Summed Probability Distributions Research Articles

Sedimentary unknowns constrain the current use of frequency analysis of radiocarbon data sets in forming regional models of demographic change

AbstractStatistical manipulation of large radiometric data sets (big data) is increasingly applied to those grand challenges in archaeology that relate to past human‐behavioural dynamics and includes frequency analysis of radiocarbon ages (summed probability distributions [SPDs]). Australian SPD studies use the radiocarbon database “AustArch” to examine regional‐ and continental‐scale demographic change. We review Australian studies, focussing on sampling bias and taphonomic bias, finding that (i) time‐averaged radiometric data cannot simply be correlated across regions, and (ii) sedimentology imposes genuine constraints upon what can be known. Internationally, flaws in SPD use occur in all main research phases, and most importantly, at the initial phase of defining research questions, logic and general approach. Major problems stem from not planning to obtain a sound understanding of the variability of past sedimentary environments, potential occupation sites and site formation processes. Thus, cultural inferences are too often made from archaeological data without due consideration of the natural processes that may explain the data. Highlighting exemplar studies, we present practical approaches to improve SPD use for exploring changes in demography, aimed at reducing uncertainties and reconnecting archaeological, chronological, geological and sedimentary data. Most important is to increase understanding of physical processes and their control on the archaeological record.

Collapse and continuity: A multi-proxy reconstruction of settlement organization and population trajectories in the Northern Fertile Crescent during the 4.2kya Rapid Climate Change event.

The rise and fall of ancient societies have been attributed to rapid climate change events. One of the most discussed of these is the 4.2kya event, a period of increased aridity and cooling posited as the cause of societal changes across the globe, including the collapse of the Akkadian Empire in Mesopotamia. Studies seeking to correlate social and climatic changes around the 4.2kya event have tended to focus either on highly localized analyses of specific sites or surveys or more synthetic overviews at pan-continental scales, and temporally on the event and its aftermath. Here we take an empirical approach at a large spatial scale to investigate trends in population and settlement organization across the entirety of Northern Fertile Crescent (Northern Mesopotamia and the Northern Levant) from 6,000 to 3,000 cal BP. We use Summed Probability Distributions of radiocarbon dates and data from eighteen archaeological surveys as proxies for population, and a dataset of all settlements over ten hectares in size as a proxy for the degree of urbanization. The goal is to examine the spatial and temporal impact of the 4.2kya event and to contextualize it within longer term patterns of settlement. We find that negative trends are visible during the event horizon in all three proxies. However, these occur against a long-term trend of increased population and urbanization supported through unsustainable overshoot and the exploitation of a drier zone with increased risk of crop failure. We argue that the 4.2kya event occurred during a period of unprecedented urban and rural growth which may have been unsustainable even without an exogenous climate forcing.

Global Processes, Regional Dynamics?

The goal of this paper is to discuss the validity of radiocarbon dates as a source of knowledge for explaining social dynamics over a large region and a long period of time. We have carefully selected c. 1000 14C dates for the time interval 8000–4000 cal BC within the northwestern Mediterranean area (NE Iberian Peninsula, SE France, N Italy) and Switzerland. Using statistical analysis, we have modelled the summed probability distribution of those dates for each of the analysed ecoregion and discussed the rhythms of neolithisation in these regions and the probability of social contact between previous Mesolithic and new Neolithic populations.

Directly modelling population dynamics in the South American Arid Diagonal using 14C dates.

Large anthropogenic 14C datasets are widely used to generate summed probability distributions (SPDs) as a proxy for past human population levels. However, SPDs are a poor proxy when datasets are small, bearing little relationship to true population dynamics. Instead, more robust inferences can be achieved by directly modelling the population and assessing the model likelihood given the data. We introduce the R package ADMUR which uses a continuous piecewise linear (CPL) model of population change, calculates the model likelihood given a 14C dataset, estimates credible intervals using Markov chain Monte Carlo, applies a goodness-of-fit test, and uses the Schwarz Criterion to compare CPL models. We demonstrate the efficacy of this method using toy data, showing that spurious dynamics are avoided when sample sizes are small, and true population dynamics are recovered as sample sizes increase. Finally, we use an improved 14C dataset for the South American Arid Diagonal to compare CPL modelling to current simulation methods, and identify three Holocene phases when population trajectory estimates changed from rapid initial growth of 4.15% per generation to a decline of 0.05% per generation between 10 821 and 7055 yr BP, then gently grew at 0.58% per generation until 2500 yr BP. This article is part of the theme issue 'Cross-disciplinary approaches to prehistoric demography'.

