1 #+TITLE: Archaeology in Oceania, Age of O18
3 #+EMAIL: tsd at tsdye dot com
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20 #+srcname: latex-preamble
21 #+begin_src latex :tangle o18_ao.tex
22 \documentclass[minion,glossaries]{tsdarticle}
24 \author{Thomas S. Dye and Jeffrey Pantaleo}
26 \title{Age of the O18 Site\thanks{Special thanks to Valerie Curtis for
27 her commitment to this project and her confidence that it would
28 yield interesting results. Dave Tuggle and Matthew Spriggs
29 offered valuable criticism that sharpened the argument
30 considerably. Caitlin Buck offered perceptive advice on Bayesian
31 modeling. Kristin Macak drafted the site map, which was prepared
32 for publication by Eric Komori. Dan Davison and Eric Schulte both
33 provided guidance on the use of Org-babel, a software environment
34 that integrates thinking, analysis, and writing that greatly
35 facilitated production of the paper.}}
38 \let\itemize\compactitem
47 #+begin_src latex :tangle o18_ao.tex
49 Seven new \rc\ age determinations on short-lived materials yield a
50 sound evidential basis for the chronology of the O18 site on O`ahu
51 Island, Hawai`i, long thought to be an early settlement site.
52 Calibration within a model-based, Bayesian framework indicates
53 that the site was established in \textsc{ad} 1040--1219, some 260--459
54 years after the current estimate of first settlement, and
55 abandoned in the late eighteenth or early nineteenth centuries.
56 Previously published age determinations are mostly too old,
57 probably due to the ``old wood'' effect. O18 appears to be the
58 oldest site on the Waim\={a}nalo Plain, but earlier sites in
59 Waim\={a}nalo likely exist inland of the plain.
64 #+srcname: latex-intro
65 #+begin_src latex :tangle o18_ao.tex
67 The age of the O18 site has been an important datum in Hawaiian
68 prehistory since the first estimate was published in the pages of
69 this journal nearly 40 years ago \citep{pearson71:_bellows}. Based
70 on an internally inconsistent set of \rc\ age determinations, the
71 site was interpreted by its excavators as having been established in
72 the seventh century \textsc{ad} and abandoned by the twelfth
73 century. The estimated date of establishment was subsequently pushed
74 back to the fourth century \textsc{ad} by \citet{kirch85}, based
75 primarily on volcanic glass hydration dates that are no longer
76 believed to be valid \citep{tuggle01:_age_bellow_dune_site_o18}.
77 Kirch considered O18 to be one of only two sites representing the
78 earliest phase of Polynesian settlement of the Hawaiian Islands.
79 This characterization exerted a strong hold on the archaeological
80 imagination. In the early 1980s, it inspired Matthew Spriggs to
81 pull additional samples from storage and have them dated. These
82 samples yielded a stratigraphically inconsistent set of \rc\ age
83 determinations that was interpreted more than a decade later
84 with some difficulty by \citet{tuggle01:_age_bellow_dune_site_o18}
85 as indicating an occupation span beginning perhaps as early as the
86 eighth century \textsc{ad} and ending in the middle of the fifteenth
89 Here, we present the results of nine new \rc\ age determinations
90 from O18, most of them on short-lived materials. The age
91 determinations on short-lived materials are internally consistent
92 and provide, for the first time, a sound evidential basis for the
93 site's chronology. The \rc\ age determinations are interpreted
94 within a model-based, Bayesian framework. An estimate of site
95 establishment yielded by the model-based analysis, supported by
96 the age of an \textit{Aleurites moluccana} nutshell dated by Spriggs,
97 indicates that O18 was established several centuries after the
98 islands were first settled by Polynesians.
100 The O18 chronology yielded by the site-specific Bayesian model is
101 extended to include \rc\ age determinations from four other sites in
102 the region. The chronologies of all five sites are broadly similar.
103 Like these other sites, O18 was abandoned late in traditional
107 * O18 in regional context [2/2]
108 ** DONE Regional context
109 #+srcname: regional-context
110 #+begin_src latex :tangle o18_ao.tex
111 \section{The O18 Site}
114 Site O18 is located on the Waim\={a}nalo Plain, at the coast
115 (fig.~\ref{fig:location}). It is a small part of a larger traditional
116 Hawaiian settlement pattern in which the coastal plain was used on a
117 regular basis, primarily for activities associated with fishing and
118 shellfishing, by people who kept more established residences inland on
119 the volcanic soils that supported their food gardens. A large portion
120 of the coastal plain was developed as a military installation in the
121 twentieth century, especially during World War II, and much of the
122 traditional Hawaiian deposit was lost during this development. The
123 pattern of sites on the plain today is probably due more to military
124 development than it is to patterns of traditional activity in the
129 \includegraphics[width=84mm]{AO_bellows_O18_landscape.png}
130 \caption{Traditional Hawaiian sites on a portion of the Waim\={a}nalo Plain.}
134 Immediately inland of Site O18, and at one time probably coterminous
135 with it, is Site 50--80--15--4853, a large expanse of discontinuous
136 cultural deposits on the north bank of Puh\={a} Stream that
137 represent primarily cooking and eating activities
138 \citep{tuggle97:_archaeol_resear_areas_propos_devel,desilets02:bellows}.
139 South of Puh\={a} Stream is Site 50--80--15--4851, which is broadly
140 similar to Site --4853, but also includes low-lying swamp deposits
141 in old stream meanders that were used to cultivate taro
142 \citep{tuggle97:_archaeol_resear_areas_propos_devel,dye98}. On the
143 north part of the plain, nearer the foothills of Keolu Hills, are
144 Sites 50--80--11--4856 and --4857, which were also likely
145 coterminous, and which appear to represent the same range of
146 activities as Site --4853.
151 #+srcname: stratigraphy
152 #+begin_src latex :tangle o18_ao.tex
153 Excavations for cultural resources management carried out at sites on
154 the plain provide data for a model of regional cultural stratigraphy.
155 The model groups deposits into one of three horizons:
156 \begin{inparaenum}[(i)]
157 \item Horizon 1 is the modern surface consisting of secondarily
158 deposited sand, historic-era and traditional Hawaiian cultural
159 materials, and pockets of volcanic fill material laid down during
160 construction of military facilities;
161 \item Horizon 2 is the traditional Hawaiian cultural deposit, often
162 truncated by heavy machinery during construction of military
164 \item Horizon 3 is the underlying basal sand that was laid down as
165 local sea level fell from its mid-Holocene +1.8~m highstand
166 \citep{fletcher96} prior to settlement of the islands.
169 The model was developed to capture variability with distance from
170 the coast, the source of trade wind-driven sand that represents the
171 primary natural mode of deposition since the plain was first
172 inhabited, and the degree to which cultural activities included
173 excavation of pits primarily for cooking fires, but also for posts
174 and trash disposal. Pit excavation is responsible for moving
175 artifacts and other cultural materials down the stratigraphic
176 profile and contribute markedly to the thickness of the cultural
177 deposit (fig.~\ref{fig:stratigraphy}).
181 \includegraphics[width=84mm]{graphics/strat-overview.png}
182 \caption{Regional cultural stratigraphy along a hypothetical
183 transect running inland from the beach, showing the relative
184 effects of ongoing sand deposition and traditional Hawaiian pit
186 \label{fig:stratigraphy}
189 At the inland edge of the plain, illustrated by profile A in
190 figure~\ref{fig:stratigraphy}, sand deposition is slight and
191 few pits were excavated in traditional Hawaiian times. The cultural
192 deposit here can be characterized as a paleosol whose surface
193 includes a low density of cultural material that appears to have
194 been discarded upon it in a more-or-less random fashion. Moving
195 toward the coast, through profiles B, C, and D, both the intensity
196 of cultural deposition and pit excavation increases, creating a
197 thicker cultural deposit beneath which individual pit features can
198 be discovered as dark stains in the light-colored basal sands.
