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#+TITLE: Archaeology in Oceania, Age of O18 #+AUTHOR: Tom Dye #+EMAIL: tsd at tsdye dot com #+DATE: 2010-07-22 Thu #+DESCRIPTION: #+KEYWORDS: #+LANGUAGE: en #+OPTIONS: H:3 num:t toc:nil \n:nil @:t ::t |:t ^:t -:t f:t *:t <:t #+OPTIONS: TeX:t LaTeX:nil skip:nil d:nil todo:nil pri:nil tags:nil #+INFOJS_OPT: view:nil toc:nil ltoc:t mouse:underline buttons:0 path:http://orgmode.org/org-info.js #+EXPORT_SELECT_TAGS: export #+EXPORT_EXCLUDE_TAGS: noexport #+LINK_UP: ../uses.php #+LINK_HOME: http://orgmode.org/worg/ #+BABEL: :exports code #+SEQ_TODO: TODO(t) STARTED(s) | DONE(d) REJECTED(r) REFTEX * LaTeX preamble #+name: latex-preamble #+begin_src latex :tangle o18_ao.tex \documentclass[minion,glossaries]{tsdarticle} \author{Thomas S. Dye and Jeffrey Pantaleo} \title{Age of the O18 Site\thanks{Special thanks to Valerie Curtis for her commitment to this project and her confidence that it would yield interesting results. Dave Tuggle and Matthew Spriggs offered valuable criticism that sharpened the argument considerably. Caitlin Buck offered perceptive advice on Bayesian modeling. Kristin Macak drafted the site map, which was prepared for publication by Eric Komori. Dan Davison and Eric Schulte both provided guidance on the use of Org-babel, a software environment that integrates thinking, analysis, and writing that greatly facilitated production of the paper.}} \let\alert\textbf \let\itemize\compactitem \begin{document} \maketitle #+end_src * Abstract #+begin_src latex :tangle o18_ao.tex \begin{abstract} Seven new \rc\ age determinations on short-lived materials yield a sound evidential basis for the chronology of the O18 site on O`ahu Island, Hawai`i, long thought to be an early settlement site. Calibration within a model-based, Bayesian framework indicates that the site was established in \textsc{ad} 1040--1219, some 260--459 years after the current estimate of first settlement, and abandoned in the late eighteenth or early nineteenth centuries. Previously published age determinations are mostly too old, probably due to the ``old wood'' effect. O18 appears to be the oldest site on the Waim\={a}nalo Plain, but earlier sites in Waim\={a}nalo likely exist inland of the plain. \end{abstract} #+end_src * Introduction #+name: latex-intro #+begin_src latex :tangle o18_ao.tex The age of the O18 site has been an important datum in Hawaiian prehistory since the first estimate was published in the pages of this journal nearly 40 years ago \citep{pearson71:_bellows}. Based on an internally inconsistent set of \rc\ age determinations, the site was interpreted by its excavators as having been established in the seventh century \textsc{ad} and abandoned by the twelfth century. The estimated date of establishment was subsequently pushed back to the fourth century \textsc{ad} by \citet{kirch85}, based primarily on volcanic glass hydration dates that are no longer believed to be valid \citep{tuggle01:_age_bellow_dune_site_o18}. Kirch considered O18 to be one of only two sites representing the earliest phase of Polynesian settlement of the Hawaiian Islands. This characterization exerted a strong hold on the archaeological imagination. In the early 1980s, it inspired Matthew Spriggs to pull additional samples from storage and have them dated. These samples yielded a stratigraphically inconsistent set of \rc\ age determinations that was interpreted more than a decade later with some difficulty by \citet{tuggle01:_age_bellow_dune_site_o18} as indicating an occupation span beginning perhaps as early as the eighth century \textsc{ad} and ending in the middle of the fifteenth century \textsc{ad}. Here, we present the results of nine new \rc\ age determinations from O18, most of them on short-lived materials. The age determinations on short-lived materials are internally consistent and provide, for the first time, a sound evidential basis for the site's chronology. The \rc\ age determinations are interpreted within a model-based, Bayesian framework. An estimate of site establishment yielded by the model-based analysis, supported by the age of an \textit{Aleurites moluccana} nutshell dated by Spriggs, indicates that O18 was established several centuries after the islands were first settled by Polynesians. The O18 chronology yielded by the site-specific Bayesian model is extended to include \rc\ age determinations from four other sites in the region. The chronologies of all five sites are broadly similar. Like these other sites, O18 was abandoned late in traditional Hawaiian times. #+end_src * O18 in regional context [2/2] ** DONE Regional context #+name: regional-context #+begin_src latex :tangle o18_ao.tex \section{The O18 Site} \label{sec:O18-site} Site O18 is located on the Waim\={a}nalo Plain, at the coast (fig.~\ref{fig:location}). It is a small part of a larger traditional Hawaiian settlement pattern in which the coastal plain was used on a regular basis, primarily for activities associated with fishing and shellfishing, by people who kept more established residences inland on the volcanic soils that supported their food gardens. A large portion of the coastal plain was developed as a military installation in the twentieth century, especially during World War II, and much of the traditional Hawaiian deposit was lost during this development. The pattern of sites on the plain today is probably due more to military development than it is to patterns of traditional activity in the past. \begin{figure}[htb!] \centering \includegraphics[width=84mm]{AO_bellows_O18_landscape.png} \caption{Traditional Hawaiian sites on a portion of the Waim\={a}nalo Plain.} \label{fig:location} \end{figure} Immediately inland of Site O18, and at one time probably coterminous with it, is Site 50--80--15--4853, a large expanse of discontinuous cultural deposits on the north bank of Puh\={a} Stream that represent primarily cooking and eating activities \citep{tuggle97:_archaeol_resear_areas_propos_devel,desilets02:bellows}. South of Puh\={a} Stream is Site 50--80--15--4851, which is broadly similar to Site --4853, but also includes low-lying swamp deposits in old stream meanders that were used to cultivate taro \citep{tuggle97:_archaeol_resear_areas_propos_devel,dye98}. On the north part of the plain, nearer the foothills of Keolu Hills, are Sites 50--80--11--4856 and --4857, which were also likely coterminous, and which appear to represent the same range of activities as Site --4853. #+end_src ** DONE Stratigraphy #+name: stratigraphy #+begin_src latex :tangle o18_ao.tex Excavations for cultural resources management carried out at sites on the plain provide data for a model of regional cultural stratigraphy. The model groups deposits into one of three horizons: \begin{inparaenum}[(i)] \item Horizon 1 is the modern surface consisting of secondarily deposited sand, historic-era and traditional Hawaiian cultural materials, and pockets of volcanic fill material laid down during construction of military facilities; \item Horizon 2 is the traditional Hawaiian cultural deposit, often truncated by heavy machinery during construction of military facilities; and \item Horizon 3 is the underlying basal sand that was laid down as local sea level fell from its mid-Holocene +1.8~m highstand \citep{fletcher96} prior to settlement of the islands. \end{inparaenum} The model was developed to capture variability with distance from the coast, the source of trade wind-driven sand that represents the primary natural mode of deposition since the plain was first inhabited, and the degree to which cultural activities included excavation of pits primarily for cooking fires, but also for posts and trash disposal. Pit excavation is responsible for moving artifacts and other cultural materials down the stratigraphic profile and contribute markedly to the thickness of the cultural deposit (fig.