Section: Archaeology
Topic: Archaeology

Analysis of the abundance of radiocarbon samples as count data

de Navascués, Miguel1, 2  ; Burgarella, Concetta2, 3 ; Jakobsson, Mattias2 
1 CBGP, INRAE, CIRAD, IRD, Institute Agro, University of Montpellier - Montpellier, France
2 Human Evolution Program, Department of Organismal Biology, Uppsala University - Uppsala, Sweden
3 AGAP Institut, University of Montpellier, CIRAD, INRAE, Institut Agro - Montpellier, France

Corresponding author(s): de Navascués, Miguel (miguel.navascues@inrae.fr)

10.24072/pcjournal.522 - Peer Community Journal, Volume 5 (2025), article no. e20.

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The analysis of the abundance of radiocarbon samples through time has become a popular method to address questions of demography in archaeology. The history of this approach is marked by the use of the Sum of Probability Distributions (SPD), a key methodological development that first allowed researchers to visualize the abundance of radiocarbon samples on a calibrated temporal scale. However, the lack of a mathematical definition hinders the use of SPD in a proper statistical framework. Recent developments of model-based approaches have allowed a more rigorous statistical analysis of the abundance of radiocarbon data. Despite these advances, these methods inherit from the SPD an interpretation of the abundance of samples as a probability distribution. In this work we propose a change of perspective by treating radiocarbon data as count data. We present an approach that models the expected number of samples occurring at each year. We argue that this model provides more interpretable parameters and better accounts for the uncertainty in the number of samples. The performance of the proposed approach is evaluated through simulations and compared to an alternative state-of-the-art approach. Our new method is competitive with the state-of-the-art model. Furthermore, we demonstrate the computational burden of using the SPD as summary statistics under an approximate Bayesian computation analysis and propose more efficient summary statistics. Finally, we use a dataset of radiocarbon samples from Ireland and Britain to provide an application example. The results of these analyses are largely congruent with previous work on the same dataset except in revealing an earlier start of the Neolithic demographic expansion.

Published online:
DOI: 10.24072/pcjournal.522
Type: Research article

de Navascués, Miguel 1, 2; Burgarella, Concetta 2, 3; Jakobsson, Mattias 2

1 CBGP, INRAE, CIRAD, IRD, Institute Agro, University of Montpellier - Montpellier, France
2 Human Evolution Program, Department of Organismal Biology, Uppsala University - Uppsala, Sweden
3 AGAP Institut, University of Montpellier, CIRAD, INRAE, Institut Agro - Montpellier, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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de Navascués, Miguel; Burgarella, Concetta; Jakobsson, Mattias. Analysis of the abundance of radiocarbon samples as count data. Peer Community Journal, Volume 5 (2025), article  no. e20. doi : 10.24072/pcjournal.522. https://peercommunityjournal.org/articles/10.24072/pcjournal.522/

PCI peer reviews and recommendation, and links to data, scripts, code and supplementary information: 10.24072/pci.archaeo.100583

Conflict of interest of the recommender and peer reviewers:
The recommender in charge of the evaluation of the article and the reviewers declared that they have no conflict of interest (as defined in the code of conduct of PCI) with the authors or with the content of the article.

[1] Bevan, A. Radiocarbon Dataset and Analysis In: Bevan, A., Colledge, S., Fuller, D., Fyfe, R., Shennan, S. and C. Stevens 2017. Holocene fluctuations in human population demonstrate repeated links to food production and climate, UCL Discovery (2017) | DOI

[2] Bevan, A.; Colledge, S.; Fuller, D.; Fyfe, R.; Shennan, S.; Stevens, C. Holocene fluctuations in human population demonstrate repeated links to food production and climate, Proceedings of the National Academy of Sciences, Volume 114 (2017) no. 49, p. E10524-E10531 | DOI

