Modeling Expansive Phenomena in Early ComplexSocieties: the Transition from Bronze Iron Agein Prehistoric Europe

J. A. Barceló & G. Capuzzo & I. Bogdanović

# Springer Science+Business Media New York 2013

Abstract The Bronze Age/Iron Age transition in Prehistoric Europe represents a perfectcase study to test different and competing hypotheses of social dynamics and economicchange in small-scale societies. The paper discusses the possibilities of modeling what couldhave happened in Europe between 1800 and 800 BC, in terms of spatiotemporal dynamics.The paper presents some theoretical aspects of the dynamic study of expansive phenomenaand gives an overview of a computer model programmed to explain the way new burialforms expanded in Europe. The main idea is comparing classic demic diffusion models(spread of population), cultural transmission models (spread of ideas), and technologicalinnovation diffusion model (spread of goods). We will present the fundamentals of apreliminary study towards the computational simulation of such hypothetical social mech-anisms, using a dataset composed of more than 1,500 georeferenced and radiocarbon datedarchaeological contexts of a period between the Early Bronze Age and the first Iron Age(1800–800 BC) from an area including theNorth-East of Iberian Peninsula, Southern France,Northern and Central Italy, Switzerland, Austria, and Southern Germany.

Keywords Computermodeling .Radiocarbon .BronzeAge .PrehistoricEurope .Demicexpansion . Cultural transmission

Introduction: the Late Bronze Age/Early Iron Age transition

In European Prehistory, the Late Bronze–Early Iron Age transition deserves attentionbecause of its historical relevance (Sørensen et al. 1989). Traditionally, the beginning of

J Archaeol Method TheoryDOI 10.1007/s10816-013-9195-2

J. A. Barceló (*) :G. Capuzzo : I. BogdanovićDepartment of Prehistory, Autonomous University of Barcelona, Faculty of Philosophy and Letters,Building B, Bellaterra, 08193 Barcelona, Spaine-mail: juanantonio.barcelo@uab.cat

G. Capuzzoe-mail: giacomo.capuzzo@uab.cat

I. Bogdanoviće-mail: igor.bogdanovic@uab.cat

Iron Age has been defined by the introduction of a new raw material and a techniquefor its manufacturing. Although in Prehistoric Europe the first sporadic finds of iron canbe dated to the twelfth century BC (Brun et al. 2009; Lopez Cachero 2008; Pons et al.2010), the adoption of iron metallurgy was a slow process (Pons 1989; Pare 2008). It isnot until the end of the sixth century BC that the new metal became common for theproduction of objects and tools of everyday utility (Brun et al. 2009). From thismoment on, the new metallurgy led to changes not only in productivity but also insocial relations of production and the social forms of capital accumulation.

Raw materials for bronze metallurgy, copper, and tin, are scarce and highly local-ized. As a result, sources were controlled and its access politically restricted. Iron, onthe contrary, is a metal with a wider diffusion in Europe, and hence, with an easieraccessibility. In fact, iron metallurgy played a main role in the breakdown of exchangenetworks through which copper and tin circulated and, as a consequence, its adoptioninduced a collapse of the political system which represented the base of the Bronze Ageeconomy. From that, we can argue that the introduction of iron did not represent just achange in technology, but a change in the social and economic strategies, in particularconcerning the circulation of goods, ideas, and people. It is not surprising then that themain features of this period would be a general trend towards settlement concentration,which is the background for the rise of Iron Age historical towns, and also the increasein the number of fortified sites, which has been suggested as an evidence of increasingsocial tension (Kristiansen 1998; Guidi 2000). This aspect has been also underlined byPatrice Brun, whose theory for the origin and the expansion of iron metallurgy takesinto account three main factors: the multiplication of conflicts on a larger scale, thedismantling of ancient exchange networks (Brun 1991; David-Elbiali 2009), and therising of a new system of commercial routes between the Mediterranean cities, inparticular Greek and Phoenician, and central European communities (Kimmig 2000;Moosauer and Bachmaier 2000; Vagnetti 2002).

How new weapons, new artifacts, and new burial practices appeared in areaspopulated by people who previously used other artifacts and practiced different funer-ary rituals? Archaeologists have identified different processes that have the potential toexplain large-scale transitions in prehistory: demic diffusion (movement of people) andcultural transmission (movement of ideas). Elite dominance (the conquest by a smallminority that takes control of institutions and imposes its language and cultural traits) isanother process that should be taken into account. Distinguishing between demicdiffusion, cultural transmission, and elite dominance in the archaeological record isproblematic, especially where there is evidence of a diffusive spread of a novel trait intoa region that has evidence of a population already in place. Cultural transmission isoften assumed to be faster than demic diffusion because social learning can occur bothwithin and across generations, whereas population growth can occur only acrossgenerations. Demic flow raises the possibility that cultural, genetic, and linguistic traitswith no intrinsic advantage may “hitchhike,” i.e., spread with the advancing newpeople (Ackland et al. 2007).

The first studies (Bosch Gimpera 1923; Childe 1927; Müller-Karpe 1959; Schauer1975), assumed a migrationist–invasionist explanation for the “adoption” of cremationburials south and east of the apparently original area, on the basis that the oldesturnfields had been discovered in Central Europe, in the Carpatho-Danubian region(Müller-Karpe 1959; Sperber 1987). Genetic data are currently used to test such

Barceló et al.

hypothesis (Plaza et al. 2003; Rootsi et al. 2004; Achilli et al. 2007). Although it hasbeen suggested, a relationship between the presence of I-L38 haplogroup in WesternEurope and the migration of Urnfield culture during the LBA and Iron Age, pointing tothe role of the Upper Rhine region in the expansion (De Beule 2010, 2011), populationmovements at the beginning of 1st millennium BC are hardly a popular hypothesistoday. The problem with a migration hypothesis to explain the “expansion” of LateBronze Age is that chronological differences for the oldest remains of cremation burialand new artifacts in each area does seem too great to follow a demic diffusion scenario.Given the obviously random nature of the demographic processes underlying theadoption of a new funerary practice, and the abundance of both random and systematicerrors in the quantitative (mainly radiometric) evidence available, it is clear that seriousstatistical analysis is required to quantify the social and cultural change at the end ofLate Bronze Age.

