Tangatatau Rockshelter

With apologies to Durrell, Zarian and the Count continue their conversation. Zarian has found an archaeology book that fascinates him, and he is eager to share it with his friend.

Zarian

I’ve brought this archaeology book with me that might interest you. It’s called Tangatatau Rockshelter: The Evolution of an Eastern Polynesian Socio-Ecosystem.

Count

Eastern Polynesia seems remote. What caught your attention?

Zarian

The Taŋatatau rockshelter is on an island named Maŋaia that is isolated and impoverished. The author has written quite a bit about Maŋaia, where he believes the social situation devolved to the point that competition for land among warriors filled the people with terror.

Count

That is surprising. The Polynesian people were among the great social organizers of their day. They designed and built the finest sailing vessels known at the time, trained crews to sail them on months long voyages, and completed modern humanity’s conquest of the Earth by discovering and settling virtually all the small islands in the vast Eastern Pacific, an area about a third of the globe’s surface. Perhaps the modern adventure that compares to this achievement is the Apollo space program organized by NASA in the US. Tell me, what does the Taŋatatau rockshelter have to do with the devolution of social organization and the terror that supposedly followed?

Zarian

(Flipping through the pages of the book) Here it is, Figure 4.8. Look at the stratification at the top of the Taŋatatau rockshelter deposit!

Count

Impressive. The top of the section looks like filo pastry from the bakery!

Zarian

Yes, that’s it. Those thin deposits at the top hold out the promise of equally fine divisions of time, and they contrast with the massive cultural deposit nearer the base. The rockshelter has been the subject of an extensive dating program; there are 71 ¹⁴C age estimates so far. The Maŋaian descent to terror ought to be exposed in exquisite detail in the fine layers at the top of the sequence.

Count

Well, I hope a chronicle of terror’s onset is a good thing. Have you studied the chronology yet? Does the stratigraphic information combined with the ¹⁴C age estimates yield a finely divided sequence? It certainly seems possible.

Zarian

Why, yes, I’ve studied the chronology closely but my study’s left me confused. I was hoping you might help.

Count

How’s that?

Zarian

I was prepared to believe the Bayesian calibration results presented in the book when I ran across a recent paper by the author and two of his colleagues that appears to throw cold seawater on the book.

Count

Bayesian calibration in the Pacific? It’s a pleasant surprise to learn the Bayesian practice is diffusing out of its Old World homeland. I hope it succeeds as splendidly as those early Polynesian seafarers! But, what’s this about seawater on the book? You lost me there.

Zarian

The recent paper reports 25 ²³⁰Th age estimates for coral artifacts recovered during excavation of the rockshelter. Many of the ²³⁰Th age estimates are extremely precise. The problem is they are a bit older than the Bayesian ¹⁴C results expect.

Count

Is that a problem?

Zarian