199 Closer to the coast, represented in the figure by profile E, the
200 thickness of the cultural deposit reaches a maximum due to a higher
201 intensity of use and a larger volume of aeolian sand deposit from
202 the nearby beach. The frequency of pit excavation here is such that
203 it is rarely possible to identify individual features in the
204 underlying basal sand. Instead, the base of the cultural deposit
205 consists entirely of the bases of pits excavated atop and through
206 one another. At Site 50--80--15--4856, where the stratigraphy
207 corresponded to the model represented by profile E, it was estimated
208 that the number and volume of pits excavated in traditional Hawaiian
209 times were sufficient to turn over the cultural deposit completely
210 three times. Closer to the beach, the level of cultural activity
211 drops somewhat and the influx of aeolian sand increases markedly,
212 creating a relatively complex stratigraphy in which cultural
213 deposits are interspersed with layers and lenses of beach sand.
214 This is the situation encountered during excavations at O18, where
215 two primary traditional Hawaiian cultural deposits, Layers II and
216 III, along with several smaller sub-layers or lenses were
219 One implication of the model is that the relatively complex
220 stratigraphy at O18 in comparison to sites farther inland on the
221 plain is not an indication of greater antiquity. Instead, it is a
222 function of the site's proximity to the beach. In this view, the
223 O18 site is the coastal fringe of traditional Hawaiian settlement on
224 the plain, where the focus of activity was a short distance inland,
225 away from the constant influx of windblown sand and from periodic
226 inundation by storm waves.
228 * Age of the site [3/3]
229 - Add interval between first settlement and site establishment
235 #+begin_src latex :tangle o18_ao.tex
236 \section{Age Determinations and Analysis}
237 \label{sec:age-determinations}
239 The nine new age determinations were processed in two batches
240 independently of one another. Five collections of wood charcoal,
241 two made by Lloyd Soehren of Bishop Museum in 1966 and three by the
242 University of Hawaii field school in 1967, were submitted by Valerie
243 Curtis, then an archaeologist with the U.S. Air Force, to Gail
244 Murakami of the International Archaeological Research Institute,
245 Inc.\ Wood Identification Laboratory for taxon identification. The
246 identified samples were submitted to Beta-Analytic, Inc.\ for \rc\
247 dating by the accelerator mass spectrometry (AMS) method
248 (table~\ref{tab:calibration}).
251 \topcaption{Age determinations on mostly short-lived specimens}
252 \label{tab:calibration}
254 \begin{tabularx}{\textwidth}{llYrrllrr}
255 \toprule \textbf{Sample} & \textbf{Unit} & \textbf{Material} &
256 $\mathbf{\delta^{13}}$\textbf{C} &
257 \multicolumn{1}{c}{\textbf{CRA}}& \textbf{Age (\textsc{ad})}\fn{1} &
258 $\mathbf{j}$ & $\mathbf{P_{j1}}$ & $\mathbf{P_{j2}}$ \\
260 \multicolumn{7}{l}{Layer II} \\
261 Beta-248821 & B-20 & Pearl shell & -1.6 & 620 $\pm$ 40 &
262 1670--1859 & $\theta_1$ & 0.14 & 0.05 \\
263 Beta-231223 & A-3 & \alert{\textit{Nestegis sandwicensis}} & -23.5
264 & \alert{710 $\pm$ 40} & \multicolumn{1}{c}{---} & $\theta_2$ &
265 \alert{0.98} & \multicolumn{1}{c}{---} \\
267 \multicolumn{7}{l}{Layer III} \\
268 Beta-231220 & EE-15 & \textit{Dodonaea viscosa} & -24.6 & 870
269 $\pm$ 40 & 1060--1279 & $\theta_3$ & 0.10 & 0.09 \\
270 Beta-231221 & EE-15 & \textit{Diospyros sandwicensis} & -26.2 &
271 \alert{680 $\pm$ 40} & 1260--1399 & $\theta_4$ & 0.11 & 0.11 \\
272 Beta-231222 & C-5 & \textit{Canthium odoratum} & -26.5 &
273 \alert{490 $\pm$ 40} & 1310--1499 & $\theta_5$ & 0.14 & 0.15 \\
274 Beta-248818 & C-6 & Pearl shell & +0.5 & 820 $\pm$ 40 &
275 1430--1689 & $\theta_6$ & 0.12 & 0.08 \\
276 Beta-248819 & C-6 & Pearl shell & +2.3 & 840 $\pm$ 40 &
277 1420--1679 & $\theta_7$ & 0.11 & 0.08 \\
278 Beta-248820 & A-6 & Pearl shell & +1.5 & 790 $\pm$ 40 &
279 1440--1699 & $\theta_8$ & 0.15 & 0.09 \\
281 \multicolumn{7}{l}{Layer not identified} \\
282 Beta-231224 & A-3 & \textit{Canthium odoratum} & -24.0 & 690 $\pm$
283 40 & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} &
284 \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---}\\
287 \multicolumn{9}{l}{\fn{1}95\% highest posterior density region.}\\
291 A second set of four age determinations on pearl shell manufacturing
292 waste was selected from the O18 collections held by the U.S. Air
293 Force and submitted by \tsdye* to Beta-Analytic, Inc.\ for AMS
294 dating (table~\ref{tab:calibration}). Pearl shell, produced by
295 mollusks in the genus \textit{Pinctada}, was a favored material for
296 fishhook manufacture in traditional Hawai`i. The cross-laminar
297 structure of the shell gives it exceptional strength for
298 applications like fishhooks that generate high levels of stress at
299 the bend. \textit{Pinctada} shell is a suitable dating material
300 because the animal is a sessile filter-feeder that takes up its
301 carbon from the general ocean water around it, and not from an old
302 limestone substrate \citep{dye94b}. The current best estimate of
303 the apparent age of the ocean water around Hawai`i yields a
304 reservoir correction factor of 110 $\pm$ 80. The large standard
305 deviation of this estimate is likely due to regional patterns of
306 variability in the apparent age of surface waters around Hawai`i
307 that are not yet understood completely. Additional information on
308 this variability might make it possible in the future to apply a
309 more precise estimate in the calibration of these samples. This
310 might yield slightly different calibrated ages for the samples, one
311 from Layer II and three from Layer III, but will not alter the fact
312 that these samples returned \rc\ age estimates that were internally
313 consistent, a first in the long history of \rc\ dating at O18.
315 % \begin{figure}[htb!]
316 % \includegraphics[width=\textwidth]{graphics/pearl-shell}
317 % \caption{Pearl shell manufacturing waste submitted for \rc\ dating:
318 % \textit{a}, Beta-248818; \textit{b}, Beta-248819; \textit{c},
319 % Beta-248820; \textit{d}, Beta-248821. The scale bar is
320 % 1~cm.} \label{fig:pearl-shell}
323 Notable features of Table~\ref{tab:calibration} have been set off in
324 boldface. One of the samples, Beta-231224, could not be assigned to
325 either Layer II or Layer III and is not considered further here.
326 The single sample from Layer II is wood charcoal from a tree known
327 in Hawai`i as \gls{olopua}. Although the life span of
328 \gls{olopua} is not known, the fact that it is a tree indicates the
329 possibility that the sample has in-built age. In fact, the age
330 determination returned by the laboratory is stratigraphically
331 inverted with two of the Layer III samples. Beta-231220, the age
332 estimate for charcoal from a shrub known in Hawai`i as
333 \gls{`a`ali`i}, does not suffer the effects of in-built age and is
334 the most reliable estimate for the antiquity of settlement at O18.
338 #+srcname: calibration
339 #+begin_src latex :tangle o18_ao.tex
340 A Bayesian model of O18 stratigraphy relates each of the dated samples
341 to the calendric ages represented by the two primary cultural
342 deposits. The symbols $\theta_{2-5}$ represent the calendar ages of
343 the archaeological events associated with burning the four dated wood
344 charcoal pieces and $\theta_1$ and $\theta_{6-8}$ represent calendar
345 ages of manufacturing events, presumably of pearl shell fishhooks
346 (table~\ref{tab:calibration}, column \textbf{j}). These are related
347 to the calendar ages of the start and end of deposition of the two
348 primary cultural deposits; $\alpha_3$ and $\beta_3$ represent the
349 start and end of deposition, respectively, of Layer III, and
350 $\alpha_2$ and $\beta_2$ represent the start and end of deposition,
351 respectively, of Layer II. The known stratigraphic relations of
352 $\theta_{2-8}$ to the layer boundaries are set out in (\ref{eq:1}),
353 where $>$ means ``is older than'' and $\geq$ means ``is older than or
358 \phi_2 \geq \alpha_3 \geq \theta_{3-8} \geq \beta_3 > \alpha_2
359 \geq \theta_{1, 2} \geq \beta_2 \geq \phi_1
363 For the sake of brevity, (\ref{eq:1}) groups the $\theta$ from each
364 layer in an unconventional way; the $\theta$ are understood to be
365 unordered so there are no stratigraphic relations among them.