[3] Bird, D.; Miranda, L.; Vander Linden, M.; Robinson, E.; Bocinsky, R. K.; Nicholson, C.; Capriles, J. M.; Finley, J. B.; Gayo, E. M.; Gil, A.; d’Alpoim Guedes, J.; Hoggarth, J. A.; Kay, A.; Loftus, E.; Lombardo, U.; Mackie, M.; Palmisano, A.; Solheim, S.; Kelly, R. L.; Freeman, J. p3k14c, a synthetic global database of archaeological radiocarbon dates, Scientific Data, Volume 9 (2022) no. 1, p. 27 | DOI

[4] Boitard, S.; Rodríguez, W.; Jay, F.; Mona, S.; Austerlitz, F. Inferring population size history from large samples of genome-wide molecular data - An approximate Bayesian computation approach, PLOS Genetics, Volume 12 (2016) no. 3 | DOI

[5] Bronk Ramsey, C. Radiocarbon dating: Revolutions in understanding, Archaeometry, Volume 50 (2008) no. 2, pp. 249-275 | DOI

[6] Broughton, J. M.; Weitzel, E. M. Population reconstructions for humans and megafauna suggest mixed causes for North American Pleistocene extinctions, Nature Communications, Volume 9 (2018) no. 1 | DOI

[7] Carleton, W. C. Evaluating Bayesian Radiocarbon-dated Event Count (REC) models for the study of long-term human and environmental processes, Journal of Quaternary Science, Volume 36 (2021) no. 1, pp. 110-123 | DOI

[8] Carleton, W. C.; Groucutt, H. S. Sum things are not what they seem: Problems with point-wise interpretations and quantitative analyses of proxies based on aggregated radiocarbon dates, The Holocene, Volume 31 (2021) no. 4, pp. 630-643 | DOI

[9] Contreras, D. A.; Codding, B. F. Landscape Taphonomy Predictably Complicates Demographic Reconstruction, Journal of Archaeological Method and Theory, Volume 31 (2023) no. 3, pp. 1102-1128 | DOI

[10] Crema, E. R. Statistical inference of prehistoric demography from frequency distributions of radiocarbon dates: A review and a guide for the perplexed, Journal of Archaeological Method and Theory, Volume 29 (2022) no. 4, pp. 1387-1418 | DOI

[11] Crema, E. R. A Bayesian alternative for aoristic analyses in archaeology, Archaeometry (2024), pp. 1-24 | DOI

[12] Crema, E. R.; Bevan, A. Inferences from large sets of radiocarbon dates: software and methods, Radiocarbon, Volume 63 (2021) no. 1, pp. 23-39 | DOI

[13] Crema, E. R.; Kobayashi, K. A multi-proxy inference of Jōmon population dynamics using bayesian phase models, residential data, and summed probability distribution of textsuperscript14C dates, Journal of Archaeological Science, Volume 117 (2020), p. 105136 | DOI

[14] Crema, E. R.; Shoda, S. A Bayesian approach for fitting and comparing demographic growth models of radiocarbon dates: A case study on the Jomon-Yayoi transition in Kyushu (Japan), PLOS ONE, Volume 16 (2021) no. 5, p. e0251695 | DOI

[15] de Navascués, M. DARth ABC: Analysis of the Dated Archaeological Record through Approximate Bayesian Computation (v1.0.1), Zenodo, 2025 | DOI

[16] DiNapoli, R. J.; Crema, E. R.; Lipo, C. P.; Rieth, T. M.; Hunt, T. L. Approximate Bayesian Computation of radiocarbon and paleoenvironmental record shows population resilience on Rapa Nui (Easter Island), Nature Communications, Volume 12 (2021) no. 1, p. 3939 | DOI

[17] Gaujoux, R. doRNG: Generic reproducible parallel backend for `foreach' loops, 2023 | DOI

[18] Geyh, M. A. Holocene Sea-Level History: Case Study of the Statistical Evaluation of textsuperscript14C Dates, Radiocarbon, Volume 22 (1980) no. 3, pp. 695-704 | DOI

