Through a filter, darkly: population size estimation, systematic error, and random error in radiocarbon-supported demographic temporal frequency analysis

Abstract Archaeologists are increasingly concerned that the non-linear relationship between the calendric and radiocarbon timelines may introduce anomalous structures into radiocarbon-supported temporal frequency distributions ( tfd s) – time series data describing temporal fluctuations in the frequency of archaeological, paleontological, or other geological deposits. This concern emphasizes a need for improved middle range theory on tfd formation, addressing the interaction between several stochastic processes. This paper outlines a Monte Carlo simulation designed to explore the influence of several variables on tfd morphology, including the nonlinear calendric-to-radiocarbon age relationship. The results indicate that this non-linear relationship entails greater variance between identically generated tfd s over some temporal intervals than others but does not predictably lead to tfd peaks over these intervals as previously suggested. Additional variance between identically generated tfd s results from small sample sizes and high values in the underlying TFD . Smoothing the tfd is a solution not only to calibration curve interference but also to sample size-dependent sampling error.

[1]  James Steele,et al.  Neolithic transition in Europe: the radiocarbon record revisited , 2003, Antiquity.

[2]  Rob Marchant,et al.  Neolithic agriculture on the European western frontier: the boom and bust of early farming in Ireland , 2014 .

[3]  A. Raftery,et al.  World population stabilization unlikely this century , 2014, Science.

[4]  A. Greenwood,et al.  Radiocarbon chronologies and extinction dynamics of the Late Quaternary mammalian megafauna of the Taimyr Peninsula, Russian Federation , 2002 .

[5]  N. Porch,et al.  Cyclical patterns in the pleistocene human occupation of Southwest Tasmania , 1995 .

[6]  A. Freeburg,et al.  A High-Resolution Chronology for the Cape Krusenstern Site Complex, Northwest Alaska , 2013, ARCTIC ANTHROPOLOGY.

[7]  K. Gajewski,et al.  Synchronous environmental and cultural change in the prehistory of the northeastern United States , 2010, Proceedings of the National Academy of Sciences.

[8]  Clive Gamble,et al.  The Archaeological and Genetic Foundations of the European Population during the Late Glacial: Implications for ‘Agricultural Thinking’ , 2005, Cambridge Archaeological Journal.

[9]  Todd A. Surovell,et al.  Global archaeological evidence for proboscidean overkill , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[10]  Todd A. Surovell,et al.  Comment on "Redefining the Age of Clovis: Implications for the Peopling of the Americas" , 2007, Science.

[11]  S. Stanley,et al.  Evidence for an extraterrestrial impact 12,900 years ago that contributed to the megafaunal extinctions and the Younger Dryas cooling , 2007, Proceedings of the National Academy of Sciences.

[12]  M. Tallavaara,et al.  Did the mid-Holocene environmental changes cause the boom and bust of hunter-gatherer population size in eastern Fennoscandia? , 2012 .

[13]  Peter Steier,et al.  New Methods and Critical Aspects in Bayesian Mathematics for 14C Calibration , 2001, Radiocarbon.

[14]  B. Culleton.  Crude demographic proxy reveals nothing about Paleoindian population , 2008, Proceedings of the National Academy of Sciences.

[15]  Martin Hinz,et al.  Demography and the intensity of cultural activities: an evaluation of Funnel Beaker Societies (4200–2800 cal BC) , 2012 .

[16]  J. Millspaugh,et al.  Wildlife Demography: Analysis of Sex, Age, and Count Data , 2005 .

[17]  Christopher Bronk Ramsey,et al.  BAYESIAN ANALYSIS OF RADIOCARBON DATES , 2009 .

[18]  M. Baillie,et al.  Holocene climatic change and past Irish societal response , 2006 .

[19]  C. Buck,et al.  IntCal13 and Marine13 Radiocarbon Age Calibration Curves 0–50,000 Years cal BP , 2013, Radiocarbon.

[20]  Todd A. Surovell,et al.  Correcting temporal frequency distributions for taphonomic bias , 2009 .

[21]  C. Latorre,et al.  Climate change and human occupation in the northernmost Chilean Altiplano over the last ca. 11 500 cal. a BP , 2009 .

[22]  C. Hirschman,et al.  POPULATION AND SOCIETY: HISTORICAL TRENDS AND FUTURE PROSPECTS , 2002 .

