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ea Edinborough Kevan ein ntplgclsqecs lhuhatmt tpoiigaslt eune for sequences Stadler absolute (e.g. providing common at increasingly becoming attempts are Although cultural sequences. largely still typological for is Europe, archaeological on basis of in reliant scales a particularly broad reasoning, such provide chronological to case, applicable to any is In enquiry. approach quantity it this and whether sufficient Europe, question Neolithic to in of open cultures is available the in constrained not patterns inter-regional stratigraphically and are regional present, characterising dates At of -consuming. analyses and Bayesian complex are analyses such aedsrbtos(als htl 07 rn asy20;Whittle 2009; Ramsey radiocarbon Bronk calibrated 2007; down Whittle possible narrow it & to making (Bayliss information by distributions dramatically other in date has and on- achieved analysis stratigraphic major be Bayesian integrate of can to of that point control application a temporal increasing remains the the improved archaeology Although in debate. chronologies going cultural of construction The Introduction http://antiquity.ac.uk/projgall/manning342/ at online provided is material Supplementary analysis and duration the Keywords: of description accurate cultures. more Neolithic and European is new that of a where intensity here gives , by analysis authors afforded resulting precision The the of greater available. the accepted distributions, generally floruit with their and with probability ranges largely cultures and Neolithic date European been ‘standard’ summed of duration series has Using a the for reasoning dates sequences. radiocarbon chronological describe compare far, typological to Thus on terms. ways reliant statistical appropriate in cultures sought archaeological long have Archaeologists Manning Katie approaches dating Neolithic European of assessment comparative a culture: of The * 2 1 n h aerne niae yalo h vial aicro vdne oeobvious Some evidence. cultures, to Ware available Corded the assigned the of (2009) dates Włodarczak of by review all end the example, by and for include, indicated exceptions beginning ranges been the date have compare there the 2011), and systematically Denaire to 2009; Thissen efforts & few Reingruber 2003; Furholt 2002; Fabian ANTIQUITY  C niut ulctosLtd. Publications Antiquity uhrfrcrepnec Eal [email protected]) (Email: Building, correspondence Darwin for Author London, UK 6BT, College WC1E UK University 0PY, Environment, London WC1H Street, and Gower London Evolution Square, Genetics, Gordon of 31–34 Department London, Research College University Archaeology, of Institute 8(04:16–00http://antiquity.ac.uk/ant/088/ant0881065.htm 1065–1080 (2014): 88 elti,clue hooois edohoooy aicro aig Bayesian dating, radiocarbon dendrochronology, chronologies, culture, Neolithic, 1 , ∗ dinTimpson Adrian , 1 ,TimKerig 1 1065 tpe Shennan Stephen & 1 , 2 u Colledge Sue , 1 nioCrema Enrico , 1 tal et 01 Raetzel- 2001; . tal et 2011), . 1 ,

