A Pan-European model of the Neolithic

UDK 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 Shukurov1 & Ganna I. Zaitseva3 1 School of Mathematics and Statistics, University of Newcastle upon Tyne, NE1 7RU, U.K. [email protected]< [email protected]< [email protected] 2 School of Historical Studies, University of Newcastle upon Tyne, NE1 7RU, U.K. [email protected] 3 Institute for the History of Material Culture, Russian Academy of Sciences, St. Petersburg, Russia ABSTRACT – 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; pottery-making spread into even broader areas. We use a population dynamics model to suggest the presence 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 Eastern Neolithic 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 pomo≠jo modela populacijske dinamike predstavljamo dva vala napredovanja, enega iz Bli∫njega Vzhoda in drugega preko Vzhodne Evrope. Z njim zagotavljamo kvantitavni okvir, v katerem lahko razvijamo enovito interpretacijo 'zahodnega' in 'vzhodnega' neolitika. KEY WORDS – Neolithic; population dynamics; radiocarbon dates; archaeology; mathematical modelling Introduction The transition to the Neolithic was a crucial period in the development of Eurasian societies, defining to a large extent their subsequent evolution. The introduction of agro-pastoral farming, which originated in the Near East about 12 000 years ago and then spread throughout Europe, is usually considered to be a key feature of this transition (Zvelebil 1996). Yet the Neolithic was not a simple, single-faceted phenomenon. In his early definition of the Neolithic, Sir John Lubbock (1865) specified its main characteristics to be the growing of crops, the taming of animals, the use of polished stone and bone tools, and potterymaking. Ceramic pottery is one of the defining characteristics of the Neolithic. It is true that there are examples of early farming communities apparently not involved in pottery-making. For example, aceramic Neolithic cultures 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 radiocarbon dates calibrated using OxCal v3.10 (Bronk Ramsey 2001) with calibration curve intcal04.14c.) Wheat, barley and legumes were cultivated at those sites; permanent houses with stone foundations were used. 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. Kozłowski, personal communication 27/03/2007). In contrast, the Neolithic in NorthEastern boreal Europe is identified with a sedentary 139 Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov & Ganna I. Zaitseva (or seasonally sedentary) settlement pattern, social hierarchy and sophisticated symbolic expression, the use of polished stone and bone tools, large-scale manufacture of ceramic ware, but not with agriculture (Oshibkina 1996): the subsistence apparently remained based on foraging. This combination of attributes 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 unified framework describing the spread of both the ‘agro-pastoral’ and ‘boreal’ Neolithic. Our quantitative model of the Neolithization is based on the large amount of relevant radiocarbon dates now available. Selection of radiocarbon dates The compilation of dates used in this study to model the spread of the Neolithic in Europe is available upon request from the authors; unlike all other similar studies known to us it includes dates from the East 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, is motivated by our attempt to understand the spread of agriculture and pottery making throughout Europe. Many archaeological sites considered have long series of radiocarbon dates: often with 3–10 dates, and occasionally with 30–50. Associated with each radiocarbon measurement is a laboratory error, which after calibration was converted into a calibration error σi. The laboratory error characterises the accuracy of the measurement of the sample radioactivity rather than the true age of the archaeological site (Dolukhanov et al. 2005) and, thus, is often unrepresentatively small, suggesting an accuracy of 30 years on occasion. Therefore, we estimated an empirical minimum error of radiocarbon age determination of the archaeological age and then used it when treating sites with multiple dates. A global minimum error of σmin = 160 years is obtained from well explored, archaeologically homogeneous sites with a large number of tightly clustered dates. Such sites are: (1) Ilipinar, 65 dates, with the standard deviation 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 σmin = 100 years for LBK sites and σmin = 130 years for the Serteya site in North-Western Russia (Dolukhanov et al. 2005); 140 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 determinations, the dates are treated and reduced to two (and rarely more) dates that are representative of the arrival of multiple Neolithic episodes to that location. For the vast majority of such sites, the radiocarbon dates available can be combined, as discussed below, to just two possible arrival dates. Examples of sites with multiple radiocarbon measurements are Ilipinar and Ivanovskoye-2 where, respectively, 65 and 21 dates have been published. Figures 1a and b indicate that for these sites the series of dates form very different distributions; different strategies are used to process these different types of date series as described below (see Dolukhanov et al. 2005 for details). If a geographical location hosts only one radiocarbon measurement associated with the early Neolithic, then this is taken to be the most likely date for the arrival of the Neolithic. The uncertainty of this radiocarbon date is taken to be the maximum of the global minimum error discussed above and the calibrated date range obtained at the 99.7 % confidence level and then divided by six (to obtain an analogue of the 1σ error). 