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Simple Calibration versus Bayesian Modeling of Archeostatigraphically Controlled 14C Ages in an Early Avar Age Cemetery from SE Hungary: Results, Advantages, Pitfalls

Published online by Cambridge University Press:  19 November 2018

Sándor Gulyás*
Affiliation:
Department of Geology and Palaeontology, University of Szeged, 2-6 Egyetem u., 6722 Szeged, Hungary
Csilla Balogh
Affiliation:
Medeniyet Üniversitesi, Sanat Tarih Bölümü, Istanbul, Turkey
Antónia Marcsik
Affiliation:
Department of Anthropology, University of Szeged, 52 Középfasor 6726 Szeged, Hungary
Pál Sümegi
Affiliation:
Department of Geology and Palaeontology, University of Szeged, 2-6 Egyetem u., 6722 Szeged, Hungary Archaeological Institute of Hungarian Academy of Sciences, 49. Úri u., 1014 Budapest, Hungary
*
*Corresponding author. Emails: gulyas.sandor@geo.u-szeged.hu, csigonc@gmail.com
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Abstract

Recent advancements in accelerator mass spectroscopic (AMS) radiocarbon (14C) analytical methods and instrumentation offer us reliable conventional 14C ages with highly reduced analytical uncertainty for archeological bone collagen. However, after calibration this may be still too high for archeologists in periods where archeochronology is capable of attaining a resolution of 25–30 yr. Furthermore, there are cases when wiggles in the calibration curve yield wider age ranges than initially expected. For the Avar Age in the Carpathian Basin (568 to early 9th century AD) reliable archeotypochronology is available for the 7th century AD alone. The date of Avar invasion (568 AD) is precisely known. Precise archeological dating for the late 6th and the 9th centuries is lacking, calling for other methods to be introduced. This paper reports the first 14C dates for an Early Avar Age cemetery, Makó-Mikócsa. According to archeotypochronology, the cemetery was in use for three generations until the mid-7th century AD. The imprecision in 14C chronology arising from wiggles in the IntCal13 curve was significantly reduced by relative stratigraphy-controlled Bayesian modeling. Introduction of further age constraints from archeotypochronology into the model reduces broad absolute age ranges providing more constraint ages.

Type
Instrumentation and Calibration
Copyright
© 2018 by the Arizona Board of Regents on behalf of the University of Arizona 

INTRODUCTION

With recent advancements in AMS 14C analytical methods and instrumentation, reliable conventional 14C ages with highly reduced uncertainty using archeological bone collagen are readily available (Tisnérat-Laborde et al. Reference Tisnérat-Laborde, Valladas, Kaltnecker and Arnold2003; Higham et al. Reference Higham, Jacobi and Bronk Ramsey2006; Brock et al. Reference Brock, Ramsey and Higham2007) compared to initial trials (Gillespie et al. Reference Gillespie, Hedges and Wand1984; Tuross et al. Reference Tuross, Fogel and Hare1988; Aitken Reference Aitken1990, Reference Aitken2003; Taylor Reference Taylor1992). However, this analytically reduced uncertainty (couple of decades) after calibration is still too wide for archeologists in periods where relative and absolute chronology, built on artifact typology and archeostratigraphy, is capable of attaining a resolution of 25–30 yr. In this case, 14C ages are not of much use on their own apart from the fact they show a general temporal trend. To attain more precise ages, other sophisticated probabilistic methods (Bayesian analysis) complemented with information from archeostratigraphy is needed (Buck et al. Reference Buck, Kenworthy, Litton and Smith1991, Reference Buck, Litton and Scott1994, Reference Buck, Cavanagh and Litton1996; Buck and Millard Reference Buck and Millard2004; Bronk Ramsey Reference Bronk Ramsey2008, Reference Bronk Ramsey2009). For the Avar Age in the Carpathian Basin covering a time-scale from 568 till the opening of the 9th century AD, reliable ages based on archeotypostratigraphy and coins are available from the 7th until 9th centuries AD alone (Garam Reference Garam1992; Martin Reference Martin2008, Somogyi Reference Somogyi2011; Zábojník Reference Zábojník2008). The exact age of the Avar invasion at 568 AD is known from Byzantine historical records (Szádeczky Kardoss Reference Szádeczky-Kardoss1992). In addition, entry of Byzantine coins to the Avar Kaganate is recorded for this date (Somogyi Reference Somogyi1997, Reference Somogyi2005, Reference Somogyi2014). Developing a reliable archeotypochronology for the period of the first two generations (568-600 AD) and the 9th century is thus still a major challenge in Migration Age archeology in Hungary. This is due on one hand to the general lack of datable coins. Lack of clearly datable typically Avar type artifact assemblages poses further hardships. Assemblages with pressed buckles are good examples. These are generally dated after 600 AD, as press stones used for producing them have been recovered from graves of that age so far (Rácz Reference Rácz2014). For the 9th century assemblages, only some buckle types with a use extending into this period give some information on the age (Szalontai Reference Szalontai1991, Reference Szalontai1996).

