139UDK 903’12\’15(4\5)“633\634”>575.17< 903’12\’15(4\5)“633\634”>574.91
Documenta Praehistorica XXXIV (2007)
A Pan-European model
of the Neolithic
Kate Davison1, Pavel M. Dolukhanov2, Graeme R. Sarson1,
Anvar Shukurov1and Ganna I. Zaitseva3
1 School of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, U.K.
kate.davison@ncl.ac.uk< g.r.sarson@ncl.ac.uk< anvar.shukurov@ncl.ac.uk
2 School of Historical Studies, University of Newcastle upon Tyne, NE1 7RU, U.K.
pavel.dolukhanov@ncl.ac.uk
3 Institute for the History of Material Culture, Russian Academy of Sciences, St. Petersburg, Russia
Introduction
The transition to the Neolithic was a crucial period
in the development of Eurasian societies, defining toa large extent their subsequent evolution. The intro-
duction of agro-pastoral farming, which originated inthe Near East about 12 000 years ago and then spreadthroughout Europe, is usually considered to be a keyfeature of this transition ( Zvelebil 1996 ). Yet the
Neolithic was not a simple, single-faceted phenome-non. In his early definition of the Neolithic, Sir JohnLubbock ( 1865) specified its main characteristics to
be the growing of crops, the taming of animals, theuse of polished stone and bone tools, and pottery-
making.
Ceramic pottery is one of the defining characteristics
of the Neolithic. It is true that there are examples ofearly farming communities apparently not involved
in pottery-making. For example, aceramic Neolithiccultures have been identified in the Levant, Upper
Mesopotamia, Anatolia (9800–7500 BC) and also in
the Peloponnese (7000–6500 BC) and Thessaly Plain(7300–6300 BC). (All BC dates supplied are radio-carbon dates calibrated using OxCal v3.10 ( Bronk
Ramsey 2001 ) with calibration curve intcal04.14c.)
Wheat, barley and legumes were cultivated at thosesites; permanent houses with stone foundations wereused. There is no widespread evidence of pottery(Perlès 2001 ) but recent excavations have revealed
the occurrence of pottery in Thessaly, albeit in small
quantities ( J. K. Koz łowski, personal communica-
tion 27/03/2007 ). In contrast, the Neolithic in North-
Eastern boreal Europe is identified with a sedentaryABSTRACT – We present a mathematical model, based on a compilation of radiocarbon dates, of the
transition to the Neolithic, from about 7000 to 4000 BC in Europe. With the arrival of the Neolithic,
hunting and food gathering gave way to agriculture and stock breeding in many parts of Europe; pot-
tery-making spread into even broader areas. We use a population dynamics model to suggest the pre-
sence of two waves of advance, one from the Near East, and another through Eastern Europe. Thus,we provide a quantitative framework in which a unified interpretation of the Western and EasternNeolithic can be developed.
IZVLE∞EK – Predstavljamo matemati≠ni model, ki temelji na kompilaciji radiokarbonskih datumov
med 7000 in 4000 BC. Ti datumi so v Evropi povezani s prehodom v neolitik, ko sta poljedelstvo in
∫ivinoreja v mnogih regijah zamenjala lov in nabiralni∏tvo; lon≠arstvo pa se je ∏irilo ∏e dlje. S po-mo≠jo modela populacijske dinamike predstavljamo dva vala napredovanja, enega iz Bli∫njega Vzho-da in drugega preko Vzhodne Evrope. Z njim zagotavljamo kvantitavni okvir, v katerem lahko raz-vijamo enovito interpretacijo 'zahodnega' in 'vzhodnega' neolitika.
KEY WORDS – Neolithic; population dynamics; radiocarbon dates; archaeology; mathematical mo-
delling
Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov and Ganna I. Zaitseva
140(or seasonally sedentary) settlement pattern, social
hierarchy and sophisticated symbolic expression, theuse of polished stone and bone tools, large-scale ma-nufacture of ceramic ware, but not with agriculture(Oshibkina 1996 ): the subsistence apparently remai-
ned based on foraging. This combination of attribu-tes is characteristic of the ‘boreal Neolithic’; of these,pottery is in practice the most easily identifiable.
In the present paper we attempt to develop a uni-
fied framework describing the spread of both the‘agro-pastoral’ and ‘boreal’ Neolithic. Our quantita-tive model of the Neolithization is based on the largeamount of relevant radiocarbon dates now available.
Selection of radiocarbon datesThe compilation of dates used in this study to model
the spread of the Neolithic in Europe is availableupon request from the authors; unlike all other si-milar studies known to us it includes dates from theEast of Europe. We used data from Gkiasta et al.(2003), Shennan and Steele ( 2000), Thissen et al
(2006) for Southern, Central and Western Europe
(SCWE) and Dolukhanov et al. ( 2005), Timofeev et
al. (2004) for Eastern Europe (EE). Our selection and
treatment of the dates, described in this section, ismotivated by our attempt to understand the spreadof agriculture and pottery making throughout Europe.
Many archaeological sites considered have long se-
ries of radiocarbon dates: often with 3–10 dates, andoccasionally with 30–50. Associated with each radio-carbon measurement is a laboratory error, whichafter calibration was converted into a calibrationerror σ
i. The laboratory error characterises the accu-
racy of the measurement of the sample radioactivity
rather than the true age of the archaeological site(Dolukhanov et al. 2005 ) and, thus, is often unrep-
resentatively small, suggesting an accuracy of 30
years on occasion. Therefore, we estimated an em-pirical minimum error of radiocarbon age deter-mination of the archaeological age and then used itwhen treating sites with multiple dates. A global mi-nimum error of σ
min= 160 years is obtained from
well explored, archaeologically homogeneous sites
with a large number of tightly clustered dates. Suchsites are: (1) Ilipinar, 65 dates, with the standard de-viation σ= 168 years (and mean date 6870 BC); (2)
Achilleion, 41 dates, σ= 169 years (mean 8682 BC);
(3) Asikli Höyük, 47 dates, σ= 156 years (mean
7206 BC). Similar estimates are σ
min= 100 years for
LBK sites and σmin= 130 years for the Serteya site
in North-Western Russia ( Dolukhanov et al. 2005 );the typical errors vary between different regions and
periods but we apply σmin= 160 years to all the data
here. 
For sites with multiple radiocarbon date determina-
tions, the dates are treated and reduced to two (and
rarely more) dates that are representative of the ar-rival of multiple Neolithic episodes to that location.For the vast majority of such sites, the radiocarbondates available can be combined, as discussed below,to just two possible arrival dates. Examples of siteswith multiple radiocarbon measurements are Ilipi-nar and Ivanovskoye-2 where, respectively, 65 and21 dates have been published. Figures 1a and b in-dicate that for these sites the series of dates form
very different distributions; different strategies areused to process these different types of date series asdescribed below (see Dolukhanov et al. 2005 for de-
tails). If a geographical location hosts only one ra-diocarbon measurement associated with the earlyNeolithic, then this is taken to be the most likelydate for the arrival of the Neolithic. The uncertaintyof this radiocarbon date is taken to be the maximumof the global minimum error discussed above andthe calibrated date range obtained at the 99.7 %confidence level and then divided by six (to obtainan analogue of the 1 σerror). There are numerous
such sites in our collection, including Casabianca,Dachstein and Inchtuthil.