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 within the calibration error, we use their mean value and characterise its uncertainty with an error equal to the maximum of each of the calibrated measurement errors σi, the standard deviation of the dates involved σ (ti), 1 ≤ i ≤ n, and the global minimum error introduced above: { ( ) } σ = max σ i , σ t i , σ min , (1) n is the total number of dates in the cluster. An example of such a site is Bademagaci, where we have 4 dates, all within 60 years of one another; Figure 1c shows the histogram of radiocarbon dates of this site. The typical calibration error of these dates is approximately 30 years, thus Eq. (1) yields σmin as 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 different approaches depending on the number of dates available and their errors. Should the cluster contain less A Pan-European model of the Neolithic than 8 dates, we take the mean of the dates (as in the previous case), as any more sophisticated statistical technique would be inappropriate for such a small sample; the error is taken as in Eq. (1). An example of such a site is Okranza Bolnica – Stara Zagora with 7 measurements, and Figure 1f shows that the 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 χ2 statistical test can be used to calculate the most likely date T of a coeval subsample as described in detail by Dolukhanov et al. (2005): n T = ∑ ti / σi 2 i =1 n , 2 ∑1 / σi i =1 where σ i = max(σi, σmin). The coeval subsample is obtained by calculating the statistic: X 2 2 ti − T ) ( =∑ n i =1 σ2i and comparing it with χ2. If X2 ≤ 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 necessarily coeval, and the dates that provide the largest contribution to X are discarded one by one until the criterion for a coeval sample is satisfied. This process is very similar to that implemented in the R_ Combine function of OxCal (Bronk Ramsey 2001). However, OxCal’s procedure first combines the uncalibrated dates into one single radiocarbon measurement and then calibrates it. Our approach on the other hand first uses the calibration scheme of OxCal and then combines the resulting calibrated dates to give T. Furthermore, our procedure adds the flexibility of identifying and discarding dates with the largest relative deviation from T. Within R_Combine the minimum error is not used in the calculation of X2 but is rather only incorporated into the final uncertainty estimate. We feel that it is more appropriate to include the minimum uncertainty into the calculation from the outset. As a check, we combined several set of dates using both OxCal and our procedure, and the results agree within a few years in most cases where such agreement could be expected. If a site has many radiocarbon determinations that do not cluster around a single date, a histogram of the dates is analyzed. If the data have a wide range and have no discernable peaks (i.e., are approximately uniformly distributed in time), they may suggest prolonged 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 identify the first appearance of the Neolithic. Examples of such sites are Mersin and Halula where there are 6 and 9 dates with a range of 550 and 1900 years, respectively, and no significant peaks (see Figs. 1d and 1e), here the oldest dates are 6950 and 8800 years BC and the associated errors are 217 and 167 years. Apart from sites with either no significant peak or only one peak, there are sites whose radiocarbon dates have a multimodal structure which may indicate multiple waves of settlement passing through this location. Ivanovskoye-2 (with 21 dates) is a typical site in this category, and Figure 1b depicts two distinct peaks. In such cases multiple dates were attributed to the site, with the above methods applied to each peak independently. Admittedly our method of assigning an individual date to a specific peak could be inaccurate in some cases as appropriate stratigraphic and/or typological data are not invoked in our procedure. In future refinements to this technique we may consider fitting bimodal normal distributions to the data to avoid the rigid assignment of measurements to one peak or another. After selection and processing, the total number of dates in our compilation is 477. In our final selection, 30 sites have two arrival dates allocated and 4 sites have three arrival dates allocated, namely Berezovaya, Osipovka, Rakushechnyi Yar and Yerpin Pudas. Modelling The mechanisms of the spread of the Neolithic in Europe remain controversial. Gordon Childe (1925) advocated direct migration of the farming population; this idea was developed in the form of the demic expansion (wave of advance) model (Ammerman and Cavalli-Sforza 1973). The Neolithization was viewed as the spread of colonist farmers who overwhelmed the indigenous hunter-gatherers or converted them to the cultivation of domesticated cereals and the rearing of animal stock (Price 2000). An alternative approach views the Neolithization as an adoption of agriculture (or other attributes) by indigenous hunter-gatherers through the diffusion of cultural novelties by means of intermarriages, assimilation and borrowing (Tilley 1994; Thomas 1996; Whittle 1996). Recent genetic evidence seems to favour cultural transmission (Haak et al. 2005). Irrespective of the particular mechanism of the spread of the Neolithic (or of its various signatu141 Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov & Ganna I. Zaitseva 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 χ2 criterion 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 Bademagaci (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 – Stara Zagora (42.43°N, 25.63°E) are not numerous enough to justify the application of the χ2 test, but they form a tight cluster, so the mean date can be used for this site. res), the underlying process can be considered as some sort of ‘random walk’, of either humans or ideas and technologies. Therefore, mathematical modelling of the spread (at suitably large scales in space and time) can arguably be based on a ‘universal’ equation (known as reaction-diffusion equation) with parameters 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, is equal to a given constant value) which advances at a constant speed (Murray 1993) (in the approximation of a homogeneous, one-dimensional habitat). This mode of spread of incipient agriculture has been confirmed 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 putative source in the Near East versus the 14C dates for early Neolithic sites in SCWE; the linear interdependence 142 is consistent with a constant propagation speed. Due to the inhomogeneous nature of the landscape we would not expect to see a very tight correlation between distance from source and time of first arrival, since there are many geographical features that naturally cause barriers to travel (e.g. the Mediterranean 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 to be –0.80; reassuringly high given the above complications. There is also a tail of older dates that originate in early Neolithic sites in the Near East, where a Neolithic tradition began and remained until it saturated the area and subsequently expanded across the landscape. In contrast to earlier models, we include the ‘boreal’, East-European (EE) Neolithic sites, which we present A Pan-European model of the Neolithic in the same format in Figure 2b. It is clear that the Eastern data