In our work, we report the first radiocarbon dates for the second largest Early Avar Age cemetery in SE Hungary: Makó-Mikócsa Hill. In addition, an attempt was made to refine the absolute chronology of the period of the first two generations using combined archeostratigraphic data and 14C dates. A grave-by-grave comparison of the results of typochronology and radiocarbon dating has also been implemented to assess inconsistencies and potential underlying causes.

Archeochronology vs. 14C Dating: Methods, Advantages, Pitfalls, Solutions

Archeotypochronology estimates the interval when certain goods, objects, tools, etc. were manufactured and uses this information to estimate the time span when these were placed into the grave (Daim Reference Daim2000; Garam Reference Garam1992; Martin Reference Martin2008; Zábojník Reference Zábojník2008; Somogyi Reference Somogyi2005, Reference Somogyi2011, Reference Somogyi2014; Balogh Reference Balogh2017). Thus, the time of death is indirectly estimated using this type of approach. The use of coins and datable artifact assemblages is the primary tool for establishing a chronology of Avar Age cemeteries in general (Garam Reference Garam1992; Somogyi Reference Somogyi2005, Reference Somogyi2011, Reference Somogyi2014; Martin Reference Martin2008; Zábojník Reference Zábojník1991, Reference Zábojník2008; Balogh Reference Balogh2017). Adoption of this method for the Avar Age is unusual, as these artifacts are rather rare in graves of this archeological period. Furthermore, graves dating to the last third of the 7th century AD, are completely lacking coins suitable for absolute dating. In addition, the derived chronologies must be confirmed by detailed numismatic examinations to be accepted. Due to these constraints, the most widely used methods in archeochronology focus on the presence of horizons, which are characterized by similar artifacts to coin-dated artifact assemblages. This method was adopted for developing a typochronology-based absolute chronology for the period of the 6th–7th centuries AD (Avar Conquest) in Hungary too (Garam Reference Garam1992; Martin Reference Martin2008; Zábojník Reference Zábojník1991, Reference Zábojník2008; Somogyi Reference Somogyi2011; Balogh Reference Balogh2017). In this chronology, the highest attainable resolution is between 25–30 yr. Nevertheless, it must be emphasized that as many artifacts are used for a longer time, they can be assigned to multiple periods. This uncertainty, which is related to the overlap of artifact use between different cultures or settlement horizons, reduces the fidelity of the created typochronology. Thus, in practice dating of complete artifact assemblages (grave goods, graves) rather than individual artifacts is adopted. In these approaches, the absolute age is given by the youngest datable artifact. As this type of analysis amalgamates a large variety of information ranging from the age of the individual artifacts, their assembly, as well as disposal into the grave, it yields short and long-span chronologies with significant discrepancies.