If only a few (less than 8) date measurements are
available for a site and those dates all agree withinthe calibration error, we use their mean value andcharacterise its uncertainty with an error equal tothe maximum of each of the calibrated measurementerrors σ
i, the standard deviation of the dates invol-
ved σ(ti), 1 ≤i≤n, and the global minimum error
introduced above:
nis the total number of dates in the cluster. An
example of such a site is Badema gaci, where we
have 4 dates, all within 60 years of one another; Fi-
gure 1c shows the histogram of radiocarbon datesof this site. The typical calibration error of thesedates is approximately 30 years, thus Eq. (1) yieldsσ
minas an uncertainty estimate. However, we apply
a slightly different procedure for clusters of dates
that do not agree within the calibration error.
For a series of dates that cluster in time but do not
agree within the calibration error, we use differentapproaches depending on the number of dates avai-lable and their errors. Should the cluster contain less  σσ σ σ= (){}max , , ,min iit (1)
A Pan-European model of the Neolithic
141than 8 dates, we take the mean of the dates (as in
the previous case), as any more sophisticated statis-tical technique would be inappropriate for such asmall sample; the error is taken as in Eq. (1). Anexample of such a site is Okranza Bolnica – Stara Za-gora with 7 measurements, and Figure 1f shows thatthe dates are tightly clustered around the mean value.
If however, the date cluster is large ( i.e.more than
8 dates, such as Ilipinar, shown in Fig. 1a), the χ
2
statistical test can be used to calculate the most likely
date Tof a coeval subsample as described in detail
by Dolukhanov et al. ( 2005):
where σi= max( σi, σmin). The coeval subsample is
obtained by calculating the statistic:
and comparing it with χ2. If X 2 ≤ χ2n–1, the sample
is coeval and the date T is the best representative of
the sample. If X2 > χ2n–1, the sample is not necessa-
rily coeval, and the dates that provide the largestcontribution to Xare discarded one by one until the
criterion for a coeval sample is satisfied. This pro-cess is very similar to that implemented in the R_
Combine function of OxCal ( Bronk Ramsey 2001 ).
However, OxCal’s procedure first combines the un-
calibrated dates into one single radiocarbon measu-rement and then calibrates it. Our approach on theother hand first uses the calibration scheme of OxCaland then combines the resulting calibrated dates togive T. Furthermore, our procedure adds the flexibi-
lity of identifying and discarding dates with the lar-
gest relative deviation from T. Within R_Combine
the minimum error is not used in the calculation of
X
2but is rather only incorporated into the final un-
certainty estimate. We feel that it is more appro-
priate to include the minimum uncertainty into thecalculation from the outset. As a check, we combinedseveral set of dates using both OxCal and our proce-
dure, and the results agree within a few years in mostcases where such agreement could be expected.
If a site has many radiocarbon determinations that
do not cluster around a single date, a histogram of thedates is analyzed. If the data have a wide range andhave no discernable peaks ( i.e., are approximately
uniformly distributed in time), they may suggest pro-longed Neolithic activity at the site, and we choose,as many other authors, the oldest date (or one of the
oldest, if there are reasons to reject outliers) to iden-tify the first appearance of the Neolithic. Examplesof such sites are Mersin and Halula where there are6 and 9 dates with a range of 550 and 1900 years,respectively, and no significant peaks (see Figs. 1dand 1e), here the oldest dates are 6950 and 8800years BC and the associated errors are 217 and 167years.
Apart from sites with either no significant peak or
only one peak, there are sites whose radiocarbondates have a multimodal structure which may indi-cate multiple waves of settlement passing throughthis location. Ivanovskoye-2 (with 21 dates) is a typi-cal site in this category, and Figure 1b depicts twodistinct peaks. In such cases multiple dates were at-tributed to the site, with the above methods appliedto each peak independently. Admittedly our methodof assigning an individual date to a specific peakcould be inaccurate in some cases as appropriatestratigraphic and/or typological data are not invo-ked in our procedure. In future refinements to thistechnique we may consider fitting bimodal normaldistributions to the data to avoid the rigid assign-ment of measurements to one peak or another. Afterselection and processing, the total number of dates
in our compilation is 477. In our final selection, 30sites have two arrival dates allocated and 4 siteshave three arrival dates allocated, namely Berezo-vaya, Osipovka, Rakushechnyi Yar and Yerpin Pudas.
Modelling
The mechanisms of the spread of the Neolithic in Eu-
rope remain controversial. Gordon Childe ( 1925) ad-
vocated direct migration of the farming population;
this idea was developed in the form of the demic ex-pansion (wave of advance) model ( Ammerman and
Cavalli-Sforza 1973 ). The Neolithization was viewed
as the spread of colonist farmers who overwhelmedthe indigenous hunter-gatherers or converted themto the cultivation of domesticated cereals and therearing of animal stock ( Price 2000 ). An alternative
approach views the Neolithization as an adoption of
agriculture (or other attributes) by indigenous hun-ter-gatherers through the diffusion of cultural nove-lties by means of intermarriages, assimilation andborrowing ( Tilley 1994; Thomas 1996; Whittle
1996). Recent genetic evidence seems to favour cul-
tural transmission ( Haak et al. 2005 ).
Irrespective of the particular mechanism of thespread of the Neolithic (or of its various signatu-  Ttii
in
i
in=∑
∑=
=/
/,σ
σ2
1
2
11
XtTi
iin22
21=−()∑
= σ
Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov and Ganna I. Zaitseva
142res), the underlying process can be considered as
some sort of ‘random walk’, of either humans orideas and technologies. Therefore, mathematical mo-delling of the spread (at suitably large scales in spaceand time) can arguably be based on a ‘universal’equation (known as reaction-diffusion equation) withparameters chosen appropriately ( Cavalli-Sforza and
Feldman 1981 ). A salient feature of this equation is
the development of a propagation front (where the
population density, or any other relevant variable, isequal to a given constant value) which advances ata constant speed ( Murray 1993 ) (in the approxima-
tion of a homogeneous, one-dimensional habitat).This mode of spread of incipient agriculture has beenconfirmed by radiocarbon dates ( Ammerman and
Biagi 2003; Ammerman and Cavalli-Sforza 1971;1973; 1984; Gkiasta et al. 2003; Pinhasi et al. 2005 ).
In Figure 2a we plot the distance from a putativesource in the Near East versus the 
14C dates for early
Neolithic sites in SCWE; the linear interdependenceis consistent with a constant propagation speed. Due
to the inhomogeneous nature of the landscape wewould not expect to see a very tight correlation be-tween distance from source and time of first arri-val, since there are many geographical features that
naturally cause barriers to travel ( e.g.the Mediterra-
nean Sea). It is also suggested in a previous work(Davison et al. 2006 ) that there are local variations
in the propagation speed near major waterways;this again detracts from the constant rate of spread.In spite of this, the correlation coefficient is found tobe –0.80; reassuringly high given the above com-plications. There is also a tail of older dates that ori-ginate in early Neolithic sites in the Near East, wherea Neolithic tradition began and remained until it sa-
turated the area and subsequently expanded acrossthe landscape.