are not all consistent with the idea of spread from a single source in the Near East. A correlation coefficient of –0.52 between the EE dates and distance to the Near East is sufficient evidence for that. Our modeling, discussed below, indicates that another wave of advance swept westward through Eastern Europe about 1500 years earlier than the conventional Near-Eastern one; we speculate that it may even have spread further to produce early ceramic sites in Western Europe (e.g. the La Hoguette and Roucadour groups). scale diffusion (Davison et al. 2006; Murray 1993): where N is the population density, γ is the intrinsic growth rate of the population, K is the carrying capacity, and ν is the diffusivity (mobility) of the population. We solve Eq. (2) numerically in two dimensions on a spherical surface with grid spacing of 1/12 degree (2–10 km, depending on latitude). All the variables in Eq. (2) can be functions of position and time, as described by Davison et al. (2006). Our population dynamics model, described in detail by (Davison et al. 2006), was refined for our present simulations. We thus solve the reaction-diffusion equation supplemented with an advection of speed V, arising from this anisotropic component of the random walk of individuals that underlies the large- We consider two non-interacting populations, each modelled with Eq. (2), but with different values of the parameters V, γ, K and ν; the difference is intended to represent differences between subsistence strategies (farmers versus hunter-gatherers) and/or between demic and cultural diffusion.  ∂N N + V ⋅ ∇ N = γN 1 −  + ∇ ⋅ ν∇N , ∂T K  ( ) ( ) (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 constant speed given below. (a) Sites from Southern, Central and Western Europe (SCWE) with respect to a Near Eastern 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 (2σ error). (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. 143 Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov & Ganna I. Zaitseva We thus numerically solve two versions of Equation (2), one for each of two non-interacting populations with different origins of dispersal. The boundaries of the computational domain are at 75°N and 25°N, and 60°E and 15°W as shown in Figure 3, they are chosen to comfortably incorporate our pan-European area. The environmental factors included into the model are the altitude, latitude, coastlines and the Danube-Rhine river system. The equation describing the farming population also includes advection velocity V along 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 inshore near the sea) which results from anisotropic diffusion in those areas. The prescription of the components of the advective velocity are given in Davison et al. (2006). The focus of our model is the speed of the front propagation U, since this quantity can be most readily linked to the radiocarbon age used to date the ‘first arrival’ of the wave of advance. This feature of the solution depends only on the linear terms in Equation (2) and, in particular, is independent of the carrying capacity K. Moreover, to a first approximation U only depends on the product γν: U = 2 γν. (3) Taking the intrinsic growth rate of a farming population 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 km2/ 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 of Paleolithic hunter-gatherers yields U ≈ 0.8 km/year; the corresponding demographic parameters are suggested to be γ = 0.02–0.03 year–1 and ν = 50–140 km2/year (Fort et al. 2004). These authors use an expression for U different from Eq. (3); it is plausible, therefore, that the intrinsic growth rate obtained by Fort et al. (2004) for hunter-gatherers is a significant overestimate; for ν = 100 km2/year and U ≈ 1.6 km/year, the nominal value of γ obtained from Eq. (3) is about 0.006 year–1. A growth rate of γ = 0.01 year–1 has been suggested for indigenous NorthAmerican populations in historical times (Young and Bettinger 1992). The range γ = 0.003–0.03 year–1 is considered in a model of Paleoindian dispersal (Ste144 ele et al. 1998). Our simulations adopt γ = 0.007 year–1 and ν = 91.4 km2/year for the hunter-gatherers. For the wave that spreads from the Near East carrying farming, K and ν smoothly tend to zero within 100 m of the altitude 1 km, above which land farming becomes impractical. For the wave spreading from the East, K and ν are similarly truncated at altitudes around 1500 km as foraging is possible up to higher altitude than farming. The low-altitude (background) values of K adopted are 0.07 persons/km2 for hunter-gatherers (Dolukhanov, 1979; Steele et al. 1998) and 3.5 persons/km2 for farmers, a value 50 times larger than that for hunter-gatherers (Ammerman 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 capacity vanish as seas are incapable of supporting a human population. The diffusivity for both farmers and hunter gatherers tails off exponentially as ν ∝ exp(–d/l), with d the shortest distance from the coast and l = 40 km, allowing the population to travel within a short distance offshore but not to have a sustained existence there. The value of l has been fine-tuned in this work in order to reproduce the delay, indicated by radiocarbon dates, in the spread of the Neolithic from the continent to Britain and Scandinavia. This provides an interesting inference regarding the sea-faring capabilities of the times, suggesting confident travel within about 40 km off the coast. The inclusion of advection along the Danube-Rhine corridor and the sea coastlines is required to reproduce the spread of the Linear Pottery and Impressed Ware cultures obtained from the radiocarbon and archaeological evidence (see Davison et al. 2006 for details). The speed of spread of farming in the Danube-Rhine corridor was as high as 4 km/yr (Ammerman and Cavalli-Sforza 1971) and that in the Mediterranean coastal areas was perhaps as high as 20 km/yr (Zilhão 2001); we set our advective velocity in these regions accordingly. However, there are no indications that similar acceleration could occur for 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 selected as follows. For the population of farmers, we position the origin and adjust the starting time so as A Pan-European model of the Neolithic to minimize the root mean square difference between the SCWE 14C dates and the arrival time of the modelled population at the corresponding locations; the procedure is repeated for all positions between 30°N, 30°E and 40°N, 40°E with a 1° step. This places the centre at 35°N, 39°E, with the propagation starting at 6700 BC. For the source