~\ref{fig:stratigraphy}). \begin{figure}[htb!] \centering \includegraphics[width=84mm]{graphics/strat-overview.png} \caption{Regional cultural stratigraphy along a hypothetical transect running inland from the beach, showing the relative effects of ongoing sand deposition and traditional Hawaiian pit excavation.} \label{fig:stratigraphy} \end{figure} At the inland edge of the plain, illustrated by profile A in figure~\ref{fig:stratigraphy}, sand deposition is slight and few pits were excavated in traditional Hawaiian times. The cultural deposit here can be characterized as a paleosol whose surface includes a low density of cultural material that appears to have been discarded upon it in a more-or-less random fashion. Moving toward the coast, through profiles B, C, and D, both the intensity of cultural deposition and pit excavation increases, creating a thicker cultural deposit beneath which individual pit features can be discovered as dark stains in the light-colored basal sands. Closer to the coast, represented in the figure by profile E, the thickness of the cultural deposit reaches a maximum due to a higher intensity of use and a larger volume of aeolian sand deposit from the nearby beach. The frequency of pit excavation here is such that it is rarely possible to identify individual features in the underlying basal sand. Instead, the base of the cultural deposit consists entirely of the bases of pits excavated atop and through one another. At Site 50--80--15--4856, where the stratigraphy corresponded to the model represented by profile E, it was estimated that the number and volume of pits excavated in traditional Hawaiian times were sufficient to turn over the cultural deposit completely three times. Closer to the beach, the level of cultural activity drops somewhat and the influx of aeolian sand increases markedly, creating a relatively complex stratigraphy in which cultural deposits are interspersed with layers and lenses of beach sand. This is the situation encountered during excavations at O18, where two primary traditional Hawaiian cultural deposits, Layers II and III, along with several smaller sub-layers or lenses were identified. One implication of the model is that the relatively complex stratigraphy at O18 in comparison to sites farther inland on the plain is not an indication of greater antiquity. Instead, it is a function of the site's proximity to the beach. In this view, the O18 site is the coastal fringe of traditional Hawaiian settlement on the plain, where the focus of activity was a short distance inland, away from the constant influx of windblown sand and from periodic inundation by storm waves. #+end_src * Age of the site [3/3] - Add interval between first settlement and site establishment - 67% hpd 260--459 - 95% hpd 100--509 ** DONE Age of O18 #+name: O18-age #+begin_src latex :tangle o18_ao.tex \section{Age Determinations and Analysis} \label{sec:age-determinations} The nine new age determinations were processed in two batches independently of one another. Five collections of wood charcoal, two made by Lloyd Soehren of Bishop Museum in 1966 and three by the University of Hawaii field school in 1967, were submitted by Valerie Curtis, then an archaeologist with the U.S. Air Force, to Gail Murakami of the International Archaeological Research Institute, Inc.\ Wood Identification Laboratory for taxon identification. The identified samples were submitted to Beta-Analytic, Inc.\ for \rc\ dating by the accelerator mass spectrometry (AMS) method (table~\ref{tab:calibration}). \begin{table}[p] \topcaption{Age determinations on mostly short-lived specimens} \label{tab:calibration} \footnotesize \begin{tabularx}{\textwidth}{llYrrllrr} \toprule \textbf{Sample} & \textbf{Unit} & \textbf{Material} & $\mathbf{\delta^{13}}$\textbf{C} & \multicolumn{1}{c}{\textbf{CRA}}& \textbf{Age (\textsc{ad})}\fn{1} & $\mathbf{j}$ & $\mathbf{P_{j1}}$ & $\mathbf{P_{j2}}$ \\ \midrule \multicolumn{7}{l}{Layer II} \\ Beta-248821 & B-20 & Pearl shell & -1.6 & 620 $\pm$ 40 & 1670--1859 & $\theta_1$ & 0.14 & 0.05 \\ Beta-231223 & A-3 & \alert{\textit{Nestegis sandwicensis}} & -23.5 & \alert{710 $\pm$ 40} & \multicolumn{1}{c}{---} & $\theta_2$ & \alert{0.98} & \multicolumn{1}{c}{---} \\ \addlinespace \multicolumn{7}{l}{Layer III} \\ Beta-231220 & EE-15 & \textit{Dodonaea viscosa} & -24.6 & 870 $\pm$ 40 & 1060--1279 & $\theta_3$ & 0.10 & 0.09 \\ Beta-231221 & EE-15 & \textit{Diospyros sandwicensis} & -26.2 & \alert{680 $\pm$ 40} & 1260--1399 & $\theta_4$ & 0.11 & 0.11 \\ Beta-231222 & C-5 & \textit{Canthium odoratum} & -26.5 & \alert{490 $\pm$ 40} & 1310--1499 & $\theta_5$ & 0.14 & 0.15 \\ Beta-248818 & C-6 & Pearl shell & +0.5 & 820 $\pm$ 40 & 1430--1689 & $\theta_6$ & 0.12 & 0.08 \\ Beta-248819 & C-6 & Pearl shell & +2.3 & 840 $\pm$ 40 & 1420--1679 & $\theta_7$ & 0.11 & 0.08 \\ Beta-248820 & A-6 & Pearl shell & +1.5 & 790 $\pm$ 40 & 1440--1699 & $\theta_8$ & 0.15 & 0.09 \\ \addlinespace \multicolumn{7}{l}{Layer not identified} \\ Beta-231224 & A-3 & \textit{Canthium odoratum} & -24.0 & 690 $\pm$ 40 & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---}\\ \bottomrule \addlinespace \multicolumn{9}{l}{\fn{1}95\% highest posterior density region.}\\ \end{tabularx} \end{table} A second set of four age determinations on pearl shell manufacturing waste was selected from the O18 collections held by the U.S. Air Force and submitted by \tsdye* to Beta-Analytic, Inc.\ for AMS dating (table~\ref{tab:calibration}). Pearl shell, produced by mollusks in the genus \textit{Pinctada}, was a favored material for fishhook manufacture in traditional Hawai`i. The cross-laminar structure of the shell gives it exceptional strength for applications like fishhooks that generate high levels of stress at the bend. \textit{Pinctada} shell is a suitable dating material because the animal is a sessile filter-feeder that takes up its carbon from the general ocean water around it, and not from an old limestone substrate \citep{dye94b}. The current best estimate of the apparent age of the ocean water around Hawai`i yields a reservoir correction factor of 110 $\pm$ 80. The large standard deviation of this estimate is likely due to regional patterns of variability in the apparent age of surface waters around Hawai`i that are not yet understood completely. Additional information on this variability might make it possible in the future to apply a more precise estimate in the calibration of these samples. This might yield slightly different calibrated ages for the samples, one from Layer II and three from Layer III, but will not alter the fact that these samples returned \rc\ age estimates that were internally consistent, a first in the long history of \rc\ dating at O18. % \begin{figure}[htb!] % \includegraphics[width=\textwidth]{graphics/pearl-shell} % \caption{Pearl shell manufacturing waste submitted for \rc\ dating: % \textit{a}, Beta-248818; \textit{b}, Beta-248819; \textit{c}, % Beta-248820; \textit{d}, Beta-248821. The scale bar is % 1~cm.