Research The chronology of culture methods, and the use of multivariate statistics in conjunction with radiocarbon data as a means of refining typochronological classifications. In particular, correspondence analysis and principal component analysis have been used to identify chronologically meaningful aspects of regional typologies, e.g. in the Mittelelbe-Saale region in (Muller¨ et al. 2000; Czebreszuk & Muller¨ 2001; Muller¨ & Van Willigen 2001, Muller¨ 2009), for Linearbandkeramik (LBK) settlements in the Netherlands (van de Velde 2012) and also for the Corded Ware (Ullrich 2008). All of these, however, are relatively localised studies of internal development. In this paper, we approach the issue at a different scale, adopting a broader and therefore lower resolution view of the relationship between different dating approaches for the European Neolithic; we then go on to estimate the underlying shape of the intensity of a culture’s presence through time. We investigate the temporal ranges of various cultural groups by analysing and comparing the estimates from three sources: the ‘standard’ date range, the radiocarbon date range, and the dendrochronological (dendro) date range, where available. We use the term ‘standard’ date range to mean the estimated start and end date for a culture as found in relevant current literature, which we consider to represent the best-informed archaeological knowledge on the subject (see online supplementary Table S1 for all ‘standard’ dates and the references used). The motivation behind our analysis came from attempting to investigate temporal patterns in subsistence data. Given that awareness of available radiocarbon dates forms an important part of that up-to-date archaeological knowledge, we were surprised to find a large difference in our results when using site phases that were dated using associated radiocarbon samples, compared to the current estimate of the ‘standard’ date range for that cultural phase. Therefore, in order to undertake a valid analysis of subsistence trends, or of any other archaeological phenomena for that matter, we must first investigate the congruency between the ‘standard’ date range and the contextually associated radiocarbon dates for a given culture. It is worth pointing out at this that our interest in the temporal ranges of different cultural groups is not intended to promote the notion of as a monolithic and unchanging entity: cultures as ‘bricks’. On the contrary, one of us has consistently argued the opposite (e.g. Shennan 1978, 1989), following Clarke’s (1968) polythetic definition of archaeological cultures. We do not need to take the traditional view of cultures as monolithic blocks to explore their chronological patterns, which may in fact relate to specific cultural packages. Just as in genetics a contrast is made between the analysis of gene trees and population trees, both of them equally valid for different purposes, so it is equally appropriate in the case of transmitted cultural variation to work at different scales of resolution for different purposes. Moreover, we do not need to subscribe to the idea that our classifications ‘carve at its joints’ in Plato’s famous phrase (Phaedrus, 265d–266a; Fowler 1925) to recognise that some categorisations are better than others. One key criterion is whether variation between the entities being analysed is significantly greater than that within them (see Shennan et al. 2014), regardless of the processes that resulted in this patterning, which often remain the focus of dispute (see Furholt 2014 for an example). In short, while archaeological ‘cultures’ may not be useful for investigating local-scale socio-economic dynamics, they have remained indispensable for characterising broad-scale spatial and temporal trends, such as those which prompted this analysis. C Antiquity Publications Ltd.

