Estimating temporal likelihood of archaeological sites in prehistoric Denmark combining typochronological and radiocarbon data

Estimating temporal likelihood of archaeological sites in prehistoric Denmark combining typochronological and radiocarbon data | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Estimating temporal likelihood of archaeological sites in prehistoric Denmark combining typochronological and radiocarbon data Giacomo Bilotti This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5656593/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The surge in data availability and methodological advancements over the last decades has enabled archaeologists to develop more robust data-driven models, which are essential for reconstructing ancient human history. However, despite their potential, these datasets pose significant challenges due to their heterogeneity and inherent uncertainties. A common limitation is the low chronological resolution of many datasets, which often compels archaeologists to rely on proxies such as radiocarbon date frequency distributions to study variations in occupation intensity. While this approach is widely used, it necessitates a large number of radiocarbon samples to construct probability curves, leading to a considerable loss of spatial resolution. To address these challenges, I propose a novel method that combines typochronological and radiocarbon datasets, preserving both temporal and spatial resolution while accounting for uncertainty. Each relatively dated site is assigned a simulated calendar date within its chronological span, based on the cumulative probability distribution of locally available radiocarbon data. The results are grouped into uniform time windows, with each site assigned a likelihood of belonging to each time period. The efficacy and functionality of the method are demonstrated using toy data, with the results compared to outputs from alternative methods. Finally, the method is applied to four case studies from prehistoric Denmark (4000 − 500 BC), showcasing its potential in addressing long-standing challenges in archaeological modelling. The results show that despite the known global trends, local variation is observed in the four different sub-regions considered. Radiocarbon Aoristic analysis summed probability distribution chronological modelling Prehistoric Denmark Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. Introduction Large archaeological databases are invaluable resources for modelling spatio-temporal patterns in site distribution and population dynamics (Bevan & Conolly, 2006 ; Brandolini & Carrer, 2020 ; Costanzo et al., 2021 ). However, these datasets often suffer from poor chronological resolution, as they typically rely on typological assessments of material culture spanning several centuries. This limitation, common in data derived from surveys, large research projects, or national databases, undermines the reliability of reconstructions of population trends and site dynamics. To address these limitations, archaeologists have explored several alternatives. One of the most common solutions is the use of radiocarbon dates, particularly through Summed Probability Distributions (SPDs). SPDs have gained widespread popularity over the past two decades as a proxy for studying population patterns (Gamble et al., 2005 ; Palmisano et al., 2021 ; Rick, 1987 ; Shennan et al., 2013 ; Shennan & Edinborough 2007 ). The growing availability of radiocarbon datasets, such as p3k14c ( https://www.p3k14c.org/ ), XRONOS ( https://r.xronos.ch ), and EUROEVOL (Manning et al., 2016 ), along with methodological advances (Edinborough et al., 2017 ; Shennan et al., 2013 ), has further driven the adoption of this method. The relative simplicity of extracting and interpreting radiocarbon data, compared to more complex or qualitative measures like artefact counts, has also contributed to its popularity (Contreras & Meadows, 2014 ). Despite the strengths of radiocarbon frequency distributions and their perception as culturally “neutral”, these methods face notable challenges (Contreras & Meadows, 2014 ; Crema, 2022 ). First, they require large sample sizes, limiting their application to medium or large regions. This constraint inherently obscures local patterns and small-scale dynamics, while results are often reduced to unidimensional curves. Studies using radiocarbon frequency distributions tend to focus on large and/or data-rich regions (Bevan et al., 2017 ; McLaughlin et al., 2021 ; Palmisano et al., 2018 , 2021 ; Riris & Arroyo-Kalin, 2019 ; Shennan et al., 2013 ; Timpson et al., 2020 ). Second, data availability is frequently uneven, reflecting modern research priorities or development project intensity rather than actual past population dynamics (Crombé & Robinson, 2014 ). An increase in available data could mitigate this issue, but data collection remains largely driven by commercial archaeology, as seen in regions like Southern Scandinavia (Bilotti, 2024 ; Friman & Lagerås, 2023 ; Mikkelsen et al., 2012 ; Olsen & Kanstrup, 2018 ), or by research projects with very specific chronological or spatial aims, which have the potential to skew actual trends (Crema, 2022 ; Crema & Bevan, 2021 ). Additional criticisms extend to the method itself, questioning whether it truly serves as a demographic proxy and highlighting statistical limitations (Crema, 2022 ; McLaughlin, 2019 ). Radiocarbon dates typically include spatial information linked to sample locations. As a result, they can be used to visualise spatial trends and to identify areas with higher or lower population densities (Crema & Bevan, 2021 ). However, this approach faces challenges similar to those of classic SPDs. In large areas, it is unrealistic to assume that dates were sampled uniformly, while in smaller areas, the limited number of dates often hinders the ability to discern local patterns or site distributions (Crombé & Robinson, 2014 ). Some adjustments can be made, but these often result in a loss of spatial resolution, ultimately returning us to the original problem (Crema & Bevan, 2021 ). A possible solution that does not neglect typochronological data is the so-called aoristic analysis. Initially developed in crime science and adopted in archaeology two decades ago, the technique has seen discrete success in generating time-frequencies of typo-chronological data while accounting for chronological uncertainty (Baxter & Cool, 2016 ; Crema, 2012 ; Hinz et al., 2019 ; Ratcliffe & McCullagh, 1998 ). Its appeal lies in its intuitive functioning and its ability to translate relative chronologies into calendar years or time blocks (Crema, 2024 ). However, aoristic analysis has significant limitations: it is prone to biases derived by how archaeological periodisations are constructed, and as a descriptive statistic, it does not account for factors such as sampling error (Crema, 2024 ; Crema & Kobayashi, 2020 ). A Bayesian phase model, as suggested by Crema and Kobayashi ( 2020 ), could help address these issues for relatively dated sites. While this solution represents a significant step forward in combining the proxy with the aim of inferring population trends across regions, it does not address variations within them. The limitations of aoristic analysis and radiocarbon-based methods require archaeologists to develop a more integrated approach. Entirely disregarding legacy data and relying only on SPDs or handling typochronological data under overly simplistic assumptions is unsatisfactory and has been widely critiqued (Contreras & Meadows, 2014 ; Crema, 2024 ; Crombé & Robinson, 2014 ). This paper proposes a novel method that integrates typochronological and radiocarbon datasets to overcome these challenges, preserving both temporal and spatial resolution while accounting for uncertainty. Specifically, the proposed approach assigns typochronologically dated sites a simulated calendar date based on the cumulative probability distribution of locally available radiocarbon data. These simulated dates are grouped into uniform time windows, and the process is iterated to produce a refined dataset. In the final output, each site is assigned a likelihood of being dated within specific chronological windows shifting the uncertainty toward a likelihood-based framework. This method only requires two datasets, radiocarbon samples from the study region and a set of relatively dated sites, allowing its implementation and replication over almost any archaeological case study. The efficacy of the model is shown on toy data, discussing its functioning. The method is then applied to four different regions in Denmark dating to the Neolithic and the Bronze Age (4000 − 500 BC). To further enhance replicability and reproducibility, the method has been coded in R, a well-known open-source software environment for statistical analyses (R Core Team 2024 ), and the necessary scripts are provided in an online repository ( https://gitlab.com/bilottigiacomo/chronological-modelling ), following the current state of the art in open science (Bilotti et al., 2024 ; Marwick, 2017 ; Marwick et al., 2018 ). The paper is organised as follows: in the next section (section 2 ) the method is introduced using the toy data. In section 3 the method is applied on prehistoric Denmark, with a brief introduction to the datasets used and the study region itself to get a more complete understanding of the implication of the model. The results are then discussed in section 4 , focusing on the performance of the models and its potential and issues. The conclusions wrap the paper up, outlining future perspectives for further advances on the topic. The Supplementary Information (SI) includes all the R scripts necessary to reproduce the model, additional figures and analyses for a more comprehensive understanding of the model and additional information on the archaeological case study. The SI is available from Zenodo ( https://zenodo.org/records/14479409 ) and the scripts are available in GitLab ( https://gitlab.com/bilottigiacomo/chronological-modelling ). 2. Methodology Overview In this section, I outline the functioning of the proposed method, detailing the types of data required, how to handle them, and the process of combining these data to generate the final results. To illustrate this, I use a toy example consisting of a dataset of radiocarbon dates and another of typochronologically dated archaeological sites. 2.1 Defining the Problem Traditional maps of site distribution for specific archaeological phases often fail to capture short term chronological changes effectively. Sites often come with an underlying uncertainty of several centuries, as seen with prehistoric sites in Denmark’s national database (Section 3.1 ). Moreover, even when sites belong to the same phase, their contemporaneity cannot be proven without direct evidence, such as radiocarbon dating. Existing methods to address these challenges include aoristic analysis and frequency distributions of radiocarbon dates. While methodologically very different, their output is somehow similar: a curve describing variation in density over time. For SPDs, the observed curve is usually complemented by a set of statistical analysis (e.g., Crema & Shoda, 2021 ; Timpson et al., 2020 ), well-suited for reconstructing regional and long-term dynamics, their focus on avoiding false positives, sampling biases, and calibration issues makes them less effective for detecting small-scale or local variations. Aoristic analysis shares many limitations with SPDs, including the loss in spatial resolution. In addition, it often lacks statistical inference, though recent methodological improvements have been proposed (Crema, 2024 ). The method proposed here aims to address these issues by combining typochronological and radiocarbon data within a likelihood-based framework. For this approach to work, a dataset with radiocarbon dates is required. This dataset should include the dating in years BP, a standard deviation measurement, a unique identifier for the site from which the sample was obtained, and the laboratory ID. In this toy example, the dataset contains 1,000 radiocarbon dates, which are not completely random. Half of the dates are distributed around the radiocarbon year 5000 BP with a broad standard deviation of 750 years, while the other half are centred around 3500 BP with a narrower standard deviation of 250 years. A subset of these radiocarbon dates is shown in Table 1 . The total number of sites is 950, simulating scenarios where some sites have been dated more than once. Table 1 Subset of the toy dataset of radiocarbon dates. The full toy dataset is provided as SI and can be reproduced by running the method.R script in the repository. Lab Site ID Years BP SD Toy-1 163 4580 20 Toy-2 497 4827 50 Toy-3 13 6169 36 Toy-4 336 5053 37 Toy-5 380 5097 29 Toy-6 284 6286 28 The second dataset consists of 1,000 relatively dated archaeological sites. The sites’ relative dates follow the chronological pattern of the radiocarbon dates, centred around the calendar years 3767 and 5721 cal BP, corresponding to the median of the two radiocarbon clusters (5000 and 3500 ± 25 BP). In this example, sites and radiocarbon dates are not directly connected. Each site is randomly assigned a precision value between 100 and 1,000 years (only 100, 200, 400, 600, 1,000 are possible). The starting and ending dates are calculated as the site year ± half of the precision, rounded to the nearest century. To avoid overlap between time blocks, end years are incremented by one unit. Each site is then assigned coordinates randomly sampled from central Jutland, one of the case studies discussed later (Table 2 ). The two dataset can be visualised in different ways, such as distribution maps (Fig. 1), aoristic count of sites per phase and as an SPD (Fig. 2). Table 2 Subset of the toy dataset of archaeological sites typochronologically dated. Coordinates were randomly taken from the actual sites in central Jutland. The toy dataset can be reproduced by running the extra_toy_data.R script from the repository. Site ID Start year BP End year BP Precision (years) Coords 1 5500 5401 100 POINT (492315.1 6286799) 2 5700 5601 100 POINT (506130 6292635) 3 6600 6401 200 POINT (493754.1 6281580) 4 5900 5701 200 POINT (509319.4 6259776) 5 5800 5701 100 POINT (504972 6282930) 6 6800 6401 400 POINT (494868.1 6285960) Figure 1 : Visualisation of the toy site dataset. Here a distribution map of four consecutive phases is shown: a) 4750 BP, b) 4500 BP, c) 4250 BP and d) 4000 BP. Sites are coloured depending on their precision in relative dating. Figure 2 : a) Aorist count of the toy sites created using the baorista package in R (Crema 2024 ). b) SPD model tested against a logistic growth model, calculated in rcarbon using the toy dataset (Crema and Bevan 2021 ). The three different types of visualisation do not always align. For example, phase maps with a resolution of 250 years—a reasonable time span for a typochronological period—appear to show a decrease in sites from 4750 to 4500 BP, followed by a peak during the 4250 BP phase, which is then maintained in the subsequent time window (Fig. 1). Simply counting the number of sites in each phase largely confirms this pattern, with 78 and 77 sites in the first two phases and 142 and 161 in the latter two. Some spatial patterns can also be outlined, with certain areas, such as the northwest and central parts of the region, experiencing a greater increase in occupation over time (Fig. 1c-d). More sophisticated spatial analyses, such as cluster or point pattern analysis, could further investigate these changes and validate assumptions about past occupation dynamics. However, these maps also include sites with a precision of 1,000 years, meaning they could be dated to any of the four periods shown in Fig. 1. If only sites with a precision equal or higher than the phase resolution (250 years) are considered, the number of sites per phase decreases