Radiocarbon dating of bones, on the other hand, can help us assess the date of death of the deceased directly (Gillespie et al. Reference Gillespie, Hedges and Wand1984; Long et al. Reference Long, Wilson, Ernst, Gore and Hare1989; Taylor Reference Taylor1992; Tuniz et al. Reference Tuniz, Zoppi and Barbetti2004). This date is however not a single calendar date, but rather a certain time interval with a certain probability expressing the error of the actual measurement (Libby Reference Libby1965; Suess Reference Suess1970; Aitken Reference Aitken1990, Reference Aitken2003; Bowman Reference Bowman1995). This measurement error is only 15–50 radiocarbon years presently for Holocene samples (Taylor and Bar-Yosef Reference Taylor and Bar-Yosef2014). However, the diet of the deceased, attributable to freshwater and marine resource intakes, can further bias the measured dates themselves (Cook et al. Reference Cook, Bonsall, Hedges, McSweeney, Boroneanţ and Pettitt2001; Schoeninger Reference Schoeninger2010; Taylor and Bar-Yosef Reference Taylor and Bar-Yosef2014; Meadows et al. Reference Meadows, Meadows, Ute, Ute, Harald, Schmölcke, Staude, Zagorska and Zarina2016). Additional uncertainty from the calibration of raw dates to calendar dates can further widen the age span due to the presence of numerous wiggles and plateaus in the calibration curve leading often to multi-decadal, multi-centennial age ranges (40–60 or even 80–100 yr). This is a serious problem in cross-validation of archeotypochronologies with an available resolution of 20–40 yr. There is an opportunity for fine tuning a series of radiocarbon dates with known stratigraphy using the method of Bayesian analysis (Buck et al. Reference Buck, Kenworthy, Litton and Smith1991; Bayliss and Bronk Ramsey Reference Bayliss and Bronk Ramsey2004; Bayliss et al. Reference Bayliss, Bronk Ramsey, van der Plicht and Whittle2007; Bayliss Reference Bayliss2007, Reference Bayliss2009). Application of this method clearly supersedes simple calibration. Simple calibration generally yields time-intervals, which are often broader than the original uncalibrated measurements themselves due to the previously mentioned reasons. However, if we have a-priori information on the stratigraphic position of the samples and their association, this knowledge can help us to adjust imprecision generated by the calibration curve using Bayesian statistics relying on the so-called Bayes theorem.

According to this theorem, the probability of the outcome is highly influenced and constantly modified by previously available and newly added knowledge from the input. The outcome is reduced time intervals which may be more in line with archeostratigraphic dates (Buck et al. Reference Buck, Kenworthy, Litton and Smith1991; Bayliss and Bronk Ramsey Reference Bayliss and Bronk Ramsey2004; Bayliss et al. Reference Bayliss, Bronk Ramsey, van der Plicht and Whittle2007; Bayliss Reference Bayliss2007, Reference Bayliss2009). Combination of the results of both methods can help us filter out outliers and establish an internally more consistent chronology than any method would yield on its own. The first application of a combination of archeotypochronology and Bayesian modeled 14C dates for Late Avar Age assemblages is from a cemetery of Szegvár-Oromdűlő in SE Hungary (Siklóssy and Lőrinczy Reference Siklóssy and Lőriczy2015). Here the start of cemetery use estimated via archeotypochronology could have been independently confirmed. The closure was estimated to be younger by the archeotypochronology than the modeled 14C ages. Authors of this paper incorrectly blamed a major supernova explosion dated at 774/775 AD, to alter radioactive carbon present at the time and thus contributing to the modification of conventional 14C ages (Siklóssy and Lőrinczy Reference Siklóssy and Lőriczy2015). However, as no OxCal code is available for this publication we have no information on how the model was built. Based on the figures and the description one may assume the construction of a simple Bayesian model in OxCal, which considered only the relative sequence of events. The dates gained were then simply compared to intervals given by archeotypochronologies of the site instead of the construction of a Bayesian model, where these constraints are actually built into the model itself.

Location and General Archeological Characteristics of the Study Site

The study site is situated in the heart of the Carpathian Basin near the middle reach of the Tisza River on the banks of the Maros (Mures) River approximately 15 km to the southeast of the city of Szeged and at the southeastern fringe of the city of Makó (Figure 1).

Figure 1 Location, archeological, geomorphological characteristics of the Makó-Mikócsa Hill study site.

The area is studded by minor rivulets representing the abandoned Pleistocene branches of the Maros River. These are inactive and act only as drainage channels for groundwater. Water appears in them only at times when groundwater percolates to the surface (Száraz creek). The cemetery is situated on top of a Pleistocene natural levee forming a loess-covered lag surface. Excavations of the site started in 2009–2010 preceding the construction of a major factory. All in all, 251 graves have been recorded making it the largest cemetery along the Maros River. According to recent magnetic surveys, 90–95% of the original cemetery has been excavated (Balogh and Gulyás Reference Balogh and Gulyás2015; Gulyás et al. Reference Gulyás, Balogh, Sümegi, Marcsik, Körössi, Rodushkin and Kelemen2015). Funerary practices observed in the cemetery (pit and chambered pit graves with an E–W orientation, large numbers of partial or complete animal remains functioning as sacrifice) as well as the various artifacts recovered are very similar to those observed in the 6th–7th century cemeteries of the Eastern European Plain. Based on the observed archeology, the community corresponds to groups characterized by the utilization of pit graves. These people must have joined the Avar tribes at the Eastern European Plain settling in the SE Great Hungarian Plain during the first phase of the Avar Invasion (after 568 AD) (Balogh Reference Balogh2017).