[23]  B. Valero-Garcés,et al.  Patterns of human occupation during the early Holocene in the Central Ebro Basin (NE Spain) in response to the 8.2 ka climatic event , 2009, Quaternary Research.

[24]  D. Michczyńska,et al.  Improvement of the Procedure for Probabilistic Calibration of Radiocarbon Dates , 1989, Radiocarbon.

[25]  Konrad Gajewski,et al.  Prehistoric demography of North America inferred from radiocarbon data , 2010 .

[26]  M. Micklin,et al.  Prologue: The Demographer’s Ken: 50 Years of Growth and Change , 2005 .

[27]  Philippe Crombé,et al.  14C dates as demographic proxies in Neolithisation models of northwestern Europe: a critical assessment using Belgium and northeast France as a case-study , 2014 .

[28]  Natasha L. Thorpe.  The Tuktu and Nogak Project: Inuit Knowledge about Caribou and Calving Areas in the Bathurst Inlet Region , 1997 .

[29]  B. Potter.  Radiocarbon Chronology of Central Alaska: Technological Continuity and Economic Change , 2008, Radiocarbon.

[30]  Michael R. Bever.  Too Little, Too Late? The Radiocarbon Chronology of Alaska and the Peopling of the New World , 2006, American Antiquity.

[31]  S. Preston,et al.  Demography: Measuring and Modeling Population Processes , 2000 .

[32]  D. W. Clark.  Kodiak Island : The later cultures , 1998 .

[33]  James Steele,et al.  Radiocarbon dates as data: quantitative strategies for estimating colonization front speeds and event densities , 2010 .

[34]  Jennifer A. Dunne,et al.  An Introduction to the Biocomplexity of Sanak Island, Western Gulf of Alaska 1 , 2009 .

[35]  S. G. Keates,et al.  Dates Are Not Just Data: Paleolithic Settlement Patterns in Siberia Derived from Radiocarbon Records , 2005, American Antiquity.

[36]  Sean S. Downey,et al.  The impact of the Neolithic agricultural transition in Britain: a comparison of pollen-based land-cover and archaeological 14C date-inferred population change , 2014 .

[37]  Y. Kuzmin,et al.  Radiocarbon Date Frequency as an Index of Intensity of Paleolithic Occupation of Siberia: Did Humans React Predictably to Climate Oscillations? , 2007, Radiocarbon.

[38]  Joel E. Cohen,et al.  How Many People Can the Earth Support , 1998 .

[39]  Clive Gamble,et al.  Radiocarbon evidence for the Lateglacial Human Recolonisation of Northern Europe , 1997, Proceedings of the Prehistoric Society.

[40]  S. Mithen,et al.  Settlement patterns in the late Mesolithic of western Scotland: the implications of Bayesian analysis of radiocarbon dates and inter-site technological comparisons , 2014 .

[41]  Christian P. Robert,et al.  Monte Carlo Statistical Methods , 2005, Springer Texts in Statistics.

[42]  Julie Esdale.  A Current Synthesis of the Northern Archaic , 2009, ARCTIC ANTHROPOLOGY.

[43]  Tim Kerig,et al.  Regional population collapse followed initial agriculture booms in mid-Holocene Europe , 2013, Nature Communications.

[44]  M. Peresani,et al.  Changes in mobility patterns as a factor for site density variation in the recent Epigravettian of Northern Italy and Southeastern France , 2014 .

[45]  Clive Gamble,et al.  Climate change and evolving human diversity in Europe during the last glacial. , 2004, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[46]  C. Sonett,et al.  The spectrum of radiocarbon , 1990, Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences.

[47]  Alan N. Williams,et al.  Human—environment interactions in Australian drylands: exploratory time-series analysis of archaeological records , 2008 .

[48]  Mike Walker,et al.  Quaternary Dating Methods , 2005 .

[49]  S. Valastro,et al.  Radiocarbon Dating and the George C. Davis Site, Texas , 1977 .

[50]  David E. Bloom,et al.  7 Billion and Counting , 2011, Science.

[51]  Enrico R. Crema,et al.  Modelling Temporal Uncertainty in Archaeological Analysis , 2012 .

[52]  P. Jeffrey Brantingham,et al.  Mind the gaps: testing for hiatuses in regional radiocarbon date sequences , 2014 .

[53]  C. Batt,et al.  Radiocarbon calibration and the peopling of North America , 1996 .