1066 fteerltosisfo h esetv fetmtn h aerneo utr,by culture, a of think range can date we the Therefore, estimating assigned. was of it perspective which its the comparing to from culture relationships the these of of date ‘standard’ the to the opposed and as it dating for basis the as dates. assignment been radiocarbon cultural own site’s have site’s a difference will the using at when ranges surprise associated results our date Hence in of themselves. ‘standard’ absence dates radiocarbon the current the by in the influenced especially strongly importantly, date, more radiocarbon of assignment its Clearly material; cultural by distribution. the diagnostic influenced since probability be properties, own may two these sample its between a with circularity of each degree date, a is ‘standard’ there a and date, calibrated l aicro aawr eie rmtedtbs oltdb h UOVLproject. EUROEVOL the by code, collated lab a database include the data from These derived were data radiocarbon All dataset and Method sindete yteecvtr aoaoyo otecvto nls.Teresultant The analyst. post-excavation culture, or associated an laboratory have excavator, to the had also by sample either the analysis, assigned this in inclusion warrant to order oete utrlrne ti ieyta l he nepeain eeue ndifferent on used were provides interpretations This three cases. all all for belonging interpretation that third of likely the probability adopted is equal have we an It nevertheless, have occasions; range. they cultural that transitional either thirdly a and to to deposits belong cultures; they the two that that between This secondly, firstly cultures). cultures; phase all interpretations: different of three two list have between a overlap for may S1 indicate assignment Table online cultural (see to of cultures assigned type these been of had second three) phases case 36 from one (2.5%) in samples (or 142 two while cultures, 71 these of one only terms. classique Linearbandkeramik—are (1968) Clarke’s ancien, and in Ware a to i.e. groups’ Corded as Cortaillod ‘culture Beaker, here treated the multi-regional, cultures—Bell refers our of is ‘culture’ of sub-phases Cortaillod Three the the term tardif. into example, and The divided for being Age. so, than Bronze entities, rather whole single Early as the cultures to archaeological far the through time that at Late course the of and scale, spatial available. larger (1987) was a Breunig information patterns. at radiocarbon archaeological although how less implications other programme, establish the of similar discuss to analysis the a and thus for had estimates, is least range follows not date findings, what these those in of between objective is Our there range. agreement date much dendro its cultures) of ape eeotie rmteEzeugdrkindsKnosBr est (Dendro website Bern Kantons des Erziehungsdirektion the n.d.). from obtained were samples Each 1NoihcadEryBoz g utrs(e iue1adoln upeetr Table supplementary online and 1 this Figure to (see addition cultures In Age S1). Bronze Early and Neolithic 71 aae o hssuyteeoecnit f59 aicro-ae ape rm1784 from samples radiocarbon-dated 5594 of consists Shennan therefore (see site-phases study archaeological this for dataset iial,ec edosml a ecniee ohv w rpris edodate dendro a properties: two have to considered be can sample dendro each Similarly, h aae nldd55 ape rm14 iepae,wihhdbe sindto assigned been had which site-phases, 1748 from samples 5452 included dataset The covers and 1) (Figure Europe north-western and central encompasses area study Our Each 14 apewsclbae i h nCl9clbaincre(Heaton curve calibration IntCal09 the via calibrated was sample C 14 apecnteeoeb osdrdt aetopoete:aradiocarbon a properties: two have to considered be therefore can sample C 14 aerne t sadr’dt ag,ad(hr vial o handful a for available (where and range, date ‘standard’ its range, date C 14 aae,ascn edohoooia aae opiig350 comprising dataset dendrochronological second a dataset, C 14 g n tnaddvain(D,lttd n longitude. and latitude (SD), deviation standard and age C ai Manning Katie tal. et 1067 03frteapiddfiiino hs) from phase), of definition applied the for 2013 tal. et  C niut ulctosLtd. Publications Antiquity tal et 09.In 2009). . 14 C

Research The chronology of culture

Figure 1. Map of north-western Europe showing the site locations from which the 14C samples were taken (black dots).

a conservative approach with the effect of erring on the side of slightly greater uncertainty in the date range. First, we investigate the broad-scale relationship between the radiocarbon date and the ‘standard’ cultural date for all samples combined (Figure 2). Both before and after calibration the exact radiocarbon date of a sample remains elusive. Instead we have a distribution, which describes the probability of each possible date. Similarly, the true ‘cultural’ date could be any date within a culture’s range, which is assumed to be a uniform distribution. We generate 1000 random realisations, such that for each realisation every sample has a random point estimate: both a discrete radiocarbon date and a discrete ‘standard’ date obtained from their C Antiquity Publications Ltd.