367 The salient points of (\ref{eq:1}) are:
369 \item the onset of Layer III deposition, $\alpha_3$, began either at,
370 or sometime after, the time Hawai`i was colonized by Polynesians,
371 which is modeled here as normally distributed, $\phi_2$ =
372 \textsc{ad} 800 $\pm$ 50
373 \citep{athens02:_avifaun_extin_veget_chang_and};
374 \item the calendar ages of three dated burning events, $\theta_{3-5}$,
375 and three dated manufacturing events, $\theta_{6-8}$, fall within
376 the period of time represented by the deposition of Layer III;
377 \item the calendar ages of the burning and manufacturing events,
378 $\theta_{3-8}$, are unordered, i.e., there is no stratigraphic
379 information on their ages relative to one another;
380 \item the calendar ages of a burning event, $\theta_{2}$, and a
381 manufacturing event, $\theta_{1}$, fall within the period of time
382 represented by the deposition of Layer II;
383 \item the calendar ages of the burning and manufacturing events,
384 $\theta_{2}$ and $\theta_{1}$, are unordered, i.e., there is no
385 stratigraphic information on their ages relative to one another;
386 \item there is a hiatus between the end of deposition of Layer III,
387 $\beta_3$, and the start of deposition of Layer II, $\alpha_2$, as
388 indicated by the $>$ symbol; and
389 \item the end of layer II deposition, $\beta_2$, was either before or
390 during the time cattle ranching was established on the Waim\={a}nalo
391 Plain, which is modeled here as normally distributed, $\phi_1$ =
392 \textsc{ad} 1830 $\pm$ 20.
395 This model was implemented with the BCal software package
396 \citep{bcal} using the most recent atmospheric and marine
397 calibration curves \citep{reimer09:_intcal_marin_radioc_age_calib}.
398 In an effort to identify outliers among the age determinations, each
399 one was assigned an uninformative outlier prior probability of 0.1,
400 following a procedure set out by
401 \citet{christen94:_summar_set_of_radioc_deter}. The intial run of
402 the software clearly identified Beta-231223 as an outlier; the value
403 of 0.98 in the column, $\mathbf{P_{j1}}$ stands out from the rest of
404 the values in the column, which differ little from their initial
405 values. Beta-231223 was omitted from the analysis and a subsequent
406 run of the software failed to detect outliers, as shown in the
407 column, $\mathbf{P_{j2}}$, where values are all close to their
408 initial values. The seven age determinations for O18 used in
409 subsequent analyses are one more than the six potentially useful age
410 determinations available previously.
412 Age estimates returned by the software for parameters of the model
413 establish a chronology for the O18 site and its constituent layers.
414 The 67\% highest posterior density region, equivalent to a one
415 standard deviation estimate, for initial settlement of the site,
416 $\alpha_3$, is \textsc{ad} 1040--1219 (fig.~\ref{fig:a3},
417 \textit{bottom left}). This initial period of deposition at the
418 site, identified by archaeologists as Layer III, came to an end in
419 \textsc{ad} 1580--1699 (fig.~\ref{fig:a3}, \textit{bottom right}).
420 After a hiatus marked stratigraphically by a layer of beach sand,
421 cultural deposition of Layer II began in \textsc{ad} 1670--1789
422 (fig.~\ref{fig:a3}, \textit{top left}) and continued until
423 \textsc{ad} 1770--1859 (fig.~\ref{fig:a3}, \textit{top right}).
424 There is little evidence that the site was abandoned in traditional
425 Hawaiian times. For example, the probability that $\beta_2$ is
426 older than \textsc{ad} 1778, the year Cook sailed to Hawai`i, is
427 0.31. Thus, given the present dating evidence and the stratigraphic
428 model of the O18 site, it is more than twice as likely that the site
429 was abandoned sometime after Cook.
433 \includegraphics[width=84mm]{o18_layers.png}
434 \caption{Estimated ages of Layers II and III at O18: \textit{top
435 left}, early boundary of Layer II; \textit{top right}, late
436 boundary of Layer II; \textit{bottom left}, early boundary of Layer
437 III; \textit{bottom right}, late boundary of Layer III.}
441 An advantage of a model-based Bayesian calibration is that it is
442 possible to derive estimates for time intervals of interest. The
443 O18 site has figured in interpretations of initial Polynesian
444 settlement of Hawai`i \citep{kirch85}; it is interesting to estimate
445 the interval between settlement and establishment of the site. The
446 67\% highest posterior density region for the time interval between
447 $\phi_2$ and $\alpha_3$ is 260--459 years
448 (fig.~\ref{fig:duration-3}, \textit{top left}). The initial period
449 of cultural deposition at the site, represented by Layer III, was
450 quite long. The 67\% highest posterior density region for the time
451 interval between $\alpha_3$ and $\beta_3$ is 400--629 years
452 (fig.~\ref{fig:duration-3}, \textit{top right}). In contrast, the
453 hiatus between Layers III and II appears to have been relatively
454 short. The estimated duration of this hiatus, which is represented
455 stratigraphically by a layer of light-colored beach sand, has a 67\%
456 highest posterior density region of 10--109 years
457 (fig.~\ref{fig:duration-3}, \textit{bottom left}). The duration of
458 Layer II was short compared to Layer III. The 67\% highest
459 posterior density region for the time interval between $\alpha_2$
460 and $\beta_2$ is 10--80 years.
464 \includegraphics[width=84mm]{o18_intervals.png}
465 \caption{Time intervals at O18: \textit{top left}, the interval
466 between Polynesian settlement of Hawai`i and establishment of
467 O18; \textit{top right}, duration of Layer III; \textit{bottom
468 left}, duration of hiatus between Layers II and III;
469 \textit{bottom right}, duration of Layer II.}
470 \label{fig:duration-3}
475 #+srcname: age-summary
476 #+begin_src latex :tangle no
477 In summary, the chronology of Site O18 as estimated by \rc\ dates on
478 short-lived materials within a Bayesian model appears to begin
479 sometime in the eleventh to thirteenth centuries \textsc{ad} and to
480 have continued, with interruptions, through to the end of the
481 traditional Hawaiian period. These interruptions, indicated
482 statigraphically by deposits of light-colored sand, appear to have
483 been relatively brief. The hiatus between Layers III and II was
484 probably less than a century and could have been as short as a
485 decade. These results fit well with the regional model of cultural
486 stratigraphy, which places O18 at the coastal fringe of widespread
487 traditional Hawaiian use of the Waim\={a}nalo Plain.
