Summed Probability Distributions Research Articles

Summed Probability Distribution of 14C Dates Suggests Regional Divergences in the Population Dynamics of the Jomon Period in Eastern Japan.

Recent advances in the use of summed probability distribution (SPD) of calibrated 14C dates have opened new possibilities for studying prehistoric demography. The degree of correlation between climate change and population dynamics can now be accurately quantified, and divergences in the demographic history of distinct geographic areas can be statistically assessed. Here we contribute to this research agenda by reconstructing the prehistoric population change of Jomon hunter-gatherers between 7,000 and 3,000 cal BP. We collected 1,433 14C dates from three different regions in Eastern Japan (Kanto, Aomori and Hokkaido) and established that the observed fluctuations in the SPDs were statistically significant. We also introduced a new non-parametric permutation test for comparing multiple sets of SPDs that highlights point of divergences in the population history of different geographic regions. Our analyses indicate a general rise-and-fall pattern shared by the three regions but also some key regional differences during the 6th millennium cal BP. The results confirm some of the patterns suggested by previous archaeological studies based on house and site counts but offer statistical significance and an absolute chronological framework that will enable future studies aiming to establish potential correlation with climatic changes.

Source Codes, Scripts, and Data for the paper "Summed Probability Distribution of 14C Dates suggests Regional Divergences in the Population Dynamics of the Jomon Period in Eastern Japan"

Source Codes, Scripts, and Data for the paper "Summed Probability Distribution of 14C Dates suggests Regional Divergences in the Population Dynamics of the Jomon Period in Eastern Japan"

Demographic Proxies for the Neolithic

The article discusses the use of summed probability distribution as a demographic proxy, and highlights several issues with this method, especially during periods of change in the exploitation of the landscape or during social transformation. With a case study from the Lange-land region in Denmark an alternative and corrective approach is applied, were number of settlements and size of settlement is included. With this approach a very different development can be described.

Source Codes, Scripts, and Data for the paper "Summed Probability Distribution of 14C Dates suggests Regional Divergences in the Population Dynamics of the Jomon Period in Eastern Japan"

Source Codes, Scripts, and Data for the paper "Summed Probability Distribution of 14C Dates suggests Regional Divergences in the Population Dynamics of the Jomon Period in Eastern Japan"

Radiocarbon dates and anthropogenic signal in the South-Central Andes (12,500–600 cal. years BP)

This paper presents the analysis of the anthropogenic signal documented by four time-series in the highlands of the South-Central Andes (Puna of Argentina and North Chile) spanning the period between 12,500 and 600 cal years BP. Our goal is to extract demographic and occupational histories from temporal data. In this way, based upon the full radiocarbon dataset and the sites of provenance of the dates, we built the following time-series: the summed probability distribution of calibrated ages; the relative frequency of calibrated ages; the relative frequency of sites per unit of time; and the frequency of new sites per unit of time. For controlling the effects of site destruction on the anthropogenic signal, we used the exponential model as well as the volcanic empirical model of taphonomic bias. The four time-series coincide in showing a regional pattern with a phase of low and fluctuating demography of relative long term duration, followed by an growth phase well evident at 5000 cal BP in a context the economic intensification. The long-term demographic success of the hunter-gatherers in the highlands many millennia before the consolidation of food production exemplifies the flexibility of this mode of subsistence for achieving human adaptation to extreme selective environments as the Puna.

Summed radiocarbon probability distributions from cereal grains: arable cultivation proxy or the ‘archaeology of us’? (a reply to Stevens and Fuller 2015)

In response to the critique in this volume (Bishop 2015), Stevens and Fuller (2015) have modified their original interpretation of Late Neolithic subsistence strategies in the British Isles (Stevens and Fuller 2012). This article highlights the key issues that remain with their analysis. It is reiterated that radiocarbon summed probability distributions from cereals are not a suitable proxy for the changing importance of arable cultivation through time.

Probability distribution of CUSUM charting statistics

In parallel to the conventional study of the distribution of the first time to signal, this paper investigates the probability distribution of the article Cumulative Sum (CUSUM) charting statistics based on a recurrence relationship. The probability distribution of the CUSUM statistic can not only provide statistical significance of observations against the null hypothesis of being in control but also facilitate the analysis of the CUSUM chart in the steady-state scenario. Both the conditional case (CUSUM chart without restarting) and the cyclical case (CUSUM chart with restarting) are considered. It is shown that the distribution of CUSUM charts both with and without restarting approaches a stationary distribution, independent of their initial values. We also show that the null steady-state distribution of the unbounded CUSUM chart previously reported in the literature is a special case of this article as the control limit approaches infinity.