1068 ape (mean samples eerqie,laigu ihte2 3% etrpeetdclue Tbe1,ec of each 1), (Table cultures best-represented (mean site-phases (31%) 329 22 and 18 the between comprised with culture which per us phases leaving 18 of required, minimum a were culture that ensure such to each representation, criterion temporal for sampling and minimum estimates geographic a good different met the that cultures between individual relationship selected We separately. the assessing to distributions. attention probability our the in uncertainty the by describe caused intervals variance confidence values, These of possible estimated. amount of be distribution. distribution the can a error (CIs) up an intervals build confidence have we which variables from 1000 both sampling calculated. since random were the regression model repeating Deming linear By two best-fitted used the a model between of linear gradient correlation The the the and R) realisation Pearson’s (using each estimates For distributions. probability respective h sadr’dt ag odr,tepooto htfl usqett h sadr’end ‘standard’ of start the the to to subsequent proportion. prior fell total fell that the that proportion and proportion (younger) the the date (older), as cultural range 1 ‘standard’ Table the date the in ‘standard’ outside and reported fell the is that phase value mass the This SPD range. the both of date of proportion the level calculated the we dates, at fair applies equally This an considered event. initially the was of sample culture. date each the as of weighted, possibility equally of distribution samples’ sample, law individual sample each knowledge the the combined the of the summing contains assumed, increases, distribution By probability is samples distribution. new the true of distributions, sampling probability the number random to the similar if increasingly as that becomes that these unity. is predicts for third, approach normalised numbers and and this large unity; summed were for behind culture normalised rationale same and the The summed in phase were Shennan every phase (see from same calibrated distributions the were in SD) sample and every (mean two- dates constructed the radiocarbon was al. SPD as raw et Each 1 first, 4. probability Table and stages: full 3 in Figures three the in reported while in plotted (SPD), are is black distribution BC) ranges probability 8000–0 a date (between summed by distribution radiocarbon a range represented of The a distribution, interval 4. as uniform 95% and reported tailed a 3 are as Figures dates plotted in ‘standard’ and with bar the bar latest, Similarly, red error. vertical and sample’s a earliest as the sample between each to with equal 3 Figure width in plotted a in are Culture and Ware date, latest Corded and earliest the comparisons to as regard long in so below culture, (see each region of relevant range Switzerland). the date within the made on light are further shed therefore can 7%,ad11 hss(81%). phases 1416 and (79%), rcso o nidvda apeta yia aicro ae(endnr error dendro (mean mean date to radiocarbon compared typical sample, a per than years sample 6.9 individual an for precision n Cortaillod aigetbihdteoealcreainbtenordt ag siae,w turned we estimates, range date our between correlation overall the established Having nodrt sestelvlo gemn ewe h aicro ae n h ‘standard’ the and dates radiocarbon the between agreement of level the assess to order In the using 1 Table in reported is range date dendro the cultures, latter these of each For oro u eetdclue lohv soitddnr ae Cre aen Ware (Corded dates dendro associated have also cultures selected our of Four 03frdtiso airto) eod h airtdpoaiiydsrbtosfrom distributions probability calibrated the second, calibration); of details for 2013 = = 6 ognn Horgen 66, 9) n osiue h aoiyo h aa opiig4281 comprising data, the of majority the constituted and 195), = 6adPy n Pfyn and 66 ai Manning Katie 14 1069 ro f74.7 of error C tal. et = 5,wihgnrlypoiegreater provide generally which 55), = 44,adbten3 n 1030 and 34 between and 64.4), 14 er) Dendrochronology years). C  C niut ulctosLtd. Publications Antiquity 14 Cdates = 73, =

Research The chronology of culture

Finally, we assessed how the intensity or ‘floruit’ of an individual culture varied through time, and the underlying shape of this change. We Z-transformed the SPD for each of the selected 22 cultures, to ensure they were on the same scale (Figure 5). This involved obtaining the mean date for the culture’s summed probabilities and the standard deviation of this distribution and then expressing the date values not on the original year scale but as numbers of standard deviations away from the mean, thus eliminating the effect created by the fact that some cultures lasted longer than others. The 22 Z-transformed SPDs were weighted by number of phases per culture, then summed and normalised to unity (Figure 5, blue line), since we can expect the ‘shape’ of those cultures with more phases to be more representative of the true culture shape. Further, for comparison we summed and normalised the 22 Z-transformed SPDs with an equal weighting (Figure 5, red line), to provide some indication of the efficacy of our minimum inclusion criterion of 18 phases per culture.

Results Overall correlation Figure 2 illustrates 10 realisations (out of the total 1000 realisations that were computed) for each of our 5594 radiocarbon samples plotted in grey. Note the ‘blocky’ nature of the scatterplot in the horizontal range, due to the ‘standard’ date being sampled from each culture’s wide uniform probability distribution. The vertical range, meanwhile, is scattered more evenly since each radiocarbon date was sampled from its own relatively narrow probability distribution. Clearly, when all samples and all cultures are included, there is a strong correlation between the two dating methods. (R = 0.859, 95% CI = 0.855–0.862), with almost three quarters of the variance in either estimate explained by the other (R squared = 0.737, 95% CI = 0.730–0.744). The gradient of the best-fitted linear model plotted in blue is 1.038 (95% CI = 1.030–1.045), which is to be expected as both the radiocarbon date range and the ‘standard’ date range are two different estimates of the same quantity (the true date range of the culture).

