The Late Glacial human reoccupation of north-western Europe: new approaches to space-time modelling. (Research).

Blackwell, Paul G. ; Buck, Caitlin E.

Introduction

In recent years there has been much interest in trying to understand how and when the north western parts of Europe were reoccupied as the ice sheets retreated during the Late Glacial period. In this paper we reinvestigate the radiocarbon data available from this period using a statistical, model-based approach. The models we adopt are simple and are only the first step towards fully spatio-temporal interpretation; much of what we advocate can be tackled within existing software. Nonetheless, our models are flexible and generalisable and thus suitable for use on a wide range of archaeological projects, in many places and periods, in which dating of occupation, colonisation or settlement is of interest. In the context of Late Glacial Europe, for example, we are able to provide probabilistic answers to the question 'in what order were the regions of north-western Europe reoccupied?'. We are also able to make suggestions for refining and tailoring existing models for future research.

The radiocarbon determinations associated with human activity during the Late Glacial period were recently assembled by Housley et al. (1997), who scrutinised the nature and quality of the dating evidence and the stratigraphic and cultural contexts of the organic samples (ibid. 34-35). These authors made suggestions about how the landscape was reoccupied as the ice sheet retreated at the end of the Wurm/Weichsel glaciation and sought to address a number of questions. Among them were two major issues:

* what is the earliest date at which we have evidence for late glacial reoccupation in northwest Europe, and

* in what order were the various regions reoccupied?

Previous approaches

In an attempt to address these issues, Housley et al. (1997) summarised the radiocarbon dates associated with each of eight regions in north-west Europe (the regions identified were Belgium, British Isles, Middle Rhine, Northern Germany, Paris Basin, Southern Germany, Thuringian Basin and Upper Rhine). They chose not to calibrate the determinations and related the dates of settlement in each region to summary histograms of all the uncalibrated radiocarbon ages. They reported the earliest non-zero cell in each histogram as the age of the onset of a 'pioneer phase' for that particular region and the cell with highest frequency as the age for a 'residential phase'. The age of the pioneer phase was seen as providing an estimate of the earliest date of reoccupation in a given region and the order in which reoccupation took place was estimated simply by chronologically ordering the regions using the earliest ages.

Blockley et al. (2000) addressed these issues in two ways. They repeated the analysis by Housley et al. (1997) with what they saw as a more appropriate allowance for error in the determinations, and showed that Housley et al.'s phases were ill-defined and uncertain in age. Blockley et al. also noted that radiocarbon determinations really need calibration before they can be seen as providing reliable estimates of the dates of events of interest. They used 'summed probability distributions' to draw together a number of calibrated radiocarbon date distributions and again concluded that 'population movement is difficult to argue and there is no clear evidence for a 'pioneer' and 'residential' phase' (ibid. 116).

The tools that Blockley et al. used to compute these 'summed probability distributions' are available in the OxCal radiocarbon calibration software, which offers the comment: 'Combining probability distributions by summing is usually difficult to justify statistically but it will generate a probability distribution which is a best estimate for the chronological distribution of the items dated.' (OxCal manual, Ramsey 2000). We agree with the first part of this statement but feel that the second part (from 'but') is unjustified.

In adopting Ramsey's terminology of a 'chronological distribution' Blockley et al. reasonably assume that the particular artefacts they are dating are sampled from some underlying distribution and then observed with dating and calibration error. However, simply averaging the calibrated radiocarbon dates from individual, randomly surviving archaeological samples does not give a good estimate of the underlying chronological distribution. In fact, since the calibrated dates being 'summed' do not relate to the same event, it is not clear what interpretation can be placed on the probabilities produced by this method.

In what follows we suggest an alternative, model-based, Bayesian approach to understanding the chronology of reoccupation. Within the Bayesian framework, probabilities based on a priori information (available before the radiocarbon dates were obtained) are updated in the light of currently available data to arrive at a posteriori probability distributions. Thus, our approach leads to fully probabilistic answers to the two major questions posed above. The data to be incorporated in this problem include not only the radiocarbon determinations but also information on the calibration curve, since, like Blockley et al. (2000), we believe that calibration is an important part of the interpretative process, uncalibrated determinations are not calendar dates and current best estimates of the radiocarbon calibration curve suggest that there is no one-to-one relationship between calendar dates and radiocarbon dates. We want to devise a framework that can be adapted and improved as more information (archaeological, radiocarbon and statistical) becomes available. It is certain that knowledge of both the process of population movement and the radiocarbon calibration curve will improve in years to come and while the current models are only 'best estimates' the methodology we suggest takes into account the uncertainty in those estimates, and should be easy to refine in the light of new information.

Which is the earliest date in a region?

In determining the earliest human activity in a region, one date that might be seen as important is the true calendar date of the earliest of the radiocarbon samples available to us from that region, which we will call T. This date is uncertain because calibrated radiocarbon dates are distributional estimates of a single point in time from which we cannot readily recover the true date of interest. Thus, we cannot be sure from calibrated radiocarbon dates alone which one of a sequence is the earliest. Blockley et al. (2000) estimate T for each region by averaging a collected set of dates, on the assumption that the calibrated dates to be combined 'represent multiple estimates of the same phenomenon' (Blockley et al. 2000: 116). We feel that this assumption is mistaken. Each organism sent for radiocarbon dating is associated with a different event (i.e. the point at which that organism ceased metabolising); they may be seen as relating to the same archaeological phenomenon, but they cannot be seen as relating to the same specific moment in time.

Given this problem (and others of a more technical statistical nature; for details see Blackwell & Buck 2001), we prefer to work within the general model-based framework outlined below. Within that framework, it is straightforward to obtain the posterior distribution for T. However, we think that it is the date of a different event which is really of greatest interest in understanding the chronology of reoccupation; not so much the earliest date of a particular post-glacial sample, as the earliest human arrival and reoccupation in a region.

We will denote the date of the human arrival in a region by [A.sub.n] for the nth region, where n = 1, 2, ..., N, N being the total number of regions under study. [A.sub.n] cannot be observed directly, since it is extremely unlikely that any of the archaeological samples we have actually represents the first post-glacial event in that particular region. Thus, to use the available radiocarbon data to make inferences about [A.sub.n], some relationship between them must be postulated. In what follows we propose a statistical model that does just this.

A simple temporal model

We posit a formal model in which the earliest arrival in each region, [A.sub.n], features as a statistical parameter about which we hope to learn on the basis of radiocarbon data. Most of the statistical theory needed to apply our methodology is not new. It is based on the Bayesian statistical framework, described in detail in Zeidler et al. (1998) and summarised in Buck et al. (1996: chap. 9) and will not be given in detail here (for another example see Needham et al. 1997). Instead we will offer intuitive explanations of the model and the way it can be used to make inferences about the process of reoccupation. We propose that each region be seen as having its own phase of reoccupation at the end of the Late Glacial period and that each phase be taken as bounded in time. The earliest boundary for the phase marks the first human arrival in the region of interest; we label the date of this boundary [A.sub.n] cal BP. The latest boundary for the phase marks the end of the reoccupation phase, say [B.sub.n] cal BP. We do not expect to obtain direct radiocarbon evidence for either [A.sub.n] or [B.sub.n] and, while it is the early boundary date ([A.sub.n]) that forms the focus of interest here, it is useful for both theoretical and practical reasons to see reoccupation as having both [A.sub.n] early and a late boundary in time. Presumably, at some point, the process of reoccupation ceased and another phase of landscape use began.

We assume a priori that [A.sub.n] and [B.sub.n] lie somewhere in the range of the current radiocarbon calibration curve and that the objects suitable for radiocarbon dating from region n were deposited uniformly throughout the period [A.sub.n] to [B.sub.n]. Since both dates are on the cal BP time scale, [A.sub.n] will always be greater than [B.sub.n]. We can then use the radiocarbon dates from a region to learn more about the most likely boundary dates. The Bayesian theory and methodology needed to implement this kind of model is already available in software such as OxCal (Ramsey 1995) and BCal (Buck et al. 1999). Both packages allow the user to define a phase (or temporal group) with early and late boundary dates. Adopting this model, as implemented in the BCal software, we re-analysed the data from Housley et al. (1997) using the INTCAL98 calibration curve (Stuiver et al. 1998) to obtain estimates of each early boundary date, [A.sub.n], as shown in Figure 1. The number of radiocarbon determinations in each phase and the 95% Highest Posterior Density (HPD) region for each [A.sub.n] are given in Table 1.

[FIGURE 1 OMITTED]

Given the simple model posited for the relationship between the available radiocarbon data and the date of first reoccupation in each region, the distributions in Figure 1 represent the best available estimates for the date of reoccupation in each region after the retreat of the ice sheets. Since we have used a model to allow us to define and learn about the parameter [A.sub.n] for each of the eight regions, our results are not directly comparable with those reported in the two previous papers. As a result, we reserve detailed interpretation and comparison until we have addressed the other main issue of concern, that of the order in which reoccupation took place.

The order in which reoccupation took place

Clearly, from Figure 1, the Upper Rhine was probably reoccupied first and the British Isles last. However, chronologically ordering the regions in between (simply on the basis of the plots of the calendar dates of first reoccupation) is quite a lot more difficult. Consequently, we felt it might be helpful to seek a probabilistic answer to the question 'in what order were the regions reoccupied?'. To this end, we worked with the posterior distribution generated by BCal for each [A.sub.n] (as shown in Figure 1). Treating the [A.sub.n]s as independent, we simulated a possible ordering for the reoccupation of the eight regions by sampling one value for each [A.sub.n] from the appropriate distribution and ranking these in ascending order. By doing this repeatedly (in our case 1,000,000 times), we generated a sample from the distribution of the order of the eight regions. In this way, we have a million examples of the likely order of the eight [A.sub.n]s, or more precisely, a sample of size one million from the posterior distribution of the orderings.

We report the results thus obtained in two different ways. The first (in Table 2) shows the probability that each of the eight regions is ranked one through eight in time (one is earliest, eight is latest). From these results, we confirm and quantify conclusions made on the basis of the plots in Figure 1. In particular, we see that the British Isles was the last region to be reoccupied with a probability of 0.79. The Upper Rhine was the first region to be reoccupied with probability 0.93. The Thuringian Basin was the second region to be reoccupied with probability 0.83.

The second mechanism we use to report the results of our simulations is Table 3. Here, we show the first ten most likely orders in which the reoccupation took place (with their probabilities). In interpreting this table, readers might like to note that the a priori probability for any particular ordering is only about 0.000025 (more precisely, it is 1/8! = 1/40320). Nonetheless, even the most likely order only has a posterior probability of 0.076 and the ten most likely orderings account for just 38% of the probability. We feel that this goes a long way towards explaining why Blockley et al. (2000: 119) concluded that 'it is not possible ... to demonstrate the movement of peoples across Europe during the last deglaciation' and yet, using the same data, Housley et al. (1997) reported a partial ordering that is consistent with some, but not all, of the orderings in Table 3: British Isles; then Paris Basin and Northern Germany; then Middle Rhine, Belgium and Southern Germany; then Thuringian Basin; and then the Upper Rhine.

Looking at all the information available in Figure 1 and Tables 2 and 3, we are not suggesting a radical new interpretation of the data. What we feel we are offering is a coherent and flexible framework in which the data might be interpreted and within which uncertainty can be readily quantified. We feel that Blockley et al. (2000) were quite right to be hesitant about making inferences, but that it was also quite natural for Housley et al. (1997) to wish to make the best assessment of the dates of reoccupation (given the currently available data) and to investigate support for the model that reoccupation occurred behind the retreating ice sheet. If readers wish to make such interpretations on the basis of the results reported here, then the Upper Rhine and Thuringian Basin are the most likely candidates for the earliest regions to have been reoccupied and the British Isles is likely to have been the latest. All other regions have reasonably high probabilities of occupying any of the remaining locations in the rank order and thus we cannot reliably place them in a single location in the chronological sequence. That said, the single most likely order (based on our model) is that reported in the first column of Table 3.

Future developments

The results reported in this paper clearly rely on the suitability and validity of the model we have suggested for the relationship between the date of first reoccupation in each region and the available radiocarbon data. We feel that it is important to point out that we have selected an archaeologically and statistically simple model more as an illustration of the kinds of tools we advocate than because it is necessarily the 'best' model for interpreting this particular data set. We hope to raise awareness of the importance of the posited relationships between data and the issues we wish to tackle. If we know that we are unlikely ever to obtain samples to date a particular event, we have a good deal to gain by seeking formal models to link the data we have available to what we wish to learn about.

In this paper we have been able to make inferences that have both a spatial and a temporal component, but would like to point out that the models we have used are not truly spatio-temporal in nature. We have simply made innovative use of existing, purely temporal tools to help us learn about the chronology of supposed phases of occupation in different (arbitrarily defined) regions. Given that there are insufficient data for us to learn all that we would like to from these simple models, this may be all that is appropriate for this problem at the present. If so, there are still issues relating to model refinement that we could usefully investigate in the near future. The most obvious of these relates to our assumption of uniform deposition rates of material between [A.sub.n] and [B.sub.n]. This is the most commonly used model in Bayesian radiocarbon calibration and is appropriate for short-lived phases at a single spatial location (which is what these tools were devised for). However, in the case of reoccupation of landscapes, it might not be so sensible. We would like to consider using models that reflect the likely sparseness of material for dating from the early stages of reoccupation in each region. A simple example might be a model in which instead of a sudden increase in deposition rate (from zero to its maximum) at [A.sub.n], and a corresponding drop at [B.sub.n], there is a gradual (perhaps sigmoidal) increase from zero at [A.sub.n] to a maximum at say [C.sub.n]s, a period of constant deposition rate until say [D.sub.n], then a gradual decrease to zero at [B.sub.n]. An example is given in Figure 2; note that the shape of such graphs need not be symmetric. This would better reflect the reality of deposition rate in many situations, with a population or technology establishing itself over a finite period of time, rather than instantaneously. Note that it also includes the simpler uniform model as a special case, when [A.sub.n] = [C.sub.n] and [B.sub.n] = [D.sub.n].

[FIGURE 2 OMITTED]

Another important step would be to explore the reoccupation question without assuming predefined regions, even though information is currently available at only a few locations. There are two ways forward, both of which can be pursued within the Bayesian framework discussed earlier. One way is simply to use a statistical model for how A and B vary with geographical location, which represents the idea that, although we may not know a priori which locations were reoccupied first, we do expect that dates for (geographically) nearby locations are likely to be more similar than those for locations a long way apart. This is simply because the reoccupation was a spatio-temporal process, rather than something occurring independently at different locations. The second way is to formulate an explicit, mechanistic model of the process of reoccupation, perhaps a stochastic version of the sort of models used by Ammerman and Cavalli-Sforza (1971, 1984) or Steele et al. (1998) and then to estimate the parameters and outcome of the process from the available data. Both of these approaches have the advantages that, as data become available from other sites within a region of interest, they can be incorporated in a natural, consistent way and that we no longer need to aggregate data over regions (as suggested by Housley et al., repeated by Blockley et al. and continued by us).

In conclusion, we advocate viewing reoccupation as a process rather than a single event and have illustrated one simple way in which this might be modelled. We have reanalysed radiocarbon data relating to

the post glacial reoccupation of north-west Europe, and attempted to lay the ground work for a robust, model-based analysis of these data within the Bayesian statistical framework. All the results obtained are probabilistic and reflect the amount of uncertainty in the information available. We are able to answer the main questions posed about the order of re-occupation, but find that, given currently available .data, models and prior information, all inferences should be seen as extremely tentative. We suggest that the fact there is so much uncertainty associated with the inferences goes some way to explaining why previous authors have reached different conclusions from the same data. Given that such tentative inferences are rather unsatisfactory, we go on to make some suggestions for future modelling work that might lead us to clearer answers to the original questions posed. Our research on this topic is ongoing.

Table 1 The numbers of radiocarbon determinations and the highest
posterior density intervals for the dates of recolonisation of the
eight regions under study

 Number of radiocarbon 95% HPD region for date
Region determinations of first colonisation

Upper Rhine 7 19480-16430
Thuringian Basin 23 17180-15990
Southern Germany 10 16900-14920
Middle Rhine 9 16710-15450
Belgium 13 17330-15330
Paris Basin 14 16090-14750
Northern Germany 16 15580-14230
British Isles 41 14900-14300

Table 2 The probability that each region is temporally ranked 1
through 8 (1 = earliest, 8 = latest)

Region 1 2 3 4 5 6

Upper Rhine 0.93 0.07 0.00 0.00 0.00 0.00
Thuringian Basin 0.06 0.83 0.11 0.00 0.00 0.00
Southern Germany 0.02 0.07 0.38 0.18 0.17 0.14
Middle Rhine 0.00 0.01 0.21 0.39 0.31 0.08
Belgium 0.00 0.02 0.22 0.32 0.31 0.12
Paris Basin 0.00 0.00 0.07 0.10 0.15 0.45
Northern Germany 0.00 0.00 0.01 0.02 0.05 0.19
British Isles 0.00 0.00 0.00 0.00 0.00 0.03

Region 7 8

Upper Rhine 0.00 0.00
Thuringian Basin 0.00 0.00
Southern Germany 0.04 0.00
Middle Rhine 0.00 0.00
Belgium 0.01 0.00
Paris Basin 0.21 0.02
Northern Germany 0.55 0.18
British Isles 0.18 0.79

Table 3 The ten most likely orders for the reoccupation of the eight
regions under study (1 = earliest, 8 = latest)

Region Position in ordering

Upper Rhine 1 1 1 1 1
Thuringian Basin 2 2 2 2 2
Southern Germany 3 3 5 3 5
Middle Rhine 4 5 4 4 3
Belgium 5 4 3 5 4
Paris Basin 6 6 6 7 6
Northern Germany 7 7 7 6 7
British Isles 8 8 8 8 8
Probability 0.076 0.065 0.036 0.035 0.032

Region Position in ordering

Upper Rhine 1 1 1 1 1
Thuringian Basin 2 2 2 2 2
Southern Germany 4 3 4 3 6
Middle Rhine 5 5 3 4 4
Belgium 3 4 5 5 3
Paris Basin 6 7 6 6 5
Northern Germany 7 6 7 8 7
British Isles 8 8 8 7 8
Probability 0.032 0.029 0.027 0.024 0.021

Received: 28 August 2001; accepted: 8 October 2001; revised: 31 January 2003

Acknowledgements

We would like to thank Rupert Housley for sending us his collated radiocarbon data. We are also grateful to Mike Baxter, Andres Christen and Andrew Millard for their insightful comments and suggestions while we were working on the text.

* Department of Probability and Statistics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH (1 Email: p. blackwell@sheffield.ac.uk; 2 Email: c.e. buck@sheffield.ac.uk)

References

AMMERMAN, A.J. & L.L. CAVALLI-SFORZA. 1971. Measurement of the rate of spread of early farming in Europe. Man 6:674-688.

-- 1984. The Neolithic transition and the genetics of populations in Europe. Princeton University Press, Princeton, New Jersey.

BLACKWELL, P.G. & C.E. BUCK. 2001. Integrating spatial and temporal information from the Late Glacial human reoccupation of North Western Europe. Department of Probability and Statistics Research Report 508/01, University of Sheffield.

BLOCKLEY, S.P.E., R.E. DONAHUE & A.M. POLLARD. 2000. Radiocarbon calibration and the Late Glacial occupation of northwest Europe. Antiquity, 74:112-119.

BUCK, C.E., W.G. CAVANAGH, & C.D. LITTON. 1996. The Bayesian Approach to Interpreting Archaeological Data. Wiley, Chichester.

BUCK, C.E., J.A. CHRISTEN & G.N. JAMES. 1999. BCal: an on-line Bayesian radiocarbon calibration tool. Internet Archaeology, 7. (http://intarch.ac.uk/ journal/issue7/buck/).

HOUSLEY, R.A., C. S. GAMBLE & P. PETTITT. 2000. Reply to Blockley, Donahue and Pollard. Antiquity, 74:119-121.

HOUSLEY, R.A., C.S. GAMBLE, M. STREET & P. PETTITT. 1997. Radiocarbon evidence for the Lateglacial Human Recolonisation of Northern Europe. Proceedings of the Prehistoric Society 63:25-54.

NEEDHAM, S., C.B. RAMSEY, D. COOMBS, C. CARTWRIGHT & P. PETTITT. 1997. An independent chronology for British Bronze Age metalwork: the results of the Oxford Radiocarbon Accelerator programme. Archaeological Journal 154: 55-107.

RAMSEY, C.B. 1995. Radiocarbon calibration and analysis of stratigraphy: the OxCal program. Radiocarbon, 37(2):425-430.

RAMSEY, C.B. 2000. OxCal Program v3.5 Manual. (http://www.rlaha.ox.ac.uk/oxcal/ arch_cmb.htm#sum).

STEELE, J., J. ADAMS & T. SLUCKIN. 1998. Modelling Paleoindian dispersals (Paleoecology and human populations). World Archaeology 30(2):286-305.

STUIVER, M., P.J. REIMER, E. BARD, J.W. BECK, G.S. BURR, K.A. HUGHEN, B. KROMER, F.G. MCCORMAC, J.V.D. PLICHT & M. SPURK. 1998. INTCAL98 radiocarbon age calibration, 24,000 -0 cal BP. Radiocarbon, 40:1041-1083.

ZEIDLER, J.A., C.E. BUCK & C.D. LITTON 1998. The integration of archaeological phase information and radiocarbon results from the Jama River Valley, Ecuador: a Bayesian approach. Latin American Antiquity 9(2):135-159.