In contrast to earlier models, we include the ‘boreal’,
East-European (EE) Neolithic sites, which we present
Fig. 1. Histograms of calibrated radiocarbon ages from archaeological sites in kyr BC, binned into 200
year intervals representing various temporal distributions. (a) The 65 dates from Ilipinar (40.47 °N,
29.30 °E) are approximately normally distributed, so the χχ2criterion can be employed to calculate the
age of this site as described by Dolukhanov et al ( 2005 ). The resulting Gaussian envelope is shown solid.
(b) Ivanovskoye-2 (56.85 °N, 39.03 °E) has 21 dates showing a multimodal structure where each peak can
be treated as above. (c) The 4 dates from Badema gaci (37.40 °N, 30.48 °E) combine into a single date when
their errors are taken into account. (d) The 6 dates from Mersin (36.78 °N, 34.60 °E) are almost uniformly
distributed in time, so the oldest date can be used as representative of the arrival of the Neolithic. (e) The
9 dates from Halula (36.40 °N, 38.17 °E) are treated as in (d). (f) The 7 dates from Okrazna Bolnica – Sta-
ra Zagora (42.43 °N, 25.63 °E) are not numerous enough to justify the application of the χχ2test, but they
form a tight cluster, so the mean date can be used for this site. 
A Pan-European model of the Neolithic
143in the same format in Figure 2b. It is clear that the
Eastern data are not all consistent with the idea ofspread from a single source in the Near East. A cor-relation coefficient of –0.52 between the EE dates anddistance to the Near East is sufficient evidence forthat. Our modeling, discussed below, indicates thatanother wave of advance swept westward throughEastern Europe about 1500 years earlier than theconventional Near-Eastern one; we speculate that itmay even have spread further to produce early cera-mic sites in Western Europe ( e.g.the La Hoguette and
Roucadour groups).
Our population dynamics model, described in detail
by (Davison et al. 2006 ), was refined for our present
simulations. We thus solve the reaction-diffusionequation supplemented with an advection of speedV, arising from this anisotropic component of the
random walk of individuals that underlies the large-scale diffusion ( Davison et al. 2006; Murray 1993 ):
where Nis the population density, 
γis the intrinsic
growth rate of the population, Kis the carrying ca-
pacity, and νis the diffusivity (mobility) of the po-
pulation. We solve Eq. (2) numerically in two dimen-
sions on a spherical surface with grid spacing of 1/12degree (2–10 km, depending on latitude). All the va-riables in Eq. (2) can be functions of position and
time, as described by Davison et al. ( 2006).
We consider two non-interacting populations, eachmodelled with Eq. (2), but with different values ofthe parameters V, 
γ, Kand ν; the difference is in-
tended to represent differences between subsistence
strategies (farmers versus hunter-gatherers) and/orbetween demic and cultural diffusion.     ∂
∂γνN
TNNN
KN +⋅ ∇() =−⎛
⎝⎜⎞
⎠⎟+∇⋅ ∇() VV1 , (2)
Fig. 2. Radiocarbon dates of early Neolithic sites versus the great-circle distance from the assumed source.
Inset maps show the location of the sites plotted, and the straight lines correspond to spread at a constantspeed given below. (a) Sites from Southern, Central and Western Europe (SCWE) with respect to a NearEastern source (Jericho). The linear correlation (cross-correlation coefficient C= –0,80) suggests a mean
speed of advance of U= 1.2 ± 0.1 km/year (2
σσerror). (b) Sites from Eastern Europe (EE) show very poor
correlation with respect to the same Near-Eastern source ( C= –0,52), so that straight-line fitting is not
useful. (c) Sites attributed, using our two-source model, to the Near-Eastern source (note a significant
number of EE sites clearly visible in the inset map) show a reasonable correlation ( C= –0,77) and a mean
speed U= 1.1 ± 0.1 km/year. (d) Sites attributed to the Eastern source (from both EE and SCWE) show a
correlation similar to that of Panel (c) ( C= –0,76), and a mean speed U= 1.7 ± 0.3 km/year.

Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov and Ganna I. Zaitseva
144We thus numerically solve two versions of Equation
(2), one for each of two non-interacting populationswith different origins of dispersal. The boundaries ofthe computational domain are at 75°N and 25°N,and 60°E and 15°W as shown in Figure 3, they arechosen to comfortably incorporate our pan-Europeanarea. The environmental factors included into themodel are the altitude, latitude, coastlines and theDanube-Rhine river system. The equation describingthe farming population also includes advection velo-city Valong the major waterways (the Danube, the
Rhine and the sea coastlines; V≠0 within corridors
10 km wide on each side of a river or 10 km inshorenear the sea) which results from anisotropic diffu-sion in those areas. The prescription of the compo-nents of the advective velocity are given in Davisonet al. ( 2006). 
The focus of our model is the speed of the front pro-pagation U, since this quantity can be most readily
linked to the radiocarbon age used to date the ‘firstarrival’ of the wave of advance. This feature of thesolution depends only on the linear terms in Equa-tion (2) and, in particular, is independent of the car-rying capacity K. Moreover, to a first approximation
Uonly depends on the product 
γν:
Taking the intrinsic growth rate of a farming popu-
lation as γ= 0.02 year –1(Birdsell 1957 ), the mean
speed of the front propagation of U≈1 km/year for
the population of farmers suggests the background
(low-latitude) value of the diffusivity ν= 12.5 km 2/
year ( Ammerman and Cavalli-Sforza 1971; Davison
et al. 2006 ). For the wave spreading from Eastern
Europe, U≈1.6 km/year is acceptable as a rough
estimate obtained from the EE radiocarbon dates
(Dolukhanov et al. 2005 ); this estimate is confirmed
by our model (see Fig. 2d). Analysis of the spread ofPaleolithic hunter-gatherers yields U≈0.8 km/year;
the corresponding demographic parameters are sug-gested to be 
γ= 0.02–0.03 year –1and ν= 50–140
km2/year ( Fort et al. 2004 ). These authors use an
expression for Udifferent from Eq. (3); it is plausi-
ble, therefore, that the intrinsic growth rate obtained
by Fort et al. ( 2004) for hunter-gatherers is a signi-
ficant overestimate; for ν= 100 km 2/year and U≈
1.6 km/year, the nominal value of γobtained from
Eq. (3) is about 0.006 year –1. A growth rate of γ=
0.01 year –1has been suggested for indigenous North-
American populations in historical times ( Young and
Bettinger 1992 ). The range γ= 0.003–0.03 year –1is
considered in a model of Paleoindian dispersal ( Ste-ele et al. 1998 ). Our simulations adopt γ= 0.007
year –1and ν= 91.4 km 2/year for the hunter-gathe-
rers. 
For the wave that spreads from the Near East carry-
ing farming, Kand νsmoothly tend to zero within
100 m of the altitude 1 km, above which land farm-ing becomes impractical. For the wave spreadingfrom the East, Kand 
νare similarly truncated at al-
titudes around 1500 km as foraging is possible up tohigher altitude than farming. The low-altitude (back-ground) values of Kadopted are 0.07 persons/km
2
for hunter-gatherers ( Dolukhanov, 1979; Steele et
al. 1998 ) and 3.5 persons/km 2for farmers, a value
50 times larger than that for hunter-gatherers ( Am-
merman and Cavalli-Sforza 1984 ). The values of K
do not affect any results reported in this paper.