dramatically, yielding 2, 3, 15, and 5 sites, respectively. It might still be possible to infer growth around 4250 BP, but any other assumption made earlier no longer holds. For instance, instead of stability, a decline seems more plausible around 4000 BP-an interpretation that does not reflect the fact that one of the two simulated peaks in the data was at around 3800 BP. Despite the dataset being relatively large (1,000 sites), these conclusions rely on a small number of well-dated sites, highlighting the difficulty of integrating underlying uncertainties: one-third of the sites have a precision of 1,000 year and another third have a precision of 400 or 600 years. As previously outlined (Section 1 ), aoristic methods and SPDs are meant to address such “dating” challenges. The results of these methods differ both from those in Fig. 1 and from one another, raising questions about the reliability of all three methods or, perhaps more importantly, about the types of questions we can ask to our data and how to interpret the results. The aoristic count provides a relatively straightforward method to visualise chronological patterns in our data (Fig. 2a), with a single line representing the summed probability over time of our typochronological data. This line reveals two major patterns of growth and decline, corresponding to the structure of the simulated data, with the other fluctations probably the results of the randomisation. A Bayesian version of the aoristic count, provided in the SI, demonstrates a better representation of the chronological distribution of the sites, even though it cannot identify the precise extent and duration of the peaks. From such visualisations, archaeologists are eager in building narratives—not only about the number of sites but also about the duration and intensity of the peaks and the reasons for their decline. The results of the SPD, tested against a logistic growth null-model, partially overlap with the aoristic results (Fig. 2b) . In particular, the first peak is not identified due to the large standard deviation, and the curve in this time frame lies within the confidence interval (CI). However, the model correctly identifies lower probabilities before and after this period. The second peak is identified by the model, with a trend not dissimilar from the aoristic sum. This brief comparison shows that each of the three methods can be useful in addressing different types of question but fail to capture one or more aspects, as summarised here: Mapping site phases provides insights into both spatial and chronological trends. However, the lack of chronological precision introduces noise, and removing this noise leaves very few sites to analyse. If not coupled with statistical analysis it lacks statistical inference. Aoristic analysis shows a more defined trend, but it lacks robustness because it is represented by a simple line without any statistical inference. Additionally, it offers no insights into spatial patterns. While a Bayesian solution might address the lack of statistical inference, it does not resolve the issue of spatial patterns. SPDs share the same limitation of aoristic analysis in failing to capture spatial trends and some of the patterns within the data. Furthermore, their results do not necessarily reflect the actual trends in site distribution, as they depend on a different proxy. 2.2 Chronological modelling The solution I propose involves the combination of both datasets, assigning typochronologically dated sites a simulated calendar date based on the cumulative probability distribution of locally available radiocarbon data. Unlike SPDs, this approach retains the spatial information of individual sites and instead of producing a curve (the SPD), the result is a dataset of sites, each one with a likelihood of being dated to predefined time windows. Furthermore, it mitigates the biases associated with radiocarbon sampling, as the simulation is not solely dependent on probability density but is also constrained by typochronology. The modelling is carried out in three steps and can be reproduced by running the method.R script in the repository: The available radiocarbon dates for the study region—or a larger area if the sample size is insufficient (a few hundred dates are typically required)—are calibrated. From the calibrated dates, a set of 1,000 calendar years is randomly sampled. The sampling process is iterated 100 times, generating 100,000 calendar years. A random calendar year is sampled for each site in the dataset, constrained by the start and end dates of the typochronological phase. For example, if a site is dated to the 1700 − 1100 BC interval, only a calendar date between these years can be sampled. The probability of sampling a specific year depends on the combination of the calibrated dates’ probability density and the site’s dating range. I created a function to perform this step, available in the ran_date_function.R script in the repository. The function requires start and end years, the simulated dates generated in the previous step, and a time range as input. The process is iterated 100 times and the results are binned into 200-year (any other value is possible) intervals defined by the user. For the toy example the first interval begins at 7000 BP and the last one ends at 2600 BP. The results of this step are shown in Table 3 . The number of times each site is simulated within each time window is counted and stored as a separate column. Table 4 shows how each site is assigned an interval compatible with its typochronological information. However, unlike aoristic analysis, the likelihood is not evenly distributed across the period but depends on the typochronological precision of the site and on the probability density of radiocarbon data. A spatial visualisation of the simulated sites and their likelihood in each time frame (based on Table 4 ) is provided in the SI. The result is a dataset containing the likelihood of each site belonging to different temporal windows, which do not need to be bounded to the existing relative chronology, allowing for fuzzier boundaries. The quality of relative dating for the sites directly impacts the level of uncertainty in the final model. Nonetheless, this approach is highly adaptable and valuable for datasets containing both accurately and inaccurately dated sites. In the next section, the model will be applied to real case studies, allowing for further exploration of its potential and a better understanding of the complexities and challenges. Table 3 Intermediate results of the simulation of a calendar date and the creation of predefined time slices. Only three out of 100 simulations are shown. For the full table refer to the SI. For the specific start/end interval of each site refer to Table 4 . id Date-1 Bin-1 Date-2 Bin-2 Date-3 Bin-3 1 5429 (5.4e + 03,5.6e + 03] 5405 (5.4e + 03,5.6e + 03] 5470 (5.4e + 03,5.6e + 03] 2 5687 (5.6e + 03,5.8e + 03] 5680 (5.6e + 03,5.8e + 03] 5667 (5.6e + 03,5.8e + 03] 3 6425 (6.4e + 03,6.6e + 03] 6406 (6.4e + 03,6.6e + 03] 6545 (6.4e + 03,6.6e + 03] 4 5870 (5.8e + 03,6e + 03] 5773 (5.6e + 03,5.8e + 03] 5854 (5.8e + 03,6e + 03] 5 5751 (5.6e + 03,5.8e + 03] 5799 (5.6e + 03,5.8e + 03] 5771 (5.6e + 03,5.8e + 03] 6 6514 (6.4e + 03,6.6e + 03] 6726 (6.6e + 03,6.8e + 03] 6419 (6.4e + 03,6.6e + 03] 7 5956 (5.8e + 03,6e + 03] 5936 (5.8e + 03,6e + 03] 5940 (5.8e + 03,6e + 03] 8 5185 (5e + 03,5.2e + 03] 5161 (5e + 03,5.2e + 03] 5148 (5e + 03,5.2e + 03] 9 5589 (5.4e + 03,5.6e + 03] 5348 (5.2e + 03,5.4e + 03] 5379 (5.2e + 03,5.4e + 03] 10 5459 (5.4e + 03,5.6e + 03] 5418 (5.4e + 03,5.6e + 03] 5434 (5.4e + 03,5.6e + 03] Table 4 Subset of the results of the simulation and slicing into time windows. Only two of the bins between 5000 BP and 4000 BP are shown. For the full table refer to the SI. id start end precision bin_4200 bin_4400 bin_4600 bin_4800 bin_4000 18 4800 4701 100 0 0 100 0 0 72 4900 4301 600 12 38 24 26 0 313 4900 4801 100 0 0 0 100 0 352 4900 4501 400 0 27 49 24 0 359 4600 4401 200 0 100 0 0 0 392 4700 4601 100 0 0 100 0 0 416 4900 3901 1000 16 18 8 7 26 439 4700 4601 100 0 0 100 0 0 449 4900 4501 400 0 26 48 26 0 456 4900 3901 1000 19 20 12 11 22 3. Modelling site likelihood in prehistoric Denmark Denmark’s nearly two-century tradition of archaeology, coupled with its recent commitment to open science, makes it an exemplary case study for the method proposed here. The abundance of data is the result of numerous research projects as well as the outputs of contract archaeology. This data is freely accessible and can be downloaded from the Fund og Fortidsminder (Finds and Ancient Monuments) website ( https://www.kulturarv.dk/fundogfortidsminder/ ), managed by the Slots- og Kulturstyrelsen (Agency for Culture and Places), which oversees Denmark’s archaeological heritage. Four different region of Denmark are selected as a case study (Fig. 3). The absolute chronological framework of this study spans from approximately 4000 BC to 500 BC, a period corresponding to the Nordic Neolithic and Bronze Age (Müller & Peterson, 2015 ; Thrane, 2013 ). This time frame was chosen primarily due to data availability, particularly: (1) the limited number of archaeological sites and radiocarbon dates during the Mesolithic and (2) the fact that during the second part of the 1st Millennium BC there is a significant decrease in radiocarbon availability, as alternative dating methods were traditionally preferred. Given the methodological nature of this paper, an in-depth examination of the region’s archaeology is not necessary. Nevertheless, a contextualisation of the archaeology of the region is provided in the SI. The four sub-regions selected for this study are: (1) Thy (Thisted municipality), central Jutland (Skive and Viborg municipalities), northwestern Zealand, and Bornholm (Fig. 4 and Fig. 3 for their location within Denmark). The selection of these regions follows a double rationale. On one hand, all regions are rich in archaeological data and have a well-established history of research. This aspect allows to better capture chronological variation and to minimise possible recovery biases. In particular, Thy was the focus of several important archaeological projects, most notably the Aas and Thy archaeological projects (Bech, 2018 ; Mikkelsen, 1996 ). Prehistoric sites are particularly abundant in central Jutland due to decades of intensive investigations led by Viborg Museum (Mikkelsen et al., 2012 ). Northwestern Zealand has a long history of research and a large number of archaeological sites, thanks to significant archaeological activity (Kristiansen, 1981 ; Mathiassen, 1959 ). On Bornholm numerous archaeological project helped reconstructing a detailed picture of local dynamics (Nielsen, 1999 ; Nielsen & Nielsen, 2020 ). At the same time, each region experienced different dynamics during prehistory. For instance, in Thy—and to some extent central Jutland—human activity intensified significantly during the Bronze Age, while earlier periods are less well-represented (Bech, 2018 ). Conversely, northwestern Zealand is particularly renowned for its abundant Neolithic sites, followed by a decline, due to the shift of the most important centres to other parts of Zealand (Kristiansen, 2022 ). Finally, Bornholm experienced a very marked neolithisation as well as Bronze Age (Nielsen & Nielsen, 2020 ). Additionally, they also represent a diverse set of geographic regions: Bornholm is a medium-sized, remote island, located far from the other regions. Northwestern Zealand is part of a large island within the Danish Isles archipelago. Central Jutland is a region with limited access to the sea, connected only via the Limfjord. Thy, by contrast, is a coastal region facing the North Sea. Figure 3 : A map of Denmark showing the four study regions in white and divided into two macro-areas used to model the radiocarbon data. The 14C samples are represented as black points on the map.” Figure 4 : The archaeological sites in each sub-area are displayed. The location of each sub-region is shown in Fig. 3. From top left to bottom right: a) Thy, b) central Jutland, c) northwestern Zealand and d) Bornholm. The colour of the sites reflects their starting year in the dataset. 3.1 Typochronological data description The dataset has a relatively simple structure, providing basic information on site locations (coordinates), administrative details, site types and chronology, including the starting and ending dates in years BC/AD. It also includes links to online sources with more detailed descriptions and, in some cases, excavation reports. An evaluation of the dataset’s chronological precision (end year minus start year) reveals that its typochronological dating is relatively coarse, potentially limiting its utility for archaeological research (Fig. 5). Even when accounting for the possibility that some sites may have been used for extended periods, it is unlikely that they were occupied for 1,000 years—the minimum median chronological resolution among the four case studies (Fig. 5) . Consequently, the dataset’s lack of precise dating poses challenges for broader archaeological interpretations. This aspect might cause most researchers to set this dataset aside in favour of more accurately dated datasets from individual research projects, which are temporally and spatially constrained. Although this is not an issue per se , here I argue that even these large dataset offer great modelling possibilities when properly handled. Figure 5 : Chronological precision of prehistoric sites in the Danish database, divided by study region. The star symbol represents the mean value, and the jittered points represent individual site precision measurements. 3.2 Radiocarbon data description Approximately 2,300 radiocarbon samples are readily available from Denmark and can be downloaded from the XRONOS database or accessed via its R package, xronos (Hinz and Roe 2024 ). While the database contains many more entries, these have been filtered to remove potential duplicates. The dates are evenly distributed between northern Jutland (ca. 1,100) and southern Jutland and the Danish Isles (ca. 1,100), as shown in Fig. 3. These two regions are modelled separately to capture as many local patterns as possible. Northern Jutland is used for Thy and central Jutland, whereas Southern Jutland and the Danish Isles is used for northwestern Zealand and Bornholm. Obviously, the total number of radiocarbon dates available in Denmark is much higher. Radiocarbon sampling is systematically conducted during rescue archaeology excavations, and thousands more dates are likely hidden in excavation reports. For example, in the nearby region of Scania (Sweden) over 6,000 radiocarbon dates from rescue excavations were recently published (Friman & Lagerås, 2023 ), compared to the 2,300 listed for all of Sweden in the XRONOS database (primarily from central and southern Sweden, as of late November 2024). In the future, it is likely that new collections of radiocarbon dates will become available for Denmark. However, as the focus here is on the methodology, this limitation is not a significant concern. In fact, the sheer number of sites or dates does not affect the method employed, although more dates and improved typochronological data will undoubtedly enhance the outcomes. 