper synthesizes decades of methodology and theory into a single, cohesive argument about the Early Bronze Age (EBA):

• From "Alternative Trajectories" (1995) to Rejection of Terms (2007): In 1995, Falconer and Savage argued that the Levant had an alternative path to urbanization compared to Mesopotamia. By 2007, with the addition of Timothy Harrison’s expertise on the EBA, they went a step further, arguing that the words "City" and "State" should not be used for the EBA Levant at all.
• Scaling Up the 1997 Simulation Methodology: The 1997 Journal of Archaeological Science paper tested small regional datasets for log-normality. The 2007 paper scaled this up drastically by running those exact Monte Carlo simulation models across the massive Jordan Antiquities Database and Information System (JADIS), analyzing hundreds of sites simultaneously to prove that settlement patterns across the entire Jordan Valley were consistently decentralized.
• Evolving from the Late Bronze Age (2003) Model: While their 2003 paper proved that the Late Bronze Age had tiny, "balkanized" city-states matching the Amarna letters, the 2007 paper demonstrated that the earlier EBA lacked even those fragmented state structures. Instead of isolated political nodes, the EBA featured overlapping, highly cooperative, and egalitarian networks.

The Monte Carlo Rank-size results indicated a continuous absence of integrated, multi-tiered regional administrative hierarchies across the Early Bronze Age. Instead of centralized, primate city-states, the data revealed:

• Segmentary, localized settlement systems that lacked high-order political integration.
• Socio-political configurations resembling corporate "house societies" or heterarchies rather than bureaucratic states.
• An urban landscape defined by walled agricultural centers that served as community storage and ritual nodes rather than despotic administrative capitals.

How the paper has been used:

• Charloux et al. use the chapter as a comparative baseline to frame their thesis of "low urbanization" and "slow urbanism" at the site of al-Natah. The authors apply this work to justify classifying the small settlement as urban, support the presence of corporate heterarchies rather than centralized states, and contrast regional timelines of social complexity. Charloux, Guillaume, Shadi Shabo, Bruno Depreux, Sylvain Colin, Kévin Guadagnini, François Guermont, Sabine Dupuy et al. "A Bronze Age town in the Khaybar walled oasis: Debating early urbanization in Northwestern Arabia." PLOS One 19, no. 10 (2024): e0309963.
• In Dolmens in the Levant (Routledge, 2018), Dr. James A. Fraser utilizes the 2007 paper to argue that the construction of massive megalithic monuments did not require a top-down, centralized state-level society. By applying the 2007 data on decentralized corporate heterarchies, Fraser demonstrates that independent agro-pastoral groups possessed sufficient social coordination to build and maintain these structures and links the spatial distribution of dolmens to localized permanent settlements as territorial anchors.
• In their 2016 study, Arıkan, Balossi Restelli, and Masi utilize Savage, Falconer, and Harrison's 2007 paper to demonstrate how varying levels of social organization influence the physical footprint of agropastoral land use. The authors employ this framework as a comparative regional baseline to evaluate decentralized settlement networks without relying strictly on centralized Mesopotamian urban models. Arıkan, Bülent, Francesca Balossi Restelli, and Alessia Masi. "Comparative modeling of Bronze Age land use in the Malatya Plain (Turkey)." Quaternary Science Reviews 136 (2016): 122-133.

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Diachronic Modeling of Peripheral Dynamics (2009)

The 2009 publication, "The Bronze Age Political Landscape of the Southern Levant", authored by Steven E. Falconer and Stephen H. Savage, served as the definitive capstone to their two-decade-long research program. Published as a central chapter in the book Polities and Power: Archaeological Perspectives on the Landscapes of Early States (edited by Falconer and Charles Redman; University of Arizona Press), this paper synthesis all of their previous regional datasets, mathematical algorithms, and theoretical models into a macro-regional history of the entire Bronze Age. By running comparative simulation arrays across the EBA, MBA, and LBA, the study provided a quantitative model showing how peripheral regions repeatedly absorb economic and environmental disruptions through the structural reconfiguration of rural settlements rather than top-down state intervention. The 2003 paper looked at the Late Bronze Age (using text + GIS), and the 2007 paper looked at the Early Bronze Age (using JADIS and cis-Jordanian database metrics). The 2009 chapter applied the already existing toolkit—K-means clustering and rank-size graphs—to provide a broad structural overview. The conclusion is environmental and structural: the fragmented topography of the southern Levant (cliffs, valleys, arid zones) simply naturally constrained the economic pooling of resources, meaning the landscape naturally favored smaller, fragmented, fluctuating networks rather than massive, sprawling river-valley empires like Egypt or Mesopotamia.