In seas, for both farmers and hunter-gatherers, both
the intrinsic growth rate and the carrying capacityvanish as seas are incapable of supporting a humanpopulation. The diffusivity for both farmers andhunter gatherers tails off exponentially as
ν∝ exp(– d/l),
with dthe shortest distance from the coast and l=
40 km, allowing the population to travel within a
short distance offshore but not to have a sustainedexistence there. The value of lhas been fine-tuned
in this work in order to reproduce the delay, indica-
ted by radiocarbon dates, in the spread of the Neo-lithic from the continent to Britain and Scandinavia.This provides an interesting inference regarding thesea-faring capabilities of the times, suggesting confi-dent travel within about 40 km off the coast. 
The inclusion of advection along the Danube-Rhine
corridor and the sea coastlines is required to repro-duce the spread of the Linear Pottery and Impressed
Ware cultures obtained from the radiocarbon andarchaeological evidence (see Davison et al. 2006 for
details). The speed of spread of farming in the Da-nube-Rhine corridor was as high as 4 km/yr ( Am-
merman and Cavalli-Sforza 1971 ) and that in the
Mediterranean coastal areas was perhaps as high as20 km/yr ( Zilhão 2001 ); we set our advective velo-
city in these regions accordingly. However, there areno indications that similar acceleration could occurfor the hunter-gatherers spreading from the East.Thus, we adopt V= 0 for this population.
The starting positions and times for the two waves
of advance – i.e., the initial conditions – were selec-
ted as follows. For the population of farmers, we po-
sition the origin and adjust the starting time so as  U=2γν. (3)
A Pan-European model of the Neolithic
145to minimize the root mean square difference be-
tween the SCWE 14C dates and the arrival time of
the modelled population at the corresponding loca-
tions; the procedure is repeated for all positions be-tween 30°N, 30°E and 40°N, 40°E with a 1° step.This places the centre at 35°N, 39°E, with the propa-
gation starting at 6700 BC. For the source in the Eastof Europe, we have tentatively selected a region cen-tered at 53°N, 56°E in the Ural mountains (to theeast of the Neolithic sites used here), so that the pro-pagation front reaches the sites in a well developedform. We do notsuggest that pottery-making inde-
pendently originated in this region. More reasonably,this technology spread, through the bottleneck be-tween the Ural Mountains and the Caspian Sea, from
a location further to the east. The starting time forthis wave of advance was fixed by trial and error at8200 BC at the above location; this reasonably fitsmost of the dates in Eastern Europe attributable tothis centre. For both populations, the initial distribu-
tion of Nis a truncated Gaussian of a radius 300 km.
Comparison of the model with radiocarbon
dates
The quality of the model was assessed by conside-
ring the time lag ΔT= T–T
mbetween the modelled
arrival time(s) of the wave(s) of advance to a site,
Tm, and the actual 14C date(s) of this site, T, obtai-
ned as described in Sect. 2. The sites were attributedto that centre (Near East or Urals) which providedthe smallest magnitude of ΔT. This procedure admit-
tedly favours the model, and the attributions have
to be carefully compared with the archaeological andtypological characteristics of each site. Such evi-dence is incomplete or insufficient in a great num-ber of cases; we leave the laborious task of incorpo-rating independent evidence in a systematic and de-
Fig. 3. Time lags, ΔΔT= T–Tm, between the actual and modelled arrival times for the early Neolithic sites
shown against their geographical position: panels (a)–(c) refer to a model with a single source in the Near
East, and panels (d)–(f) to our best model with two sources (with the second on the Eastern edge of Europe).The positions of the sources are shown in grey in panels (c) and (f). Sites with |
ΔΔT| < 500 are shown in
(a) and (d), those with 500 yr < | ΔΔT| < 1000 yr in panels (b) and (e), and those with | ΔΔT| > 1000 yr in
panels (c) and (f). There are 265, 132, 80 sites in panels (a)–(c) and 336, 113, 28 sites in (d)–(f), res-
pectively. Many data points corresponding to nearby sites overlap, diminishing the apparent differencebetween the two models. The advantage of the two-source model is nevertheless clear and significant.

Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov and Ganna I. Zaitseva
146tailed manner for future work. Our formulaic me-
thod of attribution has inevitably failed in some cases,but our preliminary checks have confirmed that theresults are still broadly consistent with the evidenceavailable, (see below).
First, we considered a model with a single source in
the Near East (see Fig. 4a for histogram of time lags).The resulting time lags are presented in Figure 3a–c.The best fit model with two sources is similarly illu-strated in Figure 3d–f. The locations of the two sour-ces are shown with grey ellipses in panels (c) and (f).
In Figure 3a the sites shown are those at which the
model arrival date and the radiocarbon date agreewithin 500 years (55 % of the pan-European dates);Figure 3d gives a similar figure for the two sourcemodel (now 70 % of the pan-European dates fit with-in 500 years). The points in the EE area are signifi-cantly more abundant in Figure 3d than in Figure 3a,while the difference in the SCWE area is less strik-ing. The SCWE sites are better fitted with the onesource model, with | ΔT| < 500 years for 68 % of
data points, but the fit is unacceptably poor for EE,where only 38 % of the radiocarbon dates can be fit-ted within 500 years. A convenient measure of thequality of the fit is the standard deviation of thetime lags
with
The standard deviation of the pan-European timelags here is s= 800 years. Outliers are numerous
when all of the European sites are included (illus-trated by the abundance of points in Figure 3c), andthey make the distribution skewed, and offset fromΔT= 0 (see Fig. 4a). The outliers are mainly located
in the east: for the SCWE sites, the distribution ismore tightly clustered ( s= 540 years), has negligible
mean value, and is quite symmetric. In contrast, thetime lags for sites in Eastern Europe (EE), with re-spect to the centre in the Near East, have a rather flatdistribution ( s= 1040 years), which is strongly ske-
wed and has a significant mean value (310 years).
  sNTTi
iN
=− ()∑
=1
1ΔΔ
  ΔΔTNTi
iN
= ∑
=1
1.
Fig. 4. Time lags, ΔΔT= T–Tm, between the actual and modelled arrival times for the early Neolithic sites.
(a)–(c): Histograms of the time lags, with a normal distribution fit (solid), for a model with a single source
in the Near East (a), for a single source in the Urals (b) and for a two-source model (c). (d)–(f): The cu-mulative probability distribution of the time lags from panels (a)–(c), respectively, rescaled such that anormal probability distribution corresponds to a straight line (known as a normal probability plot). The
straight lines show the best-fitting normal distribution, and the 95 % confidence interval. A significantreduction in the number of outliers can be seen in (f) or (c) as compared to (d) or (a) and (e) or (b).The distributions of panels (d) and (e) fail the Anderson-Darling normality test, while (f) passes the testconfirming that 
ΔΔTis normally distributed ( p-value = 0.149). 

A Pan-European model of the Neolithic
147The failure of the single-source model to accommo-
date the 14C dates from Eastern Europe justifies our
use of a more complicated model that has two sour-
ces of propagation. Attempts were made at locatingthe single source in various other locations, such asthe Urals, but this did not improve the agreement
(see Fig. 4b for the histogram of time lags for themodel with single source in the Urals). 