in the East of Europe, we have tentatively selected a region centered at 53°N, 56°E in the Ural mountains (to the east of the Neolithic sites used here), so that the propagation front reaches the sites in a well developed form. We do not suggest that pottery-making independently originated in this region. More reasonably, this technology spread, through the bottleneck between the Ural Mountains and the Caspian Sea, from a location further to the east. The starting time for this wave of advance was fixed by trial and error at 8200 BC at the above location; this reasonably fits most of the dates in Eastern Europe attributable to this centre. For both populations, the initial distribution of N is a truncated Gaussian of a radius 300 km. Comparison of the model with radiocarbon dates The quality of the model was assessed by considering the time lag ∆T = T–Tm between 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, obtained as described in Sect. 2. The sites were attributed to that centre (Near East or Urals) which provided the smallest magnitude of ∆T. This procedure admittedly favours the model, and the attributions have to be carefully compared with the archaeological and typological characteristics of each site. Such evidence is incomplete or insufficient in a great number of cases; we leave the laborious task of incorporating independent evidence in a systematic and de- Fig. 3. Time lags, ∆T = 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 |∆T| < 500 are shown in (a) and (d), those with 500 yr < |∆T| < 1000 yr in panels (b) and (e), and those with |∆T| > 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), respectively. Many data points corresponding to nearby sites overlap, diminishing the apparent difference between the two models. The advantage of the two-source model is nevertheless clear and significant. 145 Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov & Ganna I. Zaitseva tailed manner for future work. Our formulaic method of attribution has inevitably failed in some cases, but our preliminary checks have confirmed that the results are still broadly consistent with the evidence available, (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 illustrated in Figure 3d–f. The locations of the two sources 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 agree within 500 years (55 % of the pan-European dates); Figure 3d gives a similar figure for the two source model (now 70 % of the pan-European dates fit within 500 years). The points in the EE area are significantly more abundant in Figure 3d than in Figure 3a, while the difference in the SCWE area is less striking. The SCWE sites are better fitted with the one source model, with |∆T| < 500 years for 68 % of data points, but the fit is unacceptably poor for EE, where only 38 % of the radiocarbon dates can be fitted within 500 years. A convenient measure of the quality of the fit is the standard deviation of the time lags s= ( 1 N ∑ ∆Ti − ∆T N i =1 ) with ∆T = 1 N ∑ ∆Ti . N i =1 The standard deviation of the pan-European time lags here is s = 800 years. Outliers are numerous when all of the European sites are included (illustrated by the abundance of points in Figure 3c), and they make the distribution skewed, and offset from ∆T = 0 (see Fig. 4a). The outliers are mainly located in the east: for the SCWE sites, the distribution is more tightly clustered (s = 540 years), has negligible mean value, and is quite symmetric. In contrast, the time lags for sites in Eastern Europe (EE), with respect to the centre in the Near East, have a rather flat distribution (s = 1040 years), which is strongly skewed and has a significant mean value (310 years). Fig. 4. Time lags, ∆T = 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 cumulative probability distribution of the time lags from panels (a)–(c), respectively, rescaled such that a normal 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 significant reduction 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 test confirming that ∆T is normally distributed (p-value = 0.149). 146 A Pan-European model of the Neolithic The failure of the single-source model to accommodate the 14C dates from Eastern Europe justifies our use of a more complicated model that has two sources of propagation. Attempts were made at locating the single source in various other locations, such as the Urals, but this did not improve the agreement (see Fig. 4b for the histogram of time lags for the model 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 ∆T distribution 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 distributions remain similarly acceptable when calculated separately for each source (with s = 490 and 570 years for the sites attributable to the Near East and Urals, respectively). The improvement is especially striking in EE, where the sites are split almost equally between the two sources. We tentatively consider a model acceptable if the standard deviation, s, of the time lag ∆T is not larger than 3 standard dating errors σ, i.e., about 500 years, given our estimate of σ close to 160 years over the pan-European domain. This criterion cannot be satisfied with any single-source model, but is satisfied with two sources. While we would never expect a large-scale model of the sort proposed here to accurately describe the complex process of the Neolithization in fine detail (and so the resulting values of ∆T cannot be uniformly small), the degree of improvement in terms of the standard deviation of ∆T clearly favours the two-source model. The reduction in s is statistically significant, and cannot be explained by the increase in the complexity of the model alone. The confidence intervals of the sample standard deviations s for one-source and two-source models do not overlap (740 < σ < 840 and 480 < σ < 550, respectively); the F-test confirms the statistical significance of the reduction at a 99 % level. It is also instructive to perform some further basic statistical analysis of the time lags ∆T. We use the Anderson-Darling test to assess if the sample of time lags can be approximated by the Gaussian probability distribution (i.e., in particular, have a symmetric distribution with an acceptably small number of outliers). The null hypothesis of the test is that the time lags have a Gaussian distribution with the sample mean and standard deviation, while the alternative hypothesis is that they do not. This test leads us to accept the null hypothesis in the case of the twosource model (p-value = 0.149) while rejecting the null hypothesis for both one source models. Figure 4d–f show the