MATERIAL AND METHODS

Altogether, 13 human bone samples have been selected for AMS 14C dating. The samples under study were chosen to span the entire interval of the cemetery use based on archeotypochronological features on the one hand. In addition, out of the 13 samples, two had gold coins issued under the reign of Mauritius Tiberius (583/584–602). In our study, information on the dietary habits of the community are readily available from analyses of trace element markers and C and N isotope variations in human bones, including those selected for 14C dating as well (Table S1, Figure S1). According to these results, as δ13C values were higher than those for freshwater fish (>−22 ppt) (Tables S1, S2, Figure S1), exploitation of freshwater resources is negligible in the community and completely missing in the individuals selected for our study (Gulyás et al. Reference Gulyás, Balogh, Sümegi, Marcsik, Körössi, Rodushkin and Kelemen2015). So, the received conventional 14C dates are not biased by freshwater reservoir effect. The C/N ratio was higher than two indicating good collagen preservation along with the percentage of carbon in collagen. These taphonomic parameters are indicators of reliable 14C dates too.

Samples were ultrasonically washed and dried at room temperature. Surficial contaminations were removed by pretreatment with weak acid etching (2% acetic acid) followed by the ultrasonic ABA treatment before graphitization (Tuniz et al. Reference Tuniz, Zoppi and Barbetti2004; Higham et al. Reference Higham, Jacobi and Bronk Ramsey2006; Brock et al. Reference Brock, Ramsey and Higham2007). Measurements were done in the internationally renowned AMS laboratory of Seattle, WA, USA. Received conventional 14C ages were converted to calendar ages using the software OxCal 4.2 (Bronk Ramsey, Reference Bronk Ramsey2008, Reference Bronk Ramsey2009) and the most recent IntCal13 calibration curve (Reimer et al. Reference Reimer, Bard, Bayliss, Beck, Blackwell, Bronk Ramsey, Buck, Cheng, Edwards, Friedrich, Grootes, Guilderson, Haflidason, Hajdas, Hatte, Heaton, Hoffmann, Hogg, Hughen, Kaiser, Kromer, Manning, Niu, Reimer, Richards, Scott, Southon, Staff, Turney and van der Plicht2013). Calibrated ages are reported as age ranges at the 1 σ (68.2%) and 2 σ confidence level (95.4%). In archeology, the former is generally used and accepted (68.2% probability of ages). In our work dates at the 2-sigma confidence level (95.4%) were preferred to establish a more consistent absolute chronology. After calibration, the results gained were assessed to see if ranges are influenced by plateaus in the IntCal13 curve. To reduce such potential bias a single-phase Bayesian chronological model was constructed using relative archeostratigraphic information (Model 1). The received results were evaluated for integrity and congruence with those of archeotypochronology. In the second step, another model was also constructed via embedding archeotypochronological information on the assumed absolute age-span of the studied samples (Model 2) (for OxCal codes see supplement). Here dates given by archeochronology were entered into the model in the following format: the archeochronological information of last third of the 6th and first third of the 7th centuries AD was included as an age range from 570 to 633 AD besides the conventional reported 14C ages. Finally, results of the two models have been compared and differences with potential underlying causes are discussed.

RESULTS

Archeotypochronology

Table 1 lists the studied samples by feature and grave type as well as sex and age of the deceased, determined from the analysis of anthropological measurements done on femur and skull bones. In addition, the inferred archeotypochronological ages are also reported. Only four of the samples were females, the rest were males. Age groups included mainly adults (16–40 yr of age) and some seniors (>50 yr of age). Out of the 13 samples selected for 14C dating, two graves had coins issued under the reign of Emperor Maurice (583/584–602 AD) (Table 1, Figure S2). These coins are definitely older than the point in time when the studied individual died. Grave No. 54 (MM 216/208) contains a golden tremisse of Maurice (584–602 AD) from the Rome mint, which was worn as a pendant. Other clearly datable artifacts were missing with the exception of an early example of a Millefiorian-type pearl. However, the pearl-based chronology has not yet been fully established. So, its age can be put after 584–602 AD. The other grave (No. 130 (snr. 407/obnr. 386) had a solidus of Maurice (584–602 AD) deriving from the Constantinople (today Istanbul, Turkey) mint. Similarly clearly datable artifacts were likewise missing and only long-lived artifact types were noted assigning this grave again to the period after 584–602 AD.