Adding another source in the East makes the model
much more successful: the values of the time lag,shown in Fig. 3d–f, are systematically smaller; i.e.
there are significantly fewer points in Fig. 3f (5 %)compared to Fig. 3c (17 %). The resulting ΔTdistri-
bution for all the sites is quite narrow ( s= 520 years)
and almost perfectly symmetric, with a negligible
mean value (40 years), see Fig. 4c. The distributionsremain similarly acceptable when calculated sepa-rately for each source (with s= 490 and 570 years
for the sites attributable to the Near East and Urals,respectively). The improvement is especially strikingin EE, where the sites are split almost equally be-tween the two sources. 
We tentatively consider a model acceptable if the
standard deviation, s, of the time lag ΔTis not larger
than 3 standard dating errors σ, i.e., about 500
years, given our estimate of σclose to 160 years
over the pan-European domain. This criterion can-
not be satisfied with any single-source model, but is
satisfied with two sources. While we would neverexpect a large-scale model of the sort proposed hereto accurately describe the complex process of theNeolithization in fine detail (and so the resulting va-lues of ΔTcannot be uniformly small), the degree of
improvement in terms of the standard deviation ofΔTclearly favours the two-source model. The reduc-
tion in s is statistically significant, and cannot be ex-plained by the increase in the complexity of the mo-del alone. The confidence intervals of the samplestandard deviations sfor one-source and two-source
models do not overlap (740 < σ< 840 and 480 < σ
< 550, respectively); the F-test confirms the statisti-cal significance of the reduction at a 99 % level. 
It is also instructive to perform some further basic
statistical analysis of the time lags ΔT. We use the
Anderson-Darling test to assess if the sample of timelags can be approximated by the Gaussian probabi-lity distribution ( i.e., in particular, have a symmetric
distribution with an acceptably small number of out-liers). The null hypothesis of the test is that the timelags have a Gaussian distribution with the samplemean and standard deviation, while the alternativehypothesis is that they do not. This test leads us to
accept the null hypothesis in the case of the two-source model ( p-value = 0.149) while rejecting the
null hypothesis for both one source models. Figure4d–f show the cumulative probability distributions
of the time lags for each model studied, rescaled suchthat a normal probability distribution correspondsto a straight line (known as a normal probabilityplot). The straight lines show the best-fitting normaldistribution together with its 95 % confidence inter-val. As quantified by the test, the time lags more clo-sely follow the straight line in (f) than in (d) or (e);the number of outliers is reduced very significantlyin (f). Table 1 shows those sites that have | ΔT| >
1000 years, i.e., where the disagreement between
the data and the best-fit, two-source model is the
strongest. There are 28 such sites: 14 of these havenot undergone any statistical treatment, while theremaining 14 are a result of date combination or se-lection as described in Section 2. Five of the dates inTable 1 arise from the four sites (Berezovaya, Osi-povka, Rakushechnyi Yar and Yerpin Pudas) wherewe have been unable to isolate less than three rep-resentative dates (see Section 2). This may suggestthat a reinvestigation of these sites in particular isrequired and improved stratigraphic and typologicaldata are required for these sites. 
As further quantification of the quality of the model,
the χ
2statistic has been calculated for each model: 
The results are shown in Table 2.
The values of X2, given in Table 2, may then be com-
pared to the χ2value at the 5 % level with N–1 de-
grees of freedom ( χ2
N–1= 527.86). On all occasions
the value of X2significantly exceeds χ2
N–1 (at 5 % le-
vel) this is not surprising given the simplicity of our
model. The χ2statistical test would be satisfied if we
discard about one third of the sites. It should be high-lighted however that there is an approximate three-fold increase in the accuracy of the model with twosources with respect to a single-source model. Some
increase in the fit would be expected since we have in-creased the complexity of the model, but an increaseof this magnitude surpasses what we believe could beattributed simply to the increase in model comple-xity. Development and application of further statisti-cally robust techniques for comparison of our modelwith archaeological evidence is subject to our ongo-ing study.  XTi
iiN22
21=()∑
=Δ
σ. (4)
Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov and Ganna I. Zaitseva
148Sample Site Model arrival time
Site Name Lab Index Lati- Longi- Age Error Age Calib- Age Calib- Note From From
tude tude BP cal BC ration cal BC ration Near Urals,
deg. deg. yr yr Error yr Error East, yr BC
yr BC
Argisa Magula UCLA-1657A 39.64 22.47 8130 100 7100 400 7100 400 One date 6052 3975
Balma Margineda Ly-2439 42.41 1.58 6670 85 5600 130 5600 130 One date 6700 3256
Bavans LV-1415 47.47 6.70 7130 70 6000 170 6000 170 One date 4903 3777
Berezovaya LE-6706a 60.38 44.17 7840 75 6775 92 6775 92 Older date 3697 5509
Berezovaya LE-67066 60.38 44.17 8700 300 7800 267 7800 267 Oldest date 3697 5509
Bolshoe Zavetnoye LE-6556 60.98 29.63 7750 180 6650 150 6650 150 Oldest date 3836 4913
Canhasan III BM-1666R 37.50 33.50 8460 150 7450 133 7338 233 Chi-Squared 5814 3664
Canhasan III BM-1664R 8470 140 7450 133
Canhasan III BM-1660R 8390 140 7375 108
Canhasan III BM-1667R 8480 110 7450 100
Canhasan III BM-1662R 8460 110 7450 100
Canhasan III BM-1663R 8350 210 7300 233
Canhasan III BM-1665R 8270 160 7200 133
Canhasan III BM-1656R 8090 170 7050 150
Canhasan III HU-12 8543 66 7600 40
Canhasan III BM-1658R 8060 130 7025 142
Canhasan III HU-11 8584 65 7635 38
Canhasan III BM-1657R 8080 130 7050 133
Carrowmore Lu-1840 54.27 -8.53 5750 85 4575 215 4575 215 One date 3517 2445
Cashelkeelty UB-2413 51.72 -9.82 5845 100 4695 245 4695 245 One date 3585 2267
Choinovtyi-1 LE-5164 64.42 49.95 4640 25 3435 28 4070 595Average of2963 5374site one
Choinovtyi-1 LE-1729 5320 60 4160 57