Comparing individual culture date ranges Having established an overall strong relationship between the probability distributions of all radiocarbon dates and ‘standard’ culture dates, the question remains as to whether certain cultures correlate better with their associated radiocarbon dates than others. Figure 3 plots the ‘standard’, radiocarbon and dendro date ranges for the four cultures with associated dendro samples, and Figure 4 plots the ‘standard’ and radiocarbon date ranges for the remaining 18 selected cultures. Generally, there is good agreement between the dendro date ranges and the ‘standard’ date ranges, which is perhaps not surprising due to the high level of precision on dendro dates and the excellent preservation of the wetland sites where these cultures are predominantly found. The exception to this is the Corded Ware, which has a much wider ‘standard’ range than the dendro range, due to the fact that the Corded Ware is found over a much wider geographic area than the typical wetlands required for dendrochronology, and lake shore settlement ceased c. 2450 cal BC (Billamboz & Koninger¨ 2008). C Antiquity Publications Ltd.

1070 xml eaaadIink,idct noealsiti h eko aicro probability radiocarbon of peak the in shift effects. overall an wood’ indicate ‘old Iwienska, to and Veraza lead example surprising might rather that is is dates This charcoal 15% size). of and inclusion sample range our by date of weighted ‘standard’ light 23% when the in average respectively than on 12% younger ranges; and is date (22% ‘standard’ mass older the probability than radiocarbon younger ranges the date being radiocarbon of conventional towards the the skewed Overall poor. and be quite dates to remains radiocarbon tend cultures between however, Neolithic agreement note, European of general for level more ranges the a that On clear others. is than may it cultures sequences some that chronological suggests Ware) reliable range (Pitted broad more a 14.8% that Such have from 38.7%. mass of values probability mean of a radiocarbon with spread (Veraza) the 75.1% massive to of a revealing proportion range, the ‘standard’ reports the 1 exceeds Table cases. all in ranges iue2 e admraiain fec fte59 ape’rdoabndtspotdaantterrsetv ‘standard’ (blue). respective realisations their 1000 against all plotted for dates fit radiocarbon best samples’ of 5594 line the the of with each dots), (grey of date realisations random Ten 2. Figure te ifrne ntentr fti iceac o ahclueaeeiet oe for Some, evident. are culture each for discrepancy this of nature the in differences Other date ‘standard’ the than wider substantially are distributions radiocarbon the contrast, In ai Manning Katie 1071 tal. et  C niut ulctosLtd. Publications Antiquity