3.3 Results The results presented here can be analysed in two different ways. The first involves measuring the number of sites predicted within a given time frame at least once (or n times). This approach is also the most effective for spatial visualisation, as each site has its own likelihood (Fig. 6–9). The second measurement can be considered as a sort of “site count” and consists in summing the number of sites, weighted by their probability (Fig. 10b). This measure can be used as a reference value for comparison with SPDs and aoristic counts. The values measured for each period can be normalised to enhance comparability between different regions or left unnormalised. The results of the simulation are provided in the SI, alongside scripts for generating some of the numbers discussed here. The first time window (6250 − 6050 BP) has the lowest number of predicted sites across the four regions. The reason is that the precision of sites potentially dating to the Late Mesolithic is generally very low, with only 26 sites having a precision of less than 600 years and a median precision of 4,899 years. In the following time window, the situation improves, with 34 sites having a precision of less than 600 years and a median precision halves to 2,249 years. Another important difference is the nearly doubling in the total number of possible sites in all regions (see SI). Despite this, site likelihoods remain generally low, and the most significant increase is observed between 5850–5650 BP. This increase is not due to improved chronological precision or a significant rise in the total number of sites (changes are below five percent in Bornholm and Zealand and above ten percent in the other two case studies). Instead, it reflects the effect of the radiocarbon data, which shows its first spike during this period (see Fig. 11 and SI). This observation aligns with archaeological evidence from the region, which suggests an increase in population density associated with the arrival of new farmers (Gron & Sørensen, 2018 ; Sørensen, 2014 ). 3.3.1 Thy In Thy (Fig. 6), the number of simulated sites increases during the beginning of the Neolithic, reaching a local maximum probability (sum of the probabilities of all sites) between 5650–5450 BC. During this period, sites are mostly located in the east-northeastern part of the region. Following a decline in likelihood, with a minimum reached at 5050–4850 BC, there is a new peak in the subsequent time frame (Fig. 10b), with sites now more concentrated in the southern part of the region (Fig. 6). Despite oscillation in probability, the total number of sites predicted at least once remains stable (approximately 1,350 sites) between 5850–4850 BC, reflecting the (lack of) precision in the relative dating, which in this case corresponds to the Funnel Beaker (TRB) culture (6050/4950 − 4750 BP). Between 4650 − 4050 BP, the situation remains relatively stable, with most sites located in the southern part of Thy. During the Bronze Age (BA; 3650 − 2450 BP) there is a boom in settlement, with more than 1,600 sites predicted in each remaining time window (before 3650 BP sites were below 1,300). These sites also tend to have higher probabilities and are more evenly distributed across the east coast (facing the Limfjord, Fig. 6) and the northernmost part of the region. The peak in settlement is observed during the central part of the BA, and in particular during the 3250 − 2850 BP time windows, corresponding to BA periods III and IV in the relative chronology (Thrane, 2013 ). 3.3.2 Central Jutland In central Jutland, after the beginning of the Neolithic marked by an increase in the number of sites, the pattern remains relatively stable until the turn of the 5th millennium BP, when there is a boom in site likelihood (Fig. 7) peaking between 4650 − 4450 BP (Middle Neolithic - early Younger Neolithic transition). During this period, sites are distributed more or less homogeneously across the entire study region, with the exception of the southernmost part, which contains very few sites. Before 4650 BP, sites with higher likelihood were predominantly concentrated in the central part of the region, near the southeastern end of the Limfjorden (Fig. 7). During the Bronze Age, there is a marked increase in site intensity, relatively stable throughout the neolithic, with a peak between 3050–2850 BP. In this case, the difference in site count is striking, with approximately double the number of sites compared to the preceding and following periods (Fig. 7e and Fig. 10b). The spatial distribution of sites during the end of the Neolithic period and the BA also differs from earlier phases. The highest site intensity is now found in the southeastern and westernmost parts of the region, while the previously dense central area contains relatively fewer sites (Fig. 7). Figure 6 : Site likelihood in Thy. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted. Figure 7 : Site likelihood in central Jutland. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted. 3.3.3 Northwestern Zealand In northwestern Zealand, the situation differs somewhat, with the TRB period showing the highest number of simulated sites, reaching a peak during the 5850 − 5650 BP(Fig. 8). During this period, sites are distributed relatively evenly across the study area, with a slight preference for the southern-central and western parts. The number of sites predicted at least once during this time remains very stable (around 6,800–6,900 sites), reflecting the typochronological imprecision of the archaeological data, not dissimilarly to other regions. Following this initial rise, there is a general decline in site count, reaching a minimum between 4250–4050 BP (Fig. 8). During this period, the number of sites with a likelihood of 30% or higher shrinks to only a few, with the interior and eastern parts of the region showing a general lack of sites. By the end of the Late Neolithic period (4050–3850 BP), the situation changes significantly, with a marked expansion of sites with high likelihood, concentrated in the north and west but occupying most of the region (Fig. 8). During the BA the pattern becomes less uniform, with two distinct peaks (3450–3250 and 3050–2850 BP) followed by declines, with the latest aligning with observation from other regions. In general, the settlement pattern throughout the Bronze Age is characterised by a concentration around coastal areas, with the eastern and northern parts being the most intensively occupied (but with substantial differences across the various BA periods) (Fig. 8). 3.3.4 Bornholm The situation on Bornholm differs significantly from that described for Zealand, even though the same radiocarbon dataset was used for the simulation. The number of sites remains generally low throughout the Neolithic, even though a peak in site likelihood is observed following the onset of farming on the island, with a cluster of higher-likelihood sites located in the northwest and along the southern coast (Fig. 9). A second increase in site likelihood occurs between 4850 − 4450 BP, with site initially located mostly in the southeast and later on scattered throughout the island (Fig. 9). Between the end of the Neolithic period and the first BA time window (3650–3450 BP), there is a fivefold increase in site count (Fig. 10b), with the peak reached during 3450–3250 BP. During this period, sites are distributed across the island, with lower intensity in the interior and two areas of highest concentration: the south-southwest and the northwest (Fig. 9). Figure 8 : Site likelihood in northwestern Zealand. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted. Figure 9 : Site likelihood in Bornholm. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted. 4. Discussion The method proposed here allows for the retention of spatial information on areas that were more likely occupied during any given period, often neglected in the literature. This method reduces the limitations of traditional distribution maps based on relative chronology by determining varying degrees of likelihood for a site being dated to a specific period. In many cases, the measure of “sites predicted at least once” is stable across several time windows, with numbers generally aligning with relative chronologies, such in the case of the TRB. This results is a key aspect of this method, as retaining the spatial information enables the use of the sites for further analysis, such as spatial statistics. For instance, sites can be weighted by their likelihood, assigning greater importance to sites with higher probabilities. In the SI, the results of Kernel Density Estimation for likelihood-weighted sites versus unweighted density (all sites potentially belonging to the phase) shows that intensity differences can be above 10% in certain areas. This is a very important aspect to consider, as it shows the limitations of uncritical analysis of typochronological data. A comparison between the results discussed here and each proxy used individually is beneficial for better grasp the potential of the method. Testing the statistical significance between site likelihoods and the two other proxies would be worthless, as the former is a product of the tw latter. The aoristic curve and the probability density of radiocarbon dates can both be compared to the summed likelihood of sites predicted in each phase (Fig. 10 and Fig. 11). The aoristic sum has a similar pattern for each of the four regions. This similarity is unsurprising, as the simulation of calendar years depends on typochronologically dated sites. Nevertheless, when typochronological precision is low and the number of sites high, as during the 6th millennium BP in northwestern Zealand, the integration of radiocarbon data is beneficial. In this case, a peak is observed at the onset of the Neolithic, followed by stable, but lower, site likelihood during the rest of the millunnium, with a decline after 4850 − 4650 BP (Fig. 8 and Fig. 10). In Bornholm, the peak in my results is earlier than the one from the aoristic analysis, even though the global trend is roughly unchanged (Fig. 10). This improvement is further enhanced by breaking up the relative chronology into time windows that are not based on the archaeological phases, allowing to obtain a more nuanced transition between the archaeological periods. Comparing the results to SPDs is less straightforward, as using SPDs as demographic proxies requires several assumptions. However, as a visual starting point, I will compare sites to the composite kernel density estimation (CKDE; Fig. 11) (McLaughlin, 2019 ). The increase in radiocarbon dates after 6000 BP in both subregions corresponds to the onset of the Neolithic and is also reflected in the site count, particularly in northwestern Zealand (compare to Fig. 11b). A trough in CKDE probability around 4000 BP in both North Jutland and southern Jutland and Isles is not observed in the site likelihood, which remains stable during this period in three of the regions. Even more interestingly, northwestern Zealand shows a peak, thanks to the input from typochronological data. The decline after 3000 BP in the CKDEs reflects the lower number of 14C samples in later periods, a limitation long acknowledged in the literature (e.g., Shennan et al. 2013 ), which was one of the main reasons to find a way to combine these two different type of data. However, this decline is also observed in the aoristic curves (Fig. 10a), thus inevitably reflected in the results presented here. The second probability peak in northern Jutland (Fig. 11a) is not very well visible in Thy, but on the other hand is well captured in central Jutland (Fig. 10b). This differentiation might reflect distinct Neolithic settlement patterns in Thy, which would be overlooked by only looking at the CKDE (or the SPD, see SI). In both regions, the peak during the early and middle BA is similar across proxies, as the following decline. Most “could be Late BA” sites in the database have a precision of 600 years or worse, resulting in earlier calendar dates being sampled more often due to their higher frequency in the radiocarbon data. This issue is less pronounced in Bornholm due to the availability of better-dated typochronological data, demonstrating that when higher-quality data are available, the results represent an improvement compared to the single proxies. Figure 10 : a) Aoristic count calculated in R using the baorista package (Crema 2024 ) and b) the summed likelihood per each phase resulted from the simulation of this study. Legend is common for the two sub-figures. This analysis represents only a visual assessment of the trends across the different curves and does not aim to replace individual proxies for representing large-scale patterns, even though this is the ultimate goal. To infer past demographic patterns, this method would require integration into a statistically robust framework (as proposed by Crema, 2022 , 2024 ; Crema & Kobayashi, 2020 ; Timpson et al., 2020 ). An SPD for each region, generated using Timpson et al. ( 2020 )’s approach, is provided in the SI for reference. Across the different case studies, it is easy to spot the marked difference in patterns between typochronological phases, which was not present in the toy example. This issue arises from the uneven length of relatively dated archaeological periods, with better precision achieved in certain time frames depending on the available material culture. Thus, whenever possible, priority should be given to the refinement of the input data. Another potential challenge concerns the difficulty of attributing relative dates to sites, for example assigning a site to the end of the Late Neolithic or to the early BA. In the database, sites are typically well-separated between the Neolithic and Bronze Age, potentially creating an artificial divide between phases, caused by the recording strategy. A possible solution would involve providing confidence intervals for relative dating, such as “30% LN II and 70% EBA I,” as suggested by A. Bevan et al. ( 2013 ) and which could easily be implemented in the simulation carried out here. If this is not feasible, an alternative might involve integrating uncertainty within a Bayesian framework for phase allocation (Crema, 2024 ). The simulation strategy presented in this paper mitigates these effects. Sampling a calendar date for each site in the dataset and binning it into arbitrarily defined 200-year windows (generally unconnected with relative chronologies, except in the case of the BA) avoids the assumption that a site exclusively belongs to one phase. This is particularly effective when sampled dates fall near phase boundaries or when there is uncertainty in phase attribution. Iterating the process makes sure that a site with these issue will appear in more than a temporal window but in both with lower probability than a securely dated site. The within phase probability was dealt more flexibly by assuming that the probability of a site being dated in any calendar year within its relatively dated phase is correlated to the radiocarbon curve. The iteration of the process, assures the presence of sites with such uncertainties to be represented in different temporal windows. The potential for linking typochronologically dated sites with radiocarbon data has not yet been discussed. If a specific site can be linked to one or more radiocarbon samples, the code used here could be easily adapted to sample from a smaller dataset. A similar approach was recently implemented by the author to determine the dating of prehistoric houses in Scania (southern Sweden) (Bilotti, 2024 ). However, particular attention is required in this case, as it can only work when the site is securely dated to a single phase or when radiocarbon samples are available for all phases of occupation. Otherwise, some periods may be underrepresented, and if the relative chronology and the radiocarbon date do not align, the sampled date would not be representative of the site. Additionally, when the number of radiocarbon dates permits, this method can be adapted to determine the likelihood of individual structures within an excavation being dated to specific time frames (e.g., tombs in a large cemetery or buildings in a settlement). Figure 11 : CKDE of the radiocarbon data available for Denmark from the XRONOS database. a) Northern Jutland and b) Southern Jutland and the Danish Isles. The CKDE were calculated using the ckde function from the rcarbon package in R (Crema and Bevan 2021 ). 