Choinovtyi-1 LE-4495 5750 70 4615 55
DobriniöËe Bln-3785 41.83 23.57 6650 60 5575 32 5575 32 One date 6700 4199Dubokrai-5 Le-3003 55.85 30.37 4720 40 3505 45 3578 160Average of4628 5025
middle peak
Dubokrai-6 Le-6279 4820 130 3650 117
Golubjai-1 LE-4714 54.95 22.98 7060 270 5950 167 5950 167 Older date 4577 4703
Grotta del Sant R-284 40.90 15.78 5555 75 4395 155 4395 155 One date 5722 3326
della Madonna
Grotta di PortoR-1225 40.08 18.48 5850 55 4675 135 4675 135 One date 5815 3452Badisco
Kamennaya Mogila Ki-4023 47.20 35.35 5120 80 3975 92 3975 92 Younger date 5675 4984
Koshinskaya LE-6629 57.63 48.23 8350 100 7360 73 7360 73 Older date 3896 5767
Kurkijokki LE-6929 60.18 29.88 7900 80 6825 75 6825 75 One date 3973 4963
Marevka OxA-6199 48.35 35.30 7955 55 6865 62 6865 62 Older date 5566 5042
Osipovka OxA-6168 49.93 30.40 7675 70 6535 38 6535 38 Older date 5473 4896
Planta CRG-280 46.23 7.37 6500 80 5465 155 5465 155 One date 6700 3697Racquemissou44.42 2.73 7400 300 6400 233 6400 233 One date 5209 3445
VIII c1
Rakushechnyi Yar Le-5387 47.55 40.67 4830 90 3585 72 3862 283Average of5417 5209younger cluster
Rakushechnyi Yar Le-5340 5060 230 3850 183
Rakushechnyi Yar Le-5327 5290 260 4150 217Rakushechnyi Yar Le-5344 47.55 40.67 7180 250 6050 167 6600 319Average from5417 5209
older cluster
Rakushechnyi Yar Ki-6475 7690 100 6600 83
Rakushechnyi Yar Ki-955 7840 105 6750 100
Rakushechnyi Yar Ki-6477 7860 130 6775 108
Rakushechnyi Yar Ki-6476 7930 140 6825 125
Saliagos P-1311 37.05 25.08 6172 74 5080 230 5080 230 One date 6165 3471Serteya-10 Le-5260 56.22 31.57 7350 180 6200 133 6225 317Average of4571 5081
older dates
Serteya-10 Le-5261 7300 400 6250 317
Theopetra Cave DEM.576 39.68 21.68 8060 32 6980 53 6980 53 One date 5969 3980
Zapes Vs-977 54.08 23.67 4860 260 3600 233 3600 233 One date 4708 4716
A Pan-European model of the Neolithic
149It is instructive to represent the data in the same for-
mat as in Figure 2a, b, but now with each date attri-buted to one of the sources, as suggested by our mo-del. This has been done in Figure 2c, d, where theclose correlation of Figure 2a is restored for the pan-European data. Now, the dates are consistent withconstant rates of spread from one of the two sour-ces. Using straight-line fitting, we obtain the averagespeed of the front propagation of 1.1 ± 0.1 km/yearfor the wave originating in the Near East (Fig. 2c),and 1.7 ± 0.3 km/year for the source in the East (Fig.2d); 2 σvalues are given as uncertainties here and
below. The spread from the Near East slowed downin Eastern Europe to 0.7 ± 0.1 km/year; the datesfrom the west alone (as in Fig. 2a) gives a higherspeed of 1.2 ± 0.1 km/year. The estimates for the da-ta in both western and eastern Europe are compa-tible with earlier results ( Dolukhanov et al. 2005;
Gkiasta et al. 2003; Pinhasi et al. 2005 ). Care must
be taken when using such estimates, however, sincethe spread occurs in a strongly heterogeneous space,and so cannot be fully characterised by a single con-stant speed. The rate of spread varies on both pan-European scale and on smaller scales, e.g., near ma-
jor waterways ( Davison et al. 2006 ). 
Our allocation of sites to sources suggested and usedabove requires careful verification using indepen-dent evidence. Here we briefly discuss a few sites.Taking Ivanovskoye-2 (56.85°N, 39.03°E) as anexample, the data form two peaks (Fig. 1b); the timesat which each of the waves arrive at this location are4349 BC (for the Near-Eastern wave) and 5400 BC(for the Eastern wave) closely fitting the two peaksin 
14C dates. As another example, we accept two dates
for the Mayak site (68.45°N, 38.37°E); one from the
younger cluster (2601 ± 192 BC), and also the olderdate (4590 ± 47 BC) detached from the cluster. Theyounger cluster is consistent with the near-eastern
wave (arriving at 2506 BC) and the older date withthe Eastern wave (arriving at 4718 BC). We further consider those sites which are geographi-
cally in the west ( i.e., to the west of a boundary set
to join the Baltic Sea to the Black Sea) but are allo-cated to the source of pottery making in the Uralmountain area. These sites are shown in Table 3.There are 40 such sites ( i.e., 14 % of sites in the
west); they deserve further analysis in order to ve-rify the attribution suggested by the model and, ifnecessary, to further refine the model to improvethe agreement with the archaeological data. Thereare also 104 sites in the east of the above boundarythat are allocated to the source of farming in the NearEast (i.e.56 % of data points in the east). These sites
are listed in Table 4. Where a site is characterised by
a combined date obtained as described above, onlythe final age estimate is given (see entry in the col-umn labelled ‘Note’ for the selection technique ap-plied). All sites in Tables 3 and 4 should be reasses-sed both in terms of the statistical processing of mul-tiple measurements and in terms of the agreementwith independent archaeological data. 
ConclusionsOur model has significant implications for the un-
derstanding of the Neolithization of Europe. It sub-stantiates our suggestion that the spread of the Neo-lithic involved at least two waves propagating fromdistinct centres, starting at about 8200 BC in EasternEurope and 6700 BC in the Near East. The earlierwave, spreading from the east via the ‘steppe corri-
dor’, resulted in the establishment of the ‘eastern
version’ of the Neolithic in Europe. A later wave, ori-ginating in the Fertile Crescent of the Near East, isthe better-studied process that brought farming toEurope.
It is conceivable that the westernmost extension of
the earlier (eastern) wave of advance produced thepre-agricultural ceramic sites of La Hoguette type in
north-eastern France and western Germany, andRoucadour-type (also known as Epicardial) sites inwestern Mediterranean and Atlantic France ( Berg
and Hauzer 2001; Jeunesse 1987 ). The available
dates for the earlier Roucadour sites (7500–6500 BC)(Roussault-Laroque 1990 ) are not inconsistent with
Tab. 1 (on previous page). The 28 sites where the
deviation of the model arrival times from the 14C
dates exceeds 1000 years, ||ΔΔT||  > 1000 years: (1) site
name; (2) laboratory index; geographical (3) lati-