Research The chronology of culture Proportion of radiocarbon probability Radiocarbon (BC) Standard (BC) Dendrochronology (BC) mass outside the standard range ´ ´ eolithique finaleolithique moyen II 24 42 96 98 4534 3473 2973 2040 3950 2900 3500 2150 0.556 0.228 0.083 0.042 0.639 0.270 Table 1. The 22the best-represented improved cultures normally with distributed their model. start The and last end three dates columns estimated estimate using the the difference three between different ‘standard’ methods, and and radiocarbon the date mean range. and SDCulture using Bell BeakerWestern CardialChasseenCorded Ware PhasesCortaillod Samples 57 113Ertebølle StartGlobular Amphora 151 228Horgen End 189 75Iwienska 6574 3040 60Lengyel Start 341 33 213 3849Linearbandkeramik 1607 End 3251 46 145Michelsberg 4663 111 5600 Start 2500 139N 3411 1901 4950 360 4503N 2952 1800 26 23 535Peu 2009 Richard 2800 5709 2963 End 4400Pfyn 39 2050 130 5719 45 3100 131 3400Pitted 3478 Ware 2751 4100 3540 2700Rossen 4127 147 2195 3400 Older 126 5450Seine-Oise-Marne Younger 2525 3895 5080 18 5500Trichterbecher 4100 1082 2418 4529Veraza 4900 3500 3540 26 51Wartberg 2600 3158 56 2750 3517 Total 1800 0.171 19 4800 329 3482 4250 3488 39 130 0.157 20 0.062 0.264 4000 3500 1030 0.349 0.201 92 3637 0.046 2483 3730 2765 4323 0.147 50 4251 0.134 2257 3300 20 1777 22 0.233 0.138 1793 5018 0.115 2900 3138 0.506 3400 3500 0.038 0.310 0.363 38 34 4100 2350 4045 0.077 2700 0.348 0.131 3850 3000 0.072 3622 0.206 3488 3400 4750 0.249 0.313 3919 4400 0.501 1989 2205 0.000 0.169 0.613 0.115 3400 3500 0.150 0.283 3507 0.183 2850 2800 0.385 0.106 0.613 0.359 0.173 0.298 0.151 0.268 0.256 0.100 0.130 0.049 0.048 0.495 0.261 0.169 0.510 0.441 0.178 0.148 0.625 0.310 0.069 0.014 0.682 0.302 0.347 0.751 0.316

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1072 nlso rtro famnmm1 hsswsscesu nesrn ahSDwswell was SPD each the ensuring our by in that weighted successful suggesting was mean similarity, phases the remarkable 18 shows minimum show line a lines blue of Both criterion the culture. inclusion while per cultures, phases all of of number mean random the to shows them line reducing instead change and shape. and overall interference shift the to in constructive wiggles noise their background these causing removing like-for-like of a size, benefit on the distribution in had radiocarbon culture’s also each transformation each of generates This Z-transforming shape scale. often By the years). compare process 200 can cultures around calibration we (below individual SPD scale radiocarbon of short-term the the distribution on Neolithic since wiggles the of spurious ranges interpreting shape’ narrow when ‘temporal relatively taken broad-scale across be the should investigate probability Care to summing cultures. of us technique allowed the methods, also dating distributions different comparing to addition In cultures Neolithic of shape’ ‘temporal The chronological of causes underlying potential the to relation in discrepancies. for cultural these below Others, of discussed some late. of are specifics too The groups range. a or date indicating ‘standard’ early the distribution, of too radiocarbon underestimation broader potential slightly generally be a have may Seine-Oise-Marne, range example ‘standard’ the suggesting density, date ‘standard’ the and grey in sequence. (SPD) chronological distribution in probability arranged summed samples radiocarbon dendro red, black. associated in in with shown range cultures is four range the date for dendro ranges The date Comparative 3. Figure iue5sosSD fe -cr rnfrainfrec for2 utrs h red The cultures. 22 our of each for transformation Z-score after SPDs shows 5 Figure ai Manning Katie 1073 tal. et  C niut ulctosLtd. Publications Antiquity

Research The chronology of culture

Figure 4. Comparative date ranges for the remaining 18 best-represented cultures, arranged in chronological sequence according to the mean of the ‘standard’ date range.