The real point seems to be to evaluate the relative importance of both demic andcultural diffusion in different regions of Europe because in some areas both are likely tohave contributed to the social and cultural change. Our purpose in this paper is not toanalyze the origin and spread of Iron Age cultural traits. Instead, we ask a differentquestion: What do the archaeological data tell us on the relative importance of demicdiffusion and cultural transmission? An advantage of focusing our attention on theadoption rate (not on the interaction mechanisms) is that it makes direct quantitativecomparisons to archaeological data possible. Up to now, mathematical models ofpopulation spread and social learning have not been applied to the controversy betweenthe demic and cultural expansions of the Late Bronze Age–Iron Age transition,probably because of the lack of academic acceptance of the very idea of diffusion(Rahmstorf 2011).

Characterizing Expansive Phenomena

The notion of spatial diffusion through time covers all processes that contribute to thechanges in the location of some phenomenon and the reactive effects generated by thosechanges. The more complex the diffused or transmitted innovation, the more influence itsdiffusion process will have on transformation of its propagation environment, as effectsinduced by its adoption will be all the more increased. Therefore, the expansive nature ofthe historical phenomenon should be analyzed as an increase in the spatial distancebetween social agents resulting from some transformation in social ties (social fission),or a growth in the absolute number of agents. Contraction would be the reverse process;for instance, a decrease in distance between social agents as a result of an increase in socialties (social aggregation and social fusion). It brings about the intrinsic dynamic nature ofthe phenomenon, which refers to the idea of spatial change in a determined period of time.

The preliminary question to be posed is about the spatio-temporal nature of “cul-tural” changes that occurred at that time, and whether they can be defined in terms of a“demographic” or “cultural” expansion. In this paper, we will refer to expansivephenomena as dynamic systems in which every location, at some well-specifiedunderlying space, has a distinctive behavior through time. When a system expandsthrough time, we can foresee a certain degree of dependence between locations, andthis dependence is exactly what gives unity to the process.

Modeling Expansive Phenomena in Early Complex Societies

We should ask whether cremation burials in the second half of the 2nd millennium

BC and at the beginning of the 1st millennium BC “expanded,” that is, whether thedistances between their spatial locations increased with time (Hazelwood and Steele2004). We refer here to the classical idea of diffusion as a predictable space-timeprocess, suggested by the Swedish geographer Torsten Hägerstrand (1967), rather thanstandard models of diffusion of innovation based on the division of the population intoindependent adopters (“innovators”) and imitators, and that the shape of the cumulativeadoption curve will vary as a function of their relative importance (Bass 1969). Weassume that for a new practice in funerary rituals to diffuse over time and space, thereshould have existed a mechanism of contact and cultural transmission to transmit thephenomenon (Boyd and Richerson 1985): in each time period every potential adopterof the new ritual practice made contact with other persons (the number depends on thenetwork structure) with a likelihood based on the nature, intensity, and frequency ofinteractions. We also assume that the spread behavior is not determined by independentassessment but there are external constraints (economic, social, and cultural).

Obtaining archaeological estimates for demographic parameters such as populationdensity remains a very imprecise science, not least because of sampling biases anduncertainties in the documented archaeological record (Chamberlain 2009). Althoughradiocarbon data have been used with such purpose, radiocarbon estimates do notnecessary correspond with historical events. The correct inference chain is:

Isotopic event→Depositional event→Archaeological event→Social event.

What we can “see” in the archaeological record are some material consequences ofsocial actions that happened in the past. We may consider that such phenomena arearchaeological events, and such archaeological events are a palimpsest of lower-levelevents: the particular action(s) that generated the location of such item at this particularplace and moment. We call this circumstance a depositional event. A single archaeo-logical event can be composed of many different particular depositional events, withdifferent calendar dates and different durations. However, we should distinguish thepossible occurrence of an isotopically determinable death event, which is the particularmoment in which an animal or plant ceased to interact with the atmosphere andbiosphere. We assume that the most probable calendar date of a depositional eventwill be the nearest possible to the isotopically measured calendar date of the isotopicevent, with a standard error determined by the duration of the depositional event.Therefore, we should relate each isotopic event with corresponding depositional events,i.e., stratigraphic and taphonomic information of each dated sample. Defining contextreliability is a fundamental step for obtaining a true relationship between the radiocar-bon probability intervals and the depositional event we are referring to. The estimatedcalendar date and duration of all synchronous depositional events within the samearchaeological event will be used to measure the date and duration of events higher inthe hierarchy (Barceló 2008; Barceló et al. 2013) (Fig. 1).

The inference from archaeological events to proper social events is also complex. Inour case, if we go on to assume that once a region adopted the new funerary ritual(cremation), the frequency with which radiocarbon dated cremation burials occur inthat region during a given period should be proportional to the frequency of socialevents (funerals) and the frequency of social events would be related with the size of its

Barceló et al.

population. However, even in the case such assumption be plausible in terms of thearchaeological sampling processes that yielded the corpus of radiocarbon dates, wemust decide how to estimate event frequency in a way which takes account of thestatistical uncertainty inherent in each radiocarbon measurement (Steele 2010).

According to this framework we have created a georeferenced database for radio-carbon dated archaeological events that may have occurred during the Bronze Age/IronAge historical transition. The organization of our database was imposed by the natureof available data. We have related the archaeological data, expressed in terms ofisotopic events (radiocarbon measurements on charred wood and seeds, charred anduncharred bones) linked to their corresponding depositional events (spatial coordinatesof radiocarbon samples, spatial relationships with archaeological artifacts) and in manycases with the corresponding archaeological events (stratigraphic relationships). There-fore, each isotopic event is followed by spatial information (both UTM and longitude/latitude in decimal degrees), and its more probable associated archaeological event. Thedatabase currently has 1,567 isotopic events from 573 sites. The analyzed area includesall the territories between the Ebro and the Danube rivers (Eastern Iberian Peninsula,southern France, northern Italy, Switzerland, Austria, and Southern Germany). Itsextension of 525,090.51 km2 would imply one C14-dated archaeological site each916 km2 if the distribution of the sites was homogeneous. Although we have selecteddata to assume spatial homogeneity (see Capuzzo et al. 2013), there are still areas witha concentration of sites (and therefore dates) and areas (much bigger than 916 km2)

Fig. 1 From a radiocarbon estimation to the dating of the “Historical Event”

Modeling Expansive Phenomena in Early Complex Societies

without a single site. We have ensured that the temporal and spatial scales of interest arelarge enough in comparison to the intrinsic population process scales. In our case, theseprocess scales are simply the generation times of individuals and their dispersaldistances, respectively. The relevant space scales (half a continent) and the timescales (hundreds of years) are clearly orders of magnitude greater than the intrinsicprocess scales of the average individual life cycle and of the average individualmigration rate.