489 * Regional picture [2/2]
491 ** DONE Regional data
493 #+srcname: regional-data
494 #+begin_src latex :tangle o18_ao.tex
495 \section{O18 in Regional Perspective}
496 \label{sec:regional-perspective}
498 The Bayesian model can be extended to include other sites on the
499 Waim\={a}nalo Plain. Cultural resources management excavations at
500 sites 50--80--15--4851 and --4853 and 50--80--11--4856 and --4857
501 have yielded 37 \rc\ age determinations, 35 on charcoal from
502 identified short-lived taxa and two on pearl shell manufacturing
503 waste (table~\ref{tab:ages}). Each of the sites consists of the
504 remnants of a single cultural deposit that typically lacks internal
505 stratification. Because no stratigraphic relationships between the
506 deposits of these sites and the layers of O18 have been established,
507 they are each modeled as single phases independent of one another
508 and of Layers II and III at O18. Using the short-hand described
509 earlier, the model can be extended with the addition of the
510 following inequalities:
514 \alpha_{4851} \geq \theta_{9-11} \geq \beta_{4851}
519 \alpha_{4853} \geq \theta_{12-27} \geq \beta_{4853}
524 \alpha_{4856} \geq \theta_{28-41} \geq \beta_{4856}
529 \alpha_{4857} \geq \theta_{42-45} \geq \beta_{4857}
535 \topcaption{\rc\ ages of short-lived materials from other sites on the
538 \begin{tabularx}{\textwidth}{llXrrl}
539 \toprule Laboratory & Fire-pit & Material & $\delta^{13}$C &
540 CRA\fn{1} & $\mathbf{j}$ \\
542 \multicolumn{5}{l}{Site 50--80--15--4851} \\
543 Beta-111023\fn{2} & Feature 3 & cf.\ \latin{Rauvolfia
545 -26.9 & 310$\pm$40 & $\theta_9$ \\
546 Beta-111024\fn{2} & Feature 2 & \latin{Sida} cf.\ \latin{fallax} &
547 -26.8 & 140$\pm$60 & $\theta_{10}$ \\
548 Beta-111025\fn{2} & Feature 1 & \latin{Sida} cf.\ \latin{fallax} &
549 -24.2 & 540$\pm$50 & $\theta_{11}$ \\
551 \multicolumn{5}{l}{Site 50--80--15--4853} \\
552 Beta-101869\fn{2} & Feature 6 & \latin{Chamaesyce} sp. & -12.9 &
553 230$\pm$60 & $\theta_{12}$ \\
554 Beta-101871\fn{2} & Feature 9 & cf.\ \latin{Osteomeles
555 anthyllidifolia} & -25.3 & 720$\pm$40 & $\theta_{13}$ \\
556 Beta-101872\fn{2} & Feature 10 & cf.\ \latin{Osteomeles
557 anthyllidifolia} & -24.7 & 680$\pm$40 & $\theta_{14}$ \\
558 Beta-111022\fn{2} & Feature 1 & \latin{Sida} cf.\ \latin{fallax}
559 & -27.5 & 150$\pm$40 & $\theta_{15}$ \\
560 Beta-120317\fn{2} & Feature 1 & \latin{Sida} cf.\ \latin{fallax}
561 & -21.3 & 140$\pm$50 & $\theta_{16}$\\
562 Beta-120318\fn{2} & Feature 5 & \latin{Sida} cf.\ \latin{fallax}
563 & -26.1 & 150$\pm$50 & $\theta_{17}$ \\
564 Beta-120319\fn{2} & Feature 9 & \latin{Aleurites molucanna}
565 nutshell, \latin{Chenopodium oahuense}, \latin{Sida} cf.\
567 & -25.9 & 350$\pm$80 & $\theta_{18}$ \\
568 Beta-120320\fn{2} & Feature 13 & \latin{Aleurites molucanna}
569 nutshell & -25.6 & 230$\pm$50 & $\theta_{19}$ \\
570 Beta-120321\fn{2} & Feature 15 & \latin{Aleurites molucanna}
571 nutshell & -25.0 & 110$\pm$70 & $\theta_{20}$ \\
572 Beta-120322\fn{2} & Feature 16 & \latin{Chamaesyce} sp.
573 & -16.8 & 310$\pm$60 & $\theta_{21}$ \\
574 Beta-120323\fn{2} & Feature 17 & \latin{Aleurites molucanna}
575 nutshell, \latin{Chenopodium oahuense}, \latin{Sida} cf.\
576 \latin{fallax} & -27.5 & 170$\pm$60 & $\theta_{22}$ \\
577 Beta-120324\fn{2} & Feature 18 & \latin{Aleurites molucanna}
578 nutshell & -25.2 & 250$\pm$50 & $\theta_{23}$ \\
579 Beta-120325\fn{2} & Feature 19 & \latin{Aleurites molucanna}
580 nutshell & -25.2 & 270$\pm$70 & $\theta_{24}$ \\
581 Beta-120326\fn{2} & Feature 20 & \latin{Aleurites molucanna}
582 nutshell, \latin{Chenopodium oahuense}, \latin{Sida} cf.\
583 \latin{fallax} & -14.0 & 330$\pm$60 & $\theta_{25}$ \\
584 Beta-120327\fn{2} & Feature 24 & \latin{Aleurites molucanna}
585 nutshell & -23.0 & 400$\pm$70 & $\theta_{26}$ \\
586 Beta-120328\fn{2} & Feature 25 & \latin{Sida} cf.\ \latin{fallax}
587 & -25.5 & 220$\pm$50 & $\theta_{27}$ \\
590 \multicolumn{5}{l}{Site 50--80--11--4856}\\
591 Beta-208589\fn{3} & & \latin{Chenopodium oahuense} wood charcoal & -26.6 & 140$\pm$40 & $\theta_{28}$\\
592 Beta-208590\fn{3} & & \latin{Sida} cf.\ \latin{fallax} wood
593 charcoal & -24.9 & 90$\pm$40 & $\theta_{29}$\\
594 Beta-208591\fn{3} & & \latin{Aleurites moluccana} nutshell & -25.7
595 & 140$\pm$40 & $\theta_{30}$\\
596 Beta-246786\fn{4} & Feature 4 & \latin{Sida} cf.\ \latin{fallax}
597 wood charcoal & -25.4 & 380$\pm$40 & $\theta_{31}$\\
598 Beta-251245\fn{4} & Feature 5 & \latin{Chenopodium oahuense} wood
599 charcoal & -24.5 & 260$\pm$40 & $\theta_{32}$ \\
600 Beta-251243\fn{4} & Feature 9 & \latin{Aleurites moluccana}
601 nutshell charcoal & -24.9 & 350$\pm$40 & $\theta_{33}$ \\
602 Beta-251244\fn{4} & Feature 10 & \latin{Sida} cf.\ \latin{fallax}
603 wood charcoal & -24 & 250$\pm$40 & $\theta_{34}$ \\
604 Beta-251242\fn{4} & Feature 12 & \latin{Sida} cf.\ \latin{fallax}
605 wood charcoal & -24.4 & 200$\pm$40 & $\theta_{35}$ \\
606 Beta-251246\fn{4} & Feature 17 & \latin{Chenopodium oahuense} wood
607 charcoal & -21.9 & 240$\pm$40 & $\theta_{36}$ \\
608 Beta-251247\fn{4} & Feature 22 & \latin{Cordyline fruticosa} wood
609 charcoal & -22.6 & 450$\pm$40 & $\theta_{37}$ \\
610 Beta-251248\fn{4} & Feature 23 & \latin{Aleurites moluccana}
612 charcoal & -25.6 & 390$\pm$40 & $\theta_{38}$ \\
613 Beta-200230\fn{5} & Feature 22 & \latin{Chamaesyce sp.} wood charcoal
614 & -11.3 & 550$\pm$40 & $\theta_{39}$ \\
615 Beta-208588\fn{3} & & Pearl shell & -0.1 & 630$\pm$40 & $\theta_{40}$ \\
616 Beta-208587\fn{3} & & Pearl shell & -2.7 & 630$\pm$40 &
620 \multicolumn{5}{l}{Site 50--80--11--4857}\\
621 Beta-200229\fn{5} & Feature 11 & \latin{Sida} cf.\ \latin{fallax}
622 wood charcoal & -25.6 & 170$\pm$40 & $\theta_{42}$ \\
623 Beta-200228\fn{5} & Feature 12 & \latin{Chamaesyce} sp.\ wood
624 charcoal & -25.7 & 200$\pm$40 & $\theta_{43}$ \\
625 Beta-260904\fn{6} & Context 12 & cf.\ \latin{Chamaesyce} sp.\ wood
626 charcoal & -23.4 & 580$\pm$40 & $\theta_{44}$ \\
627 Beta-260905\fn{6} & Context 13 & \latin{Sida} cf.\ \latin{fallax}
628 wood charcoal & -26.4 & 400$\pm$40 & $\theta_{45}$\\
631 \bottomrule \multicolumn{5}{l}{\fn{1} Conventional \rc\ age
632 \citep{stuiver-polach77}.} \\
633 \multicolumn{5}{l}{\fn{2} \citet{dye00:_effec}.} \\
634 \multicolumn{5}{l}{\fn{3}
635 \citet*{mcelroy06:_archaeol_monit_and_inves_durin}.} \\
636 \multicolumn{5}{l}{\fn{4}
637 \citet*{zzz_lebo09:_pre_const_archaeol_survey_for}.}\\
638 \multicolumn{5}{l}{\fn{5}
639 \citet*{putzi05:_archaeol_monit_repor_for_replac}.}\\
640 \multicolumn{5}{l}{\fn{6} \citet*{dye09:_pre_archaeol_resour_survey_new}.}\\
647 ** DONE Regional analysis
648 - When other sites were established
649 - All sites presumably abandoned in early historic period
650 - Intervals between establishment of O18 and other sites
651 - 4856, 150--359 years after O18
652 - 4851, -20--349 years after O18
653 - 4857, 0--309 years after O18
654 - 4853, 70--279 years after O18
655 - p 4851 > Layer III = 0.21
656 - alpha 3 at O18, 67%, 1040--1219
657 - alpha 4853, 67% 710-571 BP, 1240--1379 AD
658 - alpha 4857, 67% 760-551 BP, 1190--1409 AD
659 - alpha 4851, 67% 770-521 BP, 1160--1429 AD
660 - alpha 4856, 67% 620-521 BP, 1360--1429 AD
663 #+srcname: regional-analysis-1
664 #+begin_src latex :tangle o18_ao.tex
665 Based on the current dating evidence, sites 50--80--15--4851 and
666 --4853 and 50--80--11--4856 and --4857 were all established after O18.