5. Conclusion In this paper, I proposed a new method to address the loss of spatial resolution when working with large archaeological datasets. I also aimed to show that, despite their limitations, typochronologically dated legacy data can - and should - be considered for quantitative analysis. Both data sources suffer from biases and issues and transferring these biases into a likelihood-based framework help mitigating them. The current approaches employed to study-or simply eyeball-site patterns in a region all have their strengths and weaknesses. Mapping sites, even when coupled with spatial statistics, lacks chronological precision or it is necessary to reduce the number of sites considered. Aoristic analysis offers better chronological trends but generally lacks statistical inference and spatial patterns are lost. Probability densities of radiocarbon data similarly fail to capture spatial trends and are further complicated by well-known biases (e.g., recovery biases, calibration issues) and methodological complexity. The method proposed here overcomes some of these issues and in particular, it keeps the spatial information available assigning to each site in the dataset a likelihood of being dated to a specific time window, based on its relative dating and the available radiocarbon data. Additionally, it overcomes the issues connected to sampling biases in the radiocarbon data, as the simulation is constrained by typochronology. Another key strength of the method is that the output can be used for further analysis, weighting the contribution of each site in a time window based on its likelihood. Using more precise data would reduce the uncertainties in the results presented here, as was evident in some of the study regions, especially during the Bronze Age. This issue was absent in the toy example, where the chronological error did not depend on relative chronologies (i.e., precision was uniformly distributed) and depends on the data in the Danish database, which could be improved by reassess the chronology of each entry. Finally, while this method has been applied to relatively large regions to study population patterns, it is not limited to any scale of operation and could be used to study scatters of materials within a site, the patterns in a large cemetery, variation of house sizes and typologies over time. Declarations Competing Interests: The author does not have any competing interest. Acknowledgments I am thankful to Roberto Ragno for the support and insightful comments during the preparation of this manuscript. This research was supported by the German Research Foundation and the Kiel University (CRC 1266) under grant number 290391021. References Artursson, M. (2005). Gårds- och bebyggelsestruktur. In P. Lagerås & B. 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Vernacular Architecture , 23 (1), 34–43. https://doi.org/10.1179/vea.1992.23.1.34 Footnotes Using SPDs to infer population dynamics is generally accepted but should not be done uncritically (Crema, 2022 ; Crema & Shoda, 2021 ; Timpson et al., 2020 ). During the period considered, the most common type of settlement were farmsteads, which were not occupied for very long times. Artursson ( 2005 ) proposed the longest time span for the study region, suggesting 100–150 years for the houses at Limensgård, Bornholm. However, in many cases, much shorter spans of 25–50 years have been proposed (Gerritsen, 1999 ; Müller, 2013 ; Zimmermann, 1992 ). Similarly, a cemetery might have been occupied for a long period (but not 1000 years), and stray finds are the products of discrete events. Additional Declarations No competing interests reported. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-5656593","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":399500291,"identity":"55def8f2-7301-48be-874b-d76b3b07400f","order_by":0,"name":"Giacomo Bilotti","email":"data:image/png;base64,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","orcid":"","institution":"Kiel University","correspondingAuthor":true,"prefix":"","firstName":"Giacomo","middleName":"","lastName":"Bilotti","suffix":""}],"badges":[],"createdAt":"2024-12-16 20:53:07","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5656593/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5656593/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":73417519,"identity":"18ce4d70-44c2-419c-88cd-7844cfd199c8","added_by":"auto","created_at":"2025-01-09 17:31:00","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":1127380,"visible":true,"origin":"","legend":"\u003cp\u003eVisualisation of the toy site dataset. Here a distribution map of four consecutive phases is shown: a) 4750 BP, b) 4500 BP, c) 4250 BP and d) 4000 BP. Sites are coloured depending on their precision in relative dating.\u003c/p\u003e","description":"","filename":"floatimage1.png","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/50b0e02dd236ed67f9a1ccb4.png"},{"id":73416519,"identity":"558ccbf8-6bfc-4643-b3b6-d36067c9ae20","added_by":"auto","created_at":"2025-01-09 17:15:00","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":108922,"visible":true,"origin":"","legend":"\u003cp\u003ea) Aorist count of the toy sites created using the baorista package in R (Crema 2024). b) SPD model tested against a logistic growth model, calculated in rcarbon using the toy dataset (Crema and Bevan 2021).\u003c/p\u003e","description":"","filename":"floatimage2.png","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/f5b7f7438d0929e5a78e0111.png"},{"id":73415897,"identity":"8a0a2be3-1020-41b1-99d2-fad88397bbec","added_by":"auto","created_at":"2025-01-09 17:07:00","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":1311290,"visible":true,"origin":"","legend":"\u003cp\u003eA map of Denmark showing the four study regions in white and divided into two macro-areas used to model the radiocarbon data. The 14C samples are represented as black points on the map.”\u003c/p\u003e","description":"","filename":"floatimage3.png","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/63dbd701e5ca52d67f7cafb6.png"},{"id":73415903,"identity":"17265f06-7b1b-4aee-9c37-990475450535","added_by":"auto","created_at":"2025-01-09 17:07:00","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":6738275,"visible":true,"origin":"","legend":"\u003cp\u003eThe archaeological sites in each sub-area are displayed. The location of each sub-region is shown in Fig. 3. From top left to bottom right: a) Thy, b) central Jutland, c) northwestern Zealand and d) Bornholm. The colour of the sites reflects their starting year in the dataset.\u003c/p\u003e","description":"","filename":"floatimage4.png","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/5df98979ae541324059270f7.png"},{"id":73415896,"identity":"93df8b1f-8bf2-4ace-82d2-84005e025c81","added_by":"auto","created_at":"2025-01-09 17:07:00","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":1146928,"visible":true,"origin":"","legend":"\u003cp\u003eChronological precision of prehistoric sites in the Danish database, divided by study region. The star symbol represents the mean value, and the jittered points represent individual site precision measurements.\u003c/p\u003e","description":"","filename":"floatimage5.png","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/ba605d9d3c2a45187648fbaf.png"},{"id":73415905,"identity":"08438ce8-5196-4d59-afb1-ee5186473d26","added_by":"auto","created_at":"2025-01-09 17:07:01","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":1016503,"visible":true,"origin":"","legend":"\u003cp\u003eSite likelihood in Thy. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted.\u003c/p\u003e","description":"","filename":"floatimage6.png","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/72696ec20ff6a9bae97e8fce.png"},{"id":73415900,"identity":"525fab1f-bd30-49b7-996d-a364ae012b8f","added_by":"auto","created_at":"2025-01-09 17:07:00","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":2207144,"visible":true,"origin":"","legend":"\u003cp\u003eSite likelihood in central Jutland. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted.\u003c/p\u003e","description":"","filename":"floatimage7.png","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/ec88e6038fa0002ea3f8be55.png"},{"id":73415902,"identity":"ef4c46e8-3360-4ffe-b40e-458f5a709f82","added_by":"auto","created_at":"2025-01-09 17:07:00","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":2236853,"visible":true,"origin":"","legend":"\u003cp\u003eSite likelihood in northwestern Zealand. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted.\u003c/p\u003e","description":"","filename":"floatimage8.png","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/6c616dd1824b89abec76f16e.png"},{"id":73415910,"identity":"c7e7646e-2ccf-4d80-9dee-5271f3d9a146","added_by":"auto","created_at":"2025-01-09 17:07:01","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":1074748,"visible":true,"origin":"","legend":"\u003cp\u003eSite likelihood in Bornholm. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted.\u003c/p\u003e","description":"","filename":"floatimage9.png","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/a08fab0a5600f66eeacfcf8a.png"},{"id":73416528,"identity":"f50b4890-5b26-4c1d-99f2-864ad55a54ae","added_by":"auto","created_at":"2025-01-09 17:15:01","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":1161537,"visible":true,"origin":"","legend":"\u003cp\u003ea) Aoristic count calculated in R using the baorista package (Crema 2024) and b) the summed likelihood per each phase resulted from the simulation of this study. Legend is common for the two sub-figures.\u003c/p\u003e","description":"","filename":"floatimage10.png","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/4df4695b85903bf19cd42531.png"},{"id":73416527,"identity":"ca351106-ada5-4738-83f3-ca64bd4a80bc","added_by":"auto","created_at":"2025-01-09 17:15:01","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":101349,"visible":true,"origin":"","legend":"\u003cp\u003eCKDE of the radiocarbon data available for Denmark from the XRONOS database. a) Northern Jutland and b) Southern Jutland and the Danish Isles. The CKDE were calculated using the ckde function from the rcarbon package in R (Crema and Bevan 2021).\u003c/p\u003e","description":"","filename":"floatimage11.png","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/9b02f5683a0bf82fd7df8c76.png"},{"id":77830751,"identity":"7a087206-c1d0-4d1b-8966-dae3a071478c","added_by":"auto","created_at":"2025-03-06 01:47:28","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":25643026,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/21f15cb2-b7cc-4885-9d93-73e07bfafe14.pdf"},{"id":73415886,"identity":"795a47ef-e092-4042-a2a3-0df2767f355c","added_by":"auto","created_at":"2025-01-09 17:07:00","extension":"xlsx","order_by":0,"title":"","display":"","copyAsset":false,"role":"supplement","size":9754,"visible":true,"origin":"","legend":"","description":"","filename":"tables.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-5656593/v1/4a5d2554fa66d0364742ae14.xlsx"}],"financialInterests":"No competing interests reported.","formattedTitle":"Estimating temporal likelihood of archaeological sites in prehistoric Denmark combining typochronological and radiocarbon data","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eLarge archaeological databases are invaluable resources for modelling spatio-temporal patterns in site distribution and population dynamics (Bevan \u0026amp; Conolly, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; Brandolini \u0026amp; Carrer, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Costanzo et al., \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). However, these datasets often suffer from poor chronological resolution, as they typically rely on typological assessments of material culture spanning several centuries. This limitation, common in data derived from surveys, large research projects, or national databases, undermines the reliability of reconstructions of population trends and site dynamics.\u003c/p\u003e \u003cp\u003eTo address these limitations, archaeologists have explored several alternatives. One of the most common solutions is the use of radiocarbon dates, particularly through Summed Probability Distributions (SPDs). SPDs have gained widespread popularity over the past two decades as a proxy for studying population patterns (Gamble et al., \u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e2005\u003c/span\u003e; Palmisano et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Rick, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e1987\u003c/span\u003e; Shennan et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Shennan \u0026amp; Edinborough \u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e2007\u003c/span\u003e). The growing availability of radiocarbon datasets, such as p3k14c (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.p3k14c.org/\u003c/span\u003e\u003cspan address=\"https://www.p3k14c.org/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e), XRONOS (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://r.xronos.ch\u003c/span\u003e\u003cspan address=\"https://r.xronos.ch\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e), and EUROEVOL (Manning et al., \u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e2016\u003c/span\u003e), along with methodological advances (Edinborough et al., \u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Shennan et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), has further driven the adoption of this method. The relative simplicity of extracting and interpreting radiocarbon data, compared to more complex or qualitative measures like artefact counts, has also contributed to its popularity (Contreras \u0026amp; Meadows, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eDespite the strengths of radiocarbon frequency distributions and their perception as culturally \u0026ldquo;neutral\u0026rdquo;, these methods face notable challenges (Contreras \u0026amp; Meadows, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Crema, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). First, they require large sample sizes, limiting their application to medium or large regions. This constraint inherently obscures local patterns and small-scale dynamics, while results are often reduced to unidimensional curves. Studies using radiocarbon frequency distributions tend to focus on large and/or data-rich regions (Bevan et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; McLaughlin et al., \u003cspan citationid=\"CR33\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Palmisano et al., \u003cspan citationid=\"CR41\" class=\"CitationRef\"\u003e2018\u003c/span\u003e, \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Riris \u0026amp; Arroyo-Kalin, \u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Shennan et al., \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Timpson et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Second, data availability is frequently uneven, reflecting modern research priorities or development project intensity rather than actual past population dynamics (Cromb\u0026eacute; \u0026amp; Robinson, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). An increase in available data could mitigate this issue, but data collection remains largely driven by commercial archaeology, as seen in regions like Southern Scandinavia (Bilotti, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Friman \u0026amp; Lager\u0026aring;s, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Mikkelsen et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Olsen \u0026amp; Kanstrup, \u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e2018\u003c/span\u003e), or by research projects with very specific chronological or spatial aims, which have the potential to skew actual trends (Crema, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Crema \u0026amp; Bevan, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). Additional criticisms extend to the method itself, questioning whether it truly serves as a demographic proxy and