[54]  I. Hutchinson,et al.  Archaeological Evidence for Village Abandonment Associated with Late Holocene Earthquakes at the Northern Cascadia Subduction Zone , 1997, Quaternary Research.

[55]  T. Guilderson,et al.  The Boon and Bane of Radiocarbon Dating , 2005, Science.

[56]  Christian P. Robert,et al.  Introducing Monte Carlo Methods with R , 2009 .

[57]  M. Collard,et al.  Paleoindian demography and the extraterrestrial impact hypothesis , 2008, Proceedings of the National Academy of Sciences.

[58]  M. Waters,et al.  The Geoarchaeology of Place: The Effect of Geological Processes on the Preservation and Interpretation of the Archaeological Record , 1996, American Antiquity.

[59]  McCulloch,et al.  Pleistocene extinction of genyornis newtoni: human impact on australian megafauna , 1999, Science.

[60]  F. Riede.  Climate and Demography in Early Prehistory: Using Calibrated 14C Dates as Population Proxies , 2009, Human biology.

[61]  M. Faught.  Archaeological Roots of Human Diversity in the New World: A Compilation of Accurate and Precise Radiocarbon Ages from Earliest Sites , 2008, American Antiquity.

[62]  Shripad Tuljapurkar,et al.  Population and prehistory II: space-limited human populations in constant environments. , 2008, Theoretical population biology.

[63]  M. Waters,et al.  Redefining the Age of Clovis: Implications for the Peopling of the Americas , 2007, Science.

[64]  A. Coale.  The history of the human population. , 1974, Scientific American.

[65]  J. Rick.  Dates as Data: An Examination of the Peruvian Preceramic Radiocarbon Record , 1987, American Antiquity.

[66]  Todd A. Surovell,et al.  A note on the use of temporal frequency distributions in studies of prehistoric demography , 2007 .

[67]  F. Hassan.  5 – Demographic Archaeology , 1981 .

[68]  P. Bartlein,et al.  Calibration of Radiocarbon Ages and the Interpretation of Paleoenvironmental Records , 1995, Quaternary Research.

[69]  Stephen Shennan,et al.  Prehistoric population history: from the Late Glacial to the Late Neolithic in Central and Northern Europe , 2007 .

[70]  T. Hunt,et al.  A radiocarbon chronology for Sāmoan prehistory , 2008 .

[71]  R. Knecht.  The Late Prehistory of the Alutiiq People: Culture Change on the Kodiak Archipelago From 1200-1750 A.D. , 1995 .

[72]  M. Tallavaara,et al.  Prehistoric population history in eastern Fennoscandia , 2010 .

[73]  John Meadows,et al.  Summed radiocarbon calibrations as a population proxy: a critical evaluation using a realistic simulation approach , 2014 .

[74]  D. Dumond.  On Eskaleutian Linguistics, Archaeology and Prehistory , 1965 .

[75]  C. Newell.  Methods and Models in Demography , 1988 .

[76]  A. Chamberlain.  Demography in Archaeology , 2006 .

[77]  A. Hrdlička.  The anthropology of Kodiak island , 1944 .

[78]  Michael J. Shott.  Radiocarbon Dating as a Probabilistic Technique: The Childers Site and Late Woodland Occupation in the Ohio Valley , 1992, American Antiquity.

[79]  A. Pazdur,et al.  14C Dates of peat for reconstruction of environmental changes in the past , 2003 .

[80]  S. Shennan,et al.  Reconstructing regional population fluctuations in the European Neolithic using radiocarbon dates: a new case-study using an improved method , 2014, Journal of Archaeological Science.

[81]  J. Stein,et al.  Big Sites, Small Sites, and Coastal Settlement Patterns in the San Juan Islands, Washington, USA , 2011 .

[82]  Shripad Tuljapurkar,et al.  Population and prehistory I: Food-dependent population growth in constant environments. , 2008, Theoretical population biology.

[83]  Todd A. Surovell,et al.  A continuous climatic impact on Holocene human population in the Rocky Mountains , 2012, Proceedings of the National Academy of Sciences.

[84]  D. Dumond.  Eskimos and Aleuts , 1970 .

[85]  F. McCormick,et al.  Statistics, sunspots and settlement: influences on sum of probability curves , 2014 .

[86]  C. Grier.  Temporality in Northwest Coast Households , 2016 .

[87]  C. Haynes,et al.  The earliest americans. , 1969, Science.