} \label{fig:pearl-shell} % \end{figure} Notable features of Table~\ref{tab:calibration} have been set off in boldface. One of the samples, Beta-231224, could not be assigned to either Layer II or Layer III and is not considered further here. The single sample from Layer II is wood charcoal from a tree known in Hawai`i as \gls{olopua}. Although the life span of \gls{olopua} is not known, the fact that it is a tree indicates the possibility that the sample has in-built age. In fact, the age determination returned by the laboratory is stratigraphically inverted with two of the Layer III samples. Beta-231220, the age estimate for charcoal from a shrub known in Hawai`i as \gls{`a`ali`i}, does not suffer the effects of in-built age and is the most reliable estimate for the antiquity of settlement at O18. #+end_src ** DONE Calibration #+name: calibration #+begin_src latex :tangle o18_ao.tex A Bayesian model of O18 stratigraphy relates each of the dated samples to the calendric ages represented by the two primary cultural deposits. The symbols $\theta_{2-5}$ represent the calendar ages of the archaeological events associated with burning the four dated wood charcoal pieces and $\theta_1$ and $\theta_{6-8}$ represent calendar ages of manufacturing events, presumably of pearl shell fishhooks (table~\ref{tab:calibration}, column \textbf{j}). These are related to the calendar ages of the start and end of deposition of the two primary cultural deposits; $\alpha_3$ and $\beta_3$ represent the start and end of deposition, respectively, of Layer III, and $\alpha_2$ and $\beta_2$ represent the start and end of deposition, respectively, of Layer II. The known stratigraphic relations of $\theta_{2-8}$ to the layer boundaries are set out in (\ref{eq:1}), where $>$ means ``is older than'' and $\geq$ means ``is older than or the same age as.'' \begin{equation} \label{eq:1} \phi_2 \geq \alpha_3 \geq \theta_{3-8} \geq \beta_3 > \alpha_2 \geq \theta_{1, 2} \geq \beta_2 \geq \phi_1 \end{equation} For the sake of brevity, (\ref{eq:1}) groups the $\theta$ from each layer in an unconventional way; the $\theta$ are understood to be unordered so there are no stratigraphic relations among them. The salient points of (\ref{eq:1}) are: \begin{itemize} \item the onset of Layer III deposition, $\alpha_3$, began either at, or sometime after, the time Hawai`i was colonized by Polynesians, which is modeled here as normally distributed, $\phi_2$ = \textsc{ad} 800 $\pm$ 50 \citep{athens02:_avifaun_extin_veget_chang_and}; \item the calendar ages of three dated burning events, $\theta_{3-5}$, and three dated manufacturing events, $\theta_{6-8}$, fall within the period of time represented by the deposition of Layer III; \item the calendar ages of the burning and manufacturing events, $\theta_{3-8}$, are unordered, i.e., there is no stratigraphic information on their ages relative to one another; \item the calendar ages of a burning event, $\theta_{2}$, and a manufacturing event, $\theta_{1}$, fall within the period of time represented by the deposition of Layer II; \item the calendar ages of the burning and manufacturing events, $\theta_{2}$ and $\theta_{1}$, are unordered, i.e., there is no stratigraphic information on their ages relative to one another; \item there is a hiatus between the end of deposition of Layer III, $\beta_3$, and the start of deposition of Layer II, $\alpha_2$, as indicated by the $>$ symbol; and \item the end of layer II deposition, $\beta_2$, was either before or during the time cattle ranching was established on the Waim\={a}nalo Plain, which is modeled here as normally distributed, $\phi_1$ = \textsc{ad} 1830 $\pm$ 20. \end{itemize} This model was implemented with the BCal software package \citep{bcal} using the most recent atmospheric and marine calibration curves \citep{reimer09:_intcal_marin_radioc_age_calib}. In an effort to identify outliers among the age determinations, each one was assigned an uninformative outlier prior probability of 0.1, following a procedure set out by \citet{christen94:_summar_set_of_radioc_deter}. The intial run of the software clearly identified Beta-231223 as an outlier; the value of 0.98 in the column, $\mathbf{P_{j1}}$ stands out from the rest of the values in the column, which differ little from their initial values. Beta-231223 was omitted from the analysis and a subsequent run of the software failed to detect outliers, as shown in the column, $\mathbf{P_{j2}}$, where values are all close to their initial values. The seven age determinations for O18 used in subsequent analyses are one more than the six potentially useful age determinations available previously. Age estimates returned by the software for parameters of the model establish a chronology for the O18 site and its constituent layers. The 67\% highest posterior density region, equivalent to a one standard deviation estimate, for initial settlement of the site, $\alpha_3$, is \textsc{ad} 1040--1219 (fig.~\ref{fig:a3}, \textit{bottom left}). This initial period of deposition at the site, identified by archaeologists as Layer III, came to an end in \textsc{ad} 1580--1699 (fig.~\ref{fig:a3}, \textit{bottom right}). After a hiatus marked stratigraphically by a layer of beach sand, cultural deposition of Layer II began in \textsc{ad} 1670--1789 (fig.~\ref{fig:a3}, \textit{top left}) and continued until \textsc{ad} 1770--1859 (fig.~\ref{fig:a3}, \textit{top right}). There is little evidence that the site was abandoned in traditional Hawaiian times. For example, the probability that $\beta_2$ is older than \textsc{ad} 1778, the year Cook sailed to Hawai`i, is 0.31. Thus, given the present dating evidence and the stratigraphic model of the O18 site, it is more than twice as likely that the site was abandoned sometime after Cook. \begin{figure}[htb!] \centering \includegraphics[width=84mm]{o18_layers.png} \caption{Estimated ages of Layers II and III at O18: \textit{top left}, early boundary of Layer II; \textit{top right}, late boundary of Layer II; \textit{bottom left}, early boundary of Layer III; \textit{bottom right}, late boundary of Layer III.} \label{fig:a3} \end{figure} An advantage of a model-based Bayesian calibration is that it is possible to derive estimates for time intervals of interest. The O18 site has figured in interpretations of initial Polynesian settlement of Hawai`i \citep{kirch85}; it is interesting to estimate the interval between settlement and establishment of the site. The 67\% highest posterior density region for the time interval between $\phi_2$ and $\alpha_3$ is 260--459 years (fig.~\ref{fig:duration-3}, \textit{top left}). The initial period of cultural deposition at the site, represented by Layer III, was quite long. The 67\% highest posterior density region for the time interval between $\alpha_3$ and $\beta_3$ is 400--629 years (fig.~\ref{fig:duration-3}, \textit{top right}). In contrast, the hiatus between Layers III and II appears to have been relatively short. The estimated duration of this hiatus, which is represented stratigraphically by a layer of light-colored beach sand, has a 67\% highest posterior density region of 10--109 years (fig.~\ref{fig:duration-3}, \textit{bottom left}). The duration of Layer II was short compared to Layer III. The 67\% highest posterior density region for the time interval between $\alpha_2$ and $\beta_2$ is 10--80 years. \begin{figure}[htb!] \centering \includegraphics[width=84mm]{o18_intervals.png} \caption{Time intervals at O18: \textit{top left}, the interval between Polynesian settlement of Hawai`i and establishment of O18; \textit{top right}, duration of Layer III; \textit{bottom left}, duration of hiatus between Layers II and III; \textit{bottom right}, duration of Layer II.