cumulative probability distributions of the time lags for each model studied, rescaled such that a normal probability distribution corresponds to a straight line (known as a normal probability plot). The straight lines show the best-fitting normal distribution together with its 95 % confidence interval. As quantified by the test, the time lags more closely follow the straight line in (f) than in (d) or (e); the number of outliers is reduced very significantly in (f). Table 1 shows those sites that have |∆T| > 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 have not undergone any statistical treatment, while the remaining 14 are a result of date combination or selection as described in Section 2. Five of the dates in Table 1 arise from the four sites (Berezovaya, Osipovka, Rakushechnyi Yar and Yerpin Pudas) where we have been unable to isolate less than three representative dates (see Section 2). This may suggest that a reinvestigation of these sites in particular is required and improved stratigraphic and typological data are required for these sites. As further quantification of the quality of the model, the χ2 statistic has been calculated for each model: N X2 = ∑ i =1 (∆Ti )2 . σ2i (4) The results are shown in Table 2. The values of X2, given in Table 2, may then be compared to the χ2 value at the 5 % level with N–1 degrees of freedom (χ2N–1 = 527.86). On all occasions the value of X2 significantly exceeds χ2N–1 (at 5 % level) this is not surprising given the simplicity of our model. The χ2 statistical test would be satisfied if we discard about one third of the sites. It should be highlighted however that there is an approximate threefold increase in the accuracy of the model with two sources with respect to a single-source model. Some increase in the fit would be expected since we have increased the complexity of the model, but an increase of this magnitude surpasses what we believe could be attributed simply to the increase in model complexity. Development and application of further statistically robust techniques for comparison of our model with archaeological evidence is subject to our ongoing study. 147 Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov & Ganna I. Zaitseva Site Name Sample Site Error Age Calib- Age Calib- Note cal BC ration cal BC ration yr Error yr Error Lab Index Latitude deg. Longitude deg. Age BP yr UCLA-1657A Ly-2439 LV-1415 LE-6706a LE-67066 LE-6556 BM-1666R BM-1664R BM-1660R BM-1667R BM-1662R BM-1663R BM-1665R BM-1656R HU-12 BM-1658R HU-11 BM-1657R Lu-1840 UB-2413 39.64 42.41 47.47 60.38 60.38 60.98 37.50 22.47 1.58 6.70 44.17 44.17 29.63 33.50 7100 5600 6000 6775 7800 6650 7450 7450 7375 7450 7450 7300 7200 7050 7600 7025 7635 7050 4575 4695 400 130 170 92 267 150 133 133 108 100 100 233 133 150 40 142 38 133 215 245 400 130 170 92 267 150 233 -8.53 -9.82 100 85 70 75 300 180 150 140 140 110 110 210 160 170 66 130 65 130 85 100 7100 5600 6000 6775 7800 6650 7338 54.27 51.72 8130 6670 7130 7840 8700 7750 8460 8470 8390 8480 8460 8350 8270 8090 8543 8060 8584 8080 5750 5845 4575 4695 215 245 Choinovtyi-1 LE-5164 64.42 49.95 4640 25 3435 28 4070 595 Choinovtyi-1 Choinovtyi-1 DobriniöËe LE-1729 LE-4495 Bln-3785 41.83 23.57 5320 5750 6650 60 70 60 4160 4615 5575 57 55 32 5575 32 Dubokrai-5 Le-3003 55.85 30.37 4720 40 3505 45 3578 160 Dubokrai-6 Golubjai-1 Grotta del Sant della Madonna Grotta di Porto Badisco Kamennaya Mogila Koshinskaya Kurkijokki Marevka Osipovka Planta Racquemissou VIII c1 Le-6279 LE-4714 R-284 54.95 40.90 22.98 15.78 4820 7060 5555 130 270 75 3650 5950 4395 117 167 155 5950 4395 R-1225 40.08 18.48 5850 55 4675 135 Ki-4023 LE-6629 LE-6929 OxA-6199 OxA-6168 CRG-280 47.20 57.63 60.18 48.35 49.93 46.23 35.35 48.23 29.88 35.30 30.40 7.37 5120 8350 7900 7955 7675 6500 80 100 80 55 70 80 3975 7360 6825 6865 6535 5465 44.42 2.73 7400 300 47.55 40.67 4830 Argisa Magula Balma Margineda Bavans Berezovaya Berezovaya Bolshoe Zavetnoye Canhasan III Canhasan III Canhasan III Canhasan III Canhasan III Canhasan III Canhasan III Canhasan III Canhasan III Canhasan III Canhasan III Canhasan III Carrowmore Cashelkeelty 3517 3585 2445 2267 2963 5374 One date Average of middle peak 6700 4199 4628 5025 167 155 Older date One date 4577 5722 4703 3326 4675 135 One date 5815 3452 92 73 75 62 38 155 3975 7360 6825 6865 6535 5465 92 73 75 62 38 155 Younger date Older date One date Older date Older date One date 5675 3896 3973 5566 5473 6700 4984 5767 4963 5042 4896 3697 6400 233 6400 233 One date 5209 3445 90 3585 72 3862 283 Average of younger cluster 5417 5209 5060 5290 230 260 3850 4150 183 217 40.67 7180 250 6050 167 6600 319 Average from older cluster 5417 5209 100 105 130 140 74 6600 6750 6775 6825 5080 83 100 108 125 230 5080 230 One date Average of older dates 6165 3471 4571 5081 One date One date 5969 4708 3980 4716 Rakushechnyi Yar Le-5387 Rakushechnyi Yar Rakushechnyi Yar Le-5340 Le-5327 Rakushechnyi Yar Le-5344 Rakushechnyi Yar Rakushechnyi Yar Rakushechnyi Yar Rakushechnyi Yar Saliagos Ki-6475 Ki-955 Ki-6477 Ki-6476 P-1311 37.05 25.08 7690 7840 7860 7930 6172 Serteya-10 Le-5260 56.22 31.57 7350 180 6200 133 6225 317 Serteya-10 Theopetra Cave Zapes Le-5261 DEM.576 Vs-977 39.68 54.08 21.68 23.67 7300 8060 4860 400 32 260 6250 6980 3600 317 53 233 6980 3600 53 233 148 47.55 Model arrival time From From Near Urals, East, yr BC yr BC One date 6052 3975 One date 6700 3256 One date 4903 3777 Older date 3697 5509 Oldest date 3697 5509 Oldest date 3836 4913 Chi-Squared 5814 3664 One date One date Average of site one A Pan-European model of the Neolithic It is instructive to represent the data in the same format as in Figure 2a, b, but now with each date attributed to one of the sources, as suggested by our model. This has been done in Figure 2c, d, where the close correlation of Figure 2a is restored for the panEuropean data. Now, the dates are consistent with constant rates of spread from one of the two sources. Using straight-line fitting, we obtain the average speed of the front propagation of 1.1 ± 0.1 km/year for the wave originating in the Near East (Fig. 2c), and 1.7 ± 0.3 km/year for the source in the East (Fig. 2d); 2σ values are given as uncertainties here and below. The spread from the Near East slowed down in Eastern Europe to 0.7 ± 0.1 km/year; the dates from the west alone (as in Fig. 2a) gives a higher speed of 1.2 ± 0.1 km/year. The estimates for the data in both western and eastern Europe are compatible with earlier results (Dolukhanov et al. 2005; Gkiasta et al. 2003; Pinhasi et al. 2005). Care must be taken when using such estimates, however, since the spread