How the paper has been used: Within Levantine archaeology, their 1995 American Antiquity paper and their 2003 BASOR paper remain their most widely cited, mathematically influential breakthroughs. The 2009 chapter is a solid re-application of those models, but it does not carry the weight of an era-defining authority. But the paper has been cited for interesting applications:

• Titolo, Andrea, and Alessio Palmisano. "A tale of two regions: Cyclical human-climate interactions in the South Levant from the Chalcolithic to the Iron Age (6500–2200 BP)." Quaternary Science Reviews 375 (2026): 109777. explicitly cites the 2009 article multiple times. They use the 2009 publication in two specific ways: 1) Contextualizing Regional Population Declines: Titolo and Palmisano use their advanced statistical models (like radiocarbon Summed Probability Distributions) to track macro-demographic shifts over thousands of years. They explicitly cite Falconer and Savage (2009) alongside classic authorities like Broshi, Gophna, and Finkelstein to provide the baseline archaeological consensus for historic population crashes in the region—specifically during the Intermediate Bronze Age (~4500–4000 BP) and the Late Bronze Age (~3400–3150 BP). 2) Factoring in Geographic Asymmetry (Urban vs. Rural): Titolo and Palmisano point out that urbanism, settlement structures, and demographic density were never evenly or symmetrically distributed across the southern Levantine landscape. They cite Falconer and Savage's 2009 work (alongside their 2003 work and Raphael Greenberg) to back up the fact that Middle Bronze Age populations heavily clustered in the Coastal Plain, leaving regions like the Central Hills and the Jordan Rift Valley with fundamentally different, lower-density socio-economic profiles. 3) Reviewing Regional Settlement Models : When discussing the computational methodologies used by past archaeologists to track how these ancient settlements grew or shrank, they list Falconer and Savage's 2009 framework as a key example of utilizing Rank-size analysis to chart macro-regional complexity.
• Ataweel and Squitieri explicitly utilize the 2009 article in Chapter 4 to establish a baseline of localized demographic reality through raw database integration and spatial modeling. The authors leverage this data to demonstrate mathematically that Bronze Age populations in the Southern Levant were heavily concentrated in specific environmental niches, illustrating structurally uneven regional settlement networks prior to imperial expansion. Altaweel, Mark, and Andrea Squitieri. Revolutionizing a world: from small states to universalism in the pre-Islamic Near East. UCL Press, 2018.
• In his paper, Pullen uses his own anisotropic cost-surface modeling (walking times based on steep terrain) to map overlapping territories in Greece. He explicitly references Falconer and Savage's 2009 work (alongside Walter Christaller's Central Place Theory) to ground his comparative discussion on how archaeologists handle contemporaneous, competing regional centers with heavily overlapping territories. Pullen points to Falconer and Savage's Levant models as a key empirical parallel: demonstrating how multiple fortified, independent political hubs can coexist and compete within a tight geographic area without automatically being subordinated to a single, monolithic palace capitalPullen, Daniel J. "The Political Geography of the Late Bronze Age Argolid States and Territories." In Political Geographies of the Bronze Age Aegean: Proceedings of the Joint Workshop of the Belgian School at Athens (EBSA) and the Netherlands Institute at Athens (NIA) May, vol. 28, pp. 75-86. 2021.

Explore Additional Citations of the 2009 Article

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Conclusions

The 18-year research trajectory detailed here marks a distinct shift in settlement archaeology toward reproducible spatial science by using custom simulation algorithms to address uneven survey recovery rates. Within the highly specialized, niche domain of quantitative settlement archaeology, the publication stream has accumulated a notable grand total of 457 citations. For a technical field focused on regional metrics, this degree of academic engagement reflects a substantial impact that spans three key areas:

• Theoretical Re-evaluation: The corrected rank-size models successfully challenged Mesopotamian-centric definitions of civilization, validating localized models of social complexity and rural resilience instead of top-down command economies. The research highlighted the rapid development of urban primacy in southern Mesopotamia's heartland and the more static rural integration of the Diyala hinterland. In contrast, Bronze Age urbanization in the southern Levant describes a mosaic of urban and rural systems following independent trajectories. As a result, greater attention to small sites is required, because the small sites often define the shape of rank-size distributions. The research stream has illuminated modest cases of urbanizatlon in terms of structure, rather than simply of reduced scale, and stresses the need to avoid thinking of such cases as derivatlve.
• Methodological Validation Against Texts: The main objective of the 2003 article was to test the computational and spatial models published in the 1995 and 1997 articles against a known historical framework—polities based on prominent places that featured in the cuneiform correspondence of the Egyptian Amarna Letters. The K-means clustering and rank-size simulations independently matched, to a surprising degree, the set of Theissen polygons Bunimovitz constructed based on the central places described in the texts. The results furnished confidence that the spatial methods employed can discern reliable, reasonable proxies of ancient settlement systems in periods where written documentation is lacking. But beyond the statistical validation of settlement patterns, the results can serve as an alternative window into past settlement systems, even where abundant textual documentation is available. By paying closer attention to actual distributions of settlements within polities, these methods can serve corrective functions vis-a-vis texts that frequently are only concerned with large settlements or central places.
• Cross-Cultural Adoption: The utility of these mathematical and spatial analytical frameworks has extended far beyond Near Eastern archaeology, seeing direct replication by global scholars investigating complex spatial networks in Mesoamerica, South America, the Aegean, and Africa. When regional scholars cite this publication stream, they explicitly use the RankSize program, the Monte Carlo simulation boundaries, and/or the K-means settlement clustering logic to solve spatial problems outside the Near East:
  • The Aegean: Scholars like Andrew Bevan (2010) and Todd Whitelaw (2014, 2018) use these exact rank-size convexity frameworks to isolate independent, competing political structures across prehistoric palatial Crete.
  Mesoamerica: Urban geographers and Mayan/Aztec specialists (e.g., Carballo & Pluckhahn 2007; Garraty 2006; Golden et al. 2008; Montiel 2010) deploy the 1997 formulas to mathematically quantify shifts in political centralization and measure decentralized market autonomy away from imperial state centers.
  • Africa: Archaeological teams mapping early state dynamics in East Africa use the software baselines to track the shifting centralizations of the Aksumite kingdom in Ethiopia (Harrower & D'Andrea 2014; Harrower et al. 2023) and decentralized town growth along the Swahili coast (Fleisher 2010).
  • South America: Specialists evaluating prehistoric households and complex networks in the Southern Brazilian highlands (De Souza 2017) and Peru's Moche Valley (Fariss 2012) cite the methodologies to filter out missing smaller settlement tiers from their raw datasets.

Because the universal problem of uneven archaeological discovery—where small sites disappear while massive centers persist—afflicts every regional survey on earth, global scholars routinely rely on this specific 18-year body of work to correct their data curves before claiming a past society was integrated or decentralized. Ultimately, turning this computational architecture into standalone software transformed localized analytical tools into permanent digital infrastructure. Alongside modern GIS, this framework continues to ensure that ancient settlement data can be evaluated as dynamic, statistically verifiable records of human organization.

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Chronological Synthesis: The Methodological Evolution

Year	Milestone / Publication	Technical / Computational Innovation	Theoretical & Disciplinary Contribution
1991	Savage (ASU Seminar Paper)	ranksize.bas in Turbo BASIC; 35,000+ Monte Carlo iterations.	Proved that incomplete survey recovery (<85%) generates artificial primacy; exposed the invalidity of standard KS tables for stepped data.
1992	Savage (Ruppé Prize Monograph)	RankSize in Turbo Pascal 6.0; linear regression model (OPerf).	Operationalized simulation on Southern Levant Chalcolithic–Bronze Age survey data; formalized the primo-convex profile.
1995	Falconer & Savage (American Antiquity)	Regional Rank-size segmentation across geomorphic zones.	Demonstrated that rural village systems maintain structural stability and log-normality despite recurring urban collapse.
1997	Savage (Journal of Archaeological Science)	Peer-reviewed formalization of Monte Carlo Rank-size simulation.	Established the discipline-wide benchmark for statistically testing departures from log-normality.
2003	Savage & Falconer (Bulletin of the American Schools of Oriental Research (BASOR))	Integration of Spatial K-means clustering with within-cluster Rank-size simulation.	Provided independent spatial-archaeological validation of the fragmented, balkanized Canaanite landscape documented in the Amarna Letters.
2007	Savage, Falconer, & Harrison (in Crossing Jordan)	Macro-regional multi-survey comparative modeling.	Deconstructed the "city-state" paradigm for the Early Bronze Age Levant, proving the existence of decentralized corporate heterarchies.
2009	Falconer & Savage (in Polities and Power)	Diachronic simulation modeling over a 2,000-year landscape baseline.	Traced the multi-millennial evolutionary cycles of peripheral settlement networks absorbing socio-economic shocks.
2000s+	RankSize (Visual Basic Edition)	32-bit graphical desktop application; automated calculation of Zipf’s q; web-based GIS infrastructure.	Transitioned proprietary analytical code into permanent, open-access research infrastructure for international archaeology.

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