highlighting statistical limitations (Crema, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; McLaughlin, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2019\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eRadiocarbon dates typically include spatial information linked to sample locations. As a result, they can be used to visualise spatial trends and to identify areas with higher or lower population densities (Crema \u0026amp; Bevan, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). However, this approach faces challenges similar to those of classic SPDs. In large areas, it is unrealistic to assume that dates were sampled uniformly, while in smaller areas, the limited number of dates often hinders the ability to discern local patterns or site distributions (Cromb\u0026eacute; \u0026amp; Robinson, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). Some adjustments can be made, but these often result in a loss of spatial resolution, ultimately returning us to the original problem (Crema \u0026amp; Bevan, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eA possible solution that does not neglect typochronological data is the so-called aoristic analysis. Initially developed in crime science and adopted in archaeology two decades ago, the technique has seen discrete success in generating time-frequencies of typo-chronological data while accounting for chronological uncertainty (Baxter \u0026amp; Cool, \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Crema, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Hinz et al., \u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e2019\u003c/span\u003e; Ratcliffe \u0026amp; McCullagh, \u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e1998\u003c/span\u003e). Its appeal lies in its intuitive functioning and its ability to translate relative chronologies into calendar years or time blocks (Crema, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). However, aoristic analysis has significant limitations: it is prone to biases derived by how archaeological periodisations are constructed, and as a descriptive statistic, it does not account for factors such as sampling error (Crema, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Crema \u0026amp; Kobayashi, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). A Bayesian phase model, as suggested by Crema and Kobayashi (\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), could help address these issues for relatively dated sites. While this solution represents a significant step forward in combining the proxy with the aim of inferring population trends across regions, it does not address variations within them.\u003c/p\u003e \u003cp\u003eThe limitations of aoristic analysis and radiocarbon-based methods require archaeologists to develop a more integrated approach. Entirely disregarding legacy data and relying only on SPDs or handling typochronological data under overly simplistic assumptions is unsatisfactory and has been widely critiqued (Contreras \u0026amp; Meadows, \u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2014\u003c/span\u003e; Crema, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Cromb\u0026eacute; \u0026amp; Robinson, \u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e2014\u003c/span\u003e). This paper proposes a novel method that integrates typochronological and radiocarbon datasets to overcome these challenges, preserving both temporal and spatial resolution while accounting for uncertainty. Specifically, the proposed approach assigns typochronologically dated sites a simulated calendar date based on the cumulative probability distribution of locally available radiocarbon data. These simulated dates are grouped into uniform time windows, and the process is iterated to produce a refined dataset. In the final output, each site is assigned a likelihood of being dated within specific chronological windows shifting the uncertainty toward a likelihood-based framework.\u003c/p\u003e \u003cp\u003eThis method only requires two datasets, radiocarbon samples from the study region and a set of relatively dated sites, allowing its implementation and replication over almost any archaeological case study. The efficacy of the model is shown on toy data, discussing its functioning. The method is then applied to four different regions in Denmark dating to the Neolithic and the Bronze Age (4000\u0026thinsp;\u0026minus;\u0026thinsp;500 BC). To further enhance replicability and reproducibility, the method has been coded in R, a well-known open-source software environment for statistical analyses (R Core Team \u003cspan citationid=\"CR43\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), and the necessary scripts are provided in an online repository (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://gitlab.com/bilottigiacomo/chronological-modelling\u003c/span\u003e\u003cspan address=\"https://gitlab.com/bilottigiacomo/chronological-modelling\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e), following the current state of the art in open science (Bilotti et al., \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Marwick, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e2017\u003c/span\u003e; Marwick et al., \u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e2018\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe paper is organised as follows: in the next section (section \u003cspan refid=\"Sec2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) the method is introduced using the toy data. In section \u003cspan refid=\"Sec5\" class=\"InternalRef\"\u003e3\u003c/span\u003e the method is applied on prehistoric Denmark, with a brief introduction to the datasets used and the study region itself to get a more complete understanding of the implication of the model. The results are then discussed in section \u003cspan refid=\"Sec13\" class=\"InternalRef\"\u003e4\u003c/span\u003e, focusing on the performance of the models and its potential and issues. The conclusions wrap the paper up, outlining future perspectives for further advances on the topic. The Supplementary Information (SI) includes all the R scripts necessary to reproduce the model, additional figures and analyses for a more comprehensive understanding of the model and additional information on the archaeological case study. The SI is available from Zenodo (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://zenodo.org/records/14479409\u003c/span\u003e\u003cspan address=\"https://zenodo.org/records/14479409\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) and the scripts are available in GitLab (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://gitlab.com/bilottigiacomo/chronological-modelling\u003c/span\u003e\u003cspan address=\"https://gitlab.com/bilottigiacomo/chronological-modelling\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e).\u003c/p\u003e"},{"header":"2. Methodology Overview","content":"\u003cp\u003eIn this section, I outline the functioning of the proposed method, detailing the types of data required, how to handle them, and the process of combining these data to generate the final results. To illustrate this, I use a toy example consisting of a dataset of radiocarbon dates and another of typochronologically dated archaeological sites.\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Defining the Problem\u003c/h2\u003e \u003cp\u003eTraditional maps of site distribution for specific archaeological phases often fail to capture short term chronological changes effectively. Sites often come with an underlying uncertainty of several centuries, as seen with prehistoric sites in Denmark\u0026rsquo;s national database (Section \u003cspan refid=\"Sec6\" class=\"InternalRef\"\u003e3.1\u003c/span\u003e). Moreover, even when sites belong to the same phase, their contemporaneity cannot be proven without direct evidence, such as radiocarbon dating.\u003c/p\u003e \u003cp\u003eExisting methods to address these challenges include aoristic analysis and frequency distributions of radiocarbon dates. While methodologically very different, their output is somehow similar: a curve describing variation in density over time. For SPDs, the observed curve is usually complemented by a set of statistical analysis (e.g., Crema \u0026amp; Shoda, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Timpson et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e), well-suited for reconstructing regional and long-term dynamics, their focus on avoiding false positives, sampling biases, and calibration issues makes them less effective for detecting small-scale or local variations. Aoristic analysis shares many limitations with SPDs, including the loss in spatial resolution. In addition, it often lacks statistical inference, though recent methodological improvements have been proposed (Crema, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe method proposed here aims to address these issues by combining typochronological and radiocarbon data within a likelihood-based framework. For this approach to work, a dataset with radiocarbon dates is required. This dataset should include the dating in years BP, a standard deviation measurement, a unique identifier for the site from which the sample was obtained, and the laboratory ID. In this toy example, the dataset contains 1,000 radiocarbon dates, which are not completely random. Half of the dates are distributed around the radiocarbon year 5000 BP with a broad standard deviation of 750 years, while the other half are centred around 3500 BP with a narrower standard deviation of 250 years. A subset of these radiocarbon dates is shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. The total number of sites is 950, simulating scenarios where some sites have been dated more than once.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSubset of the toy dataset of radiocarbon dates. The full toy dataset is provided as SI and can be reproduced by running the method.R script in the repository.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eLab\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSite ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eYears BP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSD\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eToy-1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e163\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4580\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eToy-2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e497\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4827\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eToy-3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6169\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e36\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eToy-4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e336\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5053\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eToy-5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e380\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5097\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e29\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eToy-6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e284\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6286\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e28\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe second dataset consists of 1,000 relatively dated archaeological sites. The sites\u0026rsquo; relative dates follow the chronological pattern of the radiocarbon dates, centred around the calendar years 3767 and 5721 cal BP, corresponding to the median of the two radiocarbon clusters (5000 and 3500\u0026thinsp;\u0026plusmn;\u0026thinsp;25 BP). In this example, sites and radiocarbon dates are not directly connected. Each site is randomly assigned a precision value between 100 and 1,000 years (only 100, 200, 400, 600, 1,000 are possible). The starting and ending dates are calculated as the site year\u0026thinsp;\u0026plusmn;\u0026thinsp;half of the precision, rounded to the nearest century. To avoid overlap between time blocks, end years are incremented by one unit. Each site is then assigned coordinates randomly sampled from central Jutland, one of the case studies discussed later (Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). The two dataset can be visualised in different ways, such as distribution maps (Fig.\u0026nbsp;1), aoristic count of sites per phase and as an SPD (Fig.\u0026nbsp;2).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSubset of the toy dataset of archaeological sites typochronologically dated. Coordinates were randomly taken from the actual sites in central Jutland. The toy dataset can be reproduced by running the extra_toy_data.R script from the repository.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSite ID\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eStart year BP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eEnd year BP\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePrecision (years)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCoords\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5401\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePOINT (492315.1 6286799)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5601\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePOINT (506130 6292635)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6401\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePOINT (493754.1 6281580)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5701\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePOINT (509319.4 6259776)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e5800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e5701\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePOINT (504972 6282930)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e6401\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003ePOINT (494868.1 6285960)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eFigure\u0026nbsp;1\u003c/b\u003e: Visualisation of the toy site dataset. Here a distribution map of four consecutive phases is shown: a) 4750 BP, b) 4500 BP, c) 4250 BP and d) 4000 BP. Sites are coloured depending on their precision in relative dating.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eFigure\u0026nbsp;2\u003c/b\u003e: a) Aorist count of the toy sites created using the baorista package in R (Crema \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). b) SPD model tested against a logistic growth model, calculated in rcarbon using the toy dataset (Crema and Bevan \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe three different types of visualisation do not always align. For example, phase maps with a resolution of 250 years\u0026mdash;a reasonable time span for a typochronological period\u0026mdash;appear to show a decrease in sites from 4750 to 4500 BP, followed by a peak during the 4250 BP phase, which is then maintained in the subsequent time window (Fig.\u0026nbsp;1). Simply counting the number of sites in each phase largely confirms this pattern, with 78 and 77 sites in the first two phases and 142 and 161 in the latter two. Some spatial patterns can also be outlined, with certain areas, such as the northwest and central parts of the region, experiencing a greater increase in occupation over time (Fig.\u0026nbsp;1c-d). More sophisticated spatial analyses, such as cluster or point pattern analysis, could further investigate these changes and validate assumptions about past occupation dynamics.\u003c/p\u003e \u003cp\u003eHowever, these maps also include sites with a precision of 1,000 years, meaning they could be dated to any of the four periods shown in Fig.