occurs in a strongly heterogeneous space, and so cannot be fully characterised by a single constant speed. The rate of spread varies on both panEuropean scale and on smaller scales, e.g., near major waterways (Davison et al. 2006). Our allocation of sites to sources suggested and used above requires careful verification using independent evidence. Here we briefly discuss a few sites. Taking Ivanovskoye-2 (56.85°N, 39.03°E) as an example, the data form two peaks (Fig. 1b); the times at which each of the waves arrive at this location are 4349 BC (for the Near-Eastern wave) and 5400 BC (for the Eastern wave) closely fitting the two peaks in 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 older date (4590 ± 47 BC) detached from the cluster. The younger cluster is consistent with the near-eastern wave (arriving at 2506 BC) and the older date with the Eastern wave (arriving at 4718 BC). Tab. 1 (on previous page). The 28 sites where the deviation of the model arrival times from the 14C dates exceeds 1000 years,|∆T| > 1000 years: (1) site name; (2) laboratory index; geographical (3) latitude and (4) longitude in degrees; (5) uncalibrated age and (6) its 1σ laboratory error in years (BP); (7) calibrated age and (8) its 1 σ error in years (BC); (9) combined site calibrated age and (10) its 1σ error in years (BC) obtained as discussed in Section 2; (11) method used to select this date; and the model arrival times (years BC) for the wave spreading from (12) the Near East and (13) the Urals. The data are presented in alphabetical site name order. Model Single source in Near-East Single source in Urals Two-source model X2 9553 28268 3740 Tab. 2. The X2 test statistic, given by Eq. (4), for each model. We further consider those sites which are geographically in the west (i.e., to the west of a boundary set to join the Baltic Sea to the Black Sea) but are allocated to the source of pottery making in the Ural mountain 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 verify the attribution suggested by the model and, if necessary, to further refine the model to improve the agreement with the archaeological data. There are also 104 sites in the east of the above boundary that are allocated to the source of farming in the Near East (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, only the final age estimate is given (see entry in the column labelled ‘Note’ for the selection technique applied). All sites in Tables 3 and 4 should be reassessed both in terms of the statistical processing of multiple measurements and in terms of the agreement with independent archaeological data. Conclusions Our model has significant implications for the understanding of the Neolithization of Europe. It substantiates our suggestion that the spread of the Neolithic involved at least two waves propagating from distinct centres, starting at about 8200 BC in Eastern Europe and 6700 BC in the Near East. The earlier wave, spreading from the east via the ‘steppe corridor’, resulted in the establishment of the ‘eastern version’ of the Neolithic in Europe. A later wave, originating in the Fertile Crescent of the Near East, is the better-studied process that brought farming to Europe. It is conceivable that the westernmost extension of the earlier (eastern) wave of advance produced the pre-agricultural ceramic sites of La Hoguette type in north-eastern France and western Germany, and Roucadour-type (also known as Epicardial) sites in western 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 149 Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov & Ganna I. Zaitseva Latitude deg. Abri de la Coma Franceze Gif-9080 42.83 Bridgemere BM-2565 51.21 Burntwood Farm. R6 OxA-1384 51.12 Bury Hill 50.92 Chatelliers du Viel Gif-5717 46.43 Cherhill BM-493 51.43 Coma Franceze Gif-7292 42.83 Corhampton BM-1889 50.98 Coufin Ly-3321 45.07 Derriere les Pres WM 49.07 Feldbach UCLA-1809A 47.23 Fendmeilen UCLA-1691F 47.28 Fengate GaK-4196 52.57 Frankenau VRI-207 47.50 Frigouras GIF-8479 44.13 Grande Louvre GIF-7618 48.87 Greifensee WM 47.37 Grotta dei Ciclami WM 45.70 Grotta del Sant della Madonna R-284 40.90 Grotte de la Vieille Eglise WM 45.92 Grotte du Sanglier WM 44.68 Honeygore Track GaK-1939 51.18 Horné Lefantovce Bln-304 48.42 Le Coq Galleux WM 49.40 Le Trou du Diable Ly-6505 47.32 Les Coudoumines WM 42.75 Les Longrais Ly-150 46.58 Mannlefelsen Gif-2634 47.45 Millbarrow OxA-3172 51.45 Peak Camp OxA-1622 51.83 Phyn WM 47.58 Redlands Farm OxA-5632 52.33 Sente Saillancourt Gif-5840 49.08 Shurton Hill UB-2122 50.92 Source de Reselauze WM 43.52 Windmill Hill OxA-2395 50.92 Winnall Down HAR-2196 51.08 Zurich UCLA-1772B 47.37 Zurich-Bauschanze WM 47.41 Zurich-Wollishofen WM 47.41 Site Name Lab index Longitude deg. 2.92 -2.41 -1.29 -1.37 -0.87 -1.95 2.92 -1.15 5.40 -0.05 8.78 8.63 -0.21 16.50 5.95 2.33 8.68 4.92 15.78 6.28 5.33 -2.82 18.17 2.73 4.78 2.57 2.77 7.23 -1.87 -2.15 8.93 -0.59 2.00 -0.58 4.98 -1.88 -1.32 8.58 8.52 8.52 Age BP, yr 5180 4630 4750 4750 5200 4715 5200 4790 5260 5110 5170 5415 4960 5660 5450 5260 5140 5445 5555 5295 5440 4590 5775 5300 5105 5135 5290 5140 4900 4865 4993 4825 5220 4750 5380 4730 4800 5145 5320 4993 Sample Model arrival time Age CalibraFrom From Error cal BC, tion Near East, Urals, yr Error yr BC yr BC 60 4010 220 5338 3327 50 3375 275 4291 3156 50 3510 140 4324 3232 50 3510 140 4343 3223 110 4025 325 4829 3402 90 3400 300 4276 3186 70 4025 225 5338 3327 70 3535 165 4334 3237 120 4050 300 5188 3565 70 4030 320 4576 3502 70 4010 220 4998 3861 60 4200 160 4998 3857 64 3145 225 4198 3200 100 4525 125 5377 4213 100 4250 210 5341 3506 70 4105 155 4612 3619 49 3920 130 5010 3861 60 4245 205 5114 3597 75 4395 155 5722 3326 52 4115 135 5018 3657 130 4250 300 5268 3531 40 3305 205 4298 3130 140 4700 200 5396 4318 140 4100 350 4554 3652 55 3905 135 4870 3682 36 3920 120 5309 3315 150 4100 167 4898 3561 140 3950 300 4954 3800 110 3675 325 4277 3191 80 3650 300 4224 3163 28 3820 120 5029 3883 65 3545 165 4209 3211 110 4050 300 4569 3609 50 3510 140 4346 3282 110 4210 240 5424 3460 80 3505 155 4335 3183 80 3540 180 4324 3226 70 3975 275 5010 3857 60 4155 175 5018 3857 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; geographical (3) latitude and (4) longitude in degrees; (5) uncalibrated age and (6) it’s 1σ laboratory error in years (BP); (7) calibrated age and (8) it’s 1σ error 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 alphabetical site name order. 