240 Documenta Praehistorica XLIV (2017) Introduction Radiocarbon dating is the basic method for elaborat- ing the absolute chronology of prehistoric events in the Younger Stone Age (Walanus, Goslar 2009; Tay- lor et al. 2014). Certainly, this is not an ideal me- thod. It is characterised by a number of limitations, faults, and imperfections. Awareness of their exis- tence varies among archaeologists and other scien- tists using this method. However, no method that would be a viable alternative for radiocarbon dating has been invented so far 1 1 . This is why it is very im- portant to approach the results of radiocarbon dating correctly. These results must undergo multi-dimensio- nal analyses and interpretations, which take into ac- count many internal factors (i.e. arising from the me- Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland Marek Nowak Institute of Archaeology, Jagiellonian University, Kraków, PL mniauj@interia.pl ABSTRACT – In the late 5 th , 4 th , and early 3 rd millennia BC, different archaeological units are visible in western Lesser Poland. According to traditional views, local branches of the late Lengyel-Polgár complex, the Funnel Beaker culture, and the Baden phenomena overlap chronologically in great measure. The results of investigations done with new radiocarbon dating show that in some cases a discrete mode and linearity of cultural transformation is recommended. The study demonstrates that extreme approaches in which we either approve only those dates which fit with our concepts or accept with no reservation all dates as such are incorrect. IZVLE∞EK – V obdobju poznega 5., 4. in zgodnjega 3. tiso≠letja pr. n. ∏t. lahko na obmo≠ju zahodne Malopoljske prepoznamo razli≠ne arheolo∏ke enote. Glede na tradicionalne poglede se v tem ≠asu kronolo∏ko prekrivajo enote poznega kompleksa Lengyel-Polgár, kulture zvon≠astih ≠as in badenske- ga fenomena. Novi radiokarbonski datumi ka∫ejo, da je v nekaterih primerih potreben diskreten pri- stop z linearnimi kulturnimi spremembami. V ≠lanku poka∫emo, da so ekstremni pristopi, pri kate- rih uporabimo oz. izklju≠imo bodisi tiste datume, ki sodijo v na∏e koncepte, bodisi vse datume brez zadr∫kov, pri razlagah datumov nepravilni. KEY WORDS – western Lesser Poland; Middle Neolithic; absolute chronology; 14 C dating KLJU∞NE BESEDE – Malopoljska; srednji neolitik; absolutna kronologija; 14 C datiranje Ali 14 C datumi vedno predstavljajo tudi absolutno kronologijo| Primer iz srednjega neolitika na zahodu Malopoljske 1 This inevitably connotes Winston Churchill’s famous saying about democracy: “Democracy is the worst form of government except for all those others that have been tried”. In fact, it perfectly reflects the place of the discussed method in archeology (and not only in archaeology), i.e. to paraphrase this saying, we could say that radiocarbon dating is the worst form of dating except for all those others that have been tried. DOI> 10.4312\dp.44.15 Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 241 Admittedly, this approach is only an assumption, particularly when dates do not come from the same site or context. However, the concept of a phase can be applied to many sites combined, as dates can be related to an “unordered group of events/parame- ters” and to “a random scatter of events between a start and an end boundary” (Bronk Ramsey on- line). Moreover, the supposition of continuity of de- velopment within an archaeological unit is not an illogical idea. One can conclude that the vast majo- rity of prehistoric phenomena were characterised by a consistent continuation and cohesiveness of deve- lopment (e.g., Marsch et al. 2017). Bayesian models have great potential to improve chronologies, but they have to be connected with critically analysed external circumstances (prior assumptions), i.a. with stratigraphic and typological contexts, as well as with already existing dating schemes of phenome- na important for the issue investigated. The out- come of such procedures will quite frequently be a shortening of the timeframes of archaeological units under consideration. Chronologically, they will be- come more discrete units once again, and ‘traditio- nal’, typological data will regain its importance. There may also be shifts in the dating of some pre- historic and historic events with respect to the com- mon views. To analyse problems of this kind, we decided to take into account the region of western Lesser Poland in a period that, in the local circumstances, can be cal- led ‘Middle Neolithic’ (or alternatively ‘Early Eneo- lithic’). Additionally, the ‘Late Neolithic’ Corded Ware culture will be utilised as a kind of ‘upper’ chrono- logical boundary (Fig. 1). The timeframe under scru- tiny is the period from the late 5 th to the early 3 rd millennium BC. In this period, significant changes to settlement and economic patterns took place, but probably also within the ideological and social sphe- res. These changes can be described as ‘Eneolithisa- tion’. Therefore, a comprehensive chronological in- terpretation of archaeological facts is also important and helpful for correct anthropological and historical interpretations of these processes. Archaeological setting Loess uplands covered by fertile soils predominate in western Lesser Poland, so it was and still is a very favourable area for agriculture. Hence, since the be- ginning of the Neolithic until today the area is cha- racterised by very dense human settlement. What is more, this area was and is located at a crossroads of main communication routes, intersecting basins of the Vistula and Oder rivers. In the Neolithic, cultu- thod itself) as well as external (i.e. arising from the context of a sample, and even from the specificity of a given laboratory). Perhaps, above all, we must remember that, the re- sult of radiocarbon dating and calibration, is a wider or narrower time range, and not, contrary to a com- mon view, a specific point in time. Particular seg- ments of the range are usually characterised by vary- ing probability. In our analyses, we may consider dates at face value, and determine the timeframe formally covered by ranges resulting from calibration procedures. Alter- natively, we can add up the probabilities of each cali- brated distribution. The result will usually be simi- lar to the previous one. If we rely on individually ca- librated date ranges or sum-calibrated distributions, we usually obtain longer timeframes than expected (Marsch et al. 2017.120), when based on typologi- cal premises. Consequently, it appears that many archaeological units, contrary to conventional pat- terns, develop partially or completely in parallel. However, 14 C dates treated in this way could be mis- leading. Natural imperfections and the risks con- nected with 14 C method, compounded by the laws of statistics, can result in the emergence of extreme values. These extreme values will deviate from the most typical and ordinary ones, and therefore will not reflect the actual chronology of the context from which they originate. In other words, the actual chro- nological diversity is not as advanced as it could ap- pear. In terms of the prehistoric chronology, a good illustration of this matter is the comparison of radio- carbon and dendrochronological dates, with the lat- ter giving clearly narrower intervals (Włodarczak 2008c.Fig. 7). In the quoted author’s opinion (Wło- darczak 2008c.125–126), uncritical acceptance of formal indications of radiocarbon dating results in an apparent lengthening of chronology and an ap- parent synchronicity of archaeological groupings. Based on such premises and thoughts, a ‘reductio- nist’ approach in the interpretation of radiocarbon dates may be suggested, in which extreme values are considered to be fictitious (e.g., Domboróczki 2009. 80–91; Müller 2002; Włodarczak 2008c). Therefore, modelling procedures can also be executed which will verify whether the available set of dates is cha- racterised by internal cohesiveness (grouping) and, in effect, may designate a compact period of time. Undoubtedly, Bayesian modelling has become the most prevalent in recent years (Bayliss 2015; Bay- liss et al. 2007; Bronk Ramsey 2009a; 2009b), and we will use it in this contribution. Marek Nowak 242 ral transmissions and human migration met and mingled here; they came from virtually all direc- tions. As a result, the formation of specific, syncre- tic units took place fairly frequently. It was also the output area of a number of transmissions and migra- tions, also in virtually all directions. Within the defined space and time, a number of ar- chaeological units have been recorded (Fig. 1), al- most all of which are local components of large groupings belonging to different Central-European cultural traditions. As is usual in the case of the Neo- lithic, especially in the ‘continental’ (cultural-histo- rical) approach, these units and traditions were dis- cerned long ago on the basis of pottery. From the perspective of the Anglo-American literature they would be described rather as pottery styles, not se- parate entities. Indeed, there are some shared ele- ments of ‘non-ceramic’ material culture. However, there also are some other elements of material cul- ture as well as patterns of settlement systems and, particularly, of burial practices which fit with the pot- tery classification very well (compare Włodarczak 2017). Thus, we are entitled to assume that in great measure this pottery classification reflects actual past divisions and categorisations. In the early part of the period considered we are dealing with entities that belong to the last stage of the so-called Lengyel-Polgár complex (L-PC). The term is applied to groups that developed in the 5 th millennium and in the first half of the 4 th millen- nium BC, in the basins of the Vistula and Oder rivers (e.g., Kamieńska, Kozłowski 1990). These groups were subjected to very strong influences from the Carpathian Basin, reflected primarily in pottery. However, from the perspective of other elements of material culture, settlement, economy, and the as yet few genetic analyses (Lorkiewicz et al. 2015; Ju- ras et al. 2017), they show evident connections with the first Neolithic culture in central Europe, the Li- near Band Pottery culture (LBK). For this reason, they are thought to have formed a later part of the same cultural continuum, denoted as so-called Danu- bian Neolithic, to apply Gordon Childe’s (1929.220) terminology. In Polish regions, apart from the Linear Band Pottery culture and Lengyel-Polgár complex, the Stroke Band Pottery culture is also usually in- Fig. 1. Territory of western Lesser Poland and the main archaeological units in the late 5 th , 4 th and early 3 rd mil- lennia BC: 1 borders of the area discussed in the paper; 2 sites of the Lublin-Volhynian culture; 3 the Wyciąże-Złotni- ki group; 4 the Funnel Beaker culture (a dense settlement typical of ‘loess’ upland; b more dispersed settlement typical of foothills, alluvial plains/basins and ‘jurassic’ zones; c highly dispersed set- tlement typical mainly of mountainous zone); 5 sites with the Wyciąże/Niedźwiedź materials; 6 the Baden cul- ture, 7 the Beaker/Baden as- semblages; 8 Corded Ware cul- ture (a relatively dense settle- ment typical mainly of ‘loess’ upland; b highly dispersed set- tlement typical of other ecolo- gical zones). Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 243 cluded in the Danubian Neolithic. However, it is not represented in the region under consideration. The- refore, the ultimate disappearance of the Lengyel- Polgár complex in Lesser Poland is in fact the ulti- mate disappearance of the continuous development of the Danubian Neolithic, which lasted from approx. the mid-6 th millennium BC to approx. the mid-4 th millennium BC. The late Lengyel-Polgár units in western Lesser Po- land comprise the Wyciąże-Złotniki group (W-ZG) (Fig. 2) and the Lublin-Volhynian culture (L-VC) (Fig. 3), or rather its westernmost extent, to be more pre- cise (Fig. 1) (Kadrow, Zakościelna 2000; Nowak 2009; 2014; Zakościelna 2010). The central part of our timeframe is characterised by the presence of the Funnel Beaker culture (TRB) (Figs. 4–5). This culture constitutes a quite new cultu- ral tradition, being the outcome of complicated in- teractions between the later Danubian Neolithic and still ‘non-Neolithised’ late Mesolithic societies, which took place in the south-western Baltic zone in the late 5 th millennium BC (e.g., Kabaciński et al. 2015). In lowland parts of central Europe, it indicates the further development of the Neolithic, connected on the one hand with Eneolithisation processes, but on the other, with the inclusion of late hunter-gatherer populations in the Neolithic way of life (‘second stage of neolithisation’ – Nowak 2009). The Funnel Beaker culture differs from the Danubian Neolithic not only in pottery. Sites of this culture are dispersed more evenly in the landscape, i.e. communities of this cul- ture settled and utilised almost all ecological zones (Fig. 1). A number of other factors also make a diffe- rence from the Danubian Neolithic, such as: i) the emergence of big settlements with an area of 20– 40 hectares, ii) the appearance of monumental bur- ial structures, and iii) the exten- sive pattern of agriculture of the slash-and-burn type (Kruk, Mili- sauskas 1999; Milisauskas, Kruk 1984). As a consequence of the latter factor, we have clear signs of the human transformation of the environment, mainly of de- forestation. Certainly, the emer- gence of this culture in western Lesser Poland was associated with an impact from the Polish Low- land zone. The balance between cultural transmission and migra- tion within this impact remains a matter of speculation. The last part of the period un- der discussion is characterised by phenomena connected with the Baden culture (BaC) (Fig. 6), which was a unit covering basi- cally the whole of the middle Da- nube basin. The Baden phenom- ena have an important position in the Late Eneolithic of east-cen- tral Europe, and not only because of their new ceramics. There are many new elements in settlement and economic patterns and in fu- neral rites; these can be linked to new social structures, both in the horizontal and vertical dimen- sions. For many reasons, the Ba- den cultural model must have Fig. 2. Selected pottery of the Wyciąże-Złotniki group: 1–5 Podłęże 17 (from Nowak et al. 2007); 6–13 Złotniki (from Dzieduszycka-Machni- kowa 1966). Marek Nowak 244 been attractive. This factor makes it is possible to ex- plain the relative cultural unification of almost the whole Carpathian Basin and some of the surround- ing areas in the period c. 3600–2900 cal BC. This had also to be the reason for the enthusiastic accep- tance of Baden patterns in regions situated far to the north of the middle Danube basin. This is visible in the new fashion in pottery, but also in other ele- ments, such as the enlargement of some settlements, fortifications and collective burials. The term ‘Baden phenomena’ is used here because – as a matter of fact – at least three versions of the ‘Ba- denian’ materials can be distinguished in Lesser Po- land (Fig. 1). Firstly, we are dealing with the Baden culture proper (Fig. 6) in a small area in and around Kraków (Zastawny 2015a). Secondly, features of the Baden culture can easily be noticed within the late Funnel Beaker materials. This is evident prima- rily in ceramics, but not only in western Lesser Po- land. However, only there did the Baden ceramic style became extremely popular within local late Fun- nel Beaker communities. This fashion was accepted so enthusiastically and en masse that at least some archaeologists have discerned a quite separate local cultural unit called Beaker/Baden assemblages (TRB/ BaC, B/BA on Figs. 18, 21) (Fig. 7), in the more eastern part of the area under consideration (Kruk, Milisauskas 1999; Milisauskas, Kruk 1989). Thirdly, we are also dealing with materials that com- bine some late Lengyel-Polgár, Baden and possibly Funnel Bea- ker features. They are referred to by different terms; there is no uni- versal agreement on this matter (Burchard 1977; Godłowska 1979.305–306; Kozłowski 1971; 1989b; Włodarczak 2008b; 2013; Zastawny 2011). The notion of ‘materials of the Wyciąże/Niedź- wiedź type’ (in a shorter, more convenient, version: ‘Wyciąże/ Niedźwiedź materials’) will be used in this contribution (Fig. 8) The development of Funnel Bea- ker culture and Baden phenom- ena (the Middle Neolithic devel- opment) seems to end with the appearance of the Corded Ware culture (CWC). It is obviously de- fined again by new ceramics, but frequently appear in unprece- dented forms of funeral rites (barrows and niche graves). This culture, including its branch known from southern Poland, is quite commonly considered to be evidence of nomadic, pastoral po- pulations. In contrast to previous Neolithic communities, their so- cial structure was distinguished by a greater social stratification. The ruling social stratum, endow- ed with privileges, would have Fig. 3. Collective grave of the Lublin-Volhynian culture at Bronocice (A) and pottery found there as grave goods (B) (from Kruk, Milisau- skas 1985). A B Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 245 been a stratum of adult men, warriors, who were buried under barrows (Włodarczak 2006a). There are more and more indications, including genetic ones (Allentoft et al. 2015; Haak et al. 2015), that the genesis of the Corded Ware culture in central Eu- rope was associated with western migrations from the steppe and forest-steppe zone of eastern Europe. Until around 2005, views on the absolute chronolo- gy of Middle Neolithic units in Lesser Poland were defined rather vaguely. Fairly general terms were in use, such as first or second half of the millennium, the beginning of the millennium, the middle part of the millennium, etc. These views were based first and foremost on typological premises and around 40 radiocarbon dates. Available 14 C dates were un- evenly distributed between archaeological groupings. Actually, most originated from one site of the Fun- nel Beaker culture and Beaker/Baden assemblages, i.e. from Bronocice (Kruk, Milisauskas 1983; 1990). Hence, it was difficult to make a reasonable, both de- tailed and more holistic description of absolute chro- nology. However, in recent years there has been a signifi- cant increase in the number of radiocarbon dates of the Middle (and Late) Neolithic in western Lesser Poland (Fig. 9). At present, there are over 150 dates (Tab. 1 is available at http://dx.doi.org/10.4312/ dp.44.15). More importantly, the first series of dates have been obtained for units previously almost de- prived of absolute dates, such as the Wyciąże-Złot- niki group, Lublin-Volhynian culture, and Baden cul- ture, as well as Wyciąże/Niedźwiedź materials. For this reason, it seems necessary to make a new esti- mate of the absolute chronology of this segment of the Neolithic in western Lesser Poland, making use of Bayesian modelling, among other things. Fig. 4. Pottery of the earliest Funnel Beaker culture at Bronocice (phase BR I) (from Kruk, Milisauskas 1990). Marek Nowak 246 Descriptions of all the dates used for their credibi- lity are demonstrated in Table 1, available online at http://dx.doi.org/10.4312/dp.44.15. Of course, these dates are very different in this regard. Those obtain- ed by the early 1980s usually have large standard errors and come from not very evident contexts. However, some newer dates do have the same draw- backs. On the other hand, quite a lot of our collec- tion has a high degree of credibility, i.e. dates with small standard deviations obtained from bones or short-lived plants from a certain cultural context. Taking all of this into account, it was decided to con- duct chronological analysis in three variants. The first is based on all dates; the second is based on dates with standard deviations of less than 100 years which originate from a confirmed context; this group of dates is denoted as group B (see Table 1, available online at http://dx.doi.org/10.4312/dp.44. 