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The earliest Neolithic sites in the Near Eastappeared about 13,000 calibrated yearsbefore present (cal yr B.P.) (Ozdogan and

Basgelen 1999; Pinhasi et al. 2005; Willcox et al.2009). The Neolithic transition then spread grad-ually across Europe until it reached the British Is-lands and southern Scandinavia by 6,000 cal yrB.P. (Pinhasi et al. 2005). There are two maincompeting models of the Neolithic transition inEurope. The demic diffusion model considersthat the driving force of this transition was the dis-persion of farming populations. In contrast, thecultural diffusion model assumes that the mainmechanism was the imitation of the behavior offarmers by hunter-gatherers. Whereas the demicdiffusion model does not deny the possibility ofcultural diffusion or local adoption in some spe-cific areas, it assumes that agriculture was spread

at the continental scale by dispersing farmingpopulations (Ammerman and Cavalli-Sforza1971, 1973, 1984; Renfrew 1987). On the otherhand, the cultural diffusion model accepts thatpopulation dispersal played a role in some specialplaces, but argues that the movement of ideasrather than people is essential to understanding theNeolithic transition over most of Europe (Dennell1983; Edmonson 1961; Whittle 1996; Zvelebil1986). The demic model predicts genetic clinesacross Europe with extreme gene frequencies inthe Near East (Ammerman and Cavalli-Sforza1971). This prediction of demic diffusion agreeswith synthetic maps of classical genetic markersin present Europeans (Menozzi et al. 1978). It istrue that genetic clines can also arise by othermechanisms different from Neolithic demic dif-fusion (e.g., from the arrival of modern humans

MODELLING THE NEOLITHIC TRANSITIONIN THE NEAR EAST AND EUROPE

Joaquim Fort, Toni Pujol, and Marc Vander Linden

For the Neolithic transition in the Near East and Europe, this paper compares the isochrones predicted by computational

models to those obtained by interpolating the archaeological data. This comparison reveals that there is a major inconsis-

tency between the predictions of the models and the archaeological data: according to the models, the Neolithic front would

have arrived to Greece in less than half the time interval implied by the data. Our main new results are as follows. (a) This

inconsistency can be solved by including only Pre Pottery Neolithic B/C (PPNB/C) sites in the Near East; (b) the model

that yields the lowest mean error per site in the arrival time of the Neolithic across the Near East and Europe is obtained

by allowing for sea travels up to distances of 150 km; and (c) Mountain barriers have a negligible effect on the spread rate

of the Neolithic front at the continental scale.

Para la transicin del Neoltico en el Oriente prximo y Europa, este artculo compara las isocronas predichas por modelos

computacionales a las obtenidas interpolando los datos arqueolgicos. Dicha comparacin revela una incoherencia notable

entre las predicciones de los modelos y los datos arqueolgicos: segn los modelos, el Neoltico habra llegado a Grecia en

menos de la mitad del tiempo que tard segn los datos. Nuestros principales resultados nuevos son: (i) Esta incoherencia

puede resolverse incluyendo slo yacimientos PPNB/C en el Oriente prximo; (ii) El modelo que arroja el mnimo error medio

por yacimiento en el tiempo de llegada del Neoltico en Oriente prximo y Europa se obtiene permitiendo viajes por mar con

distancias de hasta 150 km; (iii) Las barreras montaosas tienen un efecto despreciable sobre el ritmo de expansin del Neoltico

a escala continental.

Joaquim Fort and Toni Pujol Complex Systems Lab, Escola Politcnica Superior, University of Girona, 17071 Girona,Catalonia, Spain (joaquim.fort@udg.edu, toni.pujol@udg.edu)Marc Vander Linden School of Archaeology and Ancient History, University of Leicester, University Road, LE1 7RHLeicester, United Kingdom (mmagvl1@le.ac.uk)

American Antiquity 77(2), 2012, pp. 203219Copyright 2012 by the Society for American Archaeology

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204 american antiquit !V&%. 77, n&. 2, 2012