For the analysis reported here, we have used a subset of such a database, which onlyincludes well dated cremation burials. We have also included dates originating fromneighboring territories (Belgium, Northern Germany, Czech Republic, and CentralItaly). We have additionally selected only the oldest archaeological event withincircumscribed areas of less than 100 km. The resulting dataset contains 56georeferenced archaeological events. Radiocarbon dates have been calibrated usingOxCal 4.2 (Bronk Ramsey 2009), and the median of the calibrated interval has beenconsidered for statistical analysis (Table 1).

We start with a data structure consisting of a set of locations (s1, s2, etc.) in a defined“study region,” R, where a distinctive event (adoption of a “new” burial practice)occurred at different moments of time (Fig. 2). The goal of our analysis should be thento determine a meaningful relationship between difference in chronology and differencein location. This relationship, if it existed in that historical case, is essentially a measureof how the adoption of some innovation changed through time and space.

The question that now arises is whether the observed frequency of events with thesame chronology displays any systematic spatial pattern or departure from randomnesseither in the direction of clustering or regularity. In other words:

& How the spatial distribution of cremation burials depended (or “had an influence”)over the spatial distribution of other(s) value(s) or properties (grooved pottery,fortified settlements, etc.),

& How the temporal displacement of the values of cremation burials depended (or“had an influence”) over the spatial distribution of other(s) value(s) or properties

Modeling the first Occurrence of Second Millennium Cremation in PrehistoricEurope

The purpose of our research is to model the spatial trend linking differences in time forthe adoption of the new burial practice during the Bronze Age. If such a function can becalculated, then by using observations of archaeological chronologies made at somelocations, we will estimate the chronology of archaeological evidence at neighborlocations and the probabilities that a the new burial practice was adopted at some placeat a specific time.

Results are still preliminary but we can suggest an expansion to explain the adoptionof cremation burial practices during the second millennium BC. Although the regionand moment of the initial adoption of cremations in urns is still debatable fromarchaeological data, radiocarbon estimates interpolation suggests South–Western Alps,around 1400 BC, as the origin. South and Western France, Northeastern IberianPeninsula, North and Central Italy appear to be areas where the transformation took

Barceló et al.

Tab

le1

Datasetof

georeferencedradiocarbonestim

ates

forcrem

ationburialcontextsfrom

thearea

understudy

IDSite

Latitu

deLongitude

Lab

code

14CageBP

±σMedian

Materialandarchaeologicalcontext

1Altdöbern

51.652821

14.030812

Bln-3346

2690

50−8

53Unknown;

grave8

2Hexenbergle

48.254602

10.806353

UZ-3556

2790

70−9

53Wood;

burialmound

8

3Kagers

48.916667

12.583329

BM-2991

2720

45−8

70Animalbone;grave48

4Künzing-O

st48.833318

12.999994

BM-3027

2840

50−1

,005

Animalbone;grave220

5Mainzlar

50.666667

8.733333

GrA

-16041

3090

60−1

,354

Hum

anbone;burialmound

9

6Rückersdorf

51.569941

13.565511

KIA

-15666

3085

25−1

,362

Charcoal;grave16

7Saalhausen

251.010465

13.615372

Not

identified

3030

50−1

,292

Unknown;

grave104

8Franzhausen,

S33Kokoron

48.348096

15.722398

VERA-732

2931

50−1

,143

Charcoal;Pinus

sp.,grave65

9Hadersdorf

48.450135

15.716826

VERA-2069

2661

57−8

33Animalbone;grave88

10Pitten

47.712568

16.187493

VRI-93

3050

90−1

,296

Charcoal;remains

ofthepyre,area372

11Blicquy

50.588374

3.684901

KIA

-23752

3185

30−1

,459

Hum

anbone;graveF1

29

12LouetteSaint-Pierre

49.692117

4.927314

KIA

-25593

2580

25−7

85Hum

anbone;tumulus

13Mezenstraat,B

eerse

51.319233

4.836568

KIA

-33613

2945

30−1

,165

Hum

anbone;at-63cm

from

thesurface

14Paddestraat

50.872932

3.760283

KIA

-20064

2920

30−1

,119

Hum

anbone;grave18

15Provinciebann

50.886047

3.770817

KIA

-23751

2950

30−1

,172

Hum

anbone;grave12

16Tessenderlo

51.030555

5.047222

KIA

-33615

2825

25−9

76Hum

anbone;grave43

17ArroyoButarque

40.338245

−3.681337

Beta-197521

2590

40−7

81Hum

anbone;pit1

18Can

Barraca

42.208637

2.748324

Beta-216833

2620

40−8

01Charcoal;grave7,

inside

theurn

19Can

Bechde

Baix

42.405218

2.827987

CSIC-242

2770

60−9

23Crystallized

resin;

grave389,

urn15

oftheC.4

20Can

Missert

41.566381

2.012233

KIA

-35577

2815

30−9

66Hum

anbon;

urn3581,M

useo

Episcopalde

Vic

21Can

Piteu-Can

Roqueta

41.536654

2.138320

KIA

-24835

2755

30−8

94Hum

anbone;urn294-34B

22Collde

Moro

41.053401

0.390811

GrA

-23646

2630

50−8

07Hum

anbone;tumulus,g

rave

T42

23LaCodera

41.724658

0.110283

GrN

-26966

2610

40−7

95Unknown;

tumulus

6

Modeling Expansive Phenomena in Early Complex Societies

Tab

le1

(contin

ued)

IDSite

Latitu

deLongitude

Lab

code

14CageBP

±σMedian

Materialandarchaeologicalcontext

24Palomar

dePintado

39.417068

−3.361345

Beta-178469

2820

40−9

75Hum

anbone;grave76,insidetheurn

25Pedrós

41.458347

0.407092

OxA

-13565

2657

37−8

21Charcoal;tumulus

26Pi

delaLliura

41.763779

2.852027

Beta-136241

2850

40−1

,016

Charcoal;urnE-15

27Turóde

laCapsera

42.304263

0.883157

UBAR-667

2835

55−1

,000

Charcoal;tumulus

20,S

U2015

28Cam

iSalié

43.316626

−0.416666

Ly-2242

2650

140

−807

Charcoal;tumulus

1,with

urn

29Cam

pd'Alba

44.109096

1.477133

Ly-7433

2575

50−7

38Charcoal;grave79

30Errotzaté2

43.045831

−1.170259

Gif-3741

2680

100

−854

Charcoal;crom

lech

31Kastenw

ald

48.033326

7.450001

Ly-2054

2800

130

−998

Charcoal;tumulus

5,grave5

32LaCroix

delaMission

48.385384

2.996810

GrA

-17937

3130

50−1

,407

Hum

anbone;Str.48,d

oublecrem

ationin

urn

33Millagate5

43.009916

−1.030808

Gif-7559

2730

60−8

85Charcoal;mound-cromlech

34Savines-leLac

44.525571

6.404869

Poz-25712

3115

30−1

,397

Unknown;