15). The third variant is based exclusively on dates originating from the same confirmed context, but obtained only on bones and short-lived plants; such dates are labelled as group A (see Table 1, available online at http://dx.doi.org/10.4312/dp.44.15). Direct dating In the case of the Lublin-Volhynian culture in west- ern Lesser Poland, we had until recently only one radiometric date from the Bronocice site (Tab. 1.4, available online at http://dx.doi.org/10.4312/dp.44. 15), with a very broad standard deviation of 240 years (Kruk, Milisauskas 1985). Fortunately, three other dates (Tab. 1.1–3, available online at http:// dx.doi.org/10.4312/dp.44.15) obtained on bones from the same site were published in 2016 (Kruk et al. 2016; Milisauskas et al. 2016). Overall, all these dates formally cover a time range from c. 3950 to 3350 cal BC (Tab. 2; Fig. 10). For three dates of group B and also A, this range is almost the same: c. 3950– 3380 cal BC. Similarly, for the Wyciąże-Złotniki group, only one 14 C date had been obtained before 2009, from the site of Złotniki (Tab. 1.15, available online at http:// dx.doi.org/10.4312/dp.44.15), of not very high va- lue. 2 2 This unit could also be associated with a date obtained from the palynological profile at Kraków- Pleszów (Tab. 1.5, available online at http://dx.doi. org/10.4312/dp.44.15) (Wasylikowa et al. 1985.53; Godłowska et al. 1987.137). However, the number of radiocarbon dates of this group has recently increas- ed due to archaeological investigations on road works (Tab. 1.6–14, available online at http://dx.doi.org/ 10.4312/dp.44.15). All these dates formally cover a time range from c. 4300 to 3500 cal BC (Tab. 2; Fig. 11). The range for six dates included in group B has the same lower limit, while the upper is about 350 years earlier (Tab. 2). No date met group A require- ments. To the Funnel Beaker culture in western Lesser Po- land, we can attribute 59 radiocarbon dates (Tab. Fig. 5. Selected pottery of the Funnel Beaker culture: 1–4 Mozgawa (unpublished, drawn by M. Kor- czyńska); 5–7 Kraków-Prądnik Czerwony (from Rook, Nowak 1993). 2 In addition, this date is, unfortunately, often quoted with an incorrect standard deviation as 4810±120 BP (e.g., Kozłowski 1989a. 198; Kamieńska, Kozłowski 1990.85; Nowak 2009.137 – mea culpa). Its actual value is 4810±200 BP (Crane, Griffin 1970.177). Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 247 1.16–74, available online at http://dx.doi.org/10.43 12/dp.44.15). Formally, all of them outline the time span of c. 3700–3250 cal BC (Tab. 2; Fig. 12). The dates of groups B and A provided results with upper limit slightly moved down to 3280 and 3270 cal BC, respectively. At this point, an important issue must be explain- ed. In the case of the site at Bronocice, some of the radiocarbon dates attributed in the literature to the Funnel Beaker culture are from graves. However, identifying the cultures of most of these graves found there is very difficult due to a complete absence of grave goods. For this reason, we cannot be sure whether such graves should be associated with the Funnel Beaker or with Beaker/Baden phases of the settlement. If we compare consecutive publications, we see differences in this classification. There are even differences between the chapters of the same publications (compare, for example, Table 4 on p. 51 and Table 1 on p. 57 in Milisauskas et al. 2016). For this reason, a chronological evaluation of nine graves in which grave goods were not found, includ- ing Bayesian modelling (see below for a description) was performed (Tab. 2, Fig. 13). It follows that we are dealing here with three chronological horizons. The first is placed around 3700 cal BC and is repre- sented by grave no. XX. The second is situated be- tween c. 3500 and 3350 cal BC and is represented by graves no. XIV and XVIII. Finally, the third hori- zon is dated to c. 3350–2900 cal BC; graves no. VII, VIII, XV, XVI, XXIII and XXIX should be in- cluded in it. On the basis of this classification, the last group of graves was added to the Beaker/ Baden assemblages, while graves XIV, XVIII and XX were rated as connected with the Funnel Bea- ker culture. We are aware that this categorisation does not fully accord with the proposals of Kruk and Milisauskas (Kruk et al. 2016; Milisauskas et al. 2016), especially the transfer of graves VIII and XV to the Beaker/Baden assemblages. Nevertheless, we be- lieve that the presented model- ling gives the proposed categori- sation a good basis. Accordingly, dates from grave XIV, XVIII and XX were included in the group of all dates of the Funnel Beaker culture, while the remaining dates are from graves with Beaker/Ba- den assemblages. This arrange- ment will also be valid in the Ba- yesian modelling for all dates in other parts of the contribution. On the other hand, all nine dates were excluded from groups B and A, despite the fact that they were obtained from human bones. After all, we have to bear in mind that the above modelling of dates from these nine graves is merely an indirect indication of their cul- tural context. Fig. 6. Selected pottery of the Funnel Beaker culture (1) and Baden cul- ture (2–7) at Kraków-Prądnik Czerwony (from Rook, Nowak 1993). Marek Nowak 248 Three dates, which can be linked to the Wyciąże/ Niedźwiedź materials (Tab. 1.75–77, available online at http://dx.doi.org/10.4312/dp.44.15), indicate the interval of c. 3500–3000 cal BC (Tab. 2; Fig. 14); these dates meet the requirements of both group B and A. Until recently, because of the scarcity of radiocarbon dates one could encounter quite diverse views on the absolute chronology of the Baden culture in western Lesser Poland. However, quite a large num- ber of dates obtained in the past few years (Tab. 1.78–103, available online at http://dx.doi.org/10.43 12/dp.44.15) (Zastawny 2015b) allow us to set it in a relatively reliable way. The time span formally co- vered by all 26 dates should be estimated to c. 3100– 2800 cal BC (Tab. 2; Fig. 15). Interestingly, the same timeframes have been obtained in the case of 24 dates connected to group B and 19 dates classified as group A. The absolute chronology of the Beaker/Baden as- semblages can be analysed first and foremost on the basis of data from one site, Bronocice (Tab. 1.104– 127, available online at http://dx.doi.org/10.4312/ dp.44.15) (Kruk, Milisauskas 1990; Kruk et al. 2016; Milisauskas et al. 2016). To this set we should pos- Fig. 7. Selected pottery of the Beaker/Baden assemblages at Bronocice: 1–10 feature 2-B2; 11–28 feature 1-A5 (from Kruk, Milisauskas 1990). Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 249 sibly add two dates from Szarbia, a site located nearby (Tab. 1.128, 129, available online at http://dx. doi.org/10.4312/dp.44.15) (Wło- darczak 2013.379). Formally, all these 26 dates define a fairly wide interval of c. 3350–2650 cal BC (Tab. 2; Fig. 16). On the other hand, the intervals based on dates includ- ed in groups B and A are shorter, being c. 3350– 2790 cal BC and c. 3370–2900 cal BC, respectively. In both cases, the upper limit moved down, by 140 and 250 years. Regarding the Corded Ware culture, we are interested mainly in dating its origins and early stages as a background to the declining devel- opment of the previously discus- sed units. But to do so, we must use all the dates from this culture. The absolute chronology can be deter- mined on the basis of 24 radiocar- bon dates (Tab. 1.130–153, avail- able online at http://dx.doi.org/10. 4312/dp.44.15) (Jarosz, Włodar- czak 2007; Tunia, Włodarczak 2002; Włodarczak 2006a). Formal- ly, all these dates cover the period between c. 2700 and 2280 cal BC (Tab. 2; Fig. 17). The timeframes for groups A and B are c. 2650–2330 cal BC and 2630–2300 cal BC, res- pectively. By and large, radiocarbon dates, treated directly, with no modelling, support views in light of which local branches of the late Lengyel-Polgár complex, the Funnel Beaker culture and the Baden phenome- na overlap chronologically to a great extent. Admit- tedly, they are not always consistent with views based on individual (the earliest and/or the latest) dates or results from typological premises and stratigraphic observations. Separate modelling In order to determine the most precise chronologi- cal frameworks of the discussed archaeological units possible, Bayesian model simulations were perform- ed in which dates obtained for discussed archaeolo- gical units (in three groups specified above) were treated as if they constitute one phase (see ‘Intrduc- tion’). The chronological data obtained from all of these procedures were analysed and compared. As a result, we decided to discern four kinds of interval based on the properties of generated boundaries (Tab. 2): i) as the interval based on median values; ii) as the widest possible interval, based on extreme points of the 95.4% ranges; iii) as the ‘probable’ 3 3 interval, based on extreme points of the 68.2% ran- ges; and iv) as the narrowest possible interval, based on the end point of the 95.4% start boundary and the start point of the 95.4% end boundary. However, the last version may be impossible to calculate. Fig. 8. Selected pottery of the Wyciąże/Niedźwiedź materials at Nied- źwiedź (from Burchard 1977). 