667 Site 50--80--15--4851, located on the opposite bank of Puh\={a} Stream
668 from O18, is likely to be the oldest among the four. It was
669 established \textsc{ad} 1160--1429, based on the 67\% highest
670 posterior density region (fig.~\ref{fig:initial-use}, \textit{top left}).
671 Penecontemporaneously, Site 50--80--11--4857, located inland and
672 north of O18, was established in \textsc{ad} 1190--1409
673 (fig.~\ref{fig:initial-use}, \textit{bottom right}). Site 50--80--15--4853,
674 immediately inland of site O18, has been extensively dated and appears
675 to have been established at a later time. The 67\% highest posterior
676 density region for the site's establishment is \textsc{ad} 1240--1379
677 (fig.~\ref{fig:initial-use}, \textit{top right}). Finally, site
678 50--80--11--4856, located on the coast north of O18, was established
679 in \textsc{ad} 1360--1429 (fig.~\ref{fig:initial-use}, \textit{bottom left}),
680 apparently later than Site 50--80--11--4857 located immediately
681 inland. The probability that 50--80--11--4857 was established earlier
682 than 50--80--11--4856 is 0.88.
686 \includegraphics[width=84mm]{site-establishment.png}
687 \caption{Initial site use on the Waim\={a}nalo Plain: \textit{top
688 left}, 50--80--15--4851; \textit{top right}, 50--80--15--4853;
689 \textit{bottom left}, 50--80--11--4856; \textit{bottom right},
691 \label{fig:initial-use}
695 #+results: regional-analysis-1
697 Based on the current dating evidence, sites 50--80--15--4851 and
698 --4853 and 50--80--11--4856 and --4857 were all established after O18.
699 Site 50--80--15--4851, located on the opposite bank of Puh\={a} Stream
700 from O18, is likely to be the oldest among the four. It was
701 established \textsc{ad} 1160--1429, based on the 67\% highest
702 posterior density region (fig.~\ref{fig:initial-use}, \textit{top left}).
703 Pene-contemporaneously, Site 50--80--11--4857, located inland and
704 north of O18, was established in \textsc{ad} 1190--1409
705 (fig.~\ref{fig:initial-use}, \textit{bottom right}). Site 50--80--15--4853,
706 immediately inland of site O18, has been extensively dated and appears
707 to have been established at a later time. The 67\% highest posterior
708 density region for the site's establishment is \textsc{ad} 1240--1379
709 (fig.~\ref{fig:initial-use}, \textit{top right}). Finally, site
710 50--80--11--4856, located on the coast north of O18, was established
711 in \textsc{ad} 1360--1429 (fig.~\ref{fig:initial-use}, \textit{bottom left}),
712 apparently later than Site 50--80--11--4857 located immediately
713 inland. The probability that 50--80--11--4857 was established earlier
714 than 50--80--11--4856 is 0.88.
718 \includegraphics[width=84mm]{site-establishment.png}
719 \caption{Initial site use on the Waim\={a}nalo Plain: \textit{top
720 left}, 50--80--15--4851; \textit{top right}, 50--80--15--4853;
721 \textit{bottom left}, 50--80--11--4856; \textit{bottom right},
723 \label{fig:initial-use}
726 #+srcname: regional-analysis-2
727 #+begin_src latex :tangle o18_ao.tex
728 Another way to look at the site establishment estimates is relative to
729 the establishment of O18. All of the
730 posterior probability distributions have left tails that extend past
731 zero and thus each site retains some probability of having been
732 established before O18. These probabilities are all rather slim,
733 however. The site with the greatest probability of having been
734 established before O18, 50--80--11--4851, has a probability of 0.2.
735 Using 67\% highest posterior density regions: Site 50--80--15--4851
736 was settled 10 years earlier than to 349 years after O18
737 (fig.~\ref{fig:site-establishment}, \textit{top left}); site
738 50--80--11--4857 was settled at the same time as O18 to 319 years
739 later (fig.~\ref{fig:site-establishment}, \textit{bottom right}); site
740 50--80--11--4853 was settled 60--279 years after O18
741 (fig.~\ref{fig:site-establishment}, \textit{top right}); and site
742 50--80--11--4856 was settled 160--359 years after O18
743 (fig.~\ref{fig:site-establishment}, \textit{bottom left}).
745 \begin{figure}[htb!] \centering
746 \includegraphics[width=84mm]{after-o18.png} \caption[Sequence of
747 site establishment]{Sequence of site establishment---the
748 interval between establishment of O18 and other sites:
749 \textit{top left}, Site 50--80--15--4851; \textit{top right},
750 Site 50--80--15--4853; \textit{bottom left}, Site
751 50--80--11--4856; \textit{bottom right}, Site
752 50--80--11--4857. Note that there is a small probability
753 that each of the sites was established before O18.}
754 \label{fig:site-establishment} \end{figure}
757 #+srcname: conclusion
758 #+begin_src latex :tangle o18_ao.tex
759 \section{Summary and Conclusion}
760 \label{sec:conclusion}
763 ** DONE Regional prehistory [5/5]
764 - [X] O18 not an example of an early site, it was settled at least
765 240 years after Polynesian colonization and perhaps as much as
767 - [X] O18 is likely the earliest site on the plain
768 - [X] Other sites settled over the next approximately 3-4 centuries,
769 in what appears to be a piece-meal fashion, and not a radiation
771 - [X] Discuss the early date on kukui nutshell. How it got into the
772 O18 deposit is a mystery, but if it is not spuriously old due
773 to laboratory error, then it might indicate early establishment
774 of the tree on the Waimanalo plain. The calibrated age shown
775 in Table 2 accepts the material as primarily deposited in Layer
776 II. If this constraint is relaxed, and the date is calibrated
777 as constrained only by phi1 and phi2, then at 67% AD 850--1160.
778 The probability it was growing before O18 was established is
780 - [X] This carries with it the possibility that there were
781 settlements in Waimanalo that pre-dated O18
782 - [ ] Results differ by timing and by the fact that events of
783 interest are estimated directly.
784 #+srcname: prehistory
785 #+begin_src latex :tangle o18_ao.tex
786 Seven new \rc\ age determinations on short-lived materials yield a
787 chronology for O18 that differs from previous estimates. The
788 results clearly indicate that O18 was settled later than previously
789 estimated. The 67\% highest posterior density region for the true age of $\alpha_3$ is
790 \textsc{ad} 1040--1219, which is 4--9 centuries younger than
791 previous estimates. The hypothesis that O18 was occupied during an
792 early phase of Polynesian settlement is, on present evidence, false.