SU102,

grave

35Sierentz

47.654520

7.454682

Ly-4208

2990

100

−1,218

Charcoal;pitwith

crem

ation

36Tum

ulus

2de

Vix

47.898687

4.537880

Ly-1431

2890

35−1

,076

Hum

anbone;tumulus

2,grave1

37Tum

ulus

6de

Vix

47.898687

4.537880

Ly-665

2685

40−8

43Hum

anbone;tumulus

6,centralgrave

38Tum

ulus

deChaum

e-lès-Baigneux

47.898687

4.537880

Lyon-1610

2985

55−1

,222

Hum

anbone;centralgrave

39ExCasadi

Ricovero

46.603234

11.5203321

ETH-25266

2960

45−1

,185

Charcoal;individualburialin

apit

40Fo

rodi

Cesare

41.894181

12.486691

Gra-16432

2920

60−1

,126

Unknown;

grave1

41L'Oasi

44.686034

8.006393

OZE-029

3012

471267

Hum

anbone;individualburialin

apit

42Po

zzuolo

45.988092

13.195239

UD-58

2700

100

−877

Charcoal;grave2

43Rom

a,Quadrato

41.845227

12.586879

GrA

-16423

2820

50−9

79Unknown;

grave2

44S.

Palomba

41.707568

12.576605

GrA

-27028

2875

35−1

,053

Unknown;

grave1

45Trigoria

41.766800

12.479306

GrA

-27025

2870

35−1

,045

Unknown;

grave3

46VillaBruschi

Falgari

42.240853

11.759284

GrA

-23484

2885

45−1

,072

Hum

anbone;grave103

Barceló et al.

Tab

le1

(contin

ued)

IDSite

Latitu

deLongitude

Lab

code

14CageBP

±σMedian

Materialandarchaeologicalcontext

47Chodouny

50.533330

15.033328

P-1902

3080

60−1

,343

Charcoal;grave7

48Manĕtin,H

rádek

50.016659

13.249995

P-1913

2630

60−8

06Charcoal;grave164

49Přáslavice,D

ílypoddĕdinou

49.588368

17.392728

VERA-?

2990

40−1

,232

Charcoal;grave14,adultu

sindividualin

urn

50Birmensdorf-Ram

eren

47.362281

8.446312

ETH-28490

3210

50−1

,482

Charcoal;tumulus,g

rave

9

51BulleFR

,LeTerraillet

46.631112

7.061908

Ua-24629

2950

40−1

,171

Charcoal;tumulus

52Fällanden-Fröschbach

47.369438

8.644476

UZ-3910

3400

60−1

,702

Charcoal;grave12,amongthecalcined

bones

53Koppigen,

Usserfeld

47.135554

7.586912

ETH-26775/UZ-4914

3020

55−1

,276

Charcoal;grave1,

individualburialin

apit

54Murten-Löw

enberg

46.938616

7.141140

B-4994

3380

50−1

,674

Charcoal;tumulus

3,grave11

N.3

55NeftenbachII(Zürichstrasse

55)

47.525379

8.660720

KIA

-11173

3165

32−1

,443

Charcoal;grave8,

sample81

56Vidy(LausanneVD)

46.521682

6.594960

CRG-655

2870

70−1

,058

Unknown;

grave2

Extracted

from

theEUBARDatabase(Capuzzo

etal.2

013)

Modeling Expansive Phenomena in Early Complex Societies

place nearly 500 years later, including also the possible adoption of cremations withouturn.

Our preliminary results show that the first occurrence of a cremation burial isspatially auto-correlated because estimated chronologies at a distinct location areassociated with the chronology of the same phenomenon at neighboring points(Fig. 3). Dividing the hypothetical 2,354 km between the extremes of our study areainto 20 intervals (117.7 km each), Moran's I index has positive values for neighboringcemeteries, and in most cases, negative values when distance increase. That means thatchronology is spatially dependent at lower distances, and in some cases, at higherdistances, such dependency is not easily detectable. The adoption of the new funeraryritual was then clearly not stationary because the intensity of chronological differencesappears to be non-constant over the considered geographic space. Although more

Fig. 2 Spatial distribution of medians of the calibrated radiocarbon date for the oldest Second Millenniumcremation burial within a circumscribed region. Northeastern dates come from middle Danube valley, whereassouthwestern ones come from Ebro river in Spain (2,354 km between both extremes. Distance assumingmodern highways and calculated using Google Maps)

Fig. 3 Spatial Autocorrelation re-sults (Morans'I). Calculated usingthe GS+program (Gamma De-sign, Inc. http://www.gammadesign.com/)

Barceló et al.

analyses are needed, we suggest that second-order intensity seems to be dependent onthe vector difference, d (direction and distance), between spatial locations and not ontheir absolute locations, what makes reference to minimum-cost routes for physicalmovement or virtual interaction between social agents, where cost is interpretedgenerally. The expansion pattern is then much more complex than expected under abasic demic diffusion hypothesis.

In archaeology, it is usual to compute linear regression analysis between chronolog-ical estimates to describe the spatial directionality of the expansive process. A site isdesignated as the origin and its distance from each of the other sites computed;thereafter, the correlation between the distances and the ages of the other sites ismeasured. This procedure is repeated until all the sites have served as the origin. Thefinal step of the method involves comparing the correlation coefficients. The site thatyields the highest negative correlation coefficient when it is designated the origin isdeemed to be the most likely center of origin (cf. for instance, Ammerman and Cavalli-Sforza 1984; Pinhasi et al. 2005; Hamilton and Buchanan 2007; Steele 2010; Buchananet al. 2011; Collard et al. 2010a). However, our preliminary results show that the socialspace of Late Bronze Age was hardly uniform and boundless, because every spatiallocation had some degree of uniqueness relative to the other locations. This affects thespatial dependency relations and therefore the spatial process. Spatial heterogeneitymeans that overall parameters estimated for the entire system may not adequatelydescribe the process at any given location. It is important to take into account that partof this irregularity and spatial heterogeneity is not a characteristic of the historicalexpansive phenomenon but to possible errors selecting the proper radiocarbon date forthe “oldest” cremation burial in an area. Specifically in the area where oldest dates havebeen obtained (the area of Northern Alps and Danube valley), there are still many toomodern references.