[19] Hanna, J. Beyond the Sum: A Poisson Approach to Radiocarbon Analysis, Peer Community in Archaeology (2025) | DOI

[20] Harrell Jr, F. E. Hmisc: Harrell Miscellaneous, 2022 | DOI

[21] Hinz, M.; Roe, J.; Laabs, J.; Heitz, C.; Kolář, J. Bayesian inference of prehistoric population dynamics from multiple proxies: a case study from the North of the Swiss Alps, 2022 | DOI

[22] Komsta, L.; Novomestky, F. moments: Moments, Cumulants, Skewness, Kurtosis and Related Tests, 2022 | DOI

[23] Lannelongue, L.; Grealey, J.; Bateman, A.; Inouye, M. Ten simple rules to make your computing more environmentally sustainable, PLOS Computational Biology, Volume 17 (2021) no. 9 | DOI

[24] Libby, W. F.; Anderson, E. C.; Arnold, J. R. Age Determination by Radiocarbon Content: World-Wide Assay of Natural Radiocarbon, Science, Volume 110 (1949) no. 2869, pp. 678-680 | DOI

[25] Marin, J.-M.; Raynal, L.; Pudlo, P.; Robert, C. P.; Estoup, A. abcrf: Approximate Bayesian Computation via Random Forests, 2022 | DOI

[26] Marom, N.; Wolkowski, U. A note on predator-prey dynamics in radiocarbon datasets, Peer Community Journal, Volume 4 (2024) | DOI

[27] Microsoft Corporation; Weston, S. doSNOW: Foreach Parallel Adaptor for the `snow' Package, doSNOW: Foreach Parallel Adaptor for the `snow' Package, 2022 | DOI

[28] Microsoft Corporation; Weston, S. doParallel: Foreach Parallel Adaptor for the `parallel' Package, 2022 | DOI