} \label{fig:duration-3} \end{figure} #+end_src latex ** DONE Age summary #+name: age-summary #+begin_src latex :tangle no In summary, the chronology of Site O18 as estimated by \rc\ dates on short-lived materials within a Bayesian model appears to begin sometime in the eleventh to thirteenth centuries \textsc{ad} and to have continued, with interruptions, through to the end of the traditional Hawaiian period. These interruptions, indicated statigraphically by deposits of light-colored sand, appear to have been relatively brief. The hiatus between Layers III and II was probably less than a century and could have been as short as a decade. These results fit well with the regional model of cultural stratigraphy, which places O18 at the coastal fringe of widespread traditional Hawaiian use of the Waim\={a}nalo Plain. #+end_src * Regional picture [2/2] ** DONE Regional data #+name: regional-data #+begin_src latex :tangle o18_ao.tex \section{O18 in Regional Perspective} \label{sec:regional-perspective} The Bayesian model can be extended to include other sites on the Waim\={a}nalo Plain. Cultural resources management excavations at sites 50--80--15--4851 and --4853 and 50--80--11--4856 and --4857 have yielded 37 \rc\ age determinations, 35 on charcoal from identified short-lived taxa and two on pearl shell manufacturing waste (table~\ref{tab:ages}). Each of the sites consists of the remnants of a single cultural deposit that typically lacks internal stratification. Because no stratigraphic relationships between the deposits of these sites and the layers of O18 have been established, they are each modeled as single phases independent of one another and of Layers II and III at O18. Using the short-hand described earlier, the model can be extended with the addition of the following inequalities: \begin{equation} \label{eq:4851} \alpha_{4851} \geq \theta_{9-11} \geq \beta_{4851} \end{equation} \begin{equation} \label{eq:4853} \alpha_{4853} \geq \theta_{12-27} \geq \beta_{4853} \end{equation} \begin{equation} \label{eq:4856} \alpha_{4856} \geq \theta_{28-41} \geq \beta_{4856} \end{equation} \begin{equation} \label{eq:4857} \alpha_{4857} \geq \theta_{42-45} \geq \beta_{4857} \end{equation} \begin{table}[htb!] \centering \scriptsize \topcaption{\rc\ ages of short-lived materials from other sites on the Waim\={a}nalo Plain} \label{tab:ages} \begin{tabularx}{\textwidth}{llXrrl} \toprule Laboratory & Fire-pit & Material & $\delta^{13}$C & CRA\fn{1} & $\mathbf{j}$ \\ \midrule \multicolumn{5}{l}{Site 50--80--15--4851} \\ Beta-111023\fn{2} & Feature 3 & cf.\ \latin{Rauvolfia sandwicensis} & -26.9 & 310$\pm$40 & $\theta_9$ \\ Beta-111024\fn{2} & Feature 2 & \latin{Sida} cf.\ \latin{fallax} & -26.8 & 140$\pm$60 & $\theta_{10}$ \\ Beta-111025\fn{2} & Feature 1 & \latin{Sida} cf.\ \latin{fallax} & -24.2 & 540$\pm$50 & $\theta_{11}$ \\ \addlinespace \multicolumn{5}{l}{Site 50--80--15--4853} \\ Beta-101869\fn{2} & Feature 6 & \latin{Chamaesyce} sp. & -12.9 & 230$\pm$60 & $\theta_{12}$ \\ Beta-101871\fn{2} & Feature 9 & cf.\ \latin{Osteomeles anthyllidifolia} & -25.3 & 720$\pm$40 & $\theta_{13}$ \\ Beta-101872\fn{2} & Feature 10 & cf.\ \latin{Osteomeles anthyllidifolia} & -24.7 & 680$\pm$40 & $\theta_{14}$ \\ Beta-111022\fn{2} & Feature 1 & \latin{Sida} cf.\ \latin{fallax} & -27.5 & 150$\pm$40 & $\theta_{15}$ \\ Beta-120317\fn{2} & Feature 1 & \latin{Sida} cf.\ \latin{fallax} & -21.3 & 140$\pm$50 & $\theta_{16}$\\ Beta-120318\fn{2} & Feature 5 & \latin{Sida} cf.\ \latin{fallax} & -26.1 & 150$\pm$50 & $\theta_{17}$ \\ Beta-120319\fn{2} & Feature 9 & \latin{Aleurites molucanna} nutshell, \latin{Chenopodium oahuense}, \latin{Sida} cf.\ \latin{fallax} & -25.9 & 350$\pm$80 & $\theta_{18}$ \\ Beta-120320\fn{2} & Feature 13 & \latin{Aleurites molucanna} nutshell & -25.6 & 230$\pm$50 & $\theta_{19}$ \\ Beta-120321\fn{2} & Feature 15 & \latin{Aleurites molucanna} nutshell & -25.0 & 110$\pm$70 & $\theta_{20}$ \\ Beta-120322\fn{2} & Feature 16 & \latin{Chamaesyce} sp. & -16.8 & 310$\pm$60 & $\theta_{21}$ \\ Beta-120323\fn{2} & Feature 17 & \latin{Aleurites molucanna} nutshell, \latin{Chenopodium oahuense}, \latin{Sida} cf.\ \latin{fallax} & -27.5 & 170$\pm$60 & $\theta_{22}$ \\ Beta-120324\fn{2} & Feature 18 & \latin{Aleurites molucanna} nutshell & -25.2 & 250$\pm$50 & $\theta_{23}$ \\ Beta-120325\fn{2} & Feature 19 & \latin{Aleurites molucanna} nutshell & -25.2 & 270$\pm$70 & $\theta_{24}$ \\ Beta-120326\fn{2} & Feature 20 & \latin{Aleurites molucanna} nutshell, \latin{Chenopodium oahuense}, \latin{Sida} cf.\ \latin{fallax} & -14.0 & 330$\pm$60 & $\theta_{25}$ \\ Beta-120327\fn{2} & Feature 24 & \latin{Aleurites molucanna} nutshell & -23.0 & 400$\pm$70 & $\theta_{26}$ \\ Beta-120328\fn{2} & Feature 25 & \latin{Sida} cf.\ \latin{fallax} & -25.5 & 220$\pm$50 & $\theta_{27}$ \\ \addlinespace \multicolumn{5}{l}{Site 50--80--11--4856}\\ Beta-208589\fn{3} & & \latin{Chenopodium oahuense} wood charcoal & -26.6 & 140$\pm$40 & $\theta_{28}$\\ Beta-208590\fn{3} & & \latin{Sida} cf.\ \latin{fallax} wood charcoal & -24.9 & 90$\pm$40 & $\theta_{29}$\\ Beta-208591\fn{3} & & \latin{Aleurites moluccana} nutshell & -25.7 & 140$\pm$40 & $\theta_{30}$\\ Beta-246786\fn{4} & Feature 4 & \latin{Sida} cf.\ \latin{fallax} wood charcoal & -25.4 & 380$\pm$40 & $\theta_{31}$\\ Beta-251245\fn{4} & Feature 5 & \latin{Chenopodium oahuense} wood charcoal & -24.5 & 260$\pm$40 & $\theta_{32}$ \\ Beta-251243\fn{4} & Feature 9 & \latin{Aleurites moluccana} nutshell charcoal & -24.9 & 350$\pm$40 & $\theta_{33}$ \\ Beta-251244\fn{4} & Feature 10 & \latin{Sida} cf.\ \latin{fallax} wood charcoal & -24 & 250$\pm$40 & $\theta_{34}$ \\ Beta-251242\fn{4} & Feature 12 & \latin{Sida} cf.\ \latin{fallax} wood charcoal & -24.4 & 200$\pm$40 & $\theta_{35}$ \\ Beta-251246\fn{4} & Feature 17 & \latin{Chenopodium oahuense} wood charcoal & -21.9 & 240$\pm$40 & $\theta_{36}$ \\ Beta-251247\fn{4} & Feature 22 & \latin{Cordyline fruticosa} wood charcoal & -22.6 & 450$\pm$40 & $\theta_{37}$ \\ Beta-251248\fn{4} & Feature 23 & \latin{Aleurites moluccana} nutshell charcoal & -25.6 & 390$\pm$40 & $\theta_{38}$ \\ Beta-200230\fn{5} & Feature 22 & \latin{Chamaesyce sp.} wood charcoal & -11.3 & 550$\pm$40 & $\theta_{39}$ \\ Beta-208588\fn{3} & & Pearl shell & -0.1 & 630$\pm$40 & $\theta_{40}$ \\ Beta-208587\fn{3} & & Pearl shell & -2.7 & 630$\pm$40 & $\theta_{41}$ \\ \addlinespace \multicolumn{5}{l}{Site 50--80--11--4857}\\ Beta-200229\fn{5} & Feature 11 & \latin{Sida} cf.\ \latin{fallax} wood charcoal & -25.6 & 170$\pm$40 & $\theta_{42}$ \\ Beta-200228\fn{5} & Feature 12 & \latin{Chamaesyce} sp.\ wood charcoal & -25.7 & 200$\pm$40 & $\theta_{43}$ \\ Beta-260904\fn{6} & Context 12 & cf.\ \latin{Chamaesyce} sp.\ wood charcoal & -23.4 & 580$\pm$40 & $\theta_{44}$ \\ Beta-260905\fn{6} & Context 13 & \latin{Sida} cf.\ \latin{fallax} wood charcoal & -26.4 & 400$\pm$40 & $\theta_{45}$\\ \bottomrule \multicolumn{5}{l}{\fn{1} Conventional \rc\ age \citep{stuiver-polach77}.} \\ \multicolumn{5}{l}{\fn{2} \citet{dye00:_effec}.} \\ \multicolumn{5}{l}{\fn{3} \citet*{mcelroy06:_archaeol_monit_and_inves_durin}.} \\ \multicolumn{5}{l}{\fn{4} \citet*{zzz_lebo09:_pre_const_archaeol_survey_for}.}\\ \multicolumn{5}{l}{\fn{5} \citet*{putzi05:_archaeol_monit_repor_for_replac}.}\\ \multicolumn{5}{l}{\fn{6} \citet*{dye09:_pre_archaeol_resour_survey_new}.