3 After, for example, Krus et al. 2015.971, who use this term for 68.2% probability – “Activity associated with Group 1 on the site is estimated to have ended in calAD 1295–1465 (95% probability; Figure 6; End: SunWatch: Group 1), and probably in calAD 1305–1405 (68% probability)”. Fig. 9. Archaeological sites with 14 C dates used in the paper: 1 borders of the area discussed in the paper; 2 sites of the Wyciąże-Złotniki group and Lublin-Volhynian culture (only Bronocice); 3 sites of the Funnel Beaker culture; 4 sites of the Baden culture and Wyciąże/Niedź- wiedź materials (only Kra- ków-Wyciąże and Smroków); 5 sites of the Beaker/Baden assemblages; 6 sites of the Corded Ware culture; BR Bronocice, GB Gabułtów, GD Gdów, IW Iwanowice, JW Jawczyce, KM Kamiennik, KL Kolosy, KN Koniusza, K-B Kraków-Bieżanów, K-M Kra- ków-Mogiła 55, K-P Kraków- Pleszów 17: settlement and palinological profile, K-PC Kraków-Prądnik Czerwony, K-WT Kraków-Witkowice, K- WC Kraków-Wyciąże 5, K-Z Kraków-Zesławice 21 and 22, LL Lelowice, ŁP Łapszów, ML Malżyce 30 and 31, MI Miernów, MD Modlnica 1 and 5, MZ Mozgawa, ND Niedźwiedź, PŁ Pełczyska, PD Podłęże, PR Proszowice, SK Sokolina, SŁ Słonowi- ce, SM Smroków, ST Stręgoborzyce, SZ Szarbia, ZG Zagórze, ZL Zielona, ZT Złotniki, ZF Zofipole (for refe- rences see Table 1, available online at http://dx.doi.org/10.4312/dp.44.15). Marek Nowak 250 The model for the Lublin-Volhynian culture based on four dates from Bronocice is statistically signifi- cant, as are all the individual dates (Fig. 10), but gives a very broad time range (Tab. 2). At maximum span it gives 4460–2760 cal BC. ‘Probable’ values are 4000 and 3290 cal BC, whereas the ‘median’ in- terval is 3890–3400 cal BC. The shortest version of the chronology amounts to only 20 years, i.e. 3650– 3630 cal BC. Somewhat surprising is the fact that the intervals for three dates of group A and – simultane- ously – B turned out to be even longer by several do- zen years. Modelling of the 11 dates of the Wyciąże-Złotniki group also proved to be statistically significant, as did all the particular dates (Fig. 11). Again, this mo- delling allows us to accept a very large time inter- val, maximally 4530–3300 cal BC, and in the ‘prob- able’ version 4400–3480 cal BC. The narrowest ver- sion is demarcated by 4120 and 3640 cal BC, and the ‘median’ by 4310 and 3530 cal BC (Tab. 2). The above values obtained from direct dating are simi- lar to the ‘median’ ones. The modelling of group B dates gives intervals shorter by several dozen to two hundred years. The upper limit moves down fairly significantly, to 3690/3940 cal BC, except the widest interval value. Modelling of 59 dates of the Funnel Beaker culture (Fig. 12) gives the time interval of 3730–3230 cal BC, in the longest version, and the ‘probable’ inter- val of 3700–3270 cal BC. The shortest version is 3650–3330 cal BC, and the ‘median’ version is 3680– 3290 cal BC (Tab. 2). None of the intervals differ sig- nificantly from direct dating. The model for the TRB is statistically significant, but the level of agreement drops below 60% in the case of the two earliest dates from Bronocice and the latest date from Mozgawa (Fig. 12). As a comment on this observation we quote a sentence from the classic paper by Christopher Bronk Ramsey (2009b.1025): “[…] secondly, an overall agreement index is calculated A model and if this is above 60% it probably indicates that there is no problem with the model as a whole (and the- refore no samples need be rejected)”. The chronological limits modelled on 47 dates of group B do not indicate major differences; they Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 251 Archaeological units< categories of 14 C Sum 1 Interval based The widest The ‘probable’ The narrowest dates (their amounts)< agreement on medians interval interval interval indices(A overall and A model ) Lublin-Volhynian culture< all dates (4)< 101.6%, 100.3% c. 3950–3350 3890–3400 4460–2760 4000–3290 3650–3630 Lublin-Volhynian culture< dates of group B = dates of group A 2 (3)< c. 3950–3380 3930–3390 4670–2590 4070–3260 3660–3630 97.6%, 97.4% Wycia ˛z ˙e-Zl ⁄otniki group< all dates (11)< 98.5%, 99.5% c. 4300–3500 4310–3530 4530–3300 4400–3480 4120–3640 Wycia ˛z ˙e-Zl ⁄otniki group< dates of group B (6)< 88.3%, 88.0% c. 4300–3850 4290–3770 4600–3460 4380–3690 4070–3940 Funnel Beaker culture< all dates (59) 76.2%, 74.2% c. 3700–3250 3680–3290 3730–3230 3700–3270 3650–3330 Funnel Beaker culture< dates of group B (47)< 80.9%, 70.7% c. 3700–3280 3680–3280 3720–3200 3690–3260 3640–3330 Funnel Beaker culture< dates of group A (34)< 79.6%, 79.6% c. 3700–3270 3680–3290 3750–3210 3700–3260 3650–3340 Funnel Beaker culture< Bronocice c. 3900–3650 graves (9)< 91.8%, 92.0% and 3800–2870 4090–2580 3880–2790 3650–3080 c. 3520–2850 Wycia ˛z ˙e\Niedz ´wiedz ´ materials< all dates = dates of group B = dates of c. 3500–3000 3330–3130 3810–2700 3410–3030 – group A (3)<104.2%, 104.1% Baden culture< all dates (26) 74.6%, 76.7% c. 3100–2800 3070–2830 3130–2780 3100–2810 2990–2870 Baden culture< dates of group B (24)< 72.9%, 70.8% c. 3100–2800 3070–2830 3140–2780 3110–2810 2990–2870 Baden culture< dates of group A (19) 67.6%, 67.2% c. 3100–2800 3060–2820 3130–2770 3100–2800 2980–2870 Funnel Beaker\Baden assemblages< all dates (26)< 104.5%, 104.0% c. 3350–2650 3280–2770 3400–2610 3360–2720 3150–2870 Funnel Beaker\Baden assemblages< dates of group B (15)< 106.6%, 106.7% c. 3350–2790 3250–2790 3420–2610 3320–2730 3120–2880 Funnel Beaker\Baden assemblages< dates of group A (6)< 66.2%, 67.2% c. 3370–2900 3310–3030 3560–2630 3390–2850 – Corded Ware culture< all dates (24)< 64.7%, 63.6% c. 2700–2280 2670–2330 2800–2240 2720–2280 2580–2420 Corded Ware culture< dates of group B (21)< 99.9%, 98.0% c. 2650–2330 2630–2330 2710–2260 2660–2290 2580–2420 Corded Ware culture< dates of the A group (20)< 84.4%, 81.3% c. 2630–2300 2550–2360 2670–2270 2620–2310 2470–2460 1 Sum-calibrated intervals were delineated through excluding onset and tail sections of the very low probability density. 2 For characteristics of groups B and A and dates assigned to them see Table 1, available at http>\\dx.doi.org\10.4312\dp. 44.15. Tab. 2. Results of direct dating (sums) and of separate modelling of 14 C dates of the Middle and Late Neolithic units in western Lesser Poland (cal BC; rounded by 10 years). amount to no more than 30 years. The same applies to group A (34 dates); in this case, the time differ- ences do not exceed 20 years. Apart from the ear- liest date from Bronocice, which does not comply with the requirements of groups A or B, the same other two dates have agreement indices below 60%. In all versions, the differences from the sum-calibrat- ed intervals are low; only in the case of the narrow- est interval do they increase to 60/80 years. Although we have only three dates which can be con- nected with the Wyciąże/Niedźwiedź materials, the agreement indexes of modelling are above 60% (Fig. 14). The widest time interval is 3810–2700 cal BC; Marek Nowak 252 the ‘probable’ interval is 3410–3030 cal BC and the ‘median’ is based on 3330–3130 cal BC. The narrow- est version cannot be calculated (Tab. 2). As may be recalled, these three dates fit groups A and B. As a result of modelling (Fig. 15), the time span co- vered by the 26 dates from the Baden culture is con- sistent and relatively short (only one, the latest date, does not fit the model). It is delimited at 3130 cal BC and 2780 cal BC in the widest version, at 3100 and 2810 cal BC in the ‘probable’ version, at 2990– 2870 cal BC in the narrowest version, and at 3070– 2830 cal BC in the ‘median’ version. The values of direct dating are almost literally consistent with the ‘probable’ version (Tab. 2). The same can be said of the timeframes modelled on dates belonging to groups A and B; the differences amount to 10 years. As we already know, the absolute chronology of the Beaker/Baden assemblages can be analysed on the basis of 24 dates from Bronocice and 2 dates from the nearby site of Szarbia. The model for all dates is characterised by high levels of significance (Tab. 2; Fig. 16). All these dates define the widest interval as 3400–2610 cal BC. The ‘probable’ interval covers 3360–2720 cal BC (and this is almost exactly the same interval as that resulting from direct dating), whereas the narrowest one is 3150–2870 cal BC, and the ‘median’ one 3280–2770 cal BC (Tab. 2). Some values in the model based on 15 group B dates differ by no more than 40 years. On the other hand, the model generated by 6 dates in group A yields larger differences. Moreover, the values of the ‘me- dian’ (3310–3030 cal BC) and ‘probable’ (3390– 2850 cal BC) intervals are generally older. The possible dates of the beginning of the Corded Ware culture resulting from statistically significant modelling of all dates are: 2800, 2720, 2580 and 2670 cal BC (Tab. 2; Fig. 17). The corresponding va- lues for groups B and A are clearly younger. They are respectively: 2710/2670, 2660/2620, 2580/2470 and 2630/2550 cal BC. Our analyses give rise to the two basic interpreta- tions of an extreme character (Fig. 18). Firstly, we can accept the whole time or most of the time generated by the modelling procedures. In this case, all archaeological units more or less formally mesh together in time. Secondly, we can take into account only the short segments of chronological range and reject the re- maining parts of these ranges. In this case, the archa- eological units would have been arranged roughly into two groups (consisting of contemporary units), and two single units. These four groupings would be ordered linearly, but there would be even breaks in the continuity of cultural development. This scena- rio goes to some extent back to the linear (traditio- nal) vision of the development of archaeological units. One group would consist of the Lublin-Volhynian culture, the Wyciąże-Złotniki group and Funnel Bea- ker culture. The Wyciąże-Złotniki group would per- haps appear earlier, around 4100 BC, while the Lub- lin-Volhynian culture would appear around 3700 cal BC. These two units would disappear around 3600 cal BC. The Funnel Beaker culture would appear at c. 3700/3650 cal BC, so it would (partly) overlap with former units in the 37 th century BC. This culture would vanish around 3300/3250 cal BC. Another group would comprise the Baden culture and Beaker/Baden assemblages, and would be gene- rally dated to the 31 st , 30 th and part of the 29 th cen- Fig. 10. Radiocarbon chronology (cal BC) of the Lublin-Volhynian culture (L-VC). The OxCal 4.3.2 pack- age was used for all calibrations and models (Bronk Ramsey 2009a; online; Reimer et al. 2013). Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 253 turies BC, with possible earlier start of the latter unit (c. 3250 cal BC). The Wyciąże/Niedźwiedź materials would be dated to c. 3350–3100 cal BC, which would fill the poten- tial gap between the Funnel Beaker and the Baden cultures in the Kraków region in the late 33 rd and in the 32 nd centuries BC. A hiatus could also be postu- lated between the second group and the Corded Ware culture, around 2800–2650/2600 cal BC. Combined modelling In our next step, Bayesian models based on 153, 119 (group B) and 85 (group A) dates, were constructed using several relationships resulted from typological data, stratigraphic observations and general knowl- edge about Neolithic development in east-central Europe (priors). Holistic modelling is justified, be- cause the archaeological units under considerations can depend on each other, both chronologically and territorially. Such dependencies do not appear in the separate modelling. In this arrangement, “results must be seen as dependent on the assumptions built into the chronological framework” (Bronk Ramsey 2009b.348). The aforementioned relationships are as follows: Firstly, some stratigraphic observations on a few sites indicate that Lengyel-Polgár units had to be at least partially coeval with, or even later than, the early stages of the Funnel Beaker culture (Kaczanowska 1976; Kruk, Milisauskas 1985). These observations, however, do not refer to radiocarbon dated fea- tures. Stratigraphic dependencies in Bronocice demon- strate that the earliest phase of the local Funnel Bea- ker culture (phase BR I) had to be older than the lo- cal Lublin-Volhynian culture (Kruk, Milisauskas 1985). Alas, this rule can be utilised only in model- ling based on all dates, because the only date of the BR I phase does not meet the requirements of groups B and A. To be clear, there are also situations of an opposite kind in Bronocice, i.e. some Lublin-Volhy- nian features are older than Funnel Beaker features belonging only to phases BR II or BR III. Secondly, a comparison of general chronologies of the Funnel Beaker culture and Baden culture (No- wak 2009; Zastawny 2015a) suggests that the rela- tionship between them is non-linear and assumes pa- rallelism in the second half of the 4 th millennium BC. Thirdly, in case of the beginnings of the Funnel Bea- ker culture, we decided to replace ‘boundary’ with ‘sigma boundary’. This was done primarily so as to include the possible pattern of the local development of this unit, i.e. its quantitatively modest and con- spicuously early beginnings (Nowak 2009). Fourthly, some stratigraphic relations in Bronocice (see Table 1, available online at http://dx.doi.org/ Fig. 11. Radiocarbon chronology (cal BC) of the Wyciąże-Złotniki group (W-ZG); K-P Kraków-Pleszów, palynological profile, PR Proszowice, ZT Złotniki. Marek Nowak 254 Fig. 12. Radiocarbon chronology (cal BC) of the Funnel Beaker culture (TRB). Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 255 10.4312/dp.44.15) demonstrate younger chronology of the Beaker/Baden assemblages when compared to the Funnel Beaker culture, as well as their typolo- gical continuity. The typological data also suggest close continuity between the Wyciąże-Złotniki group and Wyciąże/Niedźwiedź materials. Hence, a ‘transi- tional boundary’ was used in these positions. Fifthly, no elements within the materials of the Cord- ed Ware culture in western Lesser Poland can be de- rived from other units (Włodarczak 2008b; 2011). Consequently, we believe that this culture quite radi- cally closed the earlier development and, therefore, is radically separated from earlier units. In all models constructed under these assumptions, both indexes of agreement are over the threshold value of 60% (Tab. 3; Fig. 19). Three dates ‘drop’ below 60% in the case of the ‘all dates model’ and ‘group B model’; in the case of the ‘group A model’ there are five such dates. Therefore, we can easily take these models as a basis for further analyses and interpretations. Their results have been presented in the same way as for separate modelling (Tab. 3). For the Lublin-Volhynian culture, we obtained 3990– 3100 cal BC in the widest version. The ‘probable’ va- lues are 3870 and 3360 cal BC, whereas the ‘medi- an’ ones are 3810 and 3470 cal BC. The narrowest interval covers only 3690–3630 BC. These values are shorter than those obtained in separate model- ling, except for the narrowest one. In the modelling of group B, as expected, the origins are earlier, even by over 300 years for the widest interval. By con- trast, in group A, the results are virtually identical to the modelling for all dates; differences do not ex- ceed 30 years. As for the Wyciąże-Złotniki group, modelling for all dates allows us to accept a very large time interval, the maximal version being 4460–3270 BC, and the ‘probable’ version 4370–3340 cal BC. The dates of 4110 and 3630 BC make the narrowest interval, and 4290 and 3440 cal BC the ‘median’ one. Modelling for the dates of group B gives similar values (a diffe- rence of no more than 50 years), except the narrow- est interval, which ends 270 years earlier. There are some differences with separate modelling of several dozens or over one hundred years. Interestingly, the intervals generated in combined modelling are usu- ally not shorter. Regarding the Funnel Beaker culture, its earliest phase in Bronocice can be placed at the turn of the 5 th and 4 th millennia BC, or in the first quarter of the 4 th millennium BC, as modelled on the basis of one date from the Bronocice phase BR I. Unfortuna- tely, this is the only date of this phase, and is of re- latively low reliability. The other values for the Funnel Beaker culture are very similar in all three models. The widest intervals Fig. 12. Continue ... Marek Nowak 256 covers the period of c. 3550/3530–3280/3270 cal BC, the ‘probable’ intervals 3510/3500–3300/3290 cal BC, the narrowest intervals 3490/3430–3340, and the ‘median’ intervals 3490/3480–3310 cal BC. Overall, consequently, the Funnel Beaker culture ends several decades earlier than in previous mod- els, except the narrowest interval. The values of the beginning of the Funnel Beaker culture should be calculated in a slightly different way due to the other type of distribution used, as we already know. In the ‘sigma boundary’/‘boundary’ distribution start dating, c. 3500 cal BC should be considered as the beginning of more intensive deve- lopment. We have to bear in mind that the agreement index- es of the two earliest dates of the Funnel Beaker cul- ture (DIC-719, AA-90115, see Table 1.16–17) in se- parate modelling (Fig. 12) were lower than 60%. A situation of this kind can be interpreted in two ways. Either these dates are typical deviations from the norm, appearing in numerous datasets due to the laws of statistics, or they reflect the earliest epi- sode of the presence of a given phenomenon that was isolated in time in relation to the main, conti- nued development. Since the whole model was stati- stically significant, we could in theory believe that the first alternative is more likely. Regardless, a date DIC-719, approach of this kind can also be defended for another reason. It has been proposed that in the pottery from feature 5-B6 at Bronocice (with the above-mentioned date) elements of the Lengyel-Pol- gár complex are visible (Kruk, Milisauskas 1983. 267, 282). If this is the case, it is possible even to accept the idea that the date should not be bound to the TRB at all. On the other hand, in the combined modelling, the agreement indexes of these two dates were higher than 60%, so we can say that the pattern of quanti- tatively modest and conspicuously early beginnings was tested successfully. Therefore, it should be recog- nised that dates earlier than 4900 cal BP in poste- riori version are close to reality (Fig. 20). In this case, the first Funnel Beaker culture occupation probably began around 3750 cal BC, due to the uncertainty of the date DIC-719. The widest time interval for the Wyciąże/Niedźwiedź materials is 3630–2860 cal BC, the ‘probable’ inter- val is 3570–3040 cal BC, and the ‘median’ based in- terval gives 3440–3140 cal BC. It is not possible to calculate the narrowest interval. There are no bigger differences in the case of the group A modelling, whereas the start is placed 200/300 years earlier in the group B modelling. Differences appear with se- parate modelling, which are particularly visible in the group B modelling (over 100 years). The Baden culture turned out to be delimited simi- larly in all models. We obtained 3130–2790/2780 cal BC in the widest versions, 3110/3100–2810 cal BC in ‘probable’ versions, 3000/2980–2870 cal BC in the narrowest versions, and 3070/3060–2830 cal BC in ‘median’ versions. The differences between se- parate models are negligible. Fig. 13. Radiocarbon chronology (cal BC) of graves without grave goods at Bronocice. Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 257 The models for the Beaker/Baden assemblages give the widest intervals, of 3340–2770/2690 cal BC, the ‘probable’ interval of 3330–2850/2750 cal BC, and the narrowest of 3280/3270–2880/2870 cal BC (for all dates and group B). The ‘median’ interval covers a period of 3310–3030/2790 cal BC, i.e. there is a significant difference as to the upper limit. We ob- serve differences with separate modelling up to over one hundred years. The possible dates of the beginning of Corded Ware culture are: 2740/2670, 2700/2620, 2590/2500 and 2660/2570 cal BC (Tab. 2). Except the values for the widest interval and all dates (2800 cal BC), they are quite similar to those modelled separately. A summary of this modelling again gives rise to two basic interpretations of the type analogous to the se- parate modelling (Fig. 21). Firstly, we can accept the whole period or most of the period generated by modelling procedures. In this case, archaeological units mesh together in time to a greater or lesser extent, but generally two con- centrations of coeval units can be noticed. The Wyciąże-Złotniki group would appear at c. 4400 cal BC, and would coexist with the Lublin-Volhynian cul- ture from c. 4300/4000 BC to c. 3250 cal BC. The latter unit would exist longer, until the 31 st centu- ry BC. The Funnel Beaker culture would appear to a small extent between 4350 and 4100 cal BC, but would develop substantially from c. 3750 to 3250 cal BC. In the period c. 3900/3800–3250 cal BC we could postulate the co-existence of even four units, because Wyciąże/Niedźwiedź materials would join the remaining ones. The latter unit would exist until c. 2900/2800 cal BC. At around 3350/3300 cal BC, the Beaker/Baden as- semblages would appear, i.e. it would briefly coexist with the Funnel Beaker culture and Wyciąże-Złotni- ki group (approx. 100 years) and – for a longer time – with the Lublin-Volhynian culture and Wyciąże/ Niedźwiedź materials. On the other hand, from c. 3150/3100 to 2800/2750 cal BC, Beaker/Baden as- semblages would develop simultaneously with the Baden culture. The overlapping of the Beaker/Ba- den assemblages and Corded Ware culture would be limited only to the second half of the 28 th century BC, but it could not have happened at all. If we ac- cepted the long duration of the Lublin-Volhynian cul- ture and Wyciąże/Niedźwiedź materials, to 3100/ 3000 and 2850 cal BC respectively, both these units would partially overlap with the Baden culture and Beaker/Baden assemblages. Secondly, we could again take into account only short segments, ‘hard cores’, as it were, situated with- in the widest intervals, and reject their remaining parts. In such a case, archaeological units would be separated more distinctly than in the previous inter- pretation, and be arranged roughly into four groups consisting mostly of partly contemporary units. These four groupings would be arranged linearly, but there would be even breaks in the continuity of cultural development. One group would consist of the Wyciąże-Złotniki group and Lublin-Volhynian culture. The former would appear at about 4200/4100 cal BC, and the latter only in the 38 th century BC. The end of both units should be placed at c. 3550 cal BC. The Funnel Beaker culture would come into exis- tence at c. 3750 cal BC, it would exist simultane- ously with previous units for no more than 200 years. The fundamental development of this cul- ture would start at c. 3500 cal BC and would last until c. 3300 cal BC. Because there is only one 14 C date connected with phase BR I, the question of pos- Fig. 14. Radiocarbon chronology (cal BC) of the Wyciąże/Niedźwiedź materials. Marek Nowak 258 sible the earlier appearance of the Funnel Beaker culture should be considered as rather doubtful, because stratigraphic anteriority to the Lublin-Vol- hynian culture could mean nothing more than ante- riority to the end of this culture, c. 3600/3550 cal BC. The third group would comprise the Beaker/Baden assemblages and Baden culture, and would be dated to c. 3300–2850/2800 cal BC and c. 3050–2850 cal BC, respectively. The Wyciąże/Niedźwiedź mate- rials would be placed between 3400 and 3150 cal BC, or rather somewhere within these borders. A hiatus could be postulated between the Beaker/ Baden assemblages and Baden culture on the one hand, and the fourth group, i.e. the Corded Ware culture, on the other, c. 2800–2650/2600 cal BC. Fig. 15. Radiocarbon chronology (cal BC) of the Baden culture (BaC). Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 259 Discussion While assessing which of the alternative chronolo- gical scenarios may be more akin to past reality, we should first highlight some observations and premises. Firstly, it is very easy to notice that we are dealing with very broad chronological ranges only in the cases of those units which still have a relatively low number of dates (Lublin-Volhynian culture, Wyciąże- Złotniki group, Wyciąże/Niedźwiedź materials). On the other hand, the Funnel Beaker culture, Baden culture, Beaker/Baden assemblages and Corded Ware culture, where this is not the case, give much shorter, compact ranges. In these cultures, a good compromise seems to be values close to the ‘proba- ble’ and median ones. Secondly, it is worth noting that, while we are hand- ling large datasets (in our case: radiocarbon dates) extreme values will almost always occur for various reasons (see Introduction). Certainly, Bayesian mo- delling considerably reduces this, but we cannot be sure that it does so completely. Thirdly, we must remember that the above summa- ries of the direct dating, separate modelling and com- bined modelling are of a generalised and extreme nature. In fact, in every single case, we should take into account the specificity of local conditions. Con- sequently, one can also imagine some combinations of these two extremes. Thus, some units and pheno- mena would be limited only to ‘hard cores’ indeed, but some would not. In other words, in some cases, a discrete mode of cultural transformation should be Fig. 16. Radiocarbon chronology (cal BC) of the Beaker-Baden assemblages (TRB/BaC). Marek Nowak 260 recommended, but in other cases continuous deve- lopment should be proposed. To these local conditions, as we already know, typo- logical continuations between the Funnel Beaker culture and Beaker/Baden assemblages as well as between the Wyciąże-Złotniki group and Wyciąże/ Niedźwiedź materials should be included. This means that these units had to come into contact, but on the other hand, they could not develop simultaneously for a long time. Besides, some stratigraphic observa- tions suggest some contemporaneity between the Lublin-Volhynian culture/Wyciąże-Złotniki group and the Funnel Beaker culture. The remaining assump- tions used in combined modelling (see above) are not local, but should of course also be taken into ac- count. Although these interdependencies had already been used in combined modelling, we are not concerned here with circular reasoning. The result of the com- bined modelling still gives quite a bit of uncertainty, which must still be interpreted with the application of the aforementioned local conditions. There are also no obstacles to taking these conditions into ac- count in the falsification of direct dating and sepa- rate modelling. Fourthly, reliable external data, referring to both ab- solute and relative chronology, should be included in our assessment. Lastly, the shape of the relevant part of the calibra- tion curve is also important for the final selection of timeframes of archaeological units under considera- tion. External data are particularly important for the Lub- lin-Volhynian culture and Wyciąże-Złotniki group. Their extremely early beginnings, reaching almost the mid-5 th millennium BC (Figs. 18–19), as well as late endings, reaching the early 3 rd millennium BC Archaeological units and Interval based The widest The ‘probable’ The narrowest categories of 14 C dates (their amounts) on medians interval interval interval Funnel Beaker culture, phase BR I< 1 date 3960–3810 4340–3690 4070–3720 – Lublin-Volhynia culture< all dates (4) 3810–3470 3990–3100 3870–3360 3690–3630 Lublin-Volhynia culture< dates of group B (3) 3910–3410 4300–2940 4010–3300 3700–3630 Lublin-Volhynia culture< dates of group A (3) 3800–3470 4020–3040 3870–3360 3660–3630 Wycia ˛z ˙e-Zl ⁄otniki group< all dates (11) 4290–3440 4460–3270 4370–3340 4110–3630 Wycia ˛z ˙e-Zl ⁄otniki group< dates of group B (6) 4240–3630 4450–3280 4330–3560 4070–3900 Funnel Beaker culture< all dates (58) 3480–3310 3530–3280 3510–3300 3440–3340 Funnel Beaker culture< dates of group B (47) 3480–3310 3530–3270 3500–3290 3430–3340 Funnel Beaker culture< dates of group B (34) 3490–3310 3550–3270 3510–3290 3490–3340 Wycia ˛z ˙e\Niedz ´wiedz ´ materials< all dates (3) 3440–3140 3630–2860 3570–3040 – Wycia ˛z ˙e\Niedz ´wiedz ´ materials< dates of group B (3) 3630–3120 3900–2820 3860–2990 – Wycia ˛z ˙e\Niedz ´wiedz ´ materials< dates of group A (3) 3320–3140 3630–2890 3410–3040 – Baden culture< all dates (26) 3070–2830 3130–2780 3110–2810 2990–2870 Baden culture< dates of group B (24) 3070–2830 3130–2790 3110–2810 3000–2870 Baden culture< dates of group A (19) 3060–2830 3130–2780 3100–2810 2980–2870 Funnel Beaker\Baden assemblages< all dates (26) 3310–2790 3340–2700 3330–2750 3280–2870 Funnel Beaker\Baden assemblages< 3310–2800 3340–2690 3330–2750 3270–2880 dates of group B (15) Funnel Beaker\Baden assemblages< 3310–3030 3340–2770 3330–2850 – dates of group A (6) Corded Ware culture< all dates (24) 2660–2330 2740–2250 2700–2280 2590–2410 Corded Ware culture< dates of group B (21) 2630–2330 2720–2250 2670–2290 2570–2420 Corded Ware culture< dates of group B (20) 2570–2350 2670–2260 2620–2300 2500–2440 – All dates> A model = 64.3%, A overall = 64.5%< 3 dates with agreement index lower than 60% – Modelling for dates of group B> A model = 76.2%, A overall = 75.0%< 3 dates with agreement index lower than 60% – Modelling for dates of group A> Amodel = 62.1%, A overall = 60.1%< 5 dates with agreement index lower than 60% Tab. 3. Results of combined modelling of 14 C dates of the Middle and Late Neolithic units in western Lesser Poland (cal BC; rounded by 10 years). Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 261 in the case of the former and 3300/3200 cal BC in the case of the latter (Figs. 18, 21), are impossible to accept in light of our knowledge on chronology of the Lengyel-Polgár phenomena. For instance, in the recent assessments of the chronology of the Early and Middle Eneolithic in the Carpathian Basin (Chmielewski 2008.72–76, 86; Nowak 2010.68–79, 82; Raczky, Siklósi 2013), the timeframes of the Bodrogkeresztúr and Hunyadihalom cultures were placed around 4300/4200–3700 cal BC. This is of great significance, since both these cultures can be described as ‘mother’ units of the ceramic style of the Wyciąże-Złotniki group. Similarly, new views on the chronology of the Lublin-Volhynian culture (Chmielewski 2008; Wilk 2014; 2016), based on the dates from western Volhynia, Nałęczów Plateau and Sandomierz Upland, supported by new schemes from the Carpathian Basin, prove that the traditionally defined phase III of this culture (actually, this is ra- ther pottery styles, not the phase as such) should be placed between c. 4200 and c. 3700 cal BC. Phase III is important for our subject, because Lublin-Volhy- nian materials from western Lesser Poland belong to it. It seems, therefore, that the second approach pro- posed in the summaries of separate and combined models is more correct for units which provided fewer dates. The intervals delimited by complete ranges in both models and in direct dating should Fig. 17. Radiocarbon chronology (cal BC) of the Corded Ware culture (CWC). Marek Nowak 262 be considered as indicative of approximate intervals within a segment of which given units actually deve- loped. Therefore, we should eliminate the long ‘onsets’ and ‘tails’ of the Lublin-Volhynian culture and Wyciąże- Złotniki group. If we also take into consideration, the shape of the calibration curve between c. 5100 and 4900 cal BP, we can accept the idea that the Lublin- Volhynian culture appeared in western Lesser Po- land between c. 3950 and 3700 cal BC (c. 3800 cal BC could be proposed as the most probable time), because some retardation of more western areas of this culture is highly probable. However, somewhat paradoxically, this does not necessarily refer to the Bronocice site. The Lublin-Volhynian settlement could have appeared later there. Due to stratigraphic rela- tionships, we can assume that it was later than the first phase of the Funnel Beaker culture, which we finally placed around 3750/3700 cal BC (see below). Thus, the Lublin-Volhynian culture at this site can be placed around 3700–3650/3550 cal BC. Admitted- ly, this chronological position is later than in the schedule developed by Kruk and Milisauskas; they recently dated the Lublin-Volhynian culture at Bro- nocice to 3800–3700 cal BC (Milisauskas et al. 2016.36). Overall, the end of this culture in western Lesser Poland should be placed within the period of c. 3650–3550 cal BC, due to the plateau visible in the calibration curve for 4800–4700 cal BP. Regarding the absolute dating of the Wyciąże-Złotni- ki group, the series of nine new 14 C dates led to the transformation of previous opinions. Two ‘old’ dates from Złotniki and Kraków-Pleszów suggested the late chronological position, i.e. the first half of the 4 th millennium BC, and particularly the second quar- ter of that millennium. It seemed even possible to extend this chronology slightly, by about 100/150 years, beyond the date of 3500 cal BC. However, new dates consequently point to an earlier period, i.e. at the second half of the 5 th millennium and the first quarter of the 4 th millennium BC. According to the results of both models (particularly the combin- ed one), and in light of the cited external data, the start of the Wyciąże-Złotniki group should be estab- lished at between c. 4250 and 4050 cal BC, since a plateau of this length occurs in the calibration curve and retardation to the Tisza basin is reasonable. The value for the end would be within c. 3650–3550 cal Fig. 18. Absolute chronologies (cal BC) of the Middle and Late Neolithic (Corded Ware culture) units in western Lesser Poland based on separate Bayesian modelling of all 14 C dates referring to these units (rows with abbreviations), of dates belonging to group B (B) and of dates belonging to group A (A); 1 the widest intervals, based on extreme points of the 95.4% ranges; 2 the ‘probable’ intervals, based on extreme points of the 68.2% ranges; 3 the narrowest intervals, based on the end point of the 95.4% start boundary and the starting point of the 95.4% end boundary; 4 medians. L-VC Lublin-Volhynian culture, W-ZG Wyciąże-Złotniki group, TRB Funnel Beaker culture, W/N Wyciąże/Niedźwiedź materials, BaC Ba- den culture, B/BA Beaker/Baden assemblages, CWC Corded Ware culture. Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 263 BC, at the very latest, i.a. some retardation of the cultural development, when compared to the Middle Eneolithic of the Tisza basin, is again acceptable. Moreover, the shape of the calibration curve plays a similar part as in the case of the end of the Lublin- Volhynian culture. In case of the Wyciąże/Niedźwiedź materials, the very modest amount of data makes it difficult to re- liably characterise this unit, including its chronology. We should again employ the above-mentioned ‘seg- ment’ approach. If we assume the actual presence of Lengyel-Polgár elements there, which originated from the Wyciąże-Złotniki group (Bober 2004; Fur- cholt, Machnik 2006.336, 339; Grabowska, Za- stawny 2011.134–135), as well as ther prevoiously mentioned shape of the calibrated curve, then its be- ginnings should be placed in the timeframes of c. 3650–3550 cal BC. The dating of the disappearance of these materials remains a mystery; the value of c. Fig. 19. Combined modelling of all 14 C dates of the Middle and Late Neolithic (Corded Ware culture) units in western Lesser Poland (cal BC); individual dates are not presented. 3350–3100 BC can be proposed, based mainly on median values from both models confronted with a wide plateau for 4550–4450 cal BC. Nevertheless, it gives a surprisingly long period for quantitatively in- significant archaeological phenomena. It would mean that Lengyel-Polgár elements were still in use for 400 years even after their disappearance from the Car- pathian Basin. As regards other units, we have quite a different si- tuation due to the larger sets of 14 C datings, which resulted in more compact ranges in all kinds of ana- lyses. Therefore, it seems more probable that either the whole length of these ranges or most of them should be taken into account as the real timeframes of their existence. As to the dawn of the Funnel Beaker culture, the com- bination of all analyses carried out above and the shape of the calibration curve indicate that the dates Marek Nowak 264 of c. 3750 and 3700 cal BC should be regarded as the most likely borders of its very beginning. The ceramic typology does not exclude this possibility (Nowak 2009.334–336, see further references), al- though this date is a bit later than the commonly sug- gested date of 3900/3800 cal BC (Kruk et al. 2016; Milisauskas et al. 2016; Nowak 2009; Włodarczak 2006b). However, the latter proposal was based only on single dates from ‘our’ area and other areas in Lesser Poland (Nowak 2006; Rybicka 2017) whose reliability can be challenged. The date of 3750/3700 cal BC does not contradict the above-mentioned stra- tigraphic relations recorded at Bronocice (see above). The issue of the disappearance of the Funnel Beaker culture from western Lesser Poland and of the impor- tance of the Baden influence on that process is com- plex. One way or another, it seems very likely that between this culture and the Beaker/Baden assem- blages had to function a cultural (typological) con- tinuity, which is well corroborated by separate and combined models. In other words, the Funnel Bea- ker culture proper, at least in the eastern part of the western Lesser Poland loess uplands, existed until the beginning of the Beaker/Baden assemblages. The value of 3300–3250 cal BC seems very reliable as to that transition (and remains roughly in line with the Bronocice chronology – Kruk et al. 2016; Mili- sauskas et al. 2016); however, we cannot exclude that the upper boundary of this interval of uncer- tainty should be moved up to c. 3100 cal BC, due to the shape of the calibration curve described in the case of the Wyciąże/Niedźwiedź materials. The end of the Beaker/Baden can be situated at c. 2800 cal BC, based mainly on the values of medi- Fig. 20. Prior and posterior versions of the earliest 14 C dates of the Funnel Beaker culture at of Brono- cice: 1 modelling of all dates; 2 modelling of group B dates; 3 modelling of group A dates. These diagrams are enlargements of segments of complete modelling diagrams; in the case of all dates, a simplified ver- sion of this is presented on Figure 19. Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 265 ans obtained in both models. Taking into account the calibration curve, we could transform this date into c. 2850–2750 cal BC. The postulated period of c. 3300/3250/3100–2850/2750 cal BC roughly fits with recent dating of the BR IV and BR V phases at Bronocice (3300–2900/2800 cal BC – Kruk et al. 2016; Milisauskas et al. 2016). The absolute dating of the Baden culture in western Lesser Poland should be delineated by a kind of ave- rage of all boundary values, which do not differ be- tween each other very much. The high reliability of 14 C dating enforces such a construction. Most of these dates have been obtained recently in reliable laboratories, mainly from bones, and usually have small standard deviations (Zastawny 2015b). Thus, the proposed range could be c. 3100–2800 cal BC. The first date does not have to be changed due to the calibration curve (lack of wiggle or plateau); the second can again be stretched to c. 2850–2750 cal BC. Let us recall, however, that in A. Zastawny’s opi- nion (2015.202), an even shorter slice of time, of c. 3100/3050–2900 cal BC, better reflects the Baden Fig. 21. Absolute chronologies (cal BC) of the Middle and Late Neolithic (Corded Ware culture) units in western Lesser Poland based on combined Bayesian modelling of all 14 C dates referring to these units (rows with abbreviations), of dates belonging to group B (B) and of dates belonging to group A (A); 1 the widest intervals, based on extreme points of the 95.4% ranges; 2 the ‘probable’ intervals, based on ex- treme points of the 68.2% ranges; 3 the narrowest intervals, based on the end point of the 95.4% start boundary and the starting point of the 95.4% end boundary; 4 medians; 5 evaluated beginning of the Funnel Beaker culture (see text). L-VC Lublin-Volhynian culture, W-ZG Wyciąże-Złotniki group, TRB Fun- nel Beaker culture (boundaries of the widest intervals (1), ‘probable’ intervals (2) and medians (3) of the phase BR I, based on the date DIC-719), W/N Wyciąże/Niedźwiedź materials, BaC Baden culture, B/BA Beaker/Baden assemblages, CWC Corded Ware culture. chronology, due to some typological constraints. Consequently, it is our belief that the range of c. 3100–2850 cal BC reflects the chronology of the Ba- den culture in the best way. Admittedly, this is a shorter period than might be expected. Particularly surprising are the late origins of the Baden culture in Lesser Poland. However, cre- dible dating indicates precisely this and no other si- tuation. Also, the proposed time interval does not contradict the overall principles of typological deve- lopment or current patterns of the absolute chrono- logy of the Baden phenomena (Horvath, Svingor 2015; Stadler et al. 2001; Wild et al. 2001; Zastawny 2008; 2011; 2015a). Such dating, especially the relatively late beginnings, convincingly confirm what we had long suspected, namely that the Baden culture proper in western Les- ser Poland appeared as the effect of fast (a single wave?) migration from beyond the Carpathians. This migration was of groups coming from the developed (late classic) Baden culture. These people brought Marek Nowak 266 here the model of the developed Baden culture in all its aspects. They settled in a small area within and around Kraków. Consequently, only this stage of development is represented in this area. Thus, we do not observe full cultural (typological) develop- ment, with early, developed (classic) and late phases. The cause of the sudden disappearance of Baden cul- ture and the Beaker/Baden assemblages remains un- clear. In any case, the results of analyses suggest the occurrence of a hiatus between this disappearance and the origins of the Corded Ware culture. The possible dates of the beginnings of the Corded Ware culture, resulting from statistically significant modelling, fall within a rather broad interval be- tween 2800 and 2500 cal BC. However, comparing the results of all analyses speaks, in our opinion, for the date of c. 2650 cal BC. We are aware that this date seems to be rather late when referring to gen- eral views on development of this unit in central Eu- rope, including western Lesser Poland, which usu- ally point to c. 2800 cal BC (Włodarczak 2006a). We are also aware that the calibration curve makes it possible to alternatively refer several dates earlier than c. 3100 to c. 2850–2800 cal BC. Nevertheless, we think that the presented results of separate and combined modelling allow us to evaluate the proba- bility of such an option as lower than the probability of the ‘later’ option. This problem must be analysed in depth in the future. Conclusions The final, modelled scheme of the absolute chrono- logy of the discussed archaeological units in the area under consideration is illustrated on Figure 22. This is the result of analyses which included radiocarbon, typological and contextual facts and their interpreta- tions, as well as more or less arbitrary chronological constructions based on these facts and interpreta- tions and on general knowledge, including the para- meters of the calibration curve. It should be empha- sised that this graph shows the chronology itself, not the dynamics of cultural processes. In other words, the rising and falling segments of bars reflect inter- vals of uncertainty in dating the beginning and end of a given unit. These bars do not necessarily mirror the ‘birth’, ‘heyday’ and ‘decline’ of the analysed phe- nomena. This scheme unambiguously suggests both the over- lapping and contiguous nature of cultural develop- ment in western Lesser Poland within the Middle Neolithic. The basic elements of this development are: 1) the Wyciąże-Złotniki group and the Lublin- Volhynian culture, until c. 3650–3550 cal BC; 2) the Funnel Beaker culture proper, which appeared c. 3750–3700c al BC, and existed until c. 3300–3250 cal BC, perhaps accompanied by the Wyciąże/Niedź- wiedź materials from c. 3650–3550 cal BC; and 3) the Baden culture and the Funnel Beaker/Baden as- semblages from 3100 and 3300–3100 cal BC, res- pectively, until 2850–2750 and 2850 cal BC, with – possibly – later Funnel Beaker culture and Wyciąże/ Niedźwiedź materials, existing until c. 3100 cal BC. There is an explicit suggestion in the final scheme that in some cases a discrete (radical) mode of cultu- ral transformation could be proposed; and in other cases, continuous development and/or simultaneous functioning can be suggested. In the author’s opin- ion, this arrangement (particularly the discrete one) means that some archaeological units (perhaps Ba- den culture and Corded Ware culture) should be con- sidered as reflections of real units of a cultural, po- pulation, or even political nature, which were discer- nible to prehistoric people. The final scheme shows that the Lublin-Volhynian culture could have coincided with the Wyciąże-Złot- Fig. 22. The final scheme of the absolute chronology (cal BC) of the Middle and Late Neolithic (Corded Ware culture) units in western Lesser Poland. Do 14 C dates always turn into an absolute chronology| The case of the Middle Neolithic in western Lesser Poland 267 niki group. In view of the territorial relationship between them, relations from the point of view of material culture, primarily in the field of pottery, be- come particularly interesting. It is relatively easy to see clear similarities between these units. However, the most evident similarities apply only to some ca- tegories of ceramics, including, for example, vessels with Scheibenhenkel handles. What is more, in the period between the late 38 th and early 36 th centu- ries BC, the early Funnel Beaker and possibly early Baden influences are superimposed on this Lublin- Volhynian/Wyciąże-Złotniki ‘mix’. The lack of any Funnel Beaker elements in materials of the Baden culture proper is particularly pregnant with meaning. This directly suggests that the Funnel Beaker communities in the western part of the area under consideration could have been expelled or ex- terminated. A fairly sharp geographical boundary between areas of the Baden culture and Beaker/Ba- den assemblages (Fig. 1) (see Zastawny 2008.Fig. 2; but cf. a somewhat different opinion in Włodar- czak 2008b.252) could also support an interpreta- tion of this kind. As a result, as already mentioned, one can postulate that a substantial migration of Ba- den people from the south-west took place at about 3100 cal BC. With reference to the next fundamental cultural change, i.e. the appearance of the Corded Ware cul- ture, which we use only as a kind chronological frame, we should emphasise that currently it also is difficult to point to any common or transient charac- teristics in the pottery of the Funnel Beaker culture, Beaker/Baden assemblages and Corded Ware cul- ture, not to mention the Baden culture (Włodarczak 2008b.253; 2010.208, 210; 2011.215–220), contrary to earlier hypotheses (Machnik 1966.123; Włodar- czak 2006a.90–95, 103, 105; Zastawny 2001). As a kind of summary of this issue, we can quote the opi- nion by P. Włodarczak, according to which “a short period of co-existence between the two groups is possible (c. 2850–2700 BC), although not very li- kely” (Włodarczak 2008b.253). Altogether, we take a the liberty to express the (unfashionable) view that processes connected with the disappearance of the Beaker/Baden and Baden groups and with appear- ance of Corded Ware groups were primarily histori- cal (political?) processes. “All models are wrong, some models are useful”, as George Box says (Box 1979.202 – after Bayliss et al. 2007). Hopefully, the final model is useful for many issues, despite some controversial points. Par- ticularly, the precise chronology of the Baden cul- ture, and more precise chronology of the Funnel Beaker culture, Beaker/Baden assemblages, and of the beginning of Corded Ware culture should be highlighted. It is impossible to say this about the re- maining units, but the proposed chronological limits can be useful for current knowledge and constitute a good starting point for further analyses and studies. This scheme, of course, will be more or less changed if new radiocarbon and other data appear. A very recent, extremely surprising discovery of the spec- tacular collective grave of the Globular Amphorae culture in Koszyce (approx. 30km NE of Kraków) which is dated to c. 2900–2600 cal BC (Przybyła et al. 2013) clearly proves that in western Lesser Po- land many processes and events happened in the Neolithic period, about which we have so far not ac- quired any knowledge and which were not even ex- pected. Obviously, the question posed in the title of this con- tribution should be answered negatively. Radiocar- bon dates as such usually do not determine the ac- tual absolute chronology of a given phenomena. They must pass a rigorous contextual analysis and model- ling in combination with other dates, whereby we might be able to come closer to past reality. Extreme approaches in which we either approve only those dates which fit into our concepts or accept without any reservations almost all dates are incorrect. 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