[29] Pasek, J. weights: Weighting and Weighted Statistics, 2021 | DOI

[30] Patterson, N.; Isakov, M.; Booth, T.; Büster, L.; Fischer, C.-E.; Olalde, I.; Ringbauer, H.; Akbari, A.; Cheronet, O.; Bleasdale, M.; Adamski, N.; Altena, E.; Bernardos, R.; Brace, S.; Broomandkhoshbacht, N.; Callan, K.; Candilio, F.; Culleton, B.; Curtis, E.; Demetz, L.; Carlson, K. S. D.; Edwards, C. J.; Fernandes, D. M.; Foody, M. G. B.; Freilich, S.; Goodchild, H.; Kearns, A.; Lawson, A. M.; Lazaridis, I.; Mah, M.; Mallick, S.; Mandl, K.; Micco, A.; Michel, M.; Morante, G. B.; Oppenheimer, J.; Özdoğan, K. T.; Qiu, L.; Schattke, C.; Stewardson, K.; Workman, J. N.; Zalzala, F.; Zhang, Z.; Agustí, B.; Allen, T.; Almássy, K.; Amkreutz, L.; Ash, A.; Baillif-Ducros, C.; Barclay, A.; Bartosiewicz, L.; Baxter, K.; Bernert, Z.; Blažek, J.; Bodružić, M.; Boissinot, P.; Bonsall, C.; Bradley, P.; Brittain, M.; Brookes, A.; Brown, F.; Brown, L.; Brunning, R.; Budd, C.; Burmaz, J.; Canet, S.; Carnicero-Cáceres, S.; Čaušević-Bully, M.; Chamberlain, A.; Chauvin, S.; Clough, S.; Čondić, N.; Coppa, A.; Craig, O.; Črešnar, M.; Cummings, V.; Czifra, S.; Danielisová, A.; Daniels, R.; Davies, A.; de Jersey, P.; Deacon, J.; Deminger, C.; Ditchfield, P. W.; Dizdar, M.; Dobeš, M.; Dobisíková, M.; Domboróczki, L.; Drinkall, G.; Đukić, A.; Ernée, M.; Evans, C.; Evans, J.; Fernández-Götz, M.; Filipović, S.; Fitzpatrick, A.; Fokkens, H.; Fowler, C.; Fox, A.; Gallina, Z.; Gamble, M.; González Morales, M. R.; González-Rabanal, B.; Green, A.; Gyenesei, K.; Habermehl, D.; Hajdu, T.; Hamilton, D.; Harris, J.; Hayden, C.; Hendriks, J.; Hernu, B.; Hey, G.; Horňák, M.; Ilon, G.; Istvánovits, E.; Jones, A. M.; Kavur, M. B.; Kazek, K.; Kenyon, R. A.; Khreisheh, A.; Kiss, V.; Kleijne, J.; Knight, M.; Kootker, L. M.; Kovács, P. F.; Kozubová, A.; Kulcsár, G.; Kulcsár, V.; Le Pennec, C.; Legge, M.; Leivers, M.; Loe, L.; López-Costas, O.; Lord, T.; Los, D.; Lyall, J.; Marín-Arroyo, A. B.; Mason, P.; Matošević, D.; Maxted, A.; McIntyre, L.; McKinley, J.; McSweeney, K.; Meijlink, B.; Mende, B. G.; Menđušić, M.; Metlička, M.; Meyer, S.; Mihovilić, K.; Milasinovic, L.; Minnitt, S.; Moore, J.; Morley, G.; Mullan, G.; Musilová, M.; Neil, B.; Nicholls, R.; Novak, M.; Pala, M.; Papworth, M.; Paresys, C.; Patten, R.; Perkić, D.; Pesti, K.; Petit, A.; Petriščáková, K.; Pichon, C.; Pickard, C.; Pilling, Z.; Price, T. D.; Radović, S.; Redfern, R.; Resutík, B.; Rhodes, D. T.; Richards, M. B.; Roberts, A.; Roefstra, J.; Sankot, P.; Šefčáková, A.; Sheridan, A.; Skae, S.; Šmolíková, M.; Somogyi, K.; Somogyvári, Á.; Stephens, M.; Szabó, G.; Szécsényi-Nagy, A.; Szeniczey, T.; Tabor, J.; Tankó, K.; Maria, C. T.; Terry, R.; Teržan, B.; Teschler-Nicola, M.; Torres-Martínez, J. F.; Trapp, J.; Turle, R.; Ujvári, F.; van der Heiden, M.; Veleminsky, P.; Veselka, B.; Vytlačil, Z.; Waddington, C.; Ware, P.; Wilkinson, P.; Wilson, L.; Wiseman, R.; Young, E.; Zaninović, J.; Žitňan, A.; Lalueza-Fox, C.; de Knijff, P.; Barnes, I.; Halkon, P.; Thomas, M. G.; Kennett, D. J.; Cunliffe, B.; Lillie, M.; Rohland, N.; Pinhasi, R.; Armit, I.; Reich, D. Large-scale migration into Britain during the Middle to Late Bronze Age, Nature, Volume 601 (2022) no. 7894, pp. 588-594 | DOI

[31] Pierce, J. L.; Meyer, G. A.; Timothy Jull, A. J. Fire-induced erosion and millennial-scale climate change in northern ponderosa pine forests, Nature, Volume 432 (2004) no. 7013, pp. 87-90 | DOI

[32] Porčić, M.; Blagojević, T.; Pendić, J.; Stefanović, S. The Neolithic Demographic Transition in the Central Balkans: population dynamics reconstruction based on new radiocarbon evidence, Philosophical Transactions of the Royal Society B: Biological Sciences, Volume 376 (2020) no. 1816 | DOI