To be able to create an interpolated map of chronological estimates taking intoaccount the non-stationarity and irregularity of the phenomenon under study we havecalculated the semivariance of the adoption of the new burial practice of cremationfrom Danube to the Ebro valleys. We have used a kriging algorithm, without any edgeinterpolation to predict the value of the chronology across space according to a spatiallag relationship that has both systematic and random components. Kriging is based onthe idea that the value at an unknown point should be the average of the known valuesat its neighbors; weighted by the neighbors' distance to the unknown point (Cressie1993; Stein 1999; de Smith al. 2009; Mitchell 2009).

An important feature of kriging-based interpolation methods is that they rely on thesemivariance among data. Semivariance is a property of a spatial distribution of valuesexpressing the degree of relationship between locations. The semivariance is simplyhalf the variance of the differences between all possible points spaced a constantdistance apart. The semivariance at a distance d=0 will be zero, because there are nochronological differences between spatial locations that are compared with themselves.However, as cemeteries are compared with increasingly distant points, the semivarianceof their chronology increases. At some distance, called the Range, the semivariance willbecome approximately equal to the variance of the whole spatial distribution itself. Thisis the greatest distance over which the chronology of a cremation burial is related to thechronology at another burial more distant. The range defines the maximum neighbor-hood over which control points should be selected to estimate a grid node, to take

Modeling Expansive Phenomena in Early Complex Societies

advantage of the statistical correlation among the observations. A plot of semivariancesversus distances between ordered data in a graph is known as a semivariogram (Fig. 4).

A variogram is usually characterized by three measures. The nugget refers to thevariability in the field data that cannot be explained by distance between the observa-tions. Many factors influence the magnitude of the nugget including imprecision insampling techniques and underlying variability of the attribute that is being measured.In addition, the minimum spacing between observations can influence the nuggetbecause if there are no observations located close to each other, it is impossible toestimate “close-range” spatial dependence. The sill refers to the maximum observedvariability in the data. In theory, the sill corresponds to the variance of the data asnormally estimated in statistics. The distance where the model first flattens out isknown as the range; it is just the difference between the sill and the nugget, andrepresents the amount of observed variation that can be explained by distance betweenobservations. Sample locations separated by distances closer than the range are spa-tially autocorrelated, whereas locations farther apart than the range are not.

Our data show a small nugget and a large sill; the nugget effect disappears after lag5, that means, an average distance of 885 km between cemeteries. Chronologies havemuch spatial dependence within such an area. Where spatial autocorrelation is present,semivariance is lower at smaller separation distances (autocorrelation is greater). Thistypically yields a curve like the one in Fig. 4.

We have interpolated the chronology at unknown spatial locations based on what weknow from some locations (the list of georeferenced 56 radiocarbon estimates), and theway they are related according to the previous semivariance (Fig. 5).

We may infer the “expansive” nature of the historical phenomenon because a regulartrend in the spatial probabilities of the first occurrence of cremation burials can bedetected. The model allows to identify at what spatial locations a change in theestimated temporality of the archaeological event leads to a change in the probabilityof its causing action or process. Nevertheless, instead of taking the map shown in Fig. 5as a “picture” of the expansive phenomenon at the end of Late Bronze Age, we shouldvalidate it. We need to have some idea of how well the model predicts the chronologyof the first adoption of the new burial practice at unknown locations. For all points,cross-validation compares the measured and predicted values and plots a scatter plot ofpredicted values versus true values is given (Fig. 6).

Each point on the cross-validation graph represents a location in the input data setfor which an actual and estimated value are available. The regression coefficient

Fig. 4 Second-order representa-tion of radiocarbon dates for theSecond Millennium first occur-rence of cremation(Semivariogram). Calculatedusing the GS+program (GammaDesign, Inc. http://www.gammadesign.com/)

Barceló et al.

described at the bottom of the graph represents a measure of the goodness of fit for theleast-squares model describing the linear regression equation. A nearly perfect fit hasbeen obtained (0.917) and the best-fit line (the solid line in the graph above) coincideswith the dotted 45° line on the graph. The standard error (SE=0.187, above) refers tothe standard error of the regression coefficient; the r2 value is the proportion ofvariation explained by the best-fit line (in this case 31.6 %; it is the square of thecorrelation coefficient); and the y-intercept of the best-fit line is also provided. We canconclude that the model fits conveniently available data.

Our statistical results show that the expansive nature of the adoption of a new ritualduring Late Bronze Age in Western Europe has a distinctive spatial gradient, which ischaracteristic both of demic diffusion and cultural transmission hypotheses. We canlead the analysis further by detecting significant chronological changes between neigh-boring cemeteries, suggesting the idea of non-stationarity, heterogeneity, and irregular-ity in the expansion. Hoffman and Richards (1984) have proposed that a good rule ofthumb is to divide the data array into components at maximal concavities, whichmathematically speaking, are the local minima of curvature. Formally, such a discon-tinuity in the spatial probabilities of the first occurrence of the studied event is definedas an observable edge in the first derivative of the mathematical function that describesthe archaeological frequencies over space. This task can be approached by calculatingthe spatial gradient in the data array—that is, the direction of maximum rate of changeof the perceived size of the dependent values, and a scalar measurement of this rate(Sonka et al. 1994; Palmer 1999; de Smith al. 2009). The spatial gradient associatedwith the first occurrence of cremation burial describes the modification of the densityand the size of archaeologically measured values and so regularity patterns in spatialvariation can be determined. It is calculated by finding the position of maximum slopein its intensity function (a graph of the value of time of first occurrence as a function ofspace). Thus, the intensity profile of spatial frequencies can be graphed as a curve inwhich the x-axis is the spatial dimension and the y-axis corresponds to time. Likewise,

Fig. 5 Visualizing spatial and temporal variations in the first occurrence of Second Millennium cremation(medians of the calibrated radiocarbon dates). (Software: ESRI 2011. ArcGIS Desktop: Release 10. Redlands,CA: Environmental Systems Research Institute). The numbers correspond to the ID numbers of the database.Contours represent differences of 50 years

Modeling Expansive Phenomena in Early Complex Societies

the directivity of such a probability gradient (or “aspect” of the scalar field) is simplythe polar angle described by the two orthogonal partial derivatives.