Neolithic population and summed probability distribution of 14C-dates

This paper assesses the use of radiocarbon dates as a population proxy during the north European Mesolithic–Neolithic transition. By addressing data from the Jutland peninsula, it is shown that the sum probability distributions are influenced by three human-inflicted biases. Two of these – changed ritual behaviour and changes of subsistence strategies – refer to past human activity, while the third consists of modern research strategies. The analysis questions the validity of sum probability distributions as a population proxy in a period where a society experiences a transformation process.

Temporal fluctuation of human occupation during the 7th–3rd millennium cal BP in the central-western Korean Peninsula

In this paper the population fluctuation in the central-western region of the Korean Peninsula is investigated using radiocarbon data obtained from prehistoric pit houses in residential bases or settlements during the seventh to third millennium cal BP comprising the Neolithic, Bronze and Early Iron ages in Korea. Fluctuation in radiocarbon date distribution is compared with summed probability distribution of calibrated dates as well as total numbers of settlements and dwellings arranged in chronological order. Results indicate the appearance of Neolithic and Bronze Age settlements in the early sixth and the late fourth millennium BC each followed by a rapid growth of population with a peak around 5500 and 3000 cal BP. Population decline is identified from 5300, 4900, 4500 cal BP during the Neolithic and 2800 and 2400 cal BP during the Bronze Age. The period between 4500 and 3500 cal BP corresponds with the lowest density of settlements and dwellings. Agricultural villages collapsed 2400–2000 cal BP. The paper suggests the hypothesis that climate change, especially cold or dry climate induced by weak Asian monsoon events, is possibly responsible for the fluctuation of settlements and population in prehistoric Korea.

The chronology of culture: a comparative assessment of European Neolithic dating approaches

Archaeologists have long sought appropriate ways to describe the duration and floruit of archaeological cultures in statistical terms. Thus far, chronological reasoning has been largely reliant on typological sequences. Using summed probability distributions, the authors here compare radiocarbon dates for a series of European Neolithic cultures with their generally accepted ‘standard’ date ranges and with the greater precision afforded by dendrochronology, where that is available. The resulting analysis gives a new and more accurate description of the duration and intensity of European Neolithic cultures.

The emergence of agropastoralism: Accelerated ecocultural change on the Andean altiplano, ∼3540–3120 cal BP

In the fourth millennium BP, there were major environmental and cultural changes on the Andean altiplano of South America, but the chronology remains vague. A recent synthesis describes a slow, gradual transition from hunting and gathering to agropastoralism. This proposal is tested by refining the date of the onset of more humid and stable conditions, around 3550 cal BP, based on a Bayesian model of 26 dates from Lake Wiñaymarka and an updated calculation of the lacustrine offset. This is compared to Bayesian models of 191 dates from 20 archaeological sites, which incorporate a number of recently processed radiocarbon dates. A synthesis is presented of 15 full coverage surveys, a summed probability distribution, and a Bayesian model of the transition to ceramics, which together support a scenario of a very rapid demographic increase. Fourteen models from archaeological sites are cross-referenced in a composite model, which identifies a brief, altiplano-wide emergence of agropastoralism with starting and ending boundaries of 3540 and 3120 cal BP, respectively. This starting boundary correlates strongly with the onset of improving environmental conditions, indicating synchronous cultural and environmental change. The suite of accelerating cultural changes included a marked reduction in mobility, a demographic surge, increased subsistence diversity, the adoption of ceramics, farming and the integration of camelid herding into a remarkably resilient economic strategy still in use today. This is a highly relevant but yet to be used comparative case study for the variable tempos of ‘big histories’, and ecocultural interactions that generate rapid, emergent episodes of wide-spread and enduring cultural change.