Table 1 List of selected archeological samples by age and sex and inferred archeotypochronological ages.

*Gold-coin-dated graves with no other clearly dateable artifacts.

The remaining graves contained highly similar artifact assemblages, enabling better dating. The presence of pressed buckles with masks, pressed boot mounting, Martynovka-type pressed buckles (Balogh Reference Balogh2017) puts most of the samples to the end of the 6th and first third of the 7th centuries AD. The youngest artifacts appearing in some graves are pseudo-buckle mountings with a frame of ball series assigning them to the middle of the 7th century AD.

Based on the archeochronology, most of the samples can be dated to the end of the 6th and first third of the 7th century AD (Table 1). The last two samples are dated to the transition between the two centuries.

Based on the archeochronology, the cemetery must have been opened during the late 6th century AD (after 568 AD). It must have been in use until the mid-7th century AD (630–650 AD). Burials thus span the interval of roughly three generations (80–90 yr).

Radiocarbon Dating and Modeling

Results of 14C dating are depicted on Table 2 (for pMC values see Table S2). The mean analytical error in conventional ages is within the range that may be still acceptable by archeologists (±25 yr). After calibration chronological precision of unmodeled dates is higher with the exception of the first four samples (Table 2, Table S3). Here chronological ranges are widened [121–139 yr (68.2%), 153–176 yr (95.4%)]. While in case of the rest of the samples its around ca. 50 yr (68.2%) or ca. 80 yr (95.4%) in the oldest samples (samples 5–6) and is gradually reduced to 30–40 yr (68.2%) or 70–63 yr (95.4%) toward the younger end (Table S3). This range seems acceptable in the lack of a higher resolution archeotypochronology for the site at first sight. However, there are still clear discrepancies with archeochronological dates.

Table 2 Conventional and calibrated 14C ages at the 1- and 2-sigma probability levels.*

*Conventional 14C ages have been calibrated using OxCal 4.2 and the IntCal13 calibration curve.

On the basis of simple calibrated results, the opening of the cemetery must have started between 427 and 580 AD (95.4%) and ended between 622 and 685 AD. The proposed ending is only 20 yr younger than the one established by archeotypochronology However, the opening of the cemetery is dated much earlier than expected as the first date of the Avar invasion is clearly put to 568 AD. The first acceptable age ranges appear from sample 5, with ages placed between 564 and 614 AD (Table 2, Table S3). Older dates and the twofold difference in the ranges might be attributed to various factors like contamination by organic matter or the diet of the individual (reservoir effect). However, both can be excluded on the basis of trace element and isotope analyses of bone samples (Table S1, Figure S1) (Gulyás et al. Reference Gulyás, Balogh, Sümegi, Marcsik, Körössi, Rodushkin and Kelemen2015). When the shape of the calibration curve is examined though with the results placed over (Figure S3), a clearly apparent plateau can be noted between 420 and 520 AD, which results in an unreal widening of the age span of the first four samples by ca. 100 yr.

To eliminate uncertainty due to the mentioned plateau, conventional ages were recalibrated using Bayesian modeling controlled by relative chronology of the samples derived from archeostratigraphy (Model 1) (Figure 2). The anomalously broad absolute age ranges caused by the presence of a plateau in the calibration curve was clearly reduced to 15–26 yr (68.2%) and/or 32–54 yr (95.4%) with one exception (98 yr) (Figure 2, Table S3).

Figure 2 Prior and posterior age-distribution curves of samples included in Model 1 based on relative archeostratigraphy (dark grey bands represent 2-sigma, light grey bands 1-sigma CI).

The dates produced by Model 1 show that burial at this site must have begun after 518–553 AD (68.2%) or 470–570 AD (95.4%), respectively (Figure 2, Table S3). Knowing the exact time of Avar invasion from historical records, the starting boundary’s upper limit is in the range acceptable for the first generation (570 AD). The lower limit at both confidence levels is significantly different from the expected boundary of 568, though. According to the modeled dates, the use of the cemetery as a burial site must have come to an end before 653–676 AD (68.2%) or 644–701 AD (95.4%), respectively (Figure 2, Table S3). The total estimated span of the cemetery was put between 108 and 153 yr (68.2%) and 88–209 yr (95.4%). This roughly represents three generations of use as estimated by archeotypochronological investigations.