Population density and size facilitate interactive capacity and the rise of the state.

Radiocarbon summed probability distribution (SPD) methods promise to illuminate the role of demography in shaping prehistoric social processes, but theories linking population indices to social organization are still uncommon. Here, we develop Power Theory, a formal model of political centralization that casts population density and size as key variables modulating the interactive capacity of political agents to construct power over others. To evaluate this argument, we generated an SPD from 755 radiocarbon dates for 10 000-1000 BP from Central, North Central and North Coast Peru, a period when Peruvian political form developed from 'quasi-egalitarianism' to state levels of political centralization. These data are congruent with theoretical expectations of the model but also point to an artefactual distortion previously unremarked in SPD research. This article is part of the theme issue 'Cross-disciplinary approaches to prehistoric demography'.

New evidence for early human habitation in the Nyingchi Region, Southeast Tibetan Plateau

The lack of archaeological work has long impeded our understanding of prehistoric and historical human inhabitation and East-West interactions on the southeastern Tibetan Plateau (TP). In this study, we conducted a series of systematic archaeological investigations in the Nyingchi region, on the southeastern TP. We examined archaeological stratigraphies from 10 sites and collected charred seeds and charcoals for accelerator mass spectrometry (AMS) dating. The 26 radiocarbon dates show that the earliest inhabitation in the Nyingchi region can be traced back to as early as the fifth millennium BP. In addition, results of summed probability distribution (SPD) of radiocarbon dates suggest that intensive human activities occurred between c. 2700 and 2000 cal. yr BP. Together with the pottery net sinkers found in previous investigation, the newly identified archaeobotanical assemblages, including crops such as barley ( Hordeum vulgare), naked barley ( Hordeum vulgare var. nudum), wheat ( Triticum aestivum) and pea ( Pisum sativum), also confirm that cultivation and fishing were important subsistence strategies for people living in the prehistoric Nyingchi. The discoveries of domesticated crops from Southwest Asia also suggest that the southeastern TP, represented by the Nyingchi region, was part of the early communication network between the East and the West, predating historical Highland Silk Road.

Final Pleistocene and early Holocene population dynamics and the emergence of pottery on the Korean Peninsula

The final Pleistocene and early Holocene witnessed the emergence of the earliest pottery in East Asia. Despite extensive archaeological research conducted in Korea over the last three decades, the lack of comparable pottery evidence from the early postglacial, let alone the terminal Pleistocene, on the Korean Peninsula remains an archaeological enigma. Rather than anticipating future discoveries, we feel that it is time to explain why early pottery does not appear on the Korean Peninsula and attempt to provide a workable hypothesis focusing on the spatio-temporal dynamics of mobile hunter-gatherer-fisher populations during periods of substantial environmental change. Summed probability distribution and kernel density estimation of radiocarbon dates clearly indicate significant population fluctuations: occupation density increased under cold and dry Last Glacial Maximum (LGM) conditions and declined during warmer post-LGM and postglacial periods. We argue that a significant decline in population is the main reason why Pleistocene and postglacial pottery does not appear in Korea. On the other hand, the establishment of a Neolithic pottery tradition along Korea's coasts were likely associated with the 8.2 ka cooling event.