Introduction to the Frison Institute Symposium on radiocarbon dating applications

We introduce the papers of the JAS Special Issue: Radiocarbon Dating that were presented at the First Frison Institute Symposium at the 2013 Society for American Archaeology annual meeting. Papers here fall into two categories that reflect two growing trends in archaeology: the use of summed probability distributions as measures of human population, and the use of Bayesian statistics to refine radiocarbon age estimates. While caution is required, these two methods combined offer archaeology the possibility of tracking change in the size of human populations through time and across space.

Reconstructing regional population fluctuations in the European Neolithic using radiocarbon dates: a new case-study using an improved method

In a previous study we presented a new method that used summed probability distributions (SPD) of radiocarbon dates as a proxy for population levels, and Monte-Carlo simulation to test the significance of the observed fluctuations in the context of uncertainty in the calibration curve and archaeological sampling. The method allowed us to identify periods of significant short-term population change, caveated with the fact that around 5% of these periods were false positives. In this study we present an improvement to the method by applying a criterion to remove these false positives from both the simulated and observed distributions, resulting in a substantial improvement to both its sensitivity and specificity. We also demonstrate that the method is extremely robust in the face of small sample sizes. Finally we apply this improved method to radiocarbon datasets from 12 European regions, covering the period 8000–4000 BP. As in our previous study, the results reveal a boom-bust pattern for most regions, with population levels rising rapidly after the local arrival of farming, followed by a crash to levels much lower than the peak. The prevalence of this phenomenon, combined with the dissimilarity and lack of synchronicity in the general shapes of the regional SPDs, supports the hypothesis of endogenous causes.

The demographic response to Holocene climate change in the Sahara

The timing and development of Holocene human occupation in the now hyperarid Sahara has major implications for understanding links between climate change, demography and cultural adaptation. Here we use summed probability distributions from 3287 calibrated 14C dates from 1011 archaeological sites to demonstrate a major and rapid demographic shift between 10,500 and 5500 years BP. This event corresponds with the African Humid Period (AHP) and is sub-continental in scale, indicating climate as the prime factor driving broad-scale population dynamics in northern Africa. Furthermore, by providing a high temporal resolution proxy for effective carrying capacity our population curve offers an independent estimate of environmental change in northern Africa, indicating a temporal delay in the terrestrial response to atmospheric climate change. These results highlight the degree to which human demography is a function of environment at the appropriate scale of observation in both time and space and sheds important new light on the social response to global environmental change.

Mid Holocene radiocarbon ages in the Subtropical Andes (∼29°–35° S), climatic change and implications for human space organization

This article discusses the distribution of radiocarbon age signatures obtained from archeological sites between 29° and 35° S in Central Chile and Midwest Argentina. The goal of this analysis is to establish bases from which to interpret regional trends in the distribution of the archaeological record that connect these areas, which have been traditionally considered to be geographically decoupled. We propose a standardized methodology for selecting ages that provide a reliable human signature. Variations in date frequencies in a regional scale are discussed with the use of summed probability distributions. Radiocarbon voids at the regional level previously identified in Midwest Argentina are explored. Regional chronological information is compared to the available paleoenvironmental records, thereby emphasizing the possible role of climate pulses in the spatial organization of human populations. Significant arid conditions between 7800 and 5700 cal BP are coincidental with a focused occupation of the Andes Mountains, an area which may have offered stable resources and thus was more effectively occupied than other environmental bands.

Prehistoric demographic fluctuations in China inferred from radiocarbon data and their linkage with climate change over the past 50,000 years

Historic human–climate interactions have been of interest to scholars for a long time. However, exploring the long-term relation between prehistoric demography and climate change remains challenging because of the absence of an effective proxy for population reconstruction. Recently, the summed probability distribution of archaeological radiocarbon dates has been widely used as a proxy for human population levels, although researchers recognize that such usage must be cautious. This approach is rarely applied in China due to the lack of a comprehensive archaeological radiocarbon database, and thus the relation between human population and climate change in China remains ambiguous. Herein we systematically compile an archaeological 14C database (n = 4656) for China for the first time. Using the summed probability distributions of the radiocarbon dates alongside high-resolution palaeoclimatic records, we show that: 1) the commencement of major population expansion in China was at 9 ka cal BP, occurring after the appearance of agriculture and associated with the early Holocene climate amelioration; 2) the major periods of small population size and population decline, i.e., 46–43 ka cal BP, 41–38 ka cal BP, 31–28.6 ka cal BP, 25–23.5 ka cal BP, 18–15.2 ka cal BP, and 13–11.4 ka cal BP, correspond well with the dating of abrupt cold events in the Last Glacial (LG) such as the Heinrich and Younger Dryas (YD) events, while the major periods of high-level population in the Holocene, i.e., 8.5–7 ka cal BP, 6.5–5 ka cal BP and 4.3–2.8 ka cal BP, occur at the same times as warm-moist conditions and Neolithic cultural prosperity, suggesting that abrupt cooling in the climate profoundly limited population size and that mild climate episodes spurred a growth in prehistoric populations and advances in human cultures; and 3) populations in different regions experience different growth trajectories and that their responses to climate change are varied, due to both regional environmental diversity and the attainment of different levels of adaptive strategies.