[33] Pudlo, P.; Marin, J.-M.; Estoup, A.; Cornuet, J.-M.; Gautier, M.; Robert, C. P. Reliable ABC model choice via random forests, Bioinformatics, Volume 32 (2016) no. 6, pp. 859-866 | DOI

[34] R Core Team R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing. Vienna, Austria, 2021 (https://www.R-project.org/)

[35] Raynal, L.; Marin, J.-M.; Pudlo, P.; Ribatet, M.; Robert, C. P.; Estoup, A. ABC random forests for Bayesian parameter inference, Bioinformatics, Volume 35 (2019) no. 10, pp. 1720-1728 | DOI

[36] Reimer, P. J.; Austin, W. E. N.; Bard, E.; Bayliss, A.; Blackwell, P. G.; Ramsey, C. B.; Butzin, M.; Cheng, H.; Edwards, R. L.; Friedrich, M.; Grootes, P. M.; Guilderson, T. P.; Hajdas, I.; Heaton, T. J.; Hogg, A. G.; Hughen, K. A.; Kromer, B.; Manning, S. W.; Muscheler, R.; Palmer, J. G.; Pearson, C.; Plicht, J. v. d.; Reimer, R. W.; Richards, D. A.; Scott, E. M.; Southon, J. R.; Turney, C. S. M.; Wacker, L.; Adolphi, F.; Büntgen, U.; Capano, M.; Fahrni, S. M.; Fogtmann-Schulz, A.; Friedrich, R.; Köhler, P.; Kudsk, S.; Miyake, F.; Olsen, J.; Reinig, F.; Sakamoto, M.; Sookdeo, A.; Talamo, S. The IntCal20 Northern Hemisphere Radiocarbon Age Calibration Curve (0–55 cal kBP), Radiocarbon, Volume 62 (2020) no. 4, pp. 725-757 | DOI

[37] Rick, J. W. Dates as Data: An Examination of the Peruvian Preceramic Radiocarbon Record, American Antiquity, Volume 52 (1987) no. 1, pp. 55-73 | DOI

[38] Rousset, F.; Gouy, A.; Martinez-Almoyna, C.; Courtiol, A. The summary-likelihood method and its implementation in the Infusion package, Molecular Ecology Resources, Volume 17 (2017) no. 1, pp. 110-119 | DOI

[39] Shennan, S.; Downey, S. S.; Timpson, A.; Edinborough, K.; Colledge, S.; Kerig, T.; Manning, K.; Thomas, M. G. Regional population collapse followed initial agriculture booms in mid-Holocene Europe, Nature Communications, Volume 4 (2013) no. 1 | DOI

[40] Sunnåker, M.; Busetto, A. G.; Numminen, E.; Corander, J.; Foll, M.; Dessimoz, C. Approximate Bayesian Computation, PLOS Computational Biology, Volume 9 (2013) no. 1 | DOI

[41] Taylor, R. E. Radiocarbon dating: The continuing revolution, Evolutionary Anthropology: Issues, News, and Reviews, Volume 4 (1995) no. 5, pp. 169-181 | DOI

[42] Thorndycraft, V. R.; Benito, G. The Holocene fluvial chronology of Spain: evidence from a newly compiled radiocarbon database, Quaternary Science Reviews, Volume 25 (2006) no. 3, pp. 223-234 | DOI

[43] Timpson, A.; Barberena, R.; Thomas, M. G.; Méndez, C.; Manning, K. Directly modelling population dynamics in the South American Arid Diagonal using textsuperscript14C dates, Philosophical Transactions of the Royal Society B: Biological Sciences, Volume 376 (2020) no. 1816 | DOI

[44] Williams, A. N. The use of summed radiocarbon probability distributions in archaeology: a review of methods, Journal of Archaeological Science, Volume 39 (2012) no. 3, pp. 578-589 | DOI

[45] Wolodzko, T. extraDistr: Additional Univariate and Multivariate Distributions, 2020 | DOI

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