The ups and downs of the building trade in a medieval city: Tree-ring data as proxies for economic, social and demographic dynamics in Bruges (c. 1200–1500)

The exceptional preservation of the cityscape in the medieval city of Bruges (Belgium) triggered dendrochronological research on numerous preserved roof constructions in historical buildings, that date from the Middle Ages up to the early modern period. As many of these oak timbers lack the preservation of waney edge, a method was developed to combine sapwood estimates of felling dates within each building phase and to compute a summed probability distribution (SPD) for those felling dates. These summed probabilities now allow us to reconstruct temporal trends in building trade activity in an expanding medieval city. When linked to the social status of the patrons of the building projects, it is observed that resilience to demographic crisis and political turmoil differs among the social groups and political elite of a medieval society. Furthermore the dating results of decades of tree-ring research now provide a typo-chronological framework of roof constructions and shows that it took nearly two centuries before more advanced technological skill in the construction of roofs completely replaced the traditional common rafter roofs.

INFERENCE FROM LARGE SETS OF RADIOCARBON DATES: SOFTWARE AND METHODS

ABSTRACTThe last decade has seen the development of a range of new statistical and computational techniques for analysing large collections of radiocarbon (14C) dates, often but not exclusively to make inferences about human population change in the past. Here we introducercarbon, an open-source software package for the R statistical computing language which implements many of these techniques and looks to foster transparent future study of their strengths and weaknesses. In this paper, we review the key assumptions, limitations and potentials behind statistical analyses of summed probability distribution of14C dates, including Monte-Carlo simulation-based tests, permutation tests, and spatial analyses. Supplementary material provides a fully reproducible analysis with further details not covered in the main paper.

Climate and growing season variability impacted the intensity and distribution of Fremont maize farmers during and after the Medieval Climate Anomaly based on a statistically downscaled climate model

The rise and decline of many complex, pre-European maize-farming cultures in the American Southwest coincides with the warm, climatically quiescent Medieval Climate Anomaly (MCA, ca. 850–1350 CE) and transition to the cool, hydrologically variable Little Ice Age (LIA, ca. 1350–1850 CE). The effects of drought on early subsistence agriculture in the Southwest is well studied, but the impact of temperature stress and variability on the growth of maize crops and which areas were most resilient to such stress remain open questions. We statistically downscaled outputs from a paleo-climate model experiment (CESM1 LME) to map changes to cumulative growing degree days for maize (GDD, 30/10 °C) and precipitation over Utah between 850 and 1449 CE, and downscaled GDD changes to local Fremont Culture archaeological site occupations from radiocarbon-dated contexts mapped as spatially discrete kernel density estimates of summed probability distributions (SPDs). We then analyzed correspondences between Fremont SPDs and GDD/precipitation between 850 and 1449 CE. In general, we found (1) high Fremont occupation intensity coincident with GDD that is less volatile than the long term average, and low occupation intensity coincident with, or following, periods of volatile GDD; (2) intensified occupation of high-elevation sites during the MCA, followed by a retreat to lower elevation sites coincident with a sudden rise in annual temperature volatility and increasing drought conditions; and (3) these occupation changes occurred in spite of the greater temperatures and variability in GDD at low-elevation sites. We found evidence that increased inter-annual variability of growing seasons prior to the onset of the LIA, was likely a determinant of Fremont subsistence strategy decision making, and high-elevation site occupation. The most resilient Fremont occupations in the face of these challenges were sited where growing season lengths were least variable.

Between Foragers and Farmers: Climate Change and Human Strategies in Northwestern Patagonia

In this paper we explore how changes in human strategies are differentially modulated by climate in a border area between hunter-gatherers and farmers. We analyze multiple proxies: radiocarbon summed probability distributions (SPDs), stable C and N isotopes, and zooarchaeological data from northwestern Patagonia. Based on these proxies, we discuss aspects of human population, subsistence, and dietary dynamics in relation to long-term climatic trends marked by variation in the Southern Annular Mode (SAM). Our results indicate that the farming frontier in northwestern Patagonia was dynamic in both time and space. We show how changes in temperature and precipitation over the last 1000 years cal BP have influenced the use of domestic plants and the hunting of highest-ranked wild animals, whereas no significant changes in human population size occurred. During the SAM positive phase between 900 and 550 years cal BP, warmer and drier summers are associated with an increase in C4 resource consumption (maize). After 550 years cal BP, when the SAM changes to the negative phase, wetter and cooler summer conditions are related to a change in diet focused on wild resources, especially meat. Over the past 1000 years, there was a non-significant change in the population based on the SPD.