[88]  Shripad Tuljapurkar,et al.  Population and prehistory III: food-dependent demography in variable environments. , 2009, Theoretical population biology.

[89]  R. Gould,et al.  Formation Processes of the Archaeological Record. , 1997 .

[90]  B. G. McFadgen,et al.  Radiocarbon Calibration Curve Variations and Their Implications for the Interpretation of New Zealand Prehistory , 1994, Radiocarbon.

[91]  Felix Riede,et al.  The Laacher See-eruption (12,920 BP) and material culture change at the end of the Allerød in Northern Europe , 2008 .

[92]  O. Jöris,et al.  Concepts of probability in radiocarbon analysis , 2011 .

[93]  R. Mills.  Radiocarbon calibration of archaeological dates from the Central Gulf of Alaska , 1994 .

[94]  C. West.  A Revised Radiocarbon Sequence for Karluk-1 and the Implications for Kodiak Island Prehistory , 2011, ARCTIC ANTHROPOLOGY.

[95]  C. Bae,et al.  Radiocarbon Dates Documenting the Neolithic-Bronze Age Transition in Korea , 2010, Radiocarbon.

[96]  P. Pettitt,et al.  Palaeolithic radiocarbon chronology: quantifying our confidence beyond two half-lives , 2003 .

[97]  Richard Wright,et al.  Some Archaeological Applications of Kernel Density Estimates , 1997 .

[98]  Houyuan Lu,et al.  Prehistoric demographic fluctuations in China inferred from radiocarbon data and their linkage with climate change over the past 50,000 years , 2014 .

[99]  Alan N. Williams,et al.  Human refugia in Australia during the Last Glacial Maximum and Terminal Pleistocene: a geospatial analysis of the 25–12 ka Australian archaeological record , 2013 .

[100]  M. J. O’Brien,et al.  Spatiotemporal dynamics of the Clovis–Folsom transition , 2010 .

[101]  M. Zárate,et al.  Mid-Holocene paleoenvironments and the archeological record of southern Mendoza, Argentina , 2005 .

[102]  B. Fitzhugh.  The evolution of complex hunter-gatherers : archaeological evidence from the North Pacific , 2003 .

[103]  Chris S. M. Turney,et al.  ENSO influence on Holocene Aboriginal populations in Queensland, Australia , 2006 .

[104]  Sean Ulm,et al.  Hunter‐gatherer response to late Holocene climatic variability in northern and central Australia , 2010 .

[105]  J. Rasic,et al.  A Reconsideration of Purported Holocene Bison Bones from Northern Alaska , 2009 .

[106]  R. D. Guthrie.  New carbon dates link climatic change with human colonization and Pleistocene extinctions , 2006, Nature.

[107]  R. Bras,et al.  Geoarchaeological simulation of meandering river deposits and settlement distributions: A three‐dimensional approach , 2006 .

[108]  J. Dean.  7 – Independent Dating in Archaeological Analysis , 1978 .

[109]  A. Pazdur,et al.  Shape Analysis of Cumulative Probability Density Function of Radiocarbon Dates Set in the Study of Climate Change in the Late Glacial and Holocene , 2004, Radiocarbon.

[110]  J. Southon,et al.  Standards of evidence and Paleoindian demographics , 2008, Proceedings of the National Academy of Sciences.

[111]  P. Brantingham,et al.  Late Pleistocene climate change and Paleolithic cultural evolution in northern China: Implications from the Last Glacial Maximum , 2007 .

[112]  P. Fanning,et al.  Challenging intensification: human—environment interactions in the Holocene geoarchaeological record from western New South Wales, Australia , 2008 .

[113]  Dirk P. Kroese,et al.  Simulation and the Monte Carlo method , 1981, Wiley series in probability and mathematical statistics.

[114]  M. Collard,et al.  Reply to Anderson et al., Jones, Kennett and West, Culleton, and Kennett et al.: Further evidence against the extraterrestrial impact hypothesis , 2008, Proceedings of the National Academy of Sciences.

[115]  D. Grayson,et al.  Middle-Holocene climates and human population densities in the Great Basin, western USA , 2011 .

[116]  Pedro V. Castro Martínez,et al.  Radiocarbon Dating and the Prehistory of the Balearic Islands , 1997, Proceedings of the Prehistoric Society.

[117]  Douglas B. Bamforth,et al.  Radiocarbon calibration curves, summed probability distributions, and early Paleoindian population trends in North America , 2012 .