793 The best estimate, based on present evidence, places initial site
794 use 260--459 years after the archipelago was discovered and
795 colonized. With this new, ``late'' chronology, O18 joins site H1 on
796 Hawai`i Island \citep{dye92} and the H\={a}lawa Dune site on
797 Moloka`i \citep{kirch07:_recon_hawaiian_cultur_sequen} in a growing
798 group of relatively late sites once believed to have been examples
799 of early Hawaiian settlement.
804 % the previous situation, where estimates were based on \textit{ad
805 % hoc} procedures. The initial set of five GaK dates supported two
806 % estimates that differed by three centuries. The addition of the
807 % Beta-Analytic dates did little to change the shape of the
808 % data,\footnote{The two ANU dates are clearly anomalous.} in
809 % fact it is remarkable how closely the new dates reprised the old
810 % ones. Yet, this similar but augmented data set supported a 500 year
811 % revision of the estimate. Clearly, these \textit{ad hoc} estimates
812 % were responding to information adjunct to the dates
813 % themselves---initially to now-discredited old ``dates'' on volcanic
814 % glass from O18 and subsequently to a widely-accepted
815 % paleoenvironmental estimate for first settlement in the eighth or
816 % ninth centuries \textsc{ad}. In both cases these adjunct data are
817 % not explicitly modeled in the calibration, but are instead applied
818 % idiosyncratically. The Bayesian model is sufficiently robust to
819 % accommodate both the addition of new data and a revised estimate of
820 % when the islands were initially colonized.
822 The situation is similar with respect to when O18 was abandoned.
823 The new dates on short-lived materials, calibrated and
824 interepreted within a Bayesian framework, indicate that the site was
825 abandoned at the end of traditional Hawaiian times in the late
826 eighteenth or early nineteenth centures, some 3--6 centuries later
827 than earlier estimates. The estimate brings the
828 abandonment of O18 in line with abandonment date estimates for other sites
829 on the Waim\={a}nalo Plain.
831 One reason that previous estimates of O18 chronology were too
832 old by centuries was a failure to control for the potential
833 effects of old wood during the dating process, but errors
834 assigning the dated samples to their correct archaeological
835 contexts in a field school situation, and statistical and other
836 errors in the dating laboratory probably had effects, too. It
837 is worthwhile to emphasize the ill effects of old wood; cultural
838 resources management archaeologists working in Hawaii routinely
839 date unidentified wood charcoal. There is no reason to believe
840 that their age determinations on unidentified wood charcoal will
841 perform any better than those from O18, which proved to be poor
842 estimators of site chronology. They are essentially worthless for
843 establishing archaeological chronologies.
845 In most cases, the old dates that do a poor job of estimating
846 the age of O18 provide no other useful information. An
847 exception to this is Beta-20852b on \textit{A. moluccana}
848 nutshell. This age determination does a poor job of estimating
849 the age of its archaeological context in Layer II, but because
850 the identified material derived from a tree introduced to the
851 islands by Polynesians the age estimate itself is of interest.
852 If the calendar age, $\theta_{46}$, of this age determination is
853 associated with the archaeological event of planting
854 \textit{kukui} trees in Waim\={a}nalo and calibrated in the
855 context of a model that specifies only that this event dates to
856 traditional Hawaiian times (\ref{eq:kukui}), then the 67\%
857 highest posterior density region for $\theta_{46}$ is
858 \textsc{ad} 840--1159, an estimate that has a 70\% probability
859 of dating an event older than the establishment of O18. Thus,
860 it is likely that the \textit{A. moluccana} tree was planted by
861 Hawaiians who lived at some other site in Waim\={a}nalo prior to
862 settlement at O18. Because dates from nearby sites indicate
863 that O18 was established before them, this putative earlier
864 settlement is likely to be located somewhere inland, probably on
865 the volcanic soils that supported gardens in traditional
866 Hawaiian times. Whether cultural deposits associated with this
867 putative early settlement still exist is a question for future
872 \phi_2 \geq \theta_{46} \geq \phi_1
875 Finally, development of an explicit chronological model relating
876 regional archaeological events to one another and set out in
877 inequalities (\ref{eq:1}--\ref{eq:kukui}) means that anyone can
878 replicate the estimate and explore how different parameters of
879 the model affect it. It is not possible to do this in a precise
880 way with an approach that is not strictly model-based. Changes
881 in chronological estimates for sites on the Waim\={a}nalo Plain
882 will most likely result from new dates on short-lived materials
883 from secure stratigraphic contexts both on the Waim\={a}nalo
884 Plain and beyond. Excavation of deposits at the coastal fringe
885 of Site 50--80--11--4856, for instance, might help clarify the
886 processes responsible for deposition of charcoal in this active
887 and variable environment at the fringe of traditional Hawaiian
888 settlement on the Waim\={a}nalo Plain. And certainly, any
889 change in the estimated settlement date of the Hawaiian Islands
890 would have a direct effect on the estimate of the interval
891 between this event and establishment of O18. If the change
892 in the estimated settlement date were sufficiently large, it
893 might even have an effect on the estimate of when O18 was
897 ** REJECTED The weaknesses of the present estimates
898 - Settlement dates heavily dependent on dated samples, sample size
899 potentially important in interpretation
900 - Calibration of shell dates, might change a bit, but not much
901 - Layer II represented by a single sample, if shell calibrates a
902 bit older, then the boundary between Layers II and III will change.
903 - The Layer III shell dates are all relatively young and a change
904 in calibration likely won't affect the estimated establishment
906 #+srcname: evaluation
908 The incorporation into the Bayesian calibration of a stratigraphic
909 model of traditional Hawaiian sites on the Waim\={a}nalo Plain,
910 expressed in inequalities (\ref{eq:1}) and (\ref{eq:4851}) through
911 (\ref{eq:4857}), makes it possible to answer interpretive questions
912 with probabilistic estimates, rather than with guesses or ad hoc
913 arguments. Among the probabilistic estimates
914 are: \begin{inparaenum}[(i)] \item the ages of archaeological events
915 of interest that could not be dated directly, including first
916 settlement and abandonment of the five site, as well as the upper
917 boundary of Layer III and the lower boundary of Layer II at O18;
918 \item the elapsed time between events,
919 including \begin{inparaenum}[(a)] \item the duration of Layers II,
920 III, and the hiatus between them, \item the lag between settlement
921 of O18 and other sites on the Waim\={a}nalo Plain, and \item the
922 time between first settlement of Hawai`i by Polynesians and
923 establishment of O18; and \end{inparaenum} \item the relative timing
924 of events of interest, such as the first planting of
925 \textit{A. moluccana} in Waim\={a}nalo relative to the establishment
926 of O18. \end{inparaenum} The ability of Bayesian calibration to
927 yield direct answers to interpretive questions is one of its great
930 Another strength of the model-based, Bayesian approach to
931 calibration is that new information can be used to augment and
932 refine the results. For example, a new age determination that is
933 older than others from the same site will push the estimate of site
934 establishment back in time; the Bayesian calibration will indicate
935 directly with probabilistic estimates how much effect the new date
936 has on the regional chronology. Similarly, refinement of $\Delta R$
937 for Hawai`i might change the calibrated ages of the pearl shell
938 samples by some decades. Here, the Bayesian calibration will
939 calculate the effect this has on the age of the transition from
940 Layer III to Layer II at O18. In this way, work on regional
941 chronology can be collaborative, rather than based on arguments over
942 how the ad hoc methods of chronologic hygiene might be applied in a
946 ** REJECTED Chronometric hygiene is non-scientific.
947 - Although Gak dates are often dismissed, they did no worse than
948 other laboratories did.
949 - It is possible to use dates with large standard deviations: they
950 don't mean much, but there is no intrinsic reason to discard what
951 little information they might hold.
957 ** REJECTED There are no known old sites
958 - Graph of time interval between settlement and site
959 establishment for O18
960 - H1 is late, cite Dye NZJA
961 - Halawa Dune is late, too.