150 A Pan-European model of the Neolithic Site Name Babshin Bara Bazkov Isle Bazkov Isle Berendeevo-2a Bernashovka Besovy Sledki Besovy Sledki Bilshivtsy Chapaevka Chernaya Guba-4 Chernushka-1 Choinovtyi -2 Choinovtyi-1 Daktariske Drozdovka Dubokrai-5 Dubokrai-5 Gard-3 Ivanovskoye-2 Kääpa Kamennaya Mogila Kizilevyj-5 Kodrukõla Korman Koshinskaya Krivina-3 Krivun Krivun Kuzomen Lanino-2 Lasta -8 Lasta -8 Maieri-2 Mamai Gora Marevka Marevka Mariupol Cemetry Marmuginsky Mayak Modlona Mys-7 Navolok Navolok Nerpichya Guba Nerpichya Guba Okopy Orovnavolok Ortinokh-2 Osa Oshchoy - 2 Osipovka Osipovsky Liman Pechora Latitude deg. 48.47 60.00 48.08 48.08 56.57 48.55 64.38 64.38 48.93 47.30 62.82 57.68 64.30 64.42 55.82 68.33 55.85 55.85 47.70 56.85 57.87 47.20 48.25 59.45 48.57 57.63 54.95 68.28 68.28 66.27 57.18 64.77 64.77 61.88 47.47 48.35 48.35 47.15 60.80 68.45 60.35 67.98 66.50 66.50 68.37 68.37 49.97 62.77 68.05 56.85 63.77 49.93 48.87 48.83 Site Longi- Age Calibratude cal BC, tion deg. yr Error 26.57 5160 50 40.15 2900 150 28.47 5568 160 28.47 6143 160 39.17 3883 187 27.50 5565 212 34.43 3190 60 34.43 4010 205 24.58 5307 160 35.52 5853 160 34.87 3414 316 48.77 3995 276 49.87 3668 11 49.95 4070 595 22.87 4350 100 38.28 1535 52 30.37 3578 160 30.37 4700 600 31.20 5722 160 39.03 4094 201 27.10 3509 217 35.35 5717 460 35.15 5640 53 28.08 3590 160 27.23 5193 160 48.23 3550 167 29.63 4145 58 38.43 2685 65 38.43 3375 92 36.77 2100 200 33.00 4779 533 53.73 2690 70 53.73 3500 267 30.57 2975 125 34.38 5940 160 35.30 6477 167 35.30 6865 62 37.57 5518 160 46.30 3500 47 38.37 2601 192 38.80 3067 575 34.97 2660 63 40.58 2975 125 40.58 3575 68 38.38 2275 108 38.38 3325 108 26.53 5458 223 35.08 2790 33 54.13 2035 55 24.58 4434 435 48.58 3230 47 30.40 6535 38 34.92 6400 57 28.70 6117 160 Model arrival time From Near From East, Urals, yr BC yr BC One date 5518 4680 One date 3884 5386 Average of the younger cluster 5660 4745 Average of the older cluster 5660 4745 Average of middle peak 4376 5408 Average of older cluster 5552 4722 Younger date 3310 4993 Average of older three dates 3310 4993 Average 5353 4610 Average 5663 5000 Average of younger cluster 3558 5104 Average 3875 5784 One date 2977 5379 Average of site one 2963 5374 Oldest date 4454 4707 One date 2510 4716 Average of middle peak 4628 5025 Oldest Date 4628 5025 Average 5800 4839 Weighted average of younger peak. X2 4349 5400 Average of older cluster 4299 4898 Average of older cluster 5675 4984 One date 5580 5031 Average 4081 4929 Average 5541 4712 Younger Date 3896 5767 Older date 4755 4986 Younger date 2518 4726 Older date 2518 4726 One date 2733 4791 Average of older cluster 4431 5144 One date 2780 5381 One date 2780 5381 One Date 3657 4971 Average 5664 4964 Average 5566 5042 One date 5566 5042 Average 5636 5075 One date 3564 5554 Weighted average. X2 2506 4718 Average 3873 5327 Older date 2665 4685 Younger date 2777 4922 Older date 2777 4922 Younger date 2506 4718 Older date 2506 4718 Average 5334 4730 One date 3570 5116 One date 2317 5132 Average of middle cluster 4380 4795 One date 3099 5406 One Date 5473 4896 One date 5514 5047 Average 5573 4782 Note 151 Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov & Ganna I. Zaitseva Pegrema-3 Pleshcheyevo-3 Povenchanko-15 Pugach-2 Pyalitsa-18 Rakushechnyi Yar Rakushechnyi Yar Razdolnoye Repishche Rudnya Serteyskaya Sakhtysh-8 Sarnate Savran Semenovka Semenovka-5 Serteya-10 Sev. Salma Sheltozero-10 Silino Skibinsky Sokoltsy-2 Spiginas Sukhaya Vodla-2 Sulka Suna-12 Surskoi Isle {ventoji 9 Syaberskoye-3 Tamula Tekhanovo Tokarevo Tugunda-14 Vashutinskaya Vodysh Voynavolok-24 Voynavolok-24 Vozhmarikha -4 Vyborg Yazykovo-1a Yerpin Pudas Yumizh-1 Zalavruga-4 Zapes Zarachje Zatsen’ye Zedmar-D Zejmati[ke Zolotets-6 Zveisalas Zvejnieki 62.58 56.78 62.82 47.85 66.18 47.55 47.55 47.60 58.35 55.63 56.80 57.33 48.12 48.28 45.42 56.22 68.03 61.35 60.85 48.57 48.72 56.02 62.40 56.75 62.10 48.32 56.02 58.78 57.85 57.07 60.50 64.37 57.37 58.13 62.90 62.90 63.33 60.67 57.27 63.35 62.23 62.80 54.08 56.15 54.40 54.37 55.25 62.78 57.83 57.82 34.43 38.70 34.85 31.23 39.83 40.67 40.67 38.03 33.88 31.57 40.47 21.53 30.02 30.13 29.50 31.57 35.18 35.35 29.73 29.35 29.12 21.85 37.10 27.00 34.22 35.07 21.08 29.10 26.98 39.28 28.77 33.30 40.13 41.53 34.57 34.57 35.78 28.65 33.37 34.48 44.35 36.47 23.67 38.63 27.07 22.00 26.15 36.53 27.25 25.17 3433 3505 2875 5633 3500 5456 6600 5475 3313 4381 4068 3290 5853 5863 5455 3688 3050 3000 3820 6303 6253 3850 3540 3890 4005 6110 3950 3750 4150 4100 3450 2848 3835 3275 2838 3115 3620 3260 4700 4175 3000 3333 3600 4515 4255 3898 4355 3688 3730 4211 506 45 72 160 47 333 319 160 160 233 189 233 160 262 179 200 483 117 160 160 160 167 57 346 75 160 100 217 60 47 183 160 45 125 160 72 160 80 177 160 221 286 233 52 68 250 38 442 70 273 Average of younger cluster Oldest date One date Average of older cluster One date Average from middle cluster Average from older cluster Average One Date Chi-Squared Weighted average Average Average Average Average Ave of young dates (exc. Corded) One date Youngest date Average of younger cluster Average Average Older date One date Average of middle cluster One Date Average Oldest date Older date Oldest date One date One date Average Yougest date One date Average of younger cluster Older date Average of younger cluster One date Chi Squared Average of yougest cluster Average Average of older cluster One date One date One date Weighted average. X2 Oldest date Average of older cluster One date Average of younger cluster 3598 4371 3558 5780 2823 5417 5417 5571 4252 4656 4296 4201 5720 5702 5979 4571 2661 3791 3865 5631 5600 4393 3604 4452 3677 5570 4354 4193 4298 4308 3883 3324 4243 4087 3546 3546 3477 3855 4416 3482 3446 3547 4708 4448 4778 4607 4640 3560 4302 4257 5099 5386 5104 4850 4945 5209 5209 5112 5176 5077 5465 4639 4808 4822 4615 5081 4687 5173 4919 4801 4796 4670 5194 4891 5108 5032 4653 4975 4894 5409 4904 4974 5445 5487 5092 5092 5113 4893 5157 5072 5416 5159 4716 5387 4868 4651 4841 5162 4904 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) site name; geographical (2) latitude and (3) longitude in degrees; (4) calibrated age and (5) its 1σ error in years (BC); (6) method used to select this date; and the model arrival times (years BC) for the wave spreading from (7) the Near East and (8) the Urals. For sites with multiple 14C dates only one (or a few) representative dates are given, obtained as discussed in Section 2. The selection method applied is given in the column labelled Note. The data are presented in alphabetical site name order. 