We have calculated a gradient map showing the estimated direction of chronologychanges (from locations with high chronologies to nearby locations with low chronol-ogies) with arrow lines, which show the apparent nature of expansivity in the studiedphenomenon (Fig. 7). The approach is based on the calculation of partial derivatives (orrelated functions) between the differences in chronology among locations at differentdistances to estimate “movement.” In this case, it seems well attested the existence ofsome neighborhood effect (or contagious effect): the farthest a cremation burial hasbeen discovered from the locations with highest chronologies, the lowest the chronol-ogy of the first adoption of the new burial practice. Interactions seem to be morefrequent on nearest neighbors. As such, as time passes, the innovation potentialgradually diffuses spatially.

Those statistical results are relevant to evaluate the reliability of the model. Definingthe minimum spatio-temporal gradient that may be detected archaeologically requires aclear understanding of spatial scales and resolution and is also problem dependent. Thisproblem becomes even more complex for heterogeneous topographic surfaces. Firstly,the time between any pair of events sampled must be greater than the combined sum ofradiocarbon errors and the model error. While the effect of radiocarbon errors falls ingeneral within the range 100–200 years, the modeling error is inversely dependent on

Fig. 6 Cross-validating kriging chronological estimates at unknown spatial locations. Calculated using theGS+program (Gamma Design, Inc. http://www.gammadesign.com/)

Barceló et al.

the population growth rate. Therefore, at any single location in space, we cannot becertain where the earliest dated event lies within the interval which defines thetransition period. Similarly, at any instant in time the locations of any pair of sitesbeing sampled to detect the transition of the wave front must be separated. Thenecessary spatial separation of any pair of sites being sampled will increase as thesupposed migration rate increases relative to the population growth rate. More gener-ally, in many cases where we have a radiocarbon record of a dispersal process, we cannow see that we will be severely constrained in our ability accurately to predictcolonization or innovation adoptions rates.

As a further step of our investigations, we plan to improve the model byreexamining the input data using the suggested framework.

Stationarity During Late Bronze/Iron Ages Transition

It is important to take into account that Southern Europe (North Italy, South France, andNortheast Iberian Peninsula) was not an empty uncolonized land before Urnfieldexpansion. Therefore, more than the mere existence of a spatiotemporal gradient inthe average earliest adoption times for Late Bronze Age cremation burials, the questionis whether the expansion changed the nature of the historical circumstances, that is,whether a population growth took place as a consequence of a supposed demicdiffusion.

In addition to tracking expansive phenomena from georeferenced databases ofradiocarbon estimates, archaeologists have recently begun to estimate temporal varia-tions in activity and investigate the probabilities of local population growth rates andsubsequent dynamics (including episodes of rapid depopulation, sometimes related to

Fig. 7 Map showing the directivity of the Second Millennium cremation adoption phenomenon (Software:Rockworks 16, Rockware, Inc.). The map contains small arrows at each grid node pointing down the gradient,that is, decrease in chronology: from places where cremations were older to places where such phenomenonappears to be more recent

Modeling Expansive Phenomena in Early Complex Societies

extreme climatic events). A number of recent studies have addressed this problem bygraphing summed calibrated probability distributions (SCPDs) for all the radiocarbondates in their datasets. The peaks and troughs in these SCPDs, where these aresufficiently robust to be more than mere artifacts of the inflections of the calibrationcurve, are interpreted as evidence of population fluctuations. The proxy data onpopulation numbers provided by radiocarbon dating can be combined with estimatesof fertility and migration in the construction of colonization models. There are manyapplications of those models (Housley et al. 1997; Gkiasta et al. 2003; Fort et al. 2004;Gamble et al. 2005; Mellars 2006; Shennan and Edinborough 2007; Hamilton andBuchanan 2007; Collard et al. 2010b; Hinz et al. 2012; Shennan 2013). The rationale ofthe method assumes that the number of dated archaeological contexts in a given timeperiod can be expected to be monotonically relate to population size. Consequentlyobserved peaks in the SCPD are taken as evidence of higher populations and troughs asevidence of lower populations, with the steepness of the slope of an increase ordecrease showing the rapidity of the population rise or fall. It would obviously bepossible to examine patterns like these mathematically, but archaeological practice hasgenerally been simply to examine probability distributions visually.

Nevertheless, there is no method without shortcomings. Chiverrell et al. (2011) warnof the fact that georeferenced radiocarbon databases incorporate multiple types of datedcontexts with differing chronological relationships between the 14C measurements andthe dated events, with pre-dating, dating, or post-dating chronological control eachdisplaying variable length temporal lags all mixed together in the same analysis.Ambiguities inherent in the process of radiocarbon dating can thus both create patternsin sets of radiocarbon dates that mimic those that archaeologists often interpret asevidence of long-term demographic trends and obscure real demographic patterns.Distributions of radiocarbon dates are potentially affected by sample selection and bya range of factors that condition the probability that archaeological remains aredeposited, survive, and are then discovered (Chamberlain 2009; Baggaley et al.2012). A note of caution relating to the uncritical use of temporal distributions ofradiocarbon dates has been raised by Hazelwood and Steele (2004) who have argued,with the aid of a simple model of population expansion, that such a pattern will onlysurvive in the modern archaeological record when some rather narrow conditions aremet for the demographic parameters that determined the original population expansion.Surovell and Brantingham (2007) have also pointed out that a monotonic increase inthe frequency of dates through time can be generated by a systematic taphonomic biasif (as may often be the case) the probability of archaeological site survival is negativelycorrelated with the age of the site. Furthermore, large numbers of dates from individualsites might skew the overall dataset. More serious, however, is the tendency ofarchaeologists to obtain disproportionate numbers of dates from particular site typesat the expense of other less distinctive types (Armit et al. 2012). Williams (2012) hasrecently summarized the latest developments of the method, pointed out differentproblems and proposed strategies to handle them. In our study, we tried to deal withthem in different ways according to his suggestions.

We have considered 1,366 radiocarbon dated archaeological contexts from BronzeAge (Early, Middle, and Late periods) from our area of study (Capuzzo et al. 2013).Although not all archaeological events are similar, we assume that the original depo-sitional events are comparable in that:

Barceló et al.