tude and (4) longitude in degrees; (5) uncalibra-ted age and (6) its 1
σσlaboratory error in years
(BP); (7) calibrated age and (8) its 1 σσerror in
years (BC); (9) combined site calibrated age and
(10) its 1 σσerror in years (BC) obtained as discus-
sed in Section 2; (11) method used to select this
date; and the model arrival times (years BC) forthe wave spreading from (12) the Near East and(13) the Urals. The data are presented in alphabe-
tical site name order.Tab. 2. The X2test statistic, given by Eq. (4), for
each model.Model X2
Single source in Near-East 9553
Single source in Urals 28268
Two-source model 3740
Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov and Ganna I. Zaitseva
150Sample Model arrival time
Lati- Longi- Age Age Calibra- From From
Site Name Lab index tude tude BP, Error cal BC, tion Near East, Urals,
deg. deg. yr yr Error yr BC yr BC
Abri de la Coma Franceze Gif-9080 42.83 2.92 5180 60 4010 220 5338 3327
Bridgemere BM-2565 51.21 -2.41 4630 50 3375 275 4291 3156
Burntwood Farm. R6 OxA-1384 51.12 -1.29 4750 50 3510 140 4324 3232
Bury Hill 50.92 -1.37 4750 50 3510 140 4343 3223
Chatelliers du Viel Gif-5717 46.43 -0.87 5200 110 4025 325 4829 3402
Cherhill BM-493 51.43 -1.95 4715 90 3400 300 4276 3186
Coma Franceze Gif-7292 42.83 2.92 5200 70 4025 225 5338 3327
Corhampton BM-1889 50.98 -1.15 4790 70 3535 165 4334 3237
Coufin Ly-3321 45.07 5.40 5260 120 4050 300 5188 3565
Derriere les Pres WM 49.07 -0.05 5110 70 4030 320 4576 3502
Feldbach UCLA-1809A 47.23 8.78 5170 70 4010 220 4998 3861
Fendmeilen UCLA-1691F 47.28 8.63 5415 60 4200 160 4998 3857
Fengate GaK-4196 52.57 -0.21 4960 64 3145 225 4198 3200
Frankenau VRI-207 47.50 16.50 5660 100 4525 125 5377 4213
Frigouras GIF-8479 44.13 5.95 5450 100 4250 210 5341 3506
Grande Louvre GIF-7618 48.87 2.33 5260 70 4105 155 4612 3619
Greifensee WM 47.37 8.68 5140 49 3920 130 5010 3861
Grotta dei Ciclami WM 45.70 4.92 5445 60 4245 205 5114 3597
Grotta del Sant della Madonna R-284 40.90 15.78 5555 75 4395 155 5722 3326
Grotte de la Vieille Eglise WM 45.92 6.28 5295 52 4115 135 5018 3657
Grotte du Sanglier WM 44.68 5.33 5440 130 4250 300 5268 3531
Honeygore Track GaK-1939 51.18 -2.82 4590 40 3305 205 4298 3130
Horné Lefantovce Bln-304 48.42 18.17 5775 140 4700 200 5396 4318
Le Coq Galleux WM 49.40 2.73 5300 140 4100 350 4554 3652
Le Trou du Diable Ly-6505 47.32 4.78 5105 55 3905 135 4870 3682
Les Coudoumines WM 42.75 2.57 5135 36 3920 120 5309 3315
Les Longrais Ly-150 46.58 2.77 5290 150 4100 167 4898 3561
Mannlefelsen Gif-2634 47.45 7.23 5140 140 3950 300 4954 3800
Millbarrow OxA-3172 51.45 -1.87 4900 110 3675 325 4277 3191
Peak Camp OxA-1622 51.83 -2.15 4865 80 3650 300 4224 3163
Phyn WM 47.58 8.93 4993 28 3820 120 5029 3883
Redlands Farm OxA-5632 52.33 -0.59 4825 65 3545 165 4209 3211
Sente Saillancourt Gif-5840 49.08 2.00 5220 110 4050 300 4569 3609
Shurton Hill UB-2122 50.92 -0.58 4750 50 3510 140 4346 3282
Source de Reselauze WM 43.52 4.98 5380 110 4210 240 5424 3460
Windmill Hill OxA-2395 50.92 -1.88 4730 80 3505 155 4335 3183
Winnall Down HAR-2196 51.08 -1.32 4800 80 3540 180 4324 3226
Zurich UCLA-1772B 47.37 8.58 5145 70 3975 275 5010 3857
Zurich-Bauschanze WM 47.41 8.52 5320 60 4155 175 5018 3857
Zurich-Wollishofen WM 47.41 8.52 4993 46 3805 145 5018 3857
Tab. 3. The 40 sites which are allocated to the source of spread in the Urals but are located to the west of
a west-east borderline joining the Baltic Sea to the Black Sea: (1) site name; (2) laboratory index; geogra-phical (3) latitude and (4) longitude in degrees; (5) uncalibrated age and (6) it’s 1
σσlaboratory error in
years (BP); (7) calibrated age and (8) it’s 1 σσerror in years (BC); and the model arrival times (years
BC) for the wave spreading from (9) the Near East and (10) the Urals. The data are presented in alphabe-
tical site name order.
A Pan-European model of the Neolithic
151Site Model arrival time
Site Name Lati- Longi- Age Calibra- Note From Near From
tude tude cal BC, tion East, Urals,
deg. deg. yr Error yr BC yr BC
Babshin 48.47 26.57 5160 50 One date 5518 4680
Bara 60.00 40.15 2900 150 One date 3884 5386
Bazkov Isle 48.08 28.47 5568 160 Average of the younger cluster 5660 4745
Bazkov Isle 48.08 28.47 6143 160 Average of the older cluster 5660 4745
Berendeevo-2a 56.57 39.17 3883 187 Average of middle peak 4376 5408
Bernashovka 48.55 27.50 5565 212 Average of older cluster 5552 4722
Besovy Sledki 64.38 34.43 3190 60 Younger date 3310 4993
Besovy Sledki 64.38 34.43 4010 205 Average of older three dates 3310 4993
Bilshivtsy 48.93 24.58 5307 160 Average 5353 4610
Chapaevka 47.30 35.52 5853 160 Average 5663 5000
Chernaya Guba-4 62.82 34.87 3414 316 Average of younger cluster 3558 5104
Chernushka-1 57.68 48.77 3995 276 Average 3875 5784
Choinovtyi -2 64.30 49.87 3668 11 One date 2977 5379
Choinovtyi-1 64.42 49.95 4070 595 Average of site one 2963 5374
Daktariske 55.82 22.87 4350 100 Oldest date 4454 4707
Drozdovka 68.33 38.28 1535 52 One date 2510 4716
Dubokrai-5 55.85 30.37 3578 160 Average of middle peak 4628 5025
Dubokrai-5 55.85 30.37 4700 600 Oldest Date 4628 5025
Gard-3 47.70 31.20 5722 160 Average 5800 4839
Ivanovskoye-2 56.85 39.03 4094 201 Weighted average of younger peak. X2 4349 5400
Kääpa 57.87 27.10 3509 217 Average of older cluster 4299 4898
Kamennaya Mogila 47.20 35.35 5717 460 Average of older cluster 5675 4984
Kizilevyj-5 48.25 35.15 5640 53 One date 5580 5031
Kodrukõla 59.45 28.08 3590 160 Average 4081 4929
Korman 48.57 27.23 5193 160 Average 5541 4712
Koshinskaya 57.63 48.23 3550 167 Younger Date 3896 5767
Krivina-3 54.95 29.63 4145 58 Older date 4755 4986
Krivun 68.28 38.43 2685 65 Younger date 2518 4726
Krivun 68.28 38.43 3375 92 Older date 2518 4726
Kuzomen 66.27 36.77 2100 200 One date 2733 4791
Lanino-2 57.18 33.00 4779 533 Average of older cluster 4431 5144
Lasta -8 64.77 53.73 2690 70 One date 2780 5381
Lasta -8 64.77 53.73 3500 267 One date 2780 5381
Maieri-2 61.88 30.57 2975 125 One Date 3657 4971
Mamai Gora 47.47 34.38 5940 160 Average 5664 4964
Marevka 48.35 35.30 6477 167 Average 5566 5042
Marevka 48.35 35.30 6865 62 One date 5566 5042
Mariupol Cemetry 47.15 37.57 5518 160 Average 5636 5075
Marmuginsky 60.80 46.30 3500 47 One date 3564 5554