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1074 ecie t hp,icuigiscnrltnec swl sdrto,uigmean using duration, as accurately more as distribution tendency normal central a its including contrast, shape, In its evidence. describes available the of distribution r eotdfral2 utrsi al ,adaepotdi iueS ntesupplementary the in S1 Figure in the plotted are of and SD examples and 2, Table mean shows in The information. 6 cultures cultures. 22 Figure selected all five ranges. for for date SD reported that and are end way mean and a its with start in distribution chronologies current normal cultural fitted the of with properties possible statistical not the is exploring begin to us allows SD and BC the parameters: two Linearbandkeramik requires the for only range parameters: also date start ‘standard’ two distribution using the described uses normal currently is example, range a For date while SD. ‘standard’ and date, mean the end Currently, and parameters. start of a cost extra no at compelling. extremely is fit The transformation. Z-score after distribution ersnaieo h utr’ reudryn itiuin h ahdbakln hw a shows line black dashed The (mean distribution. distribution normal underlying standard true standard culture’s a the shows line cultures’ of black 22 representative dashed all the of and mean culture; the per shows phases line of red number by the weighted (Z-transformed); mean SPD culture’s the distribution. each shows normal represent line lines blue grey the SPD; 22 The 5. Figure etecs o h ognadCre ae(ny1%ad2%of 23% and 17% (only Ware Corded and to appear Horgen does the this for Although case chronology. culture’s the a be of dendrochronology reliability by overall provided dates the comparative improve additional would the that assume to fair be may It Discussion h rnia datg fti omldsrbto sisicesdepaaoypower explanatory increased its is distribution normal this of advantage principal The = 1 r.Hne h diinlifrainta sgie,a oetacost, extra no at gained, is that information additional the Hence, yrs. 310 = 50B n end and BC 5500 ai Manning Katie = ,SD 0, 1075 = = 90B,wihtlsu iteaotteactual the about little us tells which BC, 4900 ) hc ecie h hp faynormal any of shape the describes which 1), tal. et  C niut ulctosLtd. Publications Antiquity 14 rbblt mass probability C = 5088

Research The chronology of culture

Figure 6. Examples of summed probability distributions for 5 of the 22 cultures in grey. The red line shows the best-fitted normal distribution.

outside their respective ‘standard’ dates), it does not apply to all cultures; for example, there is a discordance of 51% in the Pfyn data. This is in contrast to cultures such as the Pitted Ware, Chasseen and Michelsberg, which have no associated dendro dates, and yet show relatively good agreement between the radiocarbon and ‘standard’ date ranges (15%, 25% and 26% discordance respectively). This may be due to recent efforts aimed specifically at refining cultural chronologies such as the Michelsberg and its successive cultures (e.g. Raetzel-Fabian 2000, 2002; Geschwinde & Raetzel-Fabian 2009), or because of the archaeological visibility of particular cultural traits, e.g. the enclosures of the Michelsberg or the Chasseen, and the distinctive material and economic characteristics of the Pitted Ware. In contrast, the cultures with the highest disagreement values, such as the Veraza, Neolithique´ moyen II and Seine- Oise-Marne, are comparatively ill-defined and with relatively small sample sizes (38, 96 and 39 respectively). These results raise a number of important issues relating not only to chronological reasoning, but also to the characterisation of Neolithic cultures. On a very basic level, the amount of agreement between different dating methods at the broad level of analysis we have used seems to come down to economy and scale. The more established a culture C Antiquity Publications Ltd.

1076 ie n hr sn la orlto ewe apesz n h gemn ewe the largest between agreement the the between far and is sample by size there to sample has agreement between attributable Trichterbecher correlation more simply estimates. clear the not no two is, is is it there this and However, widespread size, accuracy. more greater the implying degree estimates, some to and is, t eprlntr,ie t outo nest Otwy17;Aitchison 1973; (Ottaway about intensity nothing us or tells floruit may it its this phenomenon, while cultural i.e. a and nature, of distribution, temporal duration uniform the its simple about a something with us only tell us provide range ‘standard’ fteSDo ahculture’s each of SPD considered the of be of and to setting needs environmental culture trajectory, historical each own discrepancy instead its for research. and of cause light estimates, clear-cut in high no date individually is is different there there culture the Cardial Hence the between (51%). of estimates spread geographic between estimates broad between discordance relatively discordance a the with Despite worse, the of even 39%. fares enjoys order of but Linearbandkeramik 535 an The of 15%. by size of sample samples highest discordance second fewer smaller a has has Ware yet Pitted (130), whilst magnitude estimates, between discordance 31% oeitrsigrsl ohv rsnfo hsaayi stecmaaieshape comparative the is analysis this from arisen have to result interesting more A ateg26 322 426 2968 2625 156 481 265 362 4620 669 3432 3779 268 2911 Wartberg 2702 Veraza Trichterbecher 3097 328 Seine-Oise-Marne 362 Rossen 340 Ware Pitted 276 3911 4499 Pfyn 310 Richard Peu 1681 624 3066 N 5088 351 N 282 Michelsberg 4583 419 281 Linearbandkeramik 3830 Lengyel 2806 Iwienska 261 3998 2513 448 Horgen SD Amphora Globular 2313 Ertebølle 5126 Mean Cortaillod Ware Corded Chasseen Cardial Western Beaker Bell Culture cultures. 22 all for based distribution SD normal and a mean on proposed The 2. Table oihqefia 65280 317 2675 4031 II moyen eolithique final eolithique ´ ´ 14 aerneetmt.Tesatadeddtso the of dates end and start The estimate. range date C ai Manning Katie 1077 itiuin(BC) distribution tal. et Normal 14 apesz 13) e suffers yet (1030), size sample C  C niut ulctosLtd. Publications Antiquity tal. et 1991).