& Dated events correspond to random accumulations around social locations (resi-dential, productive, and ritual)

& The nature of the accumulation was approximately the same,

Then,

& The amount of dated archaeological events for a single social event depends on thenumber of people generating the accumulation, the time during which the actionsgenerated material effects observable archaeologically, and the social way ofdisposing garbage (Varien and Mills 1997, p. 143).

Consequently,

& Although we are not aware of the precise rate at which each material effect wassocially produced at a specific moment, we assume the rates for the different kindsof material effects whose archaeological contexts have been dated are within a shortvariance,

& The probability that a social event happened in a short interval was proportional tothe spatial extension or temporal duration of that event,

& The probability that a social event occurring in a short interval was independent ofthe events that occurred outside that interval, and

& The probability of more than one event in a sufficiently small interval is negligible.

In such conditions, we can explain the SCPD of 1,366 radiocarbon-dated archaeo-logical contexts from Western Europe Bronze Age in terms of the absence of popula-tion growth during the period 1800–800 BC at a global scale, with peaks of higherfrequency of human activities at 1500 BC and 800 BC (Fig. 8).

We have simulated a set of radiocarbon dates with no chronological variation to testa null hypothesis of no relationship between the observed SCPD and the effects of thatparticular section of the calibration curve (Fig. 9).

Peaks in the observed distribution exactly coincide with irregularities in the calibra-tion curve around 1580 and 800 cal BC. This result should be interpreted in terms of theinfluence the calibration curve (IntCal09) has on the kinds of inferences we can drawfrom temporal patterns in the observed frequency of dated archaeological contextsbetween 1800 and 800 cal BC from Danube to the Ebro valleys. Irregularities in thecalibration curve explain both the peaks and the troughs in their curve as well as, orperhaps better than, demographic patterns can (Bamforth and Grund 2012; Chiverrellet al. 2011; Bleicher 2013).

Zolitschka et al. (2003)) observed that from the Bronze Age to the Migration period,there are reasons to assume that, at least within the margin of error in the datingmethods used, a coincidence appears between phases of unfavorable climatic condi-tions (cool and moist) and a decrease in human activities. For instance, the firstdecrease in the number of dated archaeological contexts in our observed distribution,after 1400 BC, may coincide with the palaeohydrological regional pattern establishedfor West Central Europe with phases of higher lake levels at 1600–1200 BP and 800–400 cal BC, in relation to solar-forced climatic oscillations, and the correlative aban-donment of lake-dwellings at ca. 1500 and 800 BC (Magny 1993, 2004; Magny et al.2007, 2009; Rychner et al. 1998). Tinner et al. (2003) observe the decrease of treepollen just after an apex at around 1350 BC, accompanied by peaks of Cerealia and

Modeling Expansive Phenomena in Early Complex Societies

Plantago lanceolata. This pattern suggests a temporary expansion of arable andpastoral farming during the Late Bronze Age. During the next period, at the beginningof the Iron Age (800 BC), pollen values for Cerealia and Plantago lanceolata increasedmarkedly, indicating that technical innovations during the Bronze and Iron Age (e.g.,metal ploughs, scythes, hay production, and fertilizing methods) gradually increasedagricultural productivity. Doyen et al. (2013) suggest similar dynamics in the sameregion. We have not analyzed more recent chronological estimates, and we cannotevaluate the consequences of the climate discontinuity between 850 and 750 cal. BC,characterized by a cooling period of short duration (100 years) (Geel et al. 1998; vander Plicht et al. 2004; Swindles et al. 2007).

Our data refer to an extended region in Western-Central Europe. When dividing thedataset into natural regions, the distribution has different peaks and valleys, suggestingthat demographic changes had different rhythms at different places. What at a globalscale seems stationary (no-changes), could have been much more dynamic and chang-ing at local scales. It should be taken into account that Davis et al. (2003) have shownthat temperature evolution was significatively different in Central-Western Europe thanin the Southwest. They have suggested a more relevant anomalies and irregularities forthe southern part of our region of study than for the north and west.

It is important, then to further analyze the estimates of population density at a morelocalized regional scale (Shennan 2013). However, the reduced number of datedcontexts (when dividing the dataset) prevents us further insights in this direction. Withbetter data for a region not considered in our database, the Irish Late Bronze–Iron Age

Fig. 8 Summed probability function of 1,366 radiocarbon dates included in the EUBAR database. IntCal09calibration curve. (Software: OxCal 4.2). A further investigation distinguishing the intensity of ritual activitiesthrough time (number of dated archaeological contexts from cemeteries and burials) and the quantity ofprofane activities (data from settlements) in underway (Capuzzo, forthcoming)

Barceló et al.

(Armit et al. 2012) have investigated the SCPDs of 1,500 radiocarbon estimates andhave found that that there is a substantial peak in activity, as reflected in the frequencyof radiocarbon dates, at around 1000–900 BC. Rather than any sudden collapse around800 BC, however, they see a marked but steady decline between 900 and 750 BC. Thischange is important because it suggests that activity in Ireland was already decreasingwell before the end of Late Bronze Age. If this was the product of some “event,”climatic or otherwise, then this must be placed no later than around 900 BC. The IrishEarly Iron Age, from around 800-400 BC remains a period of relatively low activitylevels, but the difference is rather less marked than before.

Further north of our study area, the Central Rhine valley, Zimmermann et al. (2009))have suggested an increasing density of sites in such a way that group size in Hallstatttimes (after 800 BC) would be a factor of 3 larger than in the Michelsberg period (ca4400–3500 BC). It is not reasonable to interpret the increasing catchment areas andtherefore also the increasing size of groups that acted collectively as a linear evolu-tionary development from the Neolithic to the Iron Age. Our data do not suggest suchpopulation growth for the period 1800–800 BC in the area under study.

To sum up, the successful adoption of yield-increasing advances cannot be explainedby climatic determinism alone. In our case, between Danube valley to the east, the Ebrovalley to the southwest, the Main valley to the North, and the Tiber Valley to the southour data does not fit the hypothesis of a Late Bronze Age cultural floruit, nor any EarlyIron Age collapse, climatically or socially induced, nor the opposite idea of a re-population at the beginning of Iron Age. This suggests that there is not strong evidenceto distinguish, demographically speaking, a so-called “Early Bronze” from the

Fig. 9 Summed probability function of 1,366 simulated radiocarbon dates under the assumption of populationuniformity: same number of dated archaeological contexts at each temporal bin. IntCal09 calibration curve(Software: OxCal 4.2)

Modeling Expansive Phenomena in Early Complex Societies

supposed “Late Bronze Age.” Therefore, one could argue the possibility of thehistorical continuity of the archaeological contexts that characterized the region sinceat least 2100 BC or, at most, from the 1600–1400 BC.