967 #+srcname: latex-ending
968 #+begin_src latex :tangle o18_ao.tex
969 % Comment or uncomment as needed
970 % style=altlist another possibility
971 %\printglossary[type=main, style=tsdlist]
972 %\printglossary[type=hawaiian, style=tsdlist]
973 % \printglossary[type=polynesian, style=tsdlist]
974 % \printglossary[type=gazetteer, style=tsdlist]
975 % \printglossary[type=acronym, style=tsdlist]
976 % \printglossary[type=oldenglish, style=tsdlist]
977 % \printglossary[type=bio, style=tsdlist]
979 \addcontentsline{toc}{section}{Bibliography}
980 \bibliographystyle{chicago}
982 % Comment or uncomment as needed
984 \bibliography{tsd,local}
989 * R code for graphics
993 - Put all the csv file names in a table, then edit the table for
994 input to the R function
1006 - thetas is a list inside the function
1008 - run lapply, use string substitution to make variable names, file
1011 - need to add cbind() an identifier that can be used to label the plot
1012 and to segregate the plots
1014 #+srcname: dated-events(files = thetas)
1015 #+begin_src R :session :file output_dated_events.png
1017 make.plot.file <- function(x, y)
1020 afile <- paste("r/",x,sep="")
1021 anobject <- strsplit(x,".",fixed=TRUE)[[1]][1]
1022 z <- read.csv(file = afile)
1023 z <- cbind(z,label=rep(anobject,dim(z)[1]))
1027 res <- data.frame(cal.BP=numeric(0),Posterior.probability=numeric(0),label=character(0))
1028 for (f in files[,1]) res <- make.plot.file(f, res)
1029 g <- ggplot(res, aes(x=1950 + cal.BP, y=Posterior.probability))
1030 png(file="output_dated_events.png",width=168,height=100,unit='mm',res=600)
1031 g + geom_bar(stat='identity') + xlab("Year AD") +
1032 ylab("Probability") + facet_wrap(~ label)
1036 #+results: dated-events
1037 [[file:output_dated_events.png]]
1039 #+srcname: single-date(x = "alpha-4856.csv")
1040 #+begin_src R :session
1041 afile <- paste("r/",x,sep="")
1042 anobject <- strsplit(x,".",fixed=TRUE)[[1]][1]
1043 ofname <- paste(anobject,".pdf",sep="")
1044 z <- read.csv(file = afile)
1045 g <- ggplot(z, aes(x=1950 + cal.BP, y=Posterior.probability))
1046 g + geom_bar(stat='identity') + xlab("Year AD") +
1052 #+results: single-date
1055 - This is a kludge that works for a one-off situation
1056 - The shell source shows all the csv files
1057 - Edit the results table to select the files to use as input to the
1059 #+srcname: intervals
1064 #+results: intervals
1065 | alpha-4851-and-alpha-3.csv |
1066 | alpha-4853-and-alpha-3.csv |
1067 | alpha-4856-and-alpha-3.csv |
1068 | alpha-4857-and-alpha-3.csv |
1070 #+srcname: interval-estimates(files = intervals)
1071 #+begin_src R :session :file output_intervals.png
1074 make.plot.file <- function(x, y)
1077 afile <- paste("r/",x,sep="")
1078 anobject <- strsplit(x,".",fixed=TRUE)[[1]][1]
1079 z <- read.csv(file = afile)
1080 z <- cbind(z,label=rep(anobject,dim(z)[1]))
1084 res <- data.frame(cal.BP=numeric(0),Posterior.probability=numeric(0),label=character(0))
1085 for (f in files[,1]) res <- make.plot.file(f, res)
1086 g <- ggplot(res, aes(x=cal.BP, y=Posterior.probability))
1087 png(file="output_intervals.png",width=168,height=100,unit='mm',res=600)
1088 g + geom_bar(stat='identity') + xlab("Time Interval (Years)") +
1089 ylab("Probability") + facet_wrap(~ label, scales = "fixed")
1093 #+results: interval-estimates
1094 [[file:output_intervals.png]]
1097 ** Regional date graph
1098 - Hard code a complex graphic
1099 #+srcname: r-regional-data
1100 #+begin_src R :session
1103 a3_gg <- cbind(a3, rep("O18",dim(a3)[1]))
1104 names(a3_gg)[3] <- "name"
1105 a4851 <- read.csv("alpha-4851.csv")
1106 a4851_gg <- cbind(a4851, rep("4851", dim(a4851)[1]))
1107 names(a4851_gg)[3] <- "name"
1108 a4853 <- read.csv("alpha-4853.csv")
1109 a4853_gg <- cbind(a4853, rep("4853", dim(a4853)[1]))
1110 names(a4853_gg)[3] <- "name"
1111 a4856 <- read.csv("alpha-4856.csv")
1112 a4856_gg <- cbind(a4856, rep("4856", dim(a4856)[1]))
1113 names(a4856_gg)[3] <- "name"
1114 a4857 <- read.csv("alpha-4857.csv")
1115 a4857_gg <- cbind(a4857, rep("4857", dim(a4857)[1]))
1116 names(a4857_gg)[3] <- "name"
1117 alpha_gg <- rbind(a3_gg, a4851_gg, a4853_gg, a4856_gg, a4857_gg)
1120 #+results: r-regional-data
1134 #+srcname: r-regional-plot
1135 #+begin_src R :session
1136 alpha_plot <- ggplot(alpha_gg, aes(x=1950 + cal.BP, y=Posterior.probability))
1137 pdf(file="alpha-regional.pdf", height=3.75, width=7.5)
1138 alpha_plot + geom_bar(stat='identity') + xlab("Year AD") +
1139 ylab("Probability") + facet_wrap(~ name)
1142 * REJECTED LaTeX article makefile
1146 <<regional-context>>
1154 <<regional-analysis-1>>
1155 <<regional-analysis-2>>
1162 * REJECTED Post-mortem on earlier data [2/2]