Population dynamics during the Neolithic transition and the onset of megalithism in Portugal according to summed probability distribution of radiocarbon determinations

As field data accumulates, the study of Neolithic Portugal has been receiving increasing attention recently, from material culture and subsistence to ideology. However, little is known about population dynamics. In this paper, we use a judicious selection of radiocarbon determinations to evaluate demographic phenomena within the 9.500–5.000 cal BP range (thus, starting in the Late Mesolithic) making use of “summed probability distribution” analysis. In greater Portugal, results show a negative deviation (i.e. demographic decrease) at 6.400–6.300 cal BP and a positive deviation (i.e. demographic increase) at 5.350–4.950 cal BP. These can be explained, respectively, by the impact of farming about one millennium after its introduction (confirming the “Neolithic demographic transition” model) and by the full establishment of the “secondary products revolution” in the Late Neolithic. However, individual analyses of the northern and southern halves of the country—i.e. using the Mondego river valley as an ecological-geographical divide—show rather contrasting trajectories, with scarce Mesolithic populations and a demographic increase in the megalithism in the North, whereas in the South a demographic crisis occurred at the onset of megalithism (which remains to be fully explained) being followed in the Late Neolithic by a sharp demographic increase. Further summed probability distribution analyses of radiocarbon determinations, particularly if combined with other populational proxies, will be able in the future to detect other demographic events taking place in space and time.

Estimating the distribution of a stochastic sum of IID random variables

Abstract Suggested is a non-parametric method and algorithm for estimating the probability distribution of a stochastic sum of independent identically distributed continuous random variables, based on combining and numerically inverting the associated empirical characteristic function (CF) derived from the observed data. This is motivated by classical problems in financial risk management, actuarial science, and hydrological modelling. This approach can be naturally generalized to more complex semi-parametric modelling and estimating approaches, e.g., by incorporating the generalized Pareto distribution fit for modelling heavy tails of the considered continuous random variables, or by considering the weighted mixture of the parametric CFs (used to incorporate the expert knowledge) and the empirical CFs (used to incorporate the knowledge based on the observed or historical data). The suggested numerical approach is based on combination of the Gil-Pelaez inversion formulae for deriving the probability distribution (PDF and CDF) from the associated CF and the trapezoidal quadrature rule used for the required numerical integration. The presented non-parametric estimation method is related to the bootstrap estimation approach, and thus, it shares similar properties. Applicability of the proposed estimation procedure is illustrated by estimating the aggregate loss distribution from the well-known Danish fire losses data.

A three-population wave-of-advance model for the European early Neolithic.

Ancient DNA studies have shown that early farming spread through most of Europe by the range expansion of farmers of Anatolian origin rather than by the conversion to farming of the local hunter-gatherers, and have confirmed that these hunter-gatherers continued to coexist with the incoming farmers. In this short report, I extend a previous three-population wave-of-advance model to accommodate these new findings, and derive the conditions supportive of such a scenario in terms of the relative magnitudes of the parameters. The revised model predicts that the conversion rate must, not surprisingly, be low, but also that the hunter-gatherers must compete more strongly with the converted farmers than with the alien farmers. Moreover, competition with the hunter-gatherers diminishes the speed of the wave-of advance of the farmers. In addition, I briefly consider how the wave-of-advance approach may contribute to interpreting the results of archaeological studies using the summed probability distribution of radiocarbon dates.