Mayak 68.45 38.37 2601 192 Weighted average. X2 2506 4718
Modlona 60.35 38.80 3067 575 Average 3873 5327
Mys-7 67.98 34.97 2660 63 Older date 2665 4685
Navolok 66.50 40.58 2975 125 Younger date 2777 4922
Navolok 66.50 40.58 3575 68 Older date 2777 4922
Nerpichya Guba 68.37 38.38 2275 108 Younger date 2506 4718
Nerpichya Guba 68.37 38.38 3325 108 Older date 2506 4718
Okopy 49.97 26.53 5458 223 Average 5334 4730
Orovnavolok 62.77 35.08 2790 33 One date 3570 5116
Ortinokh-2 68.05 54.13 2035 55 One date 2317 5132
Osa 56.85 24.58 4434 435 Average of middle cluster 4380 4795
Oshchoy - 2 63.77 48.58 3230 47 One date 3099 5406
Osipovka 49.93 30.40 6535 38 One Date 5473 4896
Osipovsky Liman 48.87 34.92 6400 57 One date 5514 5047
Pechora 48.83 28.70 6117 160 Average 5573 4782
Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov and Ganna I. Zaitseva
152Pegrema-3 62.58 34.43 3433 506 Average of younger cluster 3598 5099
Pleshcheyevo-3 56.78 38.70 3505 45 Oldest date 4371 5386
Povenchanko-15 62.82 34.85 2875 72 One date 3558 5104
Pugach-2 47.85 31.23 5633 160 Average of older cluster 5780 4850
Pyalitsa-18 66.18 39.83 3500 47 One date 2823 4945
Rakushechnyi Yar 47.55 40.67 5456 333 Average from middle cluster 5417 5209
Rakushechnyi Yar 47.55 40.67 6600 319 Average from older cluster 5417 5209
Razdolnoye 47.60 38.03 5475 160 Average 5571 5112
Repishche 58.35 33.88 3313 160 One Date 4252 5176
Rudnya Serteyskaya 55.63 31.57 4381 233 Chi-Squared 4656 5077
Sakhtysh-8 56.80 40.47 4068 189 Weighted average 4296 5465
Sarnate 57.33 21.53 3290 233 Average 4201 4639
Savran 48.12 30.02 5853 160 Average 5720 4808
Semenovka 48.28 30.13 5863 262 Average 5702 4822
Semenovka-5 45.42 29.50 5455 179 Average 5979 4615
Serteya-10 56.22 31.57 3688 200 Ave of young dates (exc. Corded) 4571 5081
Sev. Salma 68.03 35.18 3050 483 One date 2661 4687
Sheltozero-10 61.35 35.35 3000 117 Youngest date 3791 5173
Silino 60.85 29.73 3820 160 Average of younger cluster 3865 4919
Skibinsky 48.57 29.35 6303 160 Average 5631 4801
Sokoltsy-2 48.72 29.12 6253 160 Average 5600 4796
Spiginas 56.02 21.85 3850 167 Older date 4393 4670
Sukhaya Vodla-2 62.40 37.10 3540 57 One date 3604 5194
Sulka 56.75 27.00 3890 346 Average of middle cluster 4452 4891
Suna-12 62.10 34.22 4005 75 One Date 3677 5108
Surskoi Isle 48.32 35.07 6110 160 Average 5570 5032
{ventoji 9 56.02 21.08 3950 100 Oldest date 4354 4653
Syaberskoye-3 58.78 29.10 3750 217 Older date 4193 4975
Tamula 57.85 26.98 4150 60 Oldest date 4298 4894
Tekhanovo 57.07 39.28 4100 47 One date 4308 5409
Tokarevo 60.50 28.77 3450 183 One date 3883 4904
Tugunda-14 64.37 33.30 2848 160 Average 3324 4974
Vashutinskaya 57.37 40.13 3835 45 Yougest date 4243 5445
Vodysh 58.13 41.53 3275 125 One date 4087 5487
Voynavolok-24 62.90 34.57 2838 160 Average of younger cluster 3546 5092
Voynavolok-24 62.90 34.57 3115 72 Older date 3546 5092
Vozhmarikha -4 63.33 35.78 3620 160 Average of younger cluster 3477 5113
Vyborg 60.67 28.65 3260 80 One date 3855 4893
Yazykovo-1a 57.27 33.37 4700 177 Chi Squared  4416 5157
Yerpin Pudas 63.35 34.48 4175 160 Average of yougest cluster 3482 5072
Yumizh-1 62.23 44.35 3000 221 Average 3446 5416
Zalavruga-4 62.80 36.47 3333 286 Average of older cluster 3547 5159
Zapes 54.08 23.67 3600 233 One date 4708 4716
Zarachje 56.15 38.63 4515 52 One date 4448 5387
Zatsen’ye 54.40 27.07 4255 68 One date 4778 4868
Zedmar-D 54.37 22.00 3898 250 Weighted average. X2 4607 4651
Zejmati[ke 55.25 26.15 4355 38 Oldest date 4640 4841
Zolotets-6 62.78 36.53 3688 442 Average of older cluster 3560 5162
Zveisalas 57.83 27.25 3730 70 One date 4302 4904
Zvejnieki 57.82 25.17 4211 273 Average of younger cluster 4257 4824
Tab. 4 (beginning on previous page). The 104 sites which are allocated to the source of spread in the Near
East but are located to the east of a west-east borderline joining the Baltic Sea to the Black Sea: (1) sitename; geographical (2) latitude and (3) longitude in degrees; (4) calibrated age and (5) its 1
σσerror in
years (BC); (6) method used to select this date; and the model arrival times (years BC) for the wave sprea-
ding from (7) the Near East and (8) the Urals. For sites with multiple 14C dates only one (or a few) re-
presentative dates are given, obtained as discussed in Section 2. The selection method applied is given inthe column labelled Note. The data are presented in alphabetical site name order.
A Pan-European model of the Neolithic
153this idea, but a definitive conclusion needs additio-
nal work.
The nature of the eastern source needs to be further
explored. The early-pottery sites of the YelshanianCulture ( Mamonov 2000 ) have been identified in a
vast steppe area stretching between the Lower Volga
and the Ural Rivers. The oldest dates from that areaare about 8000 BC (although the peak of the cultureoccurred 1000 years later) ( Dolukhanov et al. 2005 ).
Even earlier dates have been obtained for potterybearing sites in Southern Siberia and the Russian FarEast ( Kuzmin and Orlova 2000; Timofeev et al.
2004). This empirical relation between our virtual
eastern source and the earlier pottery-bearing sitesfurther east may indicate some causal relationship.
According to our model, the early Neolithic sites in
Eastern Europe belong to both waves in roughlyequal numbers (56 % to near-eastern wave and 44 %to eastern wave). Unlike elsewhere in Europe, thewave attributable to the Near East does not seem tohave introduced farming in the East. The reason forthis is not clear and may involve the local environ-ment where low fertility of soils and prolonged win-ters are combined with the richness of aquatic andterrestrial wildlife resources ( Dolukhanov 1996 ). 
Regardless of the precise nature of the eastern source,the current work suggests the existence of a wavewhich spread into Europe from the east carrying thetradition of early Neolithic pottery-making. If confir-med by further evidence (in particular, archaeologi-cal, typological, and genetic), this suggestion will re-quire serious re-evaluation of the origins of the Neo-lithic in Europe.
Financial support from the European Community’s
Sixth Framework Programme under the grant NEST–028192–FEPRE is acknowledged.ACKNOWLEDGEMENTS
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