\u0026nbsp;1. If only sites with a precision equal or higher than the phase resolution (250 years) are considered, the number of sites per phase decreases dramatically, yielding 2, 3, 15, and 5 sites, respectively. It might still be possible to infer growth around 4250 BP, but any other assumption made earlier no longer holds. For instance, instead of stability, a decline seems more plausible around 4000 BP-an interpretation that does not reflect the fact that one of the two simulated peaks in the data was at around 3800 BP. Despite the dataset being relatively large (1,000 sites), these conclusions rely on a small number of well-dated sites, highlighting the difficulty of integrating underlying uncertainties: one-third of the sites have a precision of 1,000 year and another third have a precision of 400 or 600 years.\u003c/p\u003e \u003cp\u003eAs previously outlined (Section \u003cspan refid=\"Sec1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), aoristic methods and SPDs are meant to address such \u0026ldquo;dating\u0026rdquo; challenges. The results of these methods differ both from those in Fig.\u0026nbsp;1 and from one another, raising questions about the reliability of all three methods or, perhaps more importantly, about the types of questions we can ask to our data and how to interpret the results. The aoristic count provides a relatively straightforward method to visualise chronological patterns in our data (Fig.\u0026nbsp;2a), with a single line representing the summed probability over time of our typochronological data. This line reveals two major patterns of growth and decline, corresponding to the structure of the simulated data, with the other fluctations probably the results of the randomisation. A Bayesian version of the aoristic count, provided in the SI, demonstrates a better representation of the chronological distribution of the sites, even though it cannot identify the precise extent and duration of the peaks. From such visualisations, archaeologists are eager in building narratives\u0026mdash;not only about the number of sites but also about the duration and intensity of the peaks and the reasons for their decline.\u003c/p\u003e \u003cp\u003eThe results of the SPD, tested against a logistic growth null-model, partially overlap with the aoristic results (Fig.\u0026nbsp;2b)\u003ca class=\"FNLink\" href=\"#Fn1\" id=\"#FNLinkFn1\"\u003e\u003c/a\u003e. In particular, the first peak is not identified due to the large standard deviation, and the curve in this time frame lies within the confidence interval (CI). However, the model correctly identifies lower probabilities before and after this period. The second peak is identified by the model, with a trend not dissimilar from the aoristic sum. This brief comparison shows that each of the three methods can be useful in addressing different types of question but fail to capture one or more aspects, as summarised here:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eMapping site phases provides insights into both spatial and chronological trends. However, the lack of chronological precision introduces noise, and removing this noise leaves very few sites to analyse. If not coupled with statistical analysis it lacks statistical inference.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eAoristic analysis shows a more defined trend, but it lacks robustness because it is represented by a simple line without any statistical inference. Additionally, it offers no insights into spatial patterns. While a Bayesian solution might address the lack of statistical inference, it does not resolve the issue of spatial patterns.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eSPDs share the same limitation of aoristic analysis in failing to capture spatial trends and some of the patterns within the data. Furthermore, their results do not necessarily reflect the actual trends in site distribution, as they depend on a different proxy.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2 Chronological modelling\u003c/h2\u003e \u003cp\u003eThe solution I propose involves the combination of both datasets, assigning typochronologically dated sites a simulated calendar date based on the cumulative probability distribution of locally available radiocarbon data. Unlike SPDs, this approach retains the spatial information of individual sites and instead of producing a curve (the SPD), the result is a dataset of sites, each one with a likelihood of being dated to predefined time windows. Furthermore, it mitigates the biases associated with radiocarbon sampling, as the simulation is not solely dependent on probability density but is also constrained by typochronology.\u003c/p\u003e \u003cp\u003eThe modelling is carried out in three steps and can be reproduced by running the method.R script in the repository:\u003c/p\u003e \u003cp\u003e \u003col\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe available radiocarbon dates for the study region\u0026mdash;or a larger area if the sample size is insufficient (a few hundred dates are typically required)\u0026mdash;are calibrated. From the calibrated dates, a set of 1,000 calendar years is randomly sampled. The sampling process is iterated 100 times, generating 100,000 calendar years.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eA random calendar year is sampled for each site in the dataset, constrained by the start and end dates of the typochronological phase. For example, if a site is dated to the 1700\u0026thinsp;\u0026minus;\u0026thinsp;1100 BC interval, only a calendar date between these years can be sampled. The probability of sampling a specific year depends on the combination of the calibrated dates\u0026rsquo; probability density and the site\u0026rsquo;s dating range. I created a function to perform this step, available in the ran_date_function.R script in the repository. The function requires start and end years, the simulated dates generated in the previous step, and a time range as input. The process is iterated 100 times and the results are binned into 200-year (any other value is possible) intervals defined by the user. For the toy example the first interval begins at 7000 BP and the last one ends at 2600 BP. The results of this step are shown in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003cspan\u003e \u003cli\u003e \u003cp\u003eThe number of times each site is simulated within each time window is counted and stored as a separate column. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e shows how each site is assigned an interval compatible with its typochronological information. However, unlike aoristic analysis, the likelihood is not evenly distributed across the period but depends on the typochronological precision of the site and on the probability density of radiocarbon data. A spatial visualisation of the simulated sites and their likelihood in each time frame (based on Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e) is provided in the SI.\u003c/p\u003e \u003c/li\u003e \u003c/span\u003e \u003c/ol\u003e \u003c/p\u003e \u003cp\u003eThe result is a dataset containing the likelihood of each site belonging to different temporal windows, which do not need to be bounded to the existing relative chronology, allowing for fuzzier boundaries. The quality of relative dating for the sites directly impacts the level of uncertainty in the final model. Nonetheless, this approach is highly adaptable and valuable for datasets containing both accurately and inaccurately dated sites. In the next section, the model will be applied to real case studies, allowing for further exploration of its potential and a better understanding of the complexities and challenges.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eIntermediate results of the simulation of a calendar date and the creation of predefined time slices. Only three out of 100 simulations are shown. For the full table refer to the SI. For the specific start/end interval of each site refer to Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e 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\u003cp\u003e(5.4e\u0026thinsp;+\u0026thinsp;03,5.6e\u0026thinsp;+\u0026thinsp;03]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSubset of the results of the simulation and slicing into time windows. Only two of the bins between 5000 BP and 4000 BP are shown. For the full table refer to the SI.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eid\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003estart\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eend\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eprecision\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003ebin_4200\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ebin_4400\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003ebin_4600\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003ebin_4800\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003ebin_4000\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4800\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4701\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4301\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e38\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e313\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4801\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e352\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4501\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e27\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e359\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4401\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e392\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4601\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e416\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3901\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e439\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4700\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4601\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e449\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e4501\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e400\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e48\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e456\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4900\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e3901\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e19\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3. Modelling site likelihood in prehistoric Denmark","content":"\u003cp\u003eDenmark\u0026rsquo;s nearly two-century tradition of archaeology, coupled with its recent commitment to open science, makes it an exemplary case study for the method proposed here. The abundance of data is the result of numerous research projects as well as the outputs of contract archaeology. This data is freely accessible and can be downloaded from the Fund og Fortidsminder (Finds and Ancient Monuments) website (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.kulturarv.dk/fundogfortidsminder/\u003c/span\u003e\u003cspan address=\"https://www.kulturarv.dk/fundogfortidsminder/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e), managed by the Slots- og Kulturstyrelsen (Agency for Culture and Places), which oversees Denmark\u0026rsquo;s archaeological heritage.\u003c/p\u003e \u003cp\u003eFour different region of Denmark are selected as a case study (Fig.\u0026nbsp;3). The absolute chronological framework of this study spans from approximately 4000 BC to 500 BC, a period corresponding to the Nordic Neolithic and Bronze Age (M\u0026uuml;ller \u0026amp; Peterson, \u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Thrane, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2013\u003c/span\u003e). This time frame was chosen primarily due to data availability, particularly: (1) the limited number of archaeological sites and radiocarbon dates during the Mesolithic and (2) the fact that during the second part of the 1st Millennium BC there is a significant decrease in radiocarbon availability, as alternative dating methods were traditionally preferred. Given the methodological nature of this paper, an in-depth examination of the region\u0026rsquo;s archaeology is not necessary. Nevertheless, a contextualisation of the archaeology of the region is provided in the SI.\u003c/p\u003e \u003cp\u003eThe four sub-regions selected for this study are: (1) Thy (Thisted municipality), central Jutland (Skive and Viborg municipalities), northwestern Zealand, and Bornholm (Fig.\u0026nbsp;4 and Fig.\u0026nbsp;3 for their location within Denmark). The selection of these regions follows a double rationale. On one hand, all regions are rich in archaeological data and have a well-established history of research. This aspect allows to better capture chronological variation and to minimise possible recovery biases. In particular, Thy was the focus of several important archaeological projects, most notably the Aas and Thy archaeological projects (Bech, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; Mikkelsen, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e1996\u003c/span\u003e). Prehistoric sites are particularly abundant in central Jutland due to decades of intensive investigations led by Viborg Museum (Mikkelsen et al., \u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). Northwestern Zealand has a long history of research and a large number of archaeological sites, thanks to significant archaeological activity (Kristiansen, \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e1981\u003c/span\u003e; Mathiassen, \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e1959\u003c/span\u003e). On Bornholm numerous archaeological project helped reconstructing a detailed picture of local dynamics (Nielsen, \u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; Nielsen \u0026amp; Nielsen, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eAt the same time, each region experienced different dynamics during prehistory. For instance, in Thy\u0026mdash;and to some extent central Jutland\u0026mdash;human activity intensified significantly during the Bronze Age, while earlier periods are less well-represented (Bech, \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Conversely, northwestern Zealand is particularly renowned for its abundant Neolithic sites, followed by a decline, due to the shift of the most important centres to other parts of Zealand (Kristiansen, \u003cspan citationid=\"CR27\" class=\"CitationRef\"\u003e2022\u003c/span\u003e). Finally, Bornholm experienced a very marked neolithisation as well as Bronze Age (Nielsen \u0026amp; Nielsen, \u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). Additionally, they also represent a diverse set of geographic regions: Bornholm is a medium-sized, remote island, located far from the other regions. Northwestern Zealand is part of a large island within the Danish Isles archipelago. Central Jutland is a region with limited access to the sea, connected only via the Limfjord. Thy, by contrast, is a coastal region facing the North Sea.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eFigure\u0026nbsp;3\u003c/b\u003e: A map of Denmark showing the four study regions in white and divided into two macro-areas used to model the radiocarbon data. The 14C samples are represented as black points on the map.\u0026rdquo;\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabd\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eFigure\u0026nbsp;4\u003c/b\u003e: The archaeological sites in each sub-area are displayed. The location of each sub-region is shown in Fig.\u0026nbsp;3. From top left to bottom right: a) Thy, b) central Jutland, c) northwestern Zealand and d) Bornholm. The colour of the sites reflects their starting year in the dataset.