Conclusions

Was the first occurrence of cremation the result of an expansive process? Preliminaryresults from our analysis seem to suggest a positive answer. Was this “expansion” theconsequence of demic expansion (people movements)? Our results give for the momentno conclusive answer.

We postulate a statistically significant trend for early Urnfield sites to becomeyounger with distance from the oldest ones somewhere in Northeastern Alps. Thepresence of a clear spatial gradient in initial dates of the first adoption of cremationburials in the southern part of our study area indicates that the phenomenon can betentatively explained as an expansion. It was, by implication, fast. It is also animplication that the wave speed was determined more by unusually high exploratorymobility than by exceptionally rapid reproductive increase (i.e., there was a no evidentpopulation growth during the period).

We suggest that in this historical case, the wave width and speed cannot bedetermined only by population-averaged reproductive and dispersal rates. It isworth emphasizing that “Iron Age” was not a single phenomenon and, althoughit is often characterized by archaeologists as a “package” of related traits, theindividual elements of the package need not have been transmitted simulta-neously. This might suggest the need to model each distinct element separately.We should take into account that a new product or behavior adoption curveoften has a temporal pattern consistent with a strong frequency dependent socialbias on adopter's decisions.

If we could consider all economical, technological, cognitive, social, and politicalfactors together, we would like to model Late Bronze Age expansions using a reaction–diffusion framework. Such approach is being very popular in archaeology nowadays(Ackland et al. 2007; Hazelwood and Steele 2004; Kandler and Steele 2009; Steele2009, 2010; Fedotov et al. 2008; Fort 2012; Isern and Fort 2010, 2011; Baggaley et al.2012). If we could assume that movement (of people, ideas, and/or goods) was equallylikely in all directions and served to achieve uniform densities, regardless oflocal variation, we would conclude an average expansion speed of 0.6–1 km/year (values calculated by Neus Isern using a standard Fisher-KPP model. cf.Isern, personal communication), what is coherent in similar historical andgeographical scenarios (Zimmermann et al. 2009). This relies on two assump-tions that we cannot tenet: a nonlinear population growth locally (or reaction)term and a linear population dispersal (or migration) term. While the variationsto the travelling population wave are easy to predict, the effects on thecumulative density can be much more difficult to interpret.

There is also a possibility that expansivity at the beginning of first millennium BC inEurope was a temporally dependent but nonspatially dependent diffusion process,where spatial proximity was not influencing the behavior of the diffusion becauseabsolute location was not as important as relative position. According to this idea,

Barceló et al.

social groups would exist as personal and direct social ties that either link individualssharing values and belief or impersonal, formal, and instrumental social links. Anetwork can be used to represent those ties between social agents (Kadushin 2012;see for instance Hamilton et al. 2007, among many others). Such networks arestructures made up of discrete entities called “nodes” representing individuals ororganizations. They are tied (connected) by one or more specific links representingtypes of interdependency, such as friendship, kinship, common interest, financialexchange, dislike, sexual relationships, or relationships of beliefs, knowledge, orprestige. The resulting graph-based structures are often very complex.

In any case, we consider that the average rate of spread of new ritualpractice during the Late Bronze–Iron Age transition in Western Europe andparts of southern Europe cannot be modeled in terms of an underlying demo-graphic process in which incoming populations grow until they reach a carryingcapacity imposed by the environment and by their technological and socialstrategies, and simultaneously fission and disperse into neighboring territory(where new settlements are formed, and the process begins again from thisnew location). Our premise of is that rates of uptake of innovations during theLate Bronze/Iron Ages transition were dependent on social and political influ-ence. The classical action–reaction models should take into account part of thisadditional influence. The reaction term, which determines local rates of increasein the numbers of adopters, should consider some degree of dependence onlocal numbers of prior adopters. The diffusion term should be configured insuch a way that it takes into account some additional degree of dependence oncontact and interaction with other adopters in ones more extended neighborhoodor social network. The cultural status should enter as a parameter in the model,given its important role in the dynamics of the geographical distribution ofcultural traits (Fort and Pérez-Losada 2012).

Our analysis does not end here. We would like to model how cultural transmissionamong settlements followed kinship ties or political alliances, which is simply the ideathat similarity in behavior and artifacts may be caused by the exchange of informationusing a non-genetic mechanism. The idea is that results of individual learning (i.e.,behavior modification) can be transmitted, in the modified state, to other individuals.Through individual learning and cultural transmission, human communities can con-tinually acquire, modify, and pass on modified information. Thus, the process isfundamentally based on the interaction of both individual experimentation (i.e., inno-vation) and social learning (i.e., copying) (Boyd and Richerson 1985; Cavalli-Sforzaand Feldman 1981; Henrich 2001; Lemmen and Wirtz 2006; Ackland et al. 2007; Fortet al. 2008; Steele 2009; Eerkens and Lipo 2005; Isern and Fort 2010; Rahmstorf 2011;Rogers 1995; Fort 2012; Scholnick 2012).

Acknowledgments The authors thank Neus Isern for her estimations of the speed of expansion based on theauthors' radiocarbon estimates and assuming a classical Fisher-KPP model. The authors also acknowledge thecomments by Quim Fort, external reviewers, and the editors of this volume. This research is part of the projectPADICAT (“Patrimoni Digital Arqueològic de Catalunya), funded by the Obra Social la Caixa and theAsociació d” Universitats Catalanes (Programa RecerCaixa, RECER2010-05). Parts of it have been fundedby the project “Social and environmental transitions: Simulating the Past to understand human behavior,”funded by the Spanish Ministry for Science and Innovation, under the program CONSOLIDER-INGENIO2010, CSD2010-00034. In addition, the authors also acknowledge funds from Spanish Ministry of Science

Modeling Expansive Phenomena in Early Complex Societies

and Innovation, through grant no. HAR2009-12258 awarded to J.A. Barceló. Giacomo Capuzzo acknowl-edges his research grant from the Departament de Universitats, Investigació i Societat de la Informació of theGeneralitat de Catalunya.

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