[118]  J.M.Adams,et al.  Could Pre‐Last Glacial Maximum Humans Have Existed in North America Undetected? An Interregional Approach to the Question1 , 2001 .

[119]  Alan N. Williams,et al.  THE IMPACT OF ENSO IN THE ATACAMA DESERT AND AUSTRALIAN ARID ZONE: EXPLORATORY TIME-SERIES ANALYSIS OF ARCHAEOLOGICAL RECORDS , 2020 .

[120]  Mara A. Mulrooney.  An island-wide assessment of the chronology of settlement and land use on Rapa Nui (Easter Island) based on radiocarbon data , 2013 .

[121]  Martin Kehl,et al.  Rapid climate change and variability of settlement patterns in Iberia during the Late Pleistocene , 2012 .

[122]  Stephen Shennan,et al.  Radiocarbon evidence indicates that migrants introduced farming to Britain , 2010 .

[123]  D. Hopkins,et al.  The early Holocene Milankovitch thermal maximum and humans: adverse conditions for the Denali complex of eastern Beringia , 2001 .

[124]  Ken Lertzman,et al.  Climate Change and Culture Change on the Southern Coast of British Columbia 2400-1200 Cal. B.P.: An Hypothesis , 2005, American Antiquity.

[125]  M. J. O’Brien,et al.  A comment on Steele's (2010) "radiocarbon dates as data: quantitative strategies for estimating colonization front speeds and event densities" , 2011 .

[126]  P. Vitousek,et al.  Building and testing models of long-term agricultural intensification and population dynamics: A case study from the Leeward Kohala Field System, Hawai’i , 2012 .

[127]  P. O. Mullen.  An Archaeological Test of the Effects of the White River Ash Eruptions , 2012, ARCTIC ANTHROPOLOGY.

[128]  R. Mandel.  Geomorphic controls of the Archaic record in the Central Plains of the United States , 1995 .

[129]  M.A. Smith,et al.  What happened at 1500—1000 cal. BP in Central Australia? Timing, impact and archaeological signatures , 2008 .

[130]  J. Dean.  Independent Dating in Archaeological Analysis , 2016 .

[131]  Nick T. Thomopoulos,et al.  Essentials of Monte Carlo Simulation: Statistical Methods for Building Simulation Models , 2012 .

[132]  J. Mabry,et al.  Temporal frequency distributions of alluvium in the American Southwest: taphonomic, paleohydraulic, and demographic implications , 2011 .

[133]  A. Ballouche,et al.  A question of timing: spatio-temporal structure and mechanisms of early agriculture expansion in West Africa , 2014 .

[134]  F. Aceituno,et al.  14C data and the early colonization of Northwest South America , 2015 .

[135]  S. Mithen,et al.  The impact of the abrupt 8.2 ka cold event on the Mesolithic population of western Scotland: a Bayesian chronological analysis using ‘activity events’ as a population proxy , 2014 .

[136]  A. Williams.  The use of summed radiocarbon probability distributions in archaeology: a review of methods , 2012 .

[137]  Christopher Bronk Ramsey,et al.  DEALING WITH OUTLIERS AND OFFSETS IN RADIOCARBON DATING , 2009 .

[138]  B. Marwick.  Change or Decay? An interpretation of late Holocene archaeological evidence from the Hamersley Plateau, Western Australia , 2009 .

[139]  P. Kirch.  Feathered Gods and Fishhooks: An Introduction to Hawaiian Archaeology and Prehistory , 1987 .

[140]  Jennifer C. French,et al.  Tenfold Population Increase in Western Europe at the Neandertal–to–Modern Human Transition , 2011, Science.

[141]  P. Reimer,et al.  Extended 14C Data Base and Revised CALIB 3.0 14C Age Calibration Program , 1993, Radiocarbon: An International Journal of Cosmogenic Isotope Research.

[142]  O. Zackrisson,et al.  Radiocarbon dating of prehistoric hearths in alpine northern Sweden: problems and possibilities , 2007 .

[143]  K. Becker,et al.  From dates to demography in later prehistoric Ireland? Experimental approaches to the meta-analysis of large 14C data-sets , 2013 .

[144]  Susan R. Wilson,et al.  PROCEDURES FOR COMPARING AND COMBINING RADIOCARBON AGE DETERMINATIONS: A CRITIQUE , 1978 .

[145]  B. Bogin,et al.  Demography Part 2: Population Growth and Fertility Regulation , 2012 .