Research The chronology of culture

It is improbable that the material associated with a given culture suddenly comes into existence maintaining a constant prevalence and then suddenly ceases. Our analysis from combining all 22 SPDs suggests that a normal distribution provides a better description of the fundamental underlying shape of a culture’s rise and fall, and, therefore, the use of a mean and standard deviation would be more informative than the current start and end dates, which are so often used in the archaeological literature. Indeed, in some circumstances it may also be useful to supplement reporting the mean and SD of a cultural range by reporting the full 14C probability distribution, in order to incorporate fine-grained information about the temporal variation in the intensity of the episode. This requires caution as finer resolution may introduce undesirable artefacts from sampling error and ‘interference’ effects from wiggles in the calibration curve (Blockley et al. 2000). As such, this would only be useful where large unbiased samples are available and when the culture spans a long time period. Nevertheless, this study provides empirical support that a Gaussian model, and perhaps other unimodal distributions (Lee & Bronk Ramsey 2012), are superior to the standard uniform distribution, both as a prior for Bayesian models of archaeological chronologies (Bronk Ramsey 2009) and as a simple summary description of the cultural time-span. This improved underlying model of the expected temporal dynamics of a regional culture is of value for a range of different analyses. Bayesian analysis of 14C dates aggregated at the level of culture is reliant on the selection of a prior distribution. In the absence of other information a uniform prior is usually adopted; instead, a normally distributed prior is both more reasonable and empirically supported. Analysis requiring Monte Carlo simulation of cultural dates (e.g. Crema 2013) would also benefit greatly from this improved model. Finally, it is worth pointing out that the characteristic normal distribution we have identified bears a striking resemblance to the so-called ‘battleship curves’ produced when frequency seriations are carried out on individual artefact types that are chronologically sensitive. When cultures are taken as entities they seem to this effect. In essence, the number of dated events that archaeologists are prepared to label, for example as Horgen or Michelsberg, starts small, increases to a peak and then declines again. The pattern could arise because of the waxing and waning popularity of temporally correlated styles across a geographical region. Another possibility, supported by demographic proxies in some cases (Shennan et al. 2013), is that they reflect fluctuations in local populations; at some periods there are simply more people in the region, so the number of dated events characterised by the styles of the period is also bound to be greater. Of course, these two possibilities are not mutually exclusive, and in some cases it could be that new cultural innovations themselves result in periods of population increase. These questions remain open for subsequent analysis.

Acknowledgements We are grateful to all those who provided radiocarbon data, and to Johannes Muller¨ and Felix Riede for their constructive review comments. This research was funded by the European Research Council Advanced Grant number 249390 to Stephen Shennan for the EUROEVOL Project. Information on the EUROEVOL Project is available at http://www.ucl.ac.uk/euroevol/

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Received: 13 December 2013; Accepted: 15 April 2014; Revised: 20 June 2014

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