3040,000 years ago). However, the possibility ofa substantial contribution of Near Eastern farmersto the European gene pool has received support by

nuclear (Chikhi et al. 1998) and Y-chromosomeDNA data (Balaresque et al. 2010). Further po-tential support for the demic model can be foundin the observed correlation between genetic andarchaeological distances (Sokal et al. 1991).Moreover, very recent mitochondrial DNA(mtDNA)(Bramanti et al. 2009) and craniometric(Pinhasi et al. 2009) data from ancient humans in-dicate a limited initial admixture between farmersand hunter-gatherers. This is contrary to the pre-dictions of models based on cultural diffusion, i.e.,on the assumption that hunter-gatherers converted

into farmers (because if this had been the case, thegenetic composition of both populations shouldbe similar). Therefore, demic diffusion modelsseem necessary for a proper description of the Ne-olithic spread in the Near East and Europe. It isthus of interest to compare in detail the predic-tions of demic models with archaeological data.In fact, forty years ago it was already noted thatthe rate of spread of the Neolithic transition variessubstantially in space (Ammerman and Cavalli-Sforza 1971:table 2). This point has been alsostressed in recent years (Ammerman 2003:21;

Price 2003:280). However, detailed quantitativecomparisons of the regional trends observed tothose predicted under different demic models arestill scarce (see however, Davison et al. 2006,2007 for very interesting comparisons dealingwith the role of waterways and with the borealNeolithic, respectively).

Ammerman and Cavalli-Sforza (1973, 1984)were the first to apply a mathematical model tothe spread of farming from the Near East andacross Europe. Their model is based on Fishersequation,

(1)where s is the speed of the population front offarmers. In this equation, a is called the growth rateof farmers and is a measure of their reproductivesuccess (a is an increasing function of the numberof surviving children per generation, see Fort, Pu-

jol, and Cavalli-Sforza 2004). On the other hand,Dis the diffusion coefficient of farmers, and is ameasure of how far away they move per generation.Therefore, the speed s of the population front in-

creases with the net reproduction (parameter a) aswell as with the dispersion in space (parameterD)of the population. This was to be expected intu-

itively, but equation (1) goes beyond intuition bygiving a quantitative prediction for these depen-dencies. Indeed, reasonable values for the para-meters a andD can be estimated from ethnographicdata (Ammerman and Cavalli-Sforza 1984:155;Fort and Mndez 1999). Using such values, equa-tion (1) yields a speed s of about 1 km/yr, which isconsistent with the speed obtained by analyzing thearchaeological data (Ammerman and Cavalli-Sforza 1971, 1984; Pinhasi et al. 2005). More re-fined models yield similar results (see Steele 2009and Fort 2009 for two recent reviews).

Can a simple equation such as (1) describe allof the relevant details of the spatial propagation ofsuch a complex social process as the transition tofarming, which took place over such a huge andnon-homogeneous landscape as the Near Eastand Europe? We should expect not. Front speedequations such as (1) are useful as a first approx-imation. They can only yield a homogeneous, av-erage description of the Neolithic front propaga-tion. Thus, such models are just a first step, albeita very appealing one (because of its mathemati-cal simplicity). They cannot describe any local ef-

fects (e.g., sea travel). For this reason, non-ho-mogeneous models (i.e., taking into account seatravel, mountain barriers, etc.) have been recentlydeveloped (Davison et al. 2006). In the present pa-per we develop this line of research further bycomparing the isochrones predicted by mathe-matical models to those obtained by interpolatingthe archaeological data. We shall see that thisprocedure reveals a major inconsistency betweenthe archaeological data and the models. This prob-lem had not been noted previously, and it arisesnot only for homogeneous models (e.g., equa-

tion [1]) but also for non-homogeneous models(e.g., taking into account sea travel and/or moun-tain barriers). Based on archaeological arguments,we shall propose a reasonable solution. In ouropinion, identifying and solving this problem isnot only an interesting point in itself, but also nec-essary to develop future models of the spread ofthe Neolithic transition across the Near East andEurope. We shall also find that allowing for seatravels up to 150 km leads to the best match be-tween the model predictions and the data, and that

s aD= 2 ,

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mountain barrier effects can be neglected (as theyhave a very small effect on the global scale).