}\\ \end{tabularx} \end{table} #+end_src ** DONE Regional analysis - When other sites were established - All sites presumably abandoned in early historic period - Intervals between establishment of O18 and other sites - 4856, 150--359 years after O18 - 4851, -20--349 years after O18 - 4857, 0--309 years after O18 - 4853, 70--279 years after O18 - p 4851 > Layer III = 0.21 - alpha 3 at O18, 67%, 1040--1219 - alpha 4853, 67% 710-571 BP, 1240--1379 AD - alpha 4857, 67% 760-551 BP, 1190--1409 AD - alpha 4851, 67% 770-521 BP, 1160--1429 AD - alpha 4856, 67% 620-521 BP, 1360--1429 AD #+name: regional-analysis-1 #+begin_src latex :tangle o18_ao.tex Based on the current dating evidence, sites 50--80--15--4851 and --4853 and 50--80--11--4856 and --4857 were all established after O18. Site 50--80--15--4851, located on the opposite bank of Puh\={a} Stream from O18, is likely to be the oldest among the four. It was established \textsc{ad} 1160--1429, based on the 67\% highest posterior density region (fig.~\ref{fig:initial-use}, \textit{top left}). Penecontemporaneously, Site 50--80--11--4857, located inland and north of O18, was established in \textsc{ad} 1190--1409 (fig.~\ref{fig:initial-use}, \textit{bottom right}). Site 50--80--15--4853, immediately inland of site O18, has been extensively dated and appears to have been established at a later time. The 67\% highest posterior density region for the site's establishment is \textsc{ad} 1240--1379 (fig.~\ref{fig:initial-use}, \textit{top right}). Finally, site 50--80--11--4856, located on the coast north of O18, was established in \textsc{ad} 1360--1429 (fig.~\ref{fig:initial-use}, \textit{bottom left}), apparently later than Site 50--80--11--4857 located immediately inland. The probability that 50--80--11--4857 was established earlier than 50--80--11--4856 is 0.88. \begin{figure}[htb!] \centering \includegraphics[width=84mm]{site-establishment.png} \caption{Initial site use on the Waim\={a}nalo Plain: \textit{top left}, 50--80--15--4851; \textit{top right}, 50--80--15--4853; \textit{bottom left}, 50--80--11--4856; \textit{bottom right}, 50--80--11--4857.} \label{fig:initial-use} \end{figure} #+end_src #+results: regional-analysis-1 #+BEGIN_LaTeX Based on the current dating evidence, sites 50--80--15--4851 and --4853 and 50--80--11--4856 and --4857 were all established after O18. Site 50--80--15--4851, located on the opposite bank of Puh\={a} Stream from O18, is likely to be the oldest among the four. It was established \textsc{ad} 1160--1429, based on the 67\% highest posterior density region (fig.~\ref{fig:initial-use}, \textit{top left}). Pene-contemporaneously, Site 50--80--11--4857, located inland and north of O18, was established in \textsc{ad} 1190--1409 (fig.~\ref{fig:initial-use}, \textit{bottom right}). Site 50--80--15--4853, immediately inland of site O18, has been extensively dated and appears to have been established at a later time. The 67\% highest posterior density region for the site's establishment is \textsc{ad} 1240--1379 (fig.~\ref{fig:initial-use}, \textit{top right}). Finally, site 50--80--11--4856, located on the coast north of O18, was established in \textsc{ad} 1360--1429 (fig.~\ref{fig:initial-use}, \textit{bottom left}), apparently later than Site 50--80--11--4857 located immediately inland. The probability that 50--80--11--4857 was established earlier than 50--80--11--4856 is 0.88. \begin{figure}[htb!] \centering \includegraphics[width=84mm]{site-establishment.png} \caption{Initial site use on the Waim\={a}nalo Plain: \textit{top left}, 50--80--15--4851; \textit{top right}, 50--80--15--4853; \textit{bottom left}, 50--80--11--4856; \textit{bottom right}, 50--80--11--4857.} \label{fig:initial-use} \end{figure} #+END_LaTeX #+name: regional-analysis-2 #+begin_src latex :tangle o18_ao.tex Another way to look at the site establishment estimates is relative to the establishment of O18. All of the posterior probability distributions have left tails that extend past zero and thus each site retains some probability of having been established before O18. These probabilities are all rather slim, however. The site with the greatest probability of having been established before O18, 50--80--11--4851, has a probability of 0.2. Using 67\% highest posterior density regions: Site 50--80--15--4851 was settled 10 years earlier than to 349 years after O18 (fig.~\ref{fig:site-establishment}, \textit{top left}); site 50--80--11--4857 was settled at the same time as O18 to 319 years later (fig.~\ref{fig:site-establishment}, \textit{bottom right}); site 50--80--11--4853 was settled 60--279 years after O18 (fig.~\ref{fig:site-establishment}, \textit{top right}); and site 50--80--11--4856 was settled 160--359 years after O18 (fig.~\ref{fig:site-establishment}, \textit{bottom left}). \begin{figure}[htb!] \centering \includegraphics[width=84mm]{after-o18.png} \caption[Sequence of site establishment]{Sequence of site establishment---the interval between establishment of O18 and other sites: \textit{top left}, Site 50--80--15--4851; \textit{top right}, Site 50--80--15--4853; \textit{bottom left}, Site 50--80--11--4856; \textit{bottom right}, Site 50--80--11--4857. Note that there is a small probability that each of the sites was established before O18.} \label{fig:site-establishment} \end{figure} #+end_src * Conclusion [4/4] #+name: conclusion #+begin_src latex :tangle o18_ao.tex \section{Summary and Conclusion} \label{sec:conclusion} #+end_src ** DONE Regional prehistory [5/5] - [X] O18 not an example of an early site, it was settled at least 240 years after Polynesian colonization and perhaps as much as 449 years after - [X] O18 is likely the earliest site on the plain - [X] Other sites settled over the next approximately 3-4 centuries, in what appears to be a piece-meal fashion, and not a radiation out from O18. - [X] Discuss the early date on kukui nutshell. How it got into the O18 deposit is a mystery, but if it is not spuriously old due to laboratory error, then it might indicate early establishment of the tree on the Waimanalo plain. The calibrated age shown in Table 2 accepts the material as primarily deposited in Layer II. If this constraint is relaxed, and the date is calibrated as constrained only by phi1 and phi2, then at 67% AD 850--1160. The probability it was growing before O18 was established is XX% - [X] This carries with it the possibility that there were settlements in Waimanalo that pre-dated O18 - [ ] Results differ by timing and by the fact that events of interest are estimated directly. #+name: prehistory #+begin_src latex :tangle o18_ao.tex Seven new \rc\ age determinations on short-lived materials yield a chronology for O18 that differs from previous estimates. The results clearly indicate that O18 was settled later than previously estimated. The 67\% highest posterior density region for the true age of $\alpha_3$ is \textsc{ad} 1040--1219, which is 4--9 centuries younger than previous estimates. The hypothesis that O18 was occupied during an early phase of Polynesian settlement is, on present evidence, false. The best estimate, based on present evidence, places initial site use 260--459 years after the archipelago was discovered and colonized. With this new, ``late'' chronology, O18 joins site H1 on Hawai`i Island \citep{dye92} and the H\={a}lawa Dune site on Moloka`i \citep{kirch07:_recon_hawaiian_cultur_sequen} in a growing group of relatively late sites once believed to have been examples of early Hawaiian settlement. % Contrast this with % the previous situation, where estimates were based on \textit{ad % hoc} procedures. The initial set of five GaK dates supported two % estimates that differed by three centuries. The addition of the % Beta-Analytic dates did little to change the shape of the % data,\footnote{The two ANU dates are clearly anomalous.