1163 ** DONE Post mortem data
1164 #+srcname: post-mortem-data
1166 \section{Post-mortem on the Early Dates}
1167 \label{sec:post-mortem}
1169 The Bayesian model described in the previous section can be extended
1170 to incorporate the early age determinations reported by
1171 \citet{pearson71:_bellows} and
1172 \citet{tuggle01:_age_bellow_dune_site_o18}. The purpose of extending
1173 the model in this way is to compare the chronology produced by the
1174 early age determinations with the one produced by the new age
1175 determinations on short-lived materials. Thus, it is important that
1176 the model be extended in a way that keeps the two chronologies
1177 separate. This is accomplished in the BCal software by creating a
1178 separate set of phases for Layers II and III, as if they belonged to a
1179 separate site, and assigning the early age determinations to this
1180 separate set of phases. This extension to the model can be
1181 represented by a second inequality, (\ref{eq:2}), which establishes
1182 new layer boundaries, indicated by an \textit{o} appended to the subscript,
1183 and includes six of the early age determinations, $\theta_{2, 9-13}$
1184 (table~\ref{tab:early-dates}). GaK-1819 is clearly an outlier in
1185 Layer II and has been excluded from the analysis.
1189 \phi_2 \geq \alpha_{3o} \geq \theta_{12-13} \geq \beta_{3o} > \alpha_{2o}
1190 \geq \theta_{2, 9-11} \geq \beta_{2o} \geq \phi_1
1194 \topcaption{Early O18 age determinations}
1195 \label{tab:early-dates}
1197 \begin{tabular}{llrrllrr}
1199 \textbf{Sample} & \textbf{Material} &
1200 $\mathbf{\delta^{13}}$\textbf{C} &
1201 \multicolumn{1}{c}{\textbf{CRA}} &\multicolumn{1}{c}{\textbf{Age
1202 (\textsc{ad})}} & \multicolumn{1}{c}{\textbf{j}} &
1203 \multicolumn{1}{c}{$\mathbf{P_j}$} &
1204 \multicolumn{1}{c}{$\mathbf{P_{dep}}$} \\
1206 \multicolumn{4}{l}{Layer II} \\
1207 GaK-1818 & \alert{unidentified} & -25.0 & 1126 $\pm$ 124 &
1209 $\theta_2$ & 0.19 & 0.00002 \\
1210 GaK-1819 & \alert{unidentified} & -25.0 & \alert{1616 $\pm$ 96} & \multicolumn{1}{c}{---} &
1211 \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} \\
1212 Beta-20852a & \alert{unidentified} & -24.1 & 720 $\pm$ 130 & 1120--1309 &
1213 $\theta_9$ & 0.08 & 0.0002\\
1214 Beta-20852b & \textit{A. moluccana} nutshell & -26.4 & 1330 $\pm$
1216 & $\theta_{10}$ & 0.20 & 0.0001\\
1217 GaK-1816 & \alert{unidentified} & -25.0 & 716 $\pm$ 129 & 1120--1309 &
1218 $\theta_{11}$ & 0.09 & 0.00008\\
1220 \multicolumn{4}{l}{Layer III} \\
1221 GaK-1817 & \alert{unidentified} & -25.0 & 1046 $\pm$ 115 & 870--1019 &
1222 $\theta_{12}$ & 0.06 & 0.12 \\
1223 GaK-1820 & \alert{unidentified} & -25.0 & \alert{modern} & \multicolumn{1}{c}{---} &
1224 \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} \\
1225 Beta-20853 & \alert{unidentified} & -25.0 & 1070 $\pm$ 370 &
1227 $\theta_{13}$ & 0.04 & 0.12 \\
1228 ANU-6179 & \alert{unidentified} & -24.8 & \alert{modern} & \multicolumn{1}{c}{---} &
1229 \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} \\
1230 ANU-7027 & \textit{Cocos nucifera} & -23.1 & \alert{120 $\pm$ 132}
1231 & \multicolumn{1}{c}{---}
1232 & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} & \multicolumn{1}{c}{---} \\
1238 ** DONE Post mortem results
1239 #+srcname: post-mortem-results
1241 The Bayesian calibration of the early age determinations yields layer
1242 boundaries that correspond fairly closely to those proposed by
1243 \citet{tuggle01:_age_bellow_dune_site_o18}. According to this
1244 analysis: the site was established sometime shortly after initial
1245 settlement of the islands, \textsc{ad} 800--949, a range that is
1246 influenced strongly by the constraints imposed by $\phi_2$; the hiatus
1247 between Layers III and II began in \textsc{ad} 900--1069 and ended
1248 when Layer II began to be deposited in \textsc{ad} 990--1169; and the
1249 site was abandoned in \textsc{ad} 1160--1399.% In this case, it
1250 % appears that the ad hoc methods of ``chronological hygiene'' yielded
1251 % relatively reasonable results.
1253 A potentially more interesting question has to do with the
1254 probabilities that the early age determinations date events that
1255 took place within the period of time represented by the
1256 stratigraphic layers from which they were collected, as these are
1257 estimated by the Bayesian calibration of short-lived materials as
1258 represented by inequality (\ref{eq:1}). These probabilities are
1259 shown in the column, $P_{dep}$ of table~\ref{tab:early-dates} where
1260 it can be seen that all four of the Layer II age determinations have
1261 vanishingly small probabilities of representing events that took
1262 place while that layer was being deposited. The two Layer III age
1263 determinations have somewhat larger, but equally low probabilities
1264 of belonging to that layer. In all cases, the age determinations
1267 In the cases of two Layer III dates on unidentified wood, GaK-1817 and
1268 Beta-20853, the most likely culprit is in-built age. Both of these
1269 dates are about 200 years older than the early date on
1270 \textit{D. viscosa} (see table~\ref{tab:calibration}).
1271 \citet{dye00:_effec} has shown that controlling for in-built age
1272 yields age estimates that are, on average, about 100 years younger
1273 than age estimates on samples that don't control for in-built age.
1274 Discrepancies of 200 years are well within the range of potential
1275 in-built ages. The three other Layer III dates, GaK-1820, ANU-6179,
1276 and ANU-7027 do not differ statistically from the modern standard.
1277 Deposition of Layer III ended sometime in the late sixteenth or
1278 seventeenth centuries, so these three dates are all more than 250
1279 years too young for their stratigraphic positions. It seems unlikely
1280 that modern material could have made its way down through the fairly
1281 complex site stratigraphy to the base of the section, so problems of
1282 context are unlikely \textit{a priori}. In practical terms, this
1283 leaves some type of laboratory error as the likely culprit, where
1284 laboratory error is interpreted broadly to include both the
1285 archaeological and dating laboratories.
1287 The Layer II age determinations are all older than the period during
1288 which the layer was deposited. Two of the dates on unidentified
1289 wood charcoal, Beta-20852a and GaK-1816, are about 200 years too old
1290 and, like the Layer III samples, might be reasonably interpreted as
1291 old wood. The other three age estimates, two on unidentified wood
1292 charcoal and a third on \textit{A. moluccana} nutshell, are very old
1293 for their stratigraphic positions. Although the two estimates on
1294 unidentified wood charcoal might represent rather extreme examples
1295 of in-built age, perhaps because they are pieces of driftwood, the
1296 old age estimate on the short-lived nutshell sample suggests that
1297 other factors might be active. It is tempting to suggest that all
1298 of these samples derived from Layer III, but they are each quite a
1299 bit older than the early Layer III date on \textit{D. viscosa}, so
1300 this possibility seems unlikely. One is thrown back on laboratory
1301 error or the possibility that remnants of a deposit older than Layer
1302 III exposed material that was somehow redeposited in Layer II.
1303 Although this scenario might seem rather far-fetched, it is
1304 certainly within the realm of depositional processes at this coastal
1305 location on the fringe of traditional Hawaiian settlement.
1308 LocalWords: LaTeX src ao tex noweb srcname documentclass tsdarticle Pantaleo
1309 LocalWords: maketitle uncomment altlist printglossary tsdlist hawaiian toc rc
1310 LocalWords: polynesian oldenglish addcontentsline bibliographystyle chicago
1311 LocalWords: tsd citep pearson citet tuggle kirch Spriggs hoc Hawai Waim nalo
1312 LocalWords: htb includegraphics Puh archaeol resear propos devel desilets gg
1313 LocalWords: Keolu strat mortem
1315 ** DONE Get reference for 2009 calibration curves
1316 ** The current calibration
1317 - copy of bellows region aug
1318 - note that theta numbers do not match with paper
1319 ** DONE Correct footnotes in regional 14C table
1320 ** DONE Check all date range estimates
1321 ** DONE Regenerate graphs
1322 ** DONE Add pearl shells from project 40 to the BCal analysis
1323 - 380 208588 Pteriidae shell <0.1 63040 -0.1 ad 1682–1846
1324 - 368 208587 Pteriidae shell <0.1 63040 -2.7 ad 1682–1846
1326 ** DONE Get 95% and 67% hpd regions from BCal, put them in text
1327 ** DONE Calculate 67% hpd region for interval between alpha 2 and beta 2
1328 ** DONE Check date list for 4856
1329 ** DONE Make argument for pearl shell being a suitable dating material.
1330 ** DONE Full information for Beta-200230
1333 ** DONE Reference for Kirch and McCoy's re-dating of Halawa Dune site
1335 ** DONE Spriggs and Anderson argument against Gak dates
1336 ** Renumber \theta [28/28]
1360 - [X] 44 -> 43, then added to pearl shell dates from project 40
1365 * Changes to Page Proofs
1366 ** Page 113, column a, note
1367 - change "jeffrey.pantaleo.ctr@hickam.af.mil" to "jpanta4149@aol.com"
1368 ** Page 115, Table 1
1369 - Column *j*, all numbers following thetas should be subscripts,
1370 \theta_1, \theta_2, etc.
1371 - Column head *Pj1*, the j1 should be subscript to the P, *P_{j1}*
1372 - Column head *Pj2*, the j2 should be subscript to the P, *P_{j2}*
1373 ** Page 115, column b, line 2
1374 - Change "The single sample from Layer II is wood charcoal" to "The
1375 single wood charcoal sample from Layer II is"
1376 ** Page 117, column a, inequalities (2), (3), (4), and (5)
1377 - Need subscripts for all the greek letters,
1378 e.g. \alpha 4851\geq\theta 9-11\geq\beta 4851 should be \alpha_{4851}\geq\theta_{9-11}\geq\beta_{4851}
1379 ** Page 119, column a, inequality (6)
1380 - Need subscripts, like so, \phi_2 \geq \theta_{46} \geq \phi_1