152 A Pan-European model of the Neolithic this idea, but a definitive conclusion needs additional work. wave attributable to the Near East does not seem to have introduced farming in the East. The reason for this is not clear and may involve the local environment where low fertility of soils and prolonged winters are combined with the richness of aquatic and terrestrial wildlife resources (Dolukhanov 1996). The nature of the eastern source needs to be further explored. The early-pottery sites of the Yelshanian Culture (Mamonov 2000) have been identified in a vast steppe area stretching between the Lower Volga and the Ural Rivers. The oldest dates from that area are about 8000 BC (although the peak of the culture occurred 1000 years later) (Dolukhanov et al. 2005). Even earlier dates have been obtained for pottery bearing sites in Southern Siberia and the Russian Far East (Kuzmin and Orlova 2000; Timofeev et al. 2004). This empirical relation between our virtual eastern source and the earlier pottery-bearing sites further east may indicate some causal relationship. Regardless of the precise nature of the eastern source, the current work suggests the existence of a wave which spread into Europe from the east carrying the tradition of early Neolithic pottery-making. If confirmed by further evidence (in particular, archaeological, typological, and genetic), this suggestion will require serious re-evaluation of the origins of the Neolithic in Europe. ACKNOWLEDGEMENTS According to our model, the early Neolithic sites in Eastern Europe belong to both waves in roughly equal numbers (56 % to near-eastern wave and 44 % to eastern wave). Unlike elsewhere in Europe, the Financial support from the European Community’s Sixth Framework Programme under the grant NEST– 028192–FEPRE is acknowledged. ∴ REFERENCES AMMERMAN A. J. & BIAGI P. (eds.), 2003. The Widening Harvest. The Neolithic Transition in Europe: Looking Back, Looking Forward. Archaeological Institute of America. Boston. AMMERMAN A. J. & CAVALLI-SFORZA L. L. 1971. Measuring the rate of spread of early farming in Europe. Man 6: 674–688. 1973. A Population Model for the Diffusion of Early Farming in Europe. In C. Renfrew (ed.), The Explanation of Culture Change; Models in Prehistory. London, Duckworth. 1984. The Neolithic Transition and the Genetics of Populations in Europe. Princeton University Press. Princeton. BERG P. L. V. & HAUZER A. 2001. Le Néolithique ancien. Anthropologica et Praehistoria 112: 63–76. BIRDSELL J. B. 1957. Some population problems involving Pleistocene man. Cold Spring Harbor Symposium on Quantitative Biology 22: 47–69. BRONK RAMSEY C. 2001. Development of the Radiocarbon Program OxCal. Radiocarbon 43: 355–363. CAVALLI-SFORZA L. L. & FELDMAN M. W. 1981. Cultural Transmission and Evolution: A Quantitative Approach. Princeton University Press. Princeton. DAVISON K., DOLUKHANOV P. M., SARSON G. R. & SHUKUROV A. 2006. The role of waterways in the spread of the Neolithic. Journal of Archaeological Science 33: 641–652. DOLUKHANOV P. 1979. Ecology and Economy in Neolithic Eastern Europe. Duckworth. London. DOLUKHANOV P., SHUKUROV A., GRONENBORN D., SOKOLOFF D., TIMOFEEV V. & ZAITSEVA G. 2005. The Chronology of Neolithic Dispersal in Central and Eastern Europe. Journal of Archaeological Science 32: 1441–1458. DOLUKHANOV P. M. 1996. The Early Slavs: Eastern Europe from the Initial Settlement to the Kievan Rus. Longman. FORT J., PUJOL T. & CAVALLI-SFORZA L. L. 2004. Palaeolithic populations and waves of advance. Cambridge Archaeological Journal 14: 53–61. GKIASTA M., RUSSELL T., SHENNAN S. & STEELE J. 2003. Neolithic transition in Europe: the radiocarbon record revisited. Antiquity 77: 45–61. 153 Kate Davison, Pavel M. Dolukhanov, Graeme R. Sarson, Anvar Shukurov & Ganna I. Zaitseva GORDON CHILDE V. 1925. The Dawn of European civilization. Kegan Paul, Trench & Trubner. London. ROUSSAULT-LAROQUE J. 1990. Rubané et Cardial, le poids de l’ouest. Rubané et Cardial, ERAUL(Liège) 39: 315–360. HAAK W., FORSTER P., BRAMANTI B., MATSUMURA S., BRANDT G., TÄNZER M., VILLEMS R., RENFREW C., GRONENBORN D., ALT K. W. & BURGER J. 2005. Ancient DNA from the first European farmers in 7500-year-old Neolithic sites. Science 310: 1016–1018. SHENNAN S. & STEELE J. 2000. Spatial and Chronological Patterns in the Neolithisation of Europe. on-line: http://ads.ahds.ac.uk/catalogue/resources.html?c14_meso JEUNESSE C. 1987. Le céramique de la Hauguette. Un nouvel élément non rubané du Néolithique ancien de l’Europe de nord-ouest. Cahiers Alsasiens. KUZMIN Y. V. & ORLOVA L. 2000. The Neolithization of Siberia and the Russian Far East: Radiocarbon evidence. Antiquity 74: 356–364. LUBBOCK J. 1865. Pre-historic Times: as Illustrated by Ancient Remains, and the Manners and Customs of Modern Savages. Williams and Norgate. London. MAMONOV E. A. 2000. Khronologicheskii aspekt izucheniya yelshanskoi kul’tury. In E. N. Nosov (ed.), Khronologiya Neolita Vostochnoi Evropy. IIMK. St. Petersburg. MURRAY J. D. 1993. Mathematical Biology. Springer-Verlag. Berlin. OSHIBKINA S. V. 1996. Introduction. In S. V. Oshibkina (ed.), Neolit Severnoi Evrazii. Nauka. Moscow. PERLÈS C. 2001. The Early Neolithic in Greece. The First Farming Communities in Europe. Cambridge University Press. Cambridge. PINHASI R., FORT J. & AMMERMAN A. J. 2005. Tracing the Origin and Spread of Agriculture in Europe. P.L.O.S. Biology 3: 2220–2228. PRICE T. D. 2000. Europe’s First Farmers. Cambridge University Press. Cambridge. 154 STEELE J., ADAMS J. & SLUCKIN T. 1998. Modelling Paleoindian Dispersals. World Archaeology 30: 286–305. THISSEN L., REINGRUBER A. & BISCHOFF D. 2006. CANeW, 14C databases and chronocharts (2005–2006 updates). on-line: http://www.canew.org/data.html THOMAS J. 1996. The cultural context of the first use of domesticates in Continental and Northwest Europe. In D. R. Harris (ed.), The Origins of Spread of Agriculture and Pastoralism in Eurasia. UCL Press, London. TILLEY C. 1994. A Phenomenology of Landscape. Berg. Oxford. TIMOFEEV V. I., ZAITSEVA G. I., DOLUKHANOV P. M. & SHUKUROV A. M. 2004. Radiocarbon Chronology of the Neolithic in Northern Eurasia. Tesa. St. Petersburg. WHITTLE A. 1996. Europe in the Neolithic. The Creation of New Worlds. Cambridge University Press. Cambridge. YOUNG D. A. & BETTINGER R. L. 1992. The Numic Spread: A Computer Simulation. American Antiquity 57: 85–99. ZILHÃO J. 2001. Radiocarbon evidence for maritime pioneer colonization at the origins of farming in west Mediterranean. Proceedings of the National Academy of Sciences of the United States of America 98: 14180–14185. ZVELEBIL M. 1996. The agricultural frontier and the transition to farming in the circum-Baltic region. In D. R. Harris (ed.), The Origins and Spread of Agriculture and Pastoralism in Eurasia. UCL Press, London.