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Typochronological data description\u003c/h2\u003e \u003cp\u003eThe dataset has a relatively simple structure, providing basic information on site locations (coordinates), administrative details, site types and chronology, including the starting and ending dates in years BC/AD. It also includes links to online sources with more detailed descriptions and, in some cases, excavation reports. An evaluation of the dataset\u0026rsquo;s chronological precision (end year minus start year) reveals that its typochronological dating is relatively coarse, potentially limiting its utility for archaeological research (Fig.\u0026nbsp;5). Even when accounting for the possibility that some sites may have been used for extended periods, it is unlikely that they were occupied for 1,000 years\u0026mdash;the minimum median chronological resolution among the four case studies (Fig.\u0026nbsp;5)\u003ca class=\"FNLink\" href=\"#Fn2\" id=\"#FNLinkFn2\"\u003e\u003c/a\u003e. Consequently, the dataset\u0026rsquo;s lack of precise dating poses challenges for broader archaeological interpretations. This aspect might cause most researchers to set this dataset aside in favour of more accurately dated datasets from individual research projects, which are temporally and spatially constrained. Although this is not an issue \u003cem\u003eper se\u003c/em\u003e, here I argue that even these large dataset offer great modelling possibilities when properly handled.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabe\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eFigure\u0026nbsp;5\u003c/b\u003e: Chronological precision of prehistoric sites in the Danish database, divided by study region. The star symbol represents the mean value, and the jittered points represent individual site precision measurements.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Radiocarbon data description\u003c/h2\u003e \u003cp\u003eApproximately 2,300 radiocarbon samples are readily available from Denmark and can be downloaded from the XRONOS database or accessed via its R package, xronos (Hinz and Roe \u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). While the database contains many more entries, these have been filtered to remove potential duplicates. The dates are evenly distributed between northern Jutland (ca. 1,100) and southern Jutland and the Danish Isles (ca. 1,100), as shown in Fig.\u0026nbsp;3. These two regions are modelled separately to capture as many local patterns as possible. Northern Jutland is used for Thy and central Jutland, whereas Southern Jutland and the Danish Isles is used for northwestern Zealand and Bornholm. Obviously, the total number of radiocarbon dates available in Denmark is much higher. Radiocarbon sampling is systematically conducted during rescue archaeology excavations, and thousands more dates are likely hidden in excavation reports. For example, in the nearby region of Scania (Sweden) over 6,000 radiocarbon dates from rescue excavations were recently published (Friman \u0026amp; Lager\u0026aring;s, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), compared to the 2,300 listed for all of Sweden in the XRONOS database (primarily from central and southern Sweden, as of late November 2024). In the future, it is likely that new collections of radiocarbon dates will become available for Denmark. However, as the focus here is on the methodology, this limitation is not a significant concern. In fact, the sheer number of sites or dates does not affect the method employed, although more dates and improved typochronological data will undoubtedly enhance the outcomes.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Results\u003c/h2\u003e \u003cp\u003eThe results presented here can be analysed in two different ways. The first involves measuring the number of sites predicted within a given time frame at least once (or n times). This approach is also the most effective for spatial visualisation, as each site has its own likelihood (Fig.\u0026nbsp;6\u0026ndash;9). The second measurement can be considered as a sort of \u0026ldquo;site count\u0026rdquo; and consists in summing the number of sites, weighted by their probability (Fig.\u0026nbsp;10b). This measure can be used as a reference value for comparison with SPDs and aoristic counts. The values measured for each period can be normalised to enhance comparability between different regions or left unnormalised. The results of the simulation are provided in the SI, alongside scripts for generating some of the numbers discussed here.\u003c/p\u003e \u003cp\u003eThe first time window (6250\u0026thinsp;\u0026minus;\u0026thinsp;6050 BP) has the lowest number of predicted sites across the four regions. The reason is that the precision of sites potentially dating to the Late Mesolithic is generally very low, with only 26 sites having a precision of less than 600 years and a median precision of 4,899 years. In the following time window, the situation improves, with 34 sites having a precision of less than 600 years and a median precision halves to 2,249 years. Another important difference is the nearly doubling in the total number of possible sites in all regions (see SI). Despite this, site likelihoods remain generally low, and the most significant increase is observed between 5850\u0026ndash;5650 BP.\u003c/p\u003e \u003cp\u003eThis increase is not due to improved chronological precision or a significant rise in the total number of sites (changes are below five percent in Bornholm and Zealand and above ten percent in the other two case studies). Instead, it reflects the effect of the radiocarbon data, which shows its first spike during this period (see Fig.\u0026nbsp;11 and SI). This observation aligns with archaeological evidence from the region, which suggests an increase in population density associated with the arrival of new farmers (Gron \u0026amp; S\u0026oslash;rensen, \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2018\u003c/span\u003e; S\u0026oslash;rensen, \u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e2014\u003c/span\u003e).\u003c/p\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e3.3.1 Thy\u003c/h2\u003e \u003cp\u003eIn Thy (Fig.\u0026nbsp;6), the number of simulated sites increases during the beginning of the Neolithic, reaching a local maximum probability (sum of the probabilities of all sites) between 5650\u0026ndash;5450 BC. During this period, sites are mostly located in the east-northeastern part of the region. Following a decline in likelihood, with a minimum reached at 5050\u0026ndash;4850 BC, there is a new peak in the subsequent time frame (Fig.\u0026nbsp;10b), with sites now more concentrated in the southern part of the region (Fig.\u0026nbsp;6).\u003c/p\u003e \u003cp\u003eDespite oscillation in probability, the total number of sites predicted at least once remains stable (approximately 1,350 sites) between 5850\u0026ndash;4850 BC, reflecting the (lack of) precision in the relative dating, which in this case corresponds to the Funnel Beaker (TRB) culture (6050/4950\u0026thinsp;\u0026minus;\u0026thinsp;4750 BP). Between 4650\u0026thinsp;\u0026minus;\u0026thinsp;4050 BP, the situation remains relatively stable, with most sites located in the southern part of Thy. During the Bronze Age (BA; 3650\u0026thinsp;\u0026minus;\u0026thinsp;2450 BP) there is a boom in settlement, with more than 1,600 sites predicted in each remaining time window (before 3650 BP sites were below 1,300). These sites also tend to have higher probabilities and are more evenly distributed across the east coast (facing the Limfjord, Fig.\u0026nbsp;6) and the northernmost part of the region. The peak in settlement is observed during the central part of the BA, and in particular during the 3250\u0026thinsp;\u0026minus;\u0026thinsp;2850 BP time windows, corresponding to BA periods III and IV in the relative chronology (Thrane, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2013\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e3.3.2 Central Jutland\u003c/h2\u003e \u003cp\u003eIn central Jutland, after the beginning of the Neolithic marked by an increase in the number of sites, the pattern remains relatively stable until the turn of the 5th millennium BP, when there is a boom in site likelihood (Fig.\u0026nbsp;7) peaking between 4650\u0026thinsp;\u0026minus;\u0026thinsp;4450 BP (Middle Neolithic - early Younger Neolithic transition). During this period, sites are distributed more or less homogeneously across the entire study region, with the exception of the southernmost part, which contains very few sites. Before 4650 BP, sites with higher likelihood were predominantly concentrated in the central part of the region, near the southeastern end of the Limfjorden (Fig.\u0026nbsp;7). During the Bronze Age, there is a marked increase in site intensity, relatively stable throughout the neolithic, with a peak between 3050\u0026ndash;2850 BP. In this case, the difference in site count is striking, with approximately double the number of sites compared to the preceding and following periods (Fig.\u0026nbsp;7e and Fig.\u0026nbsp;10b). The spatial distribution of sites during the end of the Neolithic period and the BA also differs from earlier phases. The highest site intensity is now found in the southeastern and westernmost parts of the region, while the previously dense central area contains relatively fewer sites (Fig.\u0026nbsp;7).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabf\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eFigure\u0026nbsp;6\u003c/b\u003e: Site likelihood in Thy. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabg\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eFigure\u0026nbsp;7\u003c/b\u003e: Site likelihood in central Jutland. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e3.3.3 Northwestern Zealand\u003c/h2\u003e \u003cp\u003eIn northwestern Zealand, the situation differs somewhat, with the TRB period showing the highest number of simulated sites, reaching a peak during the 5850\u0026thinsp;\u0026minus;\u0026thinsp;5650 BP(Fig.\u0026nbsp;8). During this period, sites are distributed relatively evenly across the study area, with a slight preference for the southern-central and western parts. The number of sites predicted at least once during this time remains very stable (around 6,800\u0026ndash;6,900 sites), reflecting the typochronological imprecision of the archaeological data, not dissimilarly to other regions.\u003c/p\u003e \u003cp\u003eFollowing this initial rise, there is a general decline in site count, reaching a minimum between 4250\u0026ndash;4050 BP (Fig.\u0026nbsp;8). During this period, the number of sites with a likelihood of 30% or higher shrinks to only a few, with the interior and eastern parts of the region showing a general lack of sites. By the end of the Late Neolithic period (4050\u0026ndash;3850 BP), the situation changes significantly, with a marked expansion of sites with high likelihood, concentrated in the north and west but occupying most of the region (Fig.\u0026nbsp;8). During the BA the pattern becomes less uniform, with two distinct peaks (3450\u0026ndash;3250 and 3050\u0026ndash;2850 BP) followed by declines, with the latest aligning with observation from other regions. In general, the settlement pattern throughout the Bronze Age is characterised by a concentration around coastal areas, with the eastern and northern parts being the most intensively occupied (but with substantial differences across the various BA periods) (Fig.\u0026nbsp;8).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec12\" class=\"Section3\"\u003e \u003ch2\u003e3.3.4 Bornholm\u003c/h2\u003e \u003cp\u003eThe situation on Bornholm differs significantly from that described for Zealand, even though the same radiocarbon dataset was used for the simulation. The number of sites remains generally low throughout the Neolithic, even though a peak in site likelihood is observed following the onset of farming on the island, with a cluster of higher-likelihood sites located in the northwest and along the southern coast (Fig.\u0026nbsp;9). A second increase in site likelihood occurs between 4850\u0026thinsp;\u0026minus;\u0026thinsp;4450 BP, with site initially located mostly in the southeast and later on scattered throughout the island (Fig.\u0026nbsp;9). Between the end of the Neolithic period and the first BA time window (3650\u0026ndash;3450 BP), there is a fivefold increase in site count (Fig.\u0026nbsp;10b), with the peak reached during 3450\u0026ndash;3250 BP. During this period, sites are distributed across the island, with lower intensity in the interior and two areas of highest concentration: the south-southwest and the northwest (Fig.\u0026nbsp;9).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabh\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eFigure\u0026nbsp;8\u003c/b\u003e: Site likelihood in northwestern Zealand. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabi\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eFigure\u0026nbsp;9\u003c/b\u003e: Site likelihood in Bornholm. The likelihood of a site being dated to the different time frames is given by the size of the circle or by the x mark. Sites with probability below 10% are not plotted.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Discussion","content":"\u003cp\u003eThe method proposed here allows for the retention of spatial information on areas that were more likely occupied during any given period, often neglected in the literature. This method reduces the limitations of traditional distribution maps based on relative chronology by determining varying degrees of likelihood for a site being dated to a specific period. In many cases, the measure of \u0026ldquo;sites predicted at least once\u0026rdquo; is stable across several time windows, with numbers generally aligning with relative chronologies, such in the case of the TRB. This results is a key aspect of this method, as retaining the spatial information enables the use of the sites for further analysis, such as spatial statistics. For instance, sites can be weighted by their likelihood, assigning greater importance to sites with higher probabilities. In the SI, the results of Kernel Density Estimation for likelihood-weighted sites versus unweighted density (all sites potentially belonging to the phase) shows that intensity differences can be above 10% in certain areas. This is a very important aspect to consider, as it shows the limitations of uncritical analysis of typochronological data.\u003c/p\u003e \u003cp\u003eA comparison between the results discussed here and each proxy used individually is beneficial for better grasp the potential of the method. Testing the statistical significance between site likelihoods and the two other proxies would be worthless, as the former is a product of the tw latter. The aoristic curve and the probability density of radiocarbon dates can both be compared to the summed likelihood of sites predicted in each phase (Fig.\u0026nbsp;10 and Fig.\u0026nbsp;11). The aoristic sum has a similar pattern for each of the four regions. This similarity is unsurprising, as the simulation of calendar years depends on typochronologically dated sites. Nevertheless, when typochronological precision is low and the number of sites high, as during the 6th millennium BP in northwestern Zealand, the integration of radiocarbon data is beneficial. In this case, a peak is observed at the onset of the Neolithic, followed by stable, but lower, site likelihood during the rest of the millunnium, with a decline after 4850\u0026thinsp;\u0026minus;\u0026thinsp;4650 BP (Fig.\u0026nbsp;8 and Fig.\u0026nbsp;10). In Bornholm, the peak in my results is earlier than the one from the aoristic analysis, even though the global trend is roughly unchanged (Fig.\u0026nbsp;10). This improvement is further enhanced by breaking up the relative chronology into time windows that are not based on the archaeological phases, allowing to obtain a more nuanced transition between the archaeological periods.\u003c/p\u003e \u003cp\u003eComparing the results to SPDs is less straightforward, as using SPDs as demographic proxies requires several assumptions. However, as a visual starting point, I will compare sites to the composite kernel density estimation (CKDE; Fig.