Barcode seriation and concepts of Gauge Theory. The 14C-Chronology of Starčevo, LBK, and early Vinča

A new method for automated construction of 14C-based archaeological chronologies, called Barcode Seriation (BS), is introduced. The application of BS is demonstrated for medium-sized (N~50 sites) datasets of the early Neolithic cultures Starčevo/Körös/Criş, LBK-I, and Vinča A. The BS-method is easy to apply, but nevertheless allows construction of 14C-chronologies at comparatively high dating precision. The key to BS is a new timing discriminator (TD), designed for leading/trailing edge shape-analysis of summed probability distributions of 14C-ages (SPDs). In functional terms, the TD works as an Analog-to-Digital Converter. The SPD signal digitisation, in turn, supports large-scale 14C-database analysis on different levels of data confinement (e.g. by sites, periods, periods, cultures, phases) as well as on large geographic scales (regional-continental). Due to the compactness of the chosen graphic-output topology, the combined BS/TD-technology supports ordination and plotting of very large 14C-datasets, but leaving room in graphic representation for the chronology to be shown in context with other records e.g. from palaeoenvironmental, archaeobiological, and palaeaoclimatological studies. The feasibility of routine application of the new method is demonstrated by case-comparisons at high dating-resolution for the sites of Pityerdomb (Hungary), Vráble (Slowakia), Versend-Gilencsa (Hungary), Vinča-Belo-Brdo (Serbia), and at two LBK-sites (‘Lüsse’ and ‘Unteres Feld’) both located in the Ammer Valley near Tübingen (Germany). The new methodology is complemented with studies towards the application of Gauge Theory in support of archaeological 14C-analysis.

A multi-proxy inference of Jōmon population dynamics using bayesian phase models, residential data, and summed probability distribution of 14C dates

We introduce a new workflow for analysing archaeological frequency data associated with relative rather than absolute chronological time-stamps. Our approach takes into account multiple sources of uncertainty by combining Bayesian chronological models and Monte-Carlo simulation to sample possible calendar dates for each archaeological entity. We argue that when applied to settlement data, this combination of methods can bring new life to demographic proxies that are currently under-used due to their lack of chronological accuracy and precision, and provide grounds for further exploring the limits and the potential of the so-called “dates as data” approach based on the temporal frequency of radiocarbon dates. Here we employ this new workflow by re-examining a legacy dataset that has been used to describe a major population rise-and-fall that occurred in central Japan during the Jōmon period (16,000–2,800 cal BP), focusing on the temporal window between 8,000 and 3,000 cal BP. To achieve this goal we: 1) construct the first Bayesian model of forty-two Jōmon ceramic typology based cultural phases using a sample of 2,120 radiocarbon dates; 2) apply the proposed workflow on a dataset of 9,612 Jōmon pit-dwellings; and 3) compare the output to a Summed Probability Distribution (SPD) of 1,550 radiocarbon dates from the same region. Our results provide new estimates on the timing of major demographic fluctuations during the Jōmon period and reveal a generally good correlation between the two proxies, although with some notable discrepancies potentially related to changes in settlement pattern.

Spatial modeling of archaeological site locations based on summed probability distributions and hot-spot analyses: A case study from the Three Kingdoms Period, Korea

Archaeologists typically use radiocarbon ages to date human activities on archaeological sites. However, radiocarbon ages can also serve as independent proxies for human demographic patterns through space and time. Spatial modeling of archaeological data often involves taking diachronic datasets and developing synchronic views of the distribution of cultural patterns. Here, we evaluate spatial dynamics of human activity areas assayed by radiocarbon ages in the Baekje Kingdom of Korea before and after the invasion of Koguryeo, which is historically documented as occurring in AD 475. The statistical techniques used in this research apply spatial autocorrelations on archaeological sites with weighted attributes from summed probability distributions (SPDs) to evaluate regional scale diachronic changes from radiocarbon datasets. Ripley's K analysis shows an increasing tendency toward clustering of weighted SPD attributes from sites after AD 325. The Getis-Ord Gi* statistic shows the changing hot spots of Baekje settlement shift prior and concurrent to the establishment of a military zone in northern Gyeonggi Province, South Korea. The settlement systems realign from clusters in the north and south of the province to clusters in the southeast with avoidance of the north.

Demographic fluctuations and the emergence of arctic maritime adaptations

Our goal is to study the role of demographic change in the development and spread of maritime adaptations in the North American Arctic over the last 6000 years. We compile and analyze a regional radiocarbon database (n = 935) for northern Alaska, using Oxcal to analyze demographic patterns in summed probability distributions. We find that northern Alaskan populations grew significantly over the last 4500 years, although growth was punctuated by three periods of decline from approximately 3700 to 3125 cal BP, 1000 cal BP, and 600 cal BP. We assess possible alternative explanations for the observed demographic patterns (e.g. calibration and taphonomic effects, investigator bias). Region-wide erosion and calibration effects likely contribute to the dearth of radiocarbon dates around 1000 cal BP, and sampling bias may contribute to the post-600 cal BP decline. However, we conclude that the overall pattern reflects regional population growth, decline, and recovery. Population growth predates intensification of marine resource procurement by at least 1200 years; we hypothesize that population growth was a possible driver for late Holocene marine intensification in the Arctic. These findings have further implications for understanding the process of intensification and the development of complexity in coastal hunter-gatherer societies.

Chinook Salmon, Late Holocene Climate Change, and the Occupational History of Kettle Falls, a Columbia River Fishing Station

ABSTRACT Kettle Falls, located 1125 km from the mouth of the Columbia River in present-day Washington State (USA), was the second-most important salmon fishing and trading locus on that river in the early historic era. We encapsulate the late Holocene history of the fishery by deriving a summed probability distribution function (SPDF) from 50 radiocarbon ages from 13 archaeological sites within 2 km of the falls. When compared to an SPDF from 307 sites from elsewhere on the Columbia Plateau, and a null model, the Kettle Falls SPDF exhibits two phases of elevated activity at 1700–1300 cal BP and 800–500 cal BP, and an intervening lull. These phases are not related to the excavation history or differential exposure of sites to taphonomic processes, but they are concordant with episodes of glacial advance in the local mountains, which reflect hemispheric-scale changes in climate. Modern returns of summer-run Chinook salmon to the Columbia River are inversely correlated with sea-surface temperature regimes in the northeast Pacific Ocean, and we propose that the occupational history of the Kettle Falls fishery echoes long-term variations in the returns of salmon to the upper Columbia River linked to climate change.

Abrupt Holocene climate shifts in coastal East Asia, including the 8.2 ka, 4.2 ka, and 2.8 ka BP events, and societal responses on the Korean peninsula

Holocene abrupt cooling events have long attracted attention in academia due to public concern that similar rapid changes may reappear in the near future. Thus, considerable progress has been made toward understanding these short-term cooling events in the Northern Hemisphere, particularly in Europe and North America. However, few relevant studies have been conducted in coastal East Asia due to a lack of undisturbed sample materials appropriate for paleoclimate studies. In this study, we examined Holocene abrupt drying events and the Holocene climate optimum (HCO) based on a new high-resolution multi-proxy record (pollen, mean grain size, total organic carbon, carbon/nitrogen ratio) from the south coast of Korea. Possible cultural impacts of the events were also explored using summed probability distributions (SPDs) of archaeological radiocarbon dates. Our arboreal pollen percentage (AP) data clearly indicated drying events centered at 9.8 ka, 9.2 ka, 8.2 ka, 4.7 ka, 4.2 ka, 3.7 ka, 3.2 ka, 2.8 ka, and 2.4 ka BP. The AP data also indicated that forests were severely damaged by a two-step successive drying event during the period from 8.4 ka to 8 ka BP and that the HCO lasted from ca. 7.6 ka to ca. 4.8 ka BP. According to the results of a correlation analysis, climate variations on the Korean peninsula were possibly controlled by shifts in western tropical Pacific (WTP) sea surface temperatures during the past ~5500 years. Simultaneous declines in the SPDs and AP from 2.8 ka to 2.3 ka BP may reflect a demographic reduction attributable to rapid climate deterioration on the peninsula. Refugee agriculturalists might have immigrated to Japan and developed the Yayoi culture. In this study, the 2.8 ka event and its societal impact are recognized clearly for the first time in coastal East Asia.