} in % fact it is remarkable how closely the new dates reprised the old % ones. Yet, this similar but augmented data set supported a 500 year % revision of the estimate. Clearly, these \textit{ad hoc} estimates % were responding to information adjunct to the dates % themselves---initially to now-discredited old ``dates'' on volcanic % glass from O18 and subsequently to a widely-accepted % paleoenvironmental estimate for first settlement in the eighth or % ninth centuries \textsc{ad}. In both cases these adjunct data are % not explicitly modeled in the calibration, but are instead applied % idiosyncratically. The Bayesian model is sufficiently robust to % accommodate both the addition of new data and a revised estimate of % when the islands were initially colonized. The situation is similar with respect to when O18 was abandoned. The new dates on short-lived materials, calibrated and interepreted within a Bayesian framework, indicate that the site was abandoned at the end of traditional Hawaiian times in the late eighteenth or early nineteenth centures, some 3--6 centuries later than earlier estimates. The estimate brings the abandonment of O18 in line with abandonment date estimates for other sites on the Waim\={a}nalo Plain. One reason that previous estimates of O18 chronology were too old by centuries was a failure to control for the potential effects of old wood during the dating process, but errors assigning the dated samples to their correct archaeological contexts in a field school situation, and statistical and other errors in the dating laboratory probably had effects, too. It is worthwhile to emphasize the ill effects of old wood; cultural resources management archaeologists working in Hawaii routinely date unidentified wood charcoal. There is no reason to believe that their age determinations on unidentified wood charcoal will perform any better than those from O18, which proved to be poor estimators of site chronology. They are essentially worthless for establishing archaeological chronologies. In most cases, the old dates that do a poor job of estimating the age of O18 provide no other useful information. An exception to this is Beta-20852b on \textit{A. moluccana} nutshell. This age determination does a poor job of estimating the age of its archaeological context in Layer II, but because the identified material derived from a tree introduced to the islands by Polynesians the age estimate itself is of interest. If the calendar age, $\theta_{46}$, of this age determination is associated with the archaeological event of planting \textit{kukui} trees in Waim\={a}nalo and calibrated in the context of a model that specifies only that this event dates to traditional Hawaiian times (\ref{eq:kukui}), then the 67\% highest posterior density region for $\theta_{46}$ is \textsc{ad} 840--1159, an estimate that has a 70\% probability of dating an event older than the establishment of O18. Thus, it is likely that the \textit{A. moluccana} tree was planted by Hawaiians who lived at some other site in Waim\={a}nalo prior to settlement at O18. Because dates from nearby sites indicate that O18 was established before them, this putative earlier settlement is likely to be located somewhere inland, probably on the volcanic soils that supported gardens in traditional Hawaiian times. Whether cultural deposits associated with this putative early settlement still exist is a question for future research. \begin{equation} \label{eq:kukui} \phi_2 \geq \theta_{46} \geq \phi_1 \end{equation} Finally, development of an explicit chronological model relating regional archaeological events to one another and set out in inequalities (\ref{eq:1}--\ref{eq:kukui}) means that anyone can replicate the estimate and explore how different parameters of the model affect it. It is not possible to do this in a precise way with an approach that is not strictly model-based. Changes in chronological estimates for sites on the Waim\={a}nalo Plain will most likely result from new dates on short-lived materials from secure stratigraphic contexts both on the Waim\={a}nalo Plain and beyond. Excavation of deposits at the coastal fringe of Site 50--80--11--4856, for instance, might help clarify the processes responsible for deposition of charcoal in this active and variable environment at the fringe of traditional Hawaiian settlement on the Waim\={a}nalo Plain. And certainly, any change in the estimated settlement date of the Hawaiian Islands would have a direct effect on the estimate of the interval between this event and establishment of O18. If the change in the estimated settlement date were sufficiently large, it might even have an effect on the estimate of when O18 was established. #+end_src ** REJECTED The weaknesses of the present estimates - Settlement dates heavily dependent on dated samples, sample size potentially important in interpretation - Calibration of shell dates, might change a bit, but not much - Layer II represented by a single sample, if shell calibrates a bit older, then the boundary between Layers II and III will change. - The Layer III shell dates are all relatively young and a change in calibration likely won't affect the estimated establishment date #+name: evaluation #+begin_src latex The incorporation into the Bayesian calibration of a stratigraphic model of traditional Hawaiian sites on the Waim\={a}nalo Plain, expressed in inequalities (\ref{eq:1}) and (\ref{eq:4851}) through (\ref{eq:4857}), makes it possible to answer interpretive questions with probabilistic estimates, rather than with guesses or ad hoc arguments. Among the probabilistic estimates are: \begin{inparaenum}[(i)] \item the ages of archaeological events of interest that could not be dated directly, including first settlement and abandonment of the five site, as well as the upper boundary of Layer III and the lower boundary of Layer II at O18; \item the elapsed time between events, including \begin{inparaenum}[(a)] \item the duration of Layers II, III, and the hiatus between them, \item the lag between settlement of O18 and other sites on the Waim\={a}nalo Plain, and \item the time between first settlement of Hawai`i by Polynesians and establishment of O18; and \end{inparaenum} \item the relative timing of events of interest, such as the first planting of \textit{A. moluccana} in Waim\={a}nalo relative to the establishment of O18. \end{inparaenum} The ability of Bayesian calibration to yield direct answers to interpretive questions is one of its great strengths. Another strength of the model-based, Bayesian approach to calibration is that new information can be used to augment and refine the results. For example, a new age determination that is older than others from the same site will push the estimate of site establishment back in time; the Bayesian calibration will indicate directly with probabilistic estimates how much effect the new date has on the regional chronology. Similarly, refinement of $\Delta R$ for Hawai`i might change the calibrated ages of the pearl shell samples by some decades. Here, the Bayesian calibration will calculate the effect this has on the age of the transition from Layer III to Layer II at O18. In this way, work on regional chronology can be collaborative, rather than based on arguments over how the ad hoc methods of chronologic hygiene might be applied in a particular instance. #+end_src ** REJECTED Chronometric hygiene is non-scientific. - Although Gak dates are often dismissed, they did no worse than other laboratories did. - It is possible to use dates with large standard deviations: they don't mean much, but there is no intrinsic reason to discard what little information they might hold. #+name: hygiene #+begin_src latex #+end_src ** REJECTED There are no known old sites - Graph of time interval between settlement and site establishment for O18 - H1 is late, cite Dye NZJA - Halawa Dune is late, too. #+name: hawaii #+begin_src latex #+end_src * LaTeX postamble #+name: latex-ending #+begin_src latex :tangle o18_ao.tex % Comment or uncomment as needed % style=altlist another possibility %\printglossary[type=main, style=tsdlist] %\printglossary[type=hawaiian, style=tsdlist] % \printglossary[type=polynesian, style=tsdlist] % \printglossary[type=gazetteer, style=tsdlist] % \printglossary[type=acronym, style=tsdlist] % \printglossary[type=oldenglish, style=tsdlist] % \printglossary[type=bio, style=tsdlist] \addcontentsline{toc}{section}{Bibliography} \bibliographystyle{chicago} % Comment or uncomment as needed % \bibliography{tsd} \bibliography{tsd,local} \end{document} #+end_src * R code for graphics ** Dated events - A kludge - Put all the csv file names in a table, then edit the table for input to the R function #+name: thetas() #+begin_src shell cd r && ls *.csv #+End_src #+results: thetas | alpha-2.csv | | beta-2.csv | | alpha-3.csv | | beta-3.csv | - thetas is a list inside the function - run lapply, use string substitution to make variable names, file names - need to add cbind() an identifier that can be used to label the plot and to segregate the plots #+name: dated-events(files = thetas) #+begin_src R :session :file output_dated_events.png library(ggplot2) make.plot.file <- function(x, y) { r <- y afile <- paste("r/",x,sep="") anobject <- strsplit(x,".",fixed=TRUE)[[1]][1] z <- read.csv(file = afile) z <- cbind(z,label=rep(anobject,dim(z)[1])) r <- rbind(r, z) r } res <- data.frame(cal.BP=numeric(0),Posterior.probability=numeric(0),label=character(0)) for (f in files[,1]) res <- make.plot.file(f, res) g <- ggplot(res, aes(x=1950 + cal.BP, y=Posterior.probability)) png(file="output_dated_events.png",width=168,height=100,unit='mm',res=600) g + geom_bar(stat='identity') + xlab("Year AD") + ylab("Probability") + facet_wrap(~ label) dev.off() #+end_src #+results: dated-events [[file:output_dated_events.png]] #+name: single-date(x = "alpha-4856.csv") #+begin_src R :session afile <- paste("r/",x,sep="") anobject <- strsplit(x,".",fixed=TRUE)[[1]][1] ofname <- paste(anobject,".pdf",sep="") z <- read.csv(file = afile) g <- ggplot(z, aes(x=1950 + cal.BP, y=Posterior.probability)) g + geom_bar(stat='identity') + xlab("Year AD") + ylab("Probability") ggsave(ofname) ofname #+end_src #+results: single-date : theta-7.pdf ** Intervals - This is a kludge that works for a one-off situation - The shell source shows all the csv files - Edit the results table to select the files to use as input to the plotting routine #+name: intervals #+begin_src sh cd r && ls *.csv #+end_src #+results: intervals | alpha-4851-and-alpha-3.csv | | alpha-4853-and-alpha-3.csv | | alpha-4856-and-alpha-3.csv | | alpha-4857-and-alpha-3.csv | #+name: interval-estimates(files = intervals) #+begin_src R :session :file output_intervals.png library(ggplot2) make.plot.file <- function(x, y) { r <- y afile <- paste("r/",x,sep="") anobject <- strsplit(x,".",fixed=TRUE)[[1]][1] z <- read.csv(file = afile) z <- cbind(z,label=rep(anobject,dim(z)[1])) r <- rbind(r, z) r } res <- data.frame(cal.BP=numeric(0),Posterior.probability=numeric(0),label=character(0)) for (f in files[,1]) res <- make.plot.file(f, res) g <- ggplot(res, aes(x=cal.BP, y=Posterior.probability)) png(file="output_intervals.png",width=168,height=100,unit='mm',res=600) g + geom_bar(stat='identity') + xlab("Time Interval (Years)") + ylab("Probability") + facet_wrap(~ label, scales = "fixed") dev.off() #+end_src #+results: interval-estimates [[file:output_intervals.png]] ** Regional date graph - Hard code a complex graphic #+name: r-regional-data #+begin_src R :session library(ggplot2) load(".RData") a3_gg <- cbind(a3, rep("O18",dim(a3)[1])) names(a3_gg)[3] <- "name" a4851 <- read.csv("alpha-4851.csv") a4851_gg <- cbind(a4851, rep("4851", dim(a4851)[1])) names(a4851_gg)[3] <- "name" a4853 <- read.csv("alpha-4853.csv") a4853_gg <- cbind(a4853, rep("4853", dim(a4853)[1])) names(a4853_gg)[3] <- "name" a4856 <- read.csv("alpha-4856.csv") a4856_gg <- cbind(a4856, rep("4856", dim(a4856)[1])) names(a4856_gg)[3] <- "name" a4857 <- read.csv("alpha-4857.csv") a4857_gg <- cbind(a4857, rep("4857", dim(a4857)[1])) names(a4857_gg)[3] <- "name" alpha_gg <- rbind(a3_gg, a4851_gg, a4853_gg, a4856_gg, a4857_gg) #+end_src #+results: r-regional-data | ggplot2 | | reshape | | plyr | | grid | | proto | | stats | | graphics | | grDevices | | utils | | datasets | | methods | | base | #+name: r-regional-plot #+begin_src R :session alpha_plot <- ggplot(alpha_gg, aes(x=1950 + cal.BP, y=Posterior.probability)) pdf(file="alpha-regional.pdf", height=3.75, width=7.5) alpha_plot + geom_bar(stat='identity') + xlab("Year AD") + ylab("Probability") + facet_wrap(~ name) #+end_src * REJECTED LaTeX article makefile #+begin_src latex <> <> <> <> <> <> <> <> <> <> <> <> #+end_src * REJECTED Post-mortem on earlier data [2/2] ** DONE Post mortem data #+name: post-mortem-data #+begin_src latex \section{Post-mortem on the Early Dates} \label{sec:post-mortem} The Bayesian model described in the previous section can be extended to incorporate the early age determinations reported by \citet{pearson71:_bellows} and \citet{tuggle01:_age_bellow_dune_site_o18}. The purpose of extending the model in this way is to compare the chronology produced by the early age determinations with the one produced by the new age determinations on short-lived materials. Thus, it is important that the model be extended in a way that keeps the two chronologies separate. This is accomplished in the BCal software by creating a separate set of phases for Layers II and III, as if they belonged to a separate site, and assigning the early age determinations to this separate set of phases. This extension to the model can be represented by a second inequality, (\ref{eq:2}), which establishes new layer boundaries, indicated by an \textit{o} appended to the subscript, and includes six of the early age determinations, $\theta_{2, 9-13}$ (table~\ref{tab:early-dates}). GaK-1819 is clearly an outlier in Layer II and has been excluded from the analysis. \begin{equation} \label{eq:2} \phi_2 \geq \alpha_{3o} \geq \theta_{12-13} \geq \beta_{3o} > \alpha_{2o} \geq \theta_{2, 9-11} \geq \beta_{2o} \geq \phi_1 \end{equation} \begin{table}[htb!] \topcaption{Early O18 age determinations} \label{tab:early-dates} \footnotesize \begin{tabular}{llrrllrr} \toprule \textbf{Sample} & \textbf{Material} & $\mathbf{\delta^{13}}$\textbf{C} & \multicolumn{1}{c}{\textbf{CRA}} &\multicolumn{1}{c}{\textbf{Age (\textsc{ad})}} & \multicolumn{1}{c}{\textbf{j}} & \multicolumn{1}{c}{$\mathbf{P_j}$} & \multicolumn{1}{c}{$\mathbf{P_{dep}}$} \\ \midrule \multicolumn{4}{l}{Layer II} \\ GaK-1818 & \alert{unidentified} & -25.0 & 1126 $\pm$ 124 & 1070--1229 & $\theta_2$ & 0.19 & 0.00002 \\ GaK-1819 & \alert{unidentified} & -25.0 & \alert{1616 $\pm$ 96} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} \\ Beta-20852a & \alert{unidentified} & -24.1 & 720 $\pm$ 130 & 1120--1309 & $\theta_9$ & 0.08 & 0.0002\\ Beta-20852b & \textit{A. moluccana} nutshell & -26.4 & 1330 $\pm$ 230 & 1080--1259 & $\theta_{10}$ & 0.20 & 0.0001\\ GaK-1816 & \alert{unidentified} & -25.0 & 716 $\pm$ 129 & 1120--1309 & $\theta_{11}$ & 0.09 & 0.00008\\ \addlinespace \multicolumn{4}{l}{Layer III} \\ GaK-1817 & \alert{unidentified} & -25.0 & 1046 $\pm$ 115 & 870--1019 & $\theta_{12}$ & 0.06 & 0.12 \\ GaK-1820 & \alert{unidentified} & -25.0 & \alert{modern} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} \\ Beta-20853 & \alert{unidentified} & -25.0 & 1070 $\pm$ 370 & 850--1019 & $\theta_{13}$ & 0.04 & 0.12 \\ ANU-6179 & \alert{unidentified} & -24.8 & \alert{modern} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} \\ ANU-7027 & \textit{Cocos nucifera} & -23.1 & \alert{120 $\pm$ 132} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} \\ \bottomrule \end{tabular} \end{table} #+end_src ** DONE Post mortem results #+name: post-mortem-results #+begin_src latex The Bayesian calibration of the early age determinations yields layer boundaries that correspond fairly closely to those proposed by \citet{tuggle01:_age_bellow_dune_site_o18}. According to this analysis: the site was established sometime shortly after initial settlement of the islands, \textsc{ad} 800--949, a range that is influenced strongly by the constraints imposed by $\phi_2$; the hiatus between Layers III and II began in \textsc{ad} 900--1069 and ended when Layer II began to be deposited in \textsc{ad} 990--1169; and the site was abandoned in \textsc{ad} 1160--1399.% In this case, it % appears that the ad hoc methods of ``chronological hygiene'' yielded % relatively reasonable results. A potentially more interesting question has to do with the probabilities that the early age determinations date events that took place within the period of time represented by the stratigraphic layers from which they were collected, as these are estimated by the Bayesian calibration of short-lived materials as represented by inequality (\ref{eq:1}). These probabilities are shown in the column, $P_{dep}$ of table~\ref{tab:early-dates} where it can be seen that all four of the Layer II age determinations have vanishingly small probabilities of representing events that took place while that layer was being deposited. The two Layer III age determinations have somewhat larger, but equally low probabilities of belonging to that layer. In all cases, the age determinations are too old. In the cases of two Layer III dates on unidentified wood, GaK-1817 and Beta-20853, the most likely culprit is in-built age. Both of these dates are about 200 years older than the early date on \textit{D. viscosa} (see table~\ref{tab:calibration}). \citet{dye00:_effec} has shown that controlling for in-built age yields age estimates that are, on average, about 100 years younger than age estimates on samples that don't control for in-built age. Discrepancies of 200 years are well within the range of potential in-built ages. The three other Layer III dates, GaK-1820, ANU-6179, and ANU-7027 do not differ statistically from the modern standard. Deposition of Layer III ended sometime in the late sixteenth or seventeenth centuries, so these three dates are all more than 250 years too young for their stratigraphic positions. It seems unlikely that modern material could have made its way down through the fairly complex site stratigraphy to the base of the section, so problems of context are unlikely \textit{a priori}. In practical terms, this leaves some type of laboratory error as the likely culprit, where laboratory error is interpreted broadly to include both the archaeological and dating laboratories. The Layer II age determinations are all older than the period during which the layer was deposited. Two of the dates on unidentified wood charcoal, Beta-20852a and GaK-1816, are about 200 years too old and, like the Layer III samples, might be reasonably interpreted as old wood. The other three age estimates, two on unidentified wood charcoal and a third on \textit{A. moluccana} nutshell, are very old for their stratigraphic positions. Although the two estimates on unidentified wood charcoal might represent rather extreme examples of in-built age, perhaps because they are pieces of driftwood, the old age estimate on the short-lived nutshell sample suggests that other factors might be active. It is tempting to suggest that all of these samples derived from Layer III, but they are each quite a bit older than the early Layer III date on \textit{D. viscosa}, so this possibility seems unlikely. One is thrown back on laboratory error or the possibility that remnants of a deposit older than Layer III exposed material that was somehow redeposited in Layer II. Although this scenario might seem rather far-fetched, it is certainly within the realm of depositional processes at this coastal location on the fringe of traditional Hawaiian settlement. #+end_src * Spell check LocalWords: LaTeX src ao tex noweb srcname documentclass tsdarticle Pantaleo LocalWords: maketitle uncomment altlist printglossary tsdlist hawaiian toc rc LocalWords: polynesian oldenglish addcontentsline bibliographystyle chicago LocalWords: tsd citep pearson citet tuggle kirch Spriggs hoc Hawai Waim nalo LocalWords: htb includegraphics Puh archaeol resear propos devel desilets gg LocalWords: Keolu strat mortem * Notes ** DONE Get reference for 2009 calibration curves ** The current calibration - copy of bellows region aug - note that theta numbers do not match with paper ** DONE Correct footnotes in regional 14C table ** DONE Check all date range estimates ** DONE Regenerate graphs ** DONE Add pearl shells from project 40 to the BCal analysis - 380 208588 Pteriidae shell <0.1 630􏰂40 -0.1 ad 1682–1846 - 368 208587 Pteriidae shell <0.1 630􏰂40 -2.7 ad 1682–1846 ** DONE Get 95% and 67% hpd regions from BCal, put them in text ** DONE Calculate 67% hpd region for interval between alpha 2 and beta 2 ** DONE Check date list for 4856 ** DONE Make argument for pearl shell being a suitable dating material. ** DONE Full information for Beta-200230 [2010-01-31 Sun] ** DONE Reference for Kirch and McCoy's re-dating of Halawa Dune site ** DONE Spriggs and Anderson argument against Gak dates ** Renumber \theta [28/28] - [X] 45 -> 2 - [X] 15 -> 9 - [X] 14 -> 10 - [X] 46 -> 11 - [X] 31 -> 12 - [X] 30 -> 13 - [X] 29 -> 14 - [X] 28 -> 15 - [X] 47 -> 28 - [X] 48 -> 29 - [X] 49 -> 30 - [X] 32 -> 31 - [X] 33 -> 32 - [X] 34 -> 33 - [X] 35 -> 34 - [X] 36 -> 35 - [X] 37 -> 36 - [X] 38 -> 37 - [X] 39 -> 38 - [X] 40 -> 39 - [X] 41 -> 40 - [X] 44 -> 41 - [X] 43 -> 44 - [X] 44 -> 43, then added to pearl shell dates from project 40 - [X] 40 -> 44 - [X] 41 -> 43 - [X] 42 -> 44 - [X] 43 -> 45 * Changes to Page Proofs ** Page 113, column a, note - change "jeffrey.pantaleo.ctr@hickam.af.mil" to "jpanta4149@aol.com" ** Page 115, Table 1 - Column *j*, all numbers following thetas should be subscripts, \theta_1, \theta_2, etc. - Column head *Pj1*, the j1 should be subscript to the P, *P_{j1}* - Column head *Pj2*, the j2 should be subscript to the P, *P_{j2}* ** Page 115, column b, line 2 - Change "The single sample from Layer II is wood charcoal" to "The single wood charcoal sample from Layer II is" ** Page 117, column a, inequalities (2), (3), (4), and (5) - Need subscripts for all the greek letters, e.g. \alpha 4851\geq\theta 9-11\geq\beta 4851 should be \alpha_{4851}\geq\theta_{9-11}\geq\beta_{4851} ** Page 119, column a, inequality (6) - Need subscripts, like so, \phi_2 \geq \theta_{46} \geq \phi_1