Although Model 1 has managed to reduce significantly the broad absolute date ranges caused by wiggles in the IntCal13 curve yielding better ages at both probabilities, these new dates are still not fully congruent with those given by archeotypochonology. By looking at Figure 2 it can be stated that modeled ages are overlapping archeochronological ones from sample 4 at both confidence levels. Furthermore, there is a minor overlap of modeled cemetery span with merely the upper end of the estimated archeochronological one at both confidence levels.

In Model 2, the likelihood of absolute age ranges estimated by archeotypochronology and the recorded radiocarbon dates were combined to better constrain 14C ages to the expected age interval of the cemetery (Figure 3, Table S4). The agreement with the unmodeled data as well as the overall agreement indicates a high reliability of the received ages. This is also seen in reduced ranges to the previous model [6–19 yr (68.2%), 25–48 yr (95.4%)].

Figure 3 Prior and posterior age distribution curves of samples included in Model 2 based on the combination of conventional 14C ages and absolute archeochronological data (dark grey bands represent 2-sigma, light grey bands 1-sigma CI).

There is only a single date (MM 478/507) where the value of agreement is close to but still under the level of general acceptance. The starting and ending dates of site occupation are clearly congruent with assumption made on the basis of archeotypochronology, even when uncertainties are also considered at higher probabilities. All dates including the start and end of cemetery use are congruent with the archeochronology at the 1-sigma probability level, which is generally used by archeologists when reporting absolute ages. The broad absolute date ranges are also within the boundaries proposed by archeochronology at the 95.4% confidence level. The opening of the cemetery must have started between 559–578 AD (68.2%) or 545–593 AD (95.4%) (Figure 3, Table S1). The cemetery was abandoned between 641–660 AD (68.2%) or 616-656 AD (95.4%). The estimated span of cemetery use by Model 2 [67–97 yr (68.2%), 43–121 yr (95.4%)] correspond to 3 generations as proposed by archeochronology.

CONCLUDING REMARKS

Our results are clearly at odds with claims of Migration Age archeology in Hungary, which states that 14C dating cannot produce dates with high enough resolutions of 20–30 yr easily achieved by archeotypochronological methods. Bayesian modeled 14C ages do provide accurate absolute chronologies for the Early Avar Age when age constraints from archeotypochronology is included in the model. Thus, a combination of the results of the two methods with suitable evaluation techniques do provide consistent, reliable ages for those historical periods when clear-cut absolute dates are not readily available from archeotypochronologies. Our findings also point to the advantages of a collective use of both methods for periods where known archeological ages from typochronology are readily available at a resolution of 20–30 years, too. A better confinement of absolute chronologies provides information on not only the span and contemporaneity of site use but yields a firm foundation for the correlation of observed societal, archeological changes with absolute dated paleoclimatic and paleoenvironmental records.

ACKNOWLEDGMENTS

Our work was supported by the Hungarian National Scientific Fund (OTKA) project 105910 and the European Union and the State of Hungary, co-financed by the European Regional Development Fund in the project of GINOP-2.3.2.-15-2016-00009 ‘ICER’.

Supplementary materials

To view supplementary material for this article, please visit https://doi.org/10.1017/RDC.2018.116

Footnotes

Selected Papers from the 2nd Radiocarbon in the Environment Conference, Debrecen, Hungary, 3–7 July 2017

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Figure 0

Figure 1 Location, archeological, geomorphological characteristics of the Makó-Mikócsa Hill study site.

Figure 1

Table 1 List of selected archeological samples by age and sex and inferred archeotypochronological ages.

Figure 2

Table 2 Conventional and calibrated 14C ages at the 1- and 2-sigma probability levels.*

Figure 3

Figure 2 Prior and posterior age-distribution curves of samples included in Model 1 based on relative archeostratigraphy (dark grey bands represent 2-sigma, light grey bands 1-sigma CI).

Figure 4

Figure 3 Prior and posterior age distribution curves of samples included in Model 2 based on the combination of conventional 14C ages and absolute archeochronological data (dark grey bands represent 2-sigma, light grey bands 1-sigma CI).

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