We would like to stress that the direct quanti-

tative comparison of isochrone maps obtained byinterpolating archaeological data to those pre-dicted by computational models seems a poten-tially fruitful approach. Although here we focus onthe Neolithic transition in the Near East and Eu-rope (because for this phenomenon there are manydata available), our methods could be potentiallyapplied in the future to many other spatial spreadphenomena with archaeological interest, for ex-ample, the Clovis colonization of North America(Hamilton and Buchanan 2007), its possible im-plications on megafaunal mass extinctions (Al-

roy 2001), and on the terminal Pleistocene inSouth America (Anderson and Gillam 2000;Goebel et al. 2008; Steele et al. 1998); the late-glacial recolonization of Northern Europe (Fort,Pujol, and Cavalli-Sforza 2004); the AustronesianNeolithic range expansion (Fort 2003); preceramicdispersals of maize and root crops into Panama(Dickau et al. 2007); the diffusion of maize to thesouthwestern United States (Merrill et al. 2009);and so on.

Materials and Methods

Archaeological Data

The first step of our work was the realization of adatabase of 14C dates for the early Neolithic inEurope and the Near East. The starting point of ourdata collection for Europe was the database col-lated at the University College of London (Shen-nan and Steele 2000), supplemented with theRADON online database for Central Europe(Furholt et al. 2002), the IPCTE database for East-ern Europe (http://arheologie.ulbsibiu.ro/radio-

carbon/download.htm), the online inventory forPortugal provided by the Instituto Portugus de Ar-queologia (http://www.ipa.min-cultura.pt/), datelists by radiocarbon laboratories (http://c14.arch.ox.ac.uk/database/db.php; Zaitseva and Dergachev2009), and various published data surveys (Foren-baher and Miracle 2005; Jadin 2003; Lanting andvan der Plicht 2000; Manen and Sabatier 2003;Schulting and Richards 2002; Sheridan 2007;Whittle et al. 2002). For the Near East, we used theCONTEXT database (http://context-database.uni-

koeln.de/). We screened all the data, excludedthose irrelevant or incorrect, kept the oldest datefor every site such that it had a standard deviation

less than about 150 yr (otherwise we used themost reliable date available), and calibrated themusing the Calib 5.0.1 software (Stuiver et al. 2009).This yielded a total of 903 European sites and 87CONTEXT Near-Eastern sites.

Supplementary material for this paper is avail-able at http://copernic.udg.edu/QuimFort/fort.htm.The excel file Supporting Data 1 contains the 919sites and dates used in our final analysis (903European sites and 16 CONTEXT Near EasternPPNB/C sites, see the Results section below).The excel file Supporting Data 2 contains the

complete list of 87 CONTEXT sites and dates forthe Near East.

Simulation Programs

In order to convert longitude and latitude intoCartesian (x,y) coordinates and vice versa, weused a rectangular grid on an Albers conic equal-area projection. The rectangular grid is made upof squares with side 50 km, which is the valuecorresponding to the characteristic mobility pergeneration obtained from measured data for pre-industrial populations (Ammerman and Cavalli-

Sforza 1984; Fort et al. 2007). We index eachgrid node as (i,j), with 1 i 180 and 1 j 102.In the homogeneous models, we apply the fol-

lowing reactive random-walk computationscheme, which has been justified previously (Fortet al. 2007),

Step 1 (reproduction): At every node (i,j) of thegrid and time t (measured in generations), wecompute the new number of Neolithic farmersP'N(i,j,t) after reproduction from that before re-production P'N(i,j,t) at the same node as (Fort et al.2007)

(2)

whereR0N is the net reproductive rate (or fecun-dity) per generation. The second line in Eq. (2) isnecessary for the population density not to in-crease above the saturation density of farmers,

pNmax and PN

max = l 2pNmax is the maximum number

of farmers per node. In our simulations we use forpN

max the same value as that applied by Currat

=