Summed radiocarbon calibrations as a population proxy: a critical evaluation using a realistic simulation approach

The logic of using summed radiocarbon (14C) calibrations (cumulative probability density functions for large numbers of calibrated 14C dates) as proxies for past populations rests on the presumption of a proportional relationship between population size and the production, and subsequent preservation, recovery, and analysis, of 14C-datable material. Critiques of this approach have generally focused on the various problems that may undermine the validity of this assumption.Here, instead, we presume a perfect correspondence between population size and the quantity of datable material produced at any given time, and explore the question of how well summed 14C calibrations can track demographic changes under such ideal circumstances. We introduce a method of generating a random sample of simulated 14C determinations, from a specified distribution, with variable data densities and measurement errors. In other words, we generate a random sample of 14C dates not from an ideal statistical distribution but rather using a defined population curve to determine the probability distribution from which the calendar dates of the simulated 14C samples are drawn. We generate simulated 14C ages for these samples, calibrate them, and sum those calibrations. We compare the resulting proxy population curve to the known population distribution from which it was generated, to see whether known population fluctuations are unambiguously visible on a proxy curve derived from 14C data sets that are realistic in terms of the number and precision of the 14C determinations included.Results highlight 1) the critical role played by the magnitude and duration of any population fluctuation, and 2) the importance of sample size, and the reality that the numbers of samples required to detect significant population changes are generally far higher than those available to researchers proposing demographic reconstructions on the basis of literature searches for radiocarbon dates. We conclude that even if archaeological 14C data sets could be corrected for taphonomic filters and research biases, demographic signals would be difficult to distinguish from statistical noise in summed probability distributions. We suggest that simulation studies should be integral components of any attempt to reconstruct prehistoric demography from 14C dates.

Temporal Dynamics of East Texas Caddo Sites with Nine or Fewer Radiocarbon Dates

This article presents the specifics from the date combination process, and the subsequent production of summed probability distributions for radiocarbon (14C) assays from Caddo sites in East Texas. All 14C dates employed in this effort were collected from research and cultural resource management (CRM) reports and publications, were synthesized, and then recalibrated in version 4.2.2 of OxCal using IntCal09. These data are meant to augment those from previous analyses of radiocarbon samples from East Texas Caddo sites, assisting in refining these ideas further.

RADIOCARBON TRENDS AND THE EAST TEXAS CADDO TRADITION (CA. A.D. 800–1680)

Through the employment of radiocarbon (14C) dates as data, we use the date combination process to refine site-specific summed probability distributions for 555 dates from Caddo sites (n = 19) in East Texas with 10 or more 14C dates. Summed probability distributions are then contrasted across river basins and natural regions with the remainder of the East Texas Caddo Radiocarbon Database (n = 338 dates from 132 other Caddo sites), highlighting the temporal and spatial character of Caddo archaeological sites throughout East Texas.

The Bergström–Grigelionis asymptotic expansions

We consider a triangular array of independent identically distributed discrete random variables. We assume that the probability distribution of sums satisfies the necessary and sufficient conditions for the weak convergence to the compound Poisson distribution. The first known result (the case where random variables take only integer values) is due to B. Grigelionis, who estimated the convergence rate to the compound Poisson distribution. We extend the summation of random variables by including the variables taking discrete values and by using the Grigelionis ideas to obtain “lengthy” asymptotic expansions. These expansions are based on the well-known Bergstrom identity [H. Bergstrom, On asymptotic expansions of probability functions, Scand. Actuarial J., 34(1):1–33, 1951].