\u0026nbsp;11) (McLaughlin, \u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). The increase in radiocarbon dates after 6000 BP in both subregions corresponds to the onset of the Neolithic and is also reflected in the site count, particularly in northwestern Zealand (compare to Fig.\u0026nbsp;11b). A trough in CKDE probability around 4000 BP in both North Jutland and southern Jutland and Isles is not observed in the site likelihood, which remains stable during this period in three of the regions. Even more interestingly, northwestern Zealand shows a peak, thanks to the input from typochronological data. The decline after 3000 BP in the CKDEs reflects the lower number of 14C samples in later periods, a limitation long acknowledged in the literature (e.g., Shennan et al. \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e2013\u003c/span\u003e), which was one of the main reasons to find a way to combine these two different type of data. However, this decline is also observed in the aoristic curves (Fig.\u0026nbsp;10a), thus inevitably reflected in the results presented here. The second probability peak in northern Jutland (Fig.\u0026nbsp;11a) is not very well visible in Thy, but on the other hand is well captured in central Jutland (Fig.\u0026nbsp;10b). This differentiation might reflect distinct Neolithic settlement patterns in Thy, which would be overlooked by only looking at the CKDE (or the SPD, see SI). In both regions, the peak during the early and middle BA is similar across proxies, as the following decline. Most \u0026ldquo;could be Late BA\u0026rdquo; sites in the database have a precision of 600 years or worse, resulting in earlier calendar dates being sampled more often due to their higher frequency in the radiocarbon data. This issue is less pronounced in Bornholm due to the availability of better-dated typochronological data, demonstrating that when higher-quality data are available, the results represent an improvement compared to the single proxies.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabj\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eFigure\u0026nbsp;10\u003c/b\u003e: a) Aoristic count calculated in R using the baorista package (Crema \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) and b) the summed likelihood per each phase resulted from the simulation of this study. Legend is common for the two sub-figures.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThis analysis represents only a visual assessment of the trends across the different curves and does not aim to replace individual proxies for representing large-scale patterns, even though this is the ultimate goal. To infer past demographic patterns, this method would require integration into a statistically robust framework (as proposed by Crema, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2022\u003c/span\u003e, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Crema \u0026amp; Kobayashi, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2020\u003c/span\u003e; Timpson et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). An SPD for each region, generated using Timpson et al. (\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e)\u0026rsquo;s approach, is provided in the SI for reference.\u003c/p\u003e \u003cp\u003eAcross the different case studies, it is easy to spot the marked difference in patterns between typochronological phases, which was not present in the toy example. This issue arises from the uneven length of relatively dated archaeological periods, with better precision achieved in certain time frames depending on the available material culture. Thus, whenever possible, priority should be given to the refinement of the input data. Another potential challenge concerns the difficulty of attributing relative dates to sites, for example assigning a site to the end of the Late Neolithic or to the early BA. In the database, sites are typically well-separated between the Neolithic and Bronze Age, potentially creating an artificial divide between phases, caused by the recording strategy. A possible solution would involve providing confidence intervals for relative dating, such as \u0026ldquo;30% LN II and 70% EBA I,\u0026rdquo; as suggested by A. Bevan et al. (\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2013\u003c/span\u003e) and which could easily be implemented in the simulation carried out here. If this is not feasible, an alternative might involve integrating uncertainty within a Bayesian framework for phase allocation (Crema, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe simulation strategy presented in this paper mitigates these effects. Sampling a calendar date for each site in the dataset and binning it into arbitrarily defined 200-year windows (generally unconnected with relative chronologies, except in the case of the BA) avoids the assumption that a site exclusively belongs to one phase. This is particularly effective when sampled dates fall near phase boundaries or when there is uncertainty in phase attribution. Iterating the process makes sure that a site with these issue will appear in more than a temporal window but in both with lower probability than a securely dated site. The within phase probability was dealt more flexibly by assuming that the probability of a site being dated in any calendar year within its relatively dated phase is correlated to the radiocarbon curve. The iteration of the process, assures the presence of sites with such uncertainties to be represented in different temporal windows.\u003c/p\u003e \u003cp\u003eThe potential for linking typochronologically dated sites with radiocarbon data has not yet been discussed. If a specific site can be linked to one or more radiocarbon samples, the code used here could be easily adapted to sample from a smaller dataset. A similar approach was recently implemented by the author to determine the dating of prehistoric houses in Scania (southern Sweden) (Bilotti, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). However, particular attention is required in this case, as it can only work when the site is securely dated to a single phase or when radiocarbon samples are available for all phases of occupation. Otherwise, some periods may be underrepresented, and if the relative chronology and the radiocarbon date do not align, the sampled date would not be representative of the site. Additionally, when the number of radiocarbon dates permits, this method can be adapted to determine the likelihood of individual structures within an excavation being dated to specific time frames (e.g., tombs in a large cemetery or buildings in a settlement).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabk\" border=\"1\"\u003e \u003ccolgroup cols=\"1\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003c/p\u003e \u003cp\u003e\u003cb\u003eFigure\u0026nbsp;11\u003c/b\u003e: CKDE of the radiocarbon data available for Denmark from the XRONOS database. a) Northern Jutland and b) Southern Jutland and the Danish Isles. The CKDE were calculated using the ckde function from the rcarbon package in R (Crema and Bevan \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2021\u003c/span\u003e).\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e"},{"header":"5. Conclusion","content":"\u003cp\u003eIn this paper, I proposed a new method to address the loss of spatial resolution when working with large archaeological datasets. I also aimed to show that, despite their limitations, typochronologically dated legacy data can - and should - be considered for quantitative analysis.\u003c/p\u003e \u003cp\u003eBoth data sources suffer from biases and issues and transferring these biases into a likelihood-based framework help mitigating them. The current approaches employed to study-or simply eyeball-site patterns in a region all have their strengths and weaknesses. Mapping sites, even when coupled with spatial statistics, lacks chronological precision or it is necessary to reduce the number of sites considered. Aoristic analysis offers better chronological trends but generally lacks statistical inference and spatial patterns are lost. Probability densities of radiocarbon data similarly fail to capture spatial trends and are further complicated by well-known biases (e.g., recovery biases, calibration issues) and methodological complexity. The method proposed here overcomes some of these issues and in particular, it keeps the spatial information available assigning to each site in the dataset a likelihood of being dated to a specific time window, based on its relative dating and the available radiocarbon data. Additionally, it overcomes the issues connected to sampling biases in the radiocarbon data, as the simulation is constrained by typochronology. Another key strength of the method is that the output can be used for further analysis, weighting the contribution of each site in a time window based on its likelihood.\u003c/p\u003e \u003cp\u003eUsing more precise data would reduce the uncertainties in the results presented here, as was evident in some of the study regions, especially during the Bronze Age. This issue was absent in the toy example, where the chronological error did not depend on relative chronologies (i.e., precision was uniformly distributed) and depends on the data in the Danish database, which could be improved by reassess the chronology of each entry.\u003c/p\u003e \u003cp\u003eFinally, while this method has been applied to relatively large regions to study population patterns, it is not limited to any scale of operation and could be used to study scatters of materials within a site, the patterns in a large cemetery, variation of house sizes and typologies over time.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003eCompeting Interests:\u003c/p\u003e\n\u003cp\u003eThe author does not have any competing interest.\u003c/p\u003e\n\u003cp\u003eAcknowledgments\u003c/p\u003e\n\u003cp\u003eI am thankful to Roberto Ragno for the support and insightful comments during the preparation of this manuscript. This research was supported by the German Research Foundation and the Kiel University (CRC 1266) under grant number 290391021.\u003c/p\u003e"},{"header":"References","content":"\u003cp\u003eArtursson, M. (2005). G\u0026aring;rds- och bebyggelsestruktur. In P. Lager\u0026aring;s \u0026amp; B. Str\u0026ouml;mberg (Eds.), \u003cem\u003eBrons\u0026aring;ldersbygd. 2300\u0026ndash;500 f.kr. Sk\u0026aring;nska sp\u0026aring;r \u0026ndash; arkeologi l\u0026auml;ngs v\u0026auml;stkustbanan\u003c/em\u003e (pp. 84\u0026ndash;155). Lund: Riksantikvarie\u0026auml;mbetet.\u003c/p\u003e\n\u003cp\u003eBaxter, M. J., \u0026amp; Cool, H. E. M. (2016). Reinventing the wheel? 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Oxford University Press.\u0026nbsp;\u003ca href=\"https://doi.org/10.1093/oxfordhb/9780199572861.013.0041\"\u003ehttps://doi.org/10.1093/oxfordhb/9780199572861.013.0041\u003c/a\u003e\u003c/p\u003e\n\u003cp\u003eTimpson, A., Barberena, R., Thomas, M. G., M\u0026eacute;ndez, C., \u0026amp; Manning, K. (2020). Directly modelling population dynamics in the south american arid diagonal using 14C dates. \u003cem\u003ePhilosophical Transactions of the Royal Society B: Biological Sciences\u003c/em\u003e, \u003cem\u003e376\u003c/em\u003e(1816), 20190723.\u0026nbsp;\u003ca href=\"https://doi.org/10.1098/rstb.2019.0723\"\u003ehttps://doi.org/10.1098/rstb.2019.0723\u003c/a\u003e\u003c/p\u003e\n\u003cp\u003eZimmermann, H. W. (1992). The \u0026rsquo;Helm\u0026rsquo; in England, Wales, Scandinavia and North America. \u003cem\u003eVernacular Architecture\u003c/em\u003e, \u003cem\u003e23\u003c/em\u003e(1), 34\u0026ndash;43.\u0026nbsp;\u003ca href=\"https://doi.org/10.1179/vea.1992.23.1.34\"\u003ehttps://doi.org/10.1179/vea.1992.23.1.34\u003c/a\u003e\u003c/p\u003e"},{"header":"Footnotes","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003e Using SPDs to infer population dynamics is generally accepted but should not be done uncritically (Crema, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2022\u003c/span\u003e; Crema \u0026amp; Shoda, \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; Timpson et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2020\u003c/span\u003e).\u003c/span\u003e\u003c/li\u003e\u003cli\u003e\u003cspan\u003e During the period considered, the most common type of settlement were farmsteads, which were not occupied for very long times. Artursson (\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2005\u003c/span\u003e) proposed the longest time span for the study region, suggesting 100\u0026ndash;150 years for the houses at Limensg\u0026aring;rd, Bornholm. However, in many cases, much shorter spans of 25\u0026ndash;50 years have been proposed (Gerritsen, \u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e1999\u003c/span\u003e; M\u0026uuml;ller, \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2013\u003c/span\u003e; Zimmermann, \u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e1992\u003c/span\u003e). Similarly, a cemetery might have been occupied for a long period (but not 1000 years), and stray finds are the products of discrete events.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Radiocarbon, Aoristic analysis, summed probability distribution, chronological modelling, Prehistoric Denmark","lastPublishedDoi":"10.21203/rs.3.rs-5656593/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5656593/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThe surge in data availability and methodological advancements over the last decades has enabled archaeologists to develop more robust data-driven models, which are essential for reconstructing ancient human history. However, despite their potential, these datasets pose significant challenges due to their heterogeneity and inherent uncertainties. A common limitation is the low chronological resolution of many datasets, which often compels archaeologists to rely on proxies such as radiocarbon date frequency distributions to study variations in occupation intensity. While this approach is widely used, it necessitates a large number of radiocarbon samples to construct probability curves, leading to a considerable loss of spatial resolution. To address these challenges, I propose a novel method that combines typochronological and radiocarbon datasets, preserving both temporal and spatial resolution while accounting for uncertainty. Each relatively dated site is assigned a simulated calendar date within its chronological span, based on the cumulative probability distribution of locally available radiocarbon data. The results are grouped into uniform time windows, with each site assigned a likelihood of belonging to each time period. The efficacy and functionality of the method are demonstrated using toy data, with the results compared to outputs from alternative methods. Finally, the method is applied to four case studies from prehistoric Denmark (4000\u0026thinsp;\u0026minus;\u0026thinsp;500 BC), showcasing its potential in addressing long-standing challenges in archaeological modelling. The results show that despite the known global trends, local variation is observed in the four different sub-regions considered.\u003c/p\u003e","manuscriptTitle":"Estimating temporal likelihood of archaeological sites in prehistoric Denmark combining typochronological and radiocarbon data","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-01-09 17:06:55","doi":"10.21203/rs.3.rs-5656593/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ec9bf3f3-12f1-43d0-b2ae-4130fb186818","owner":[],"postedDate":"January 9th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2025-03-06T01:38:40+00:00","versionOfRecord":[],"versionCreatedAt":"2025-01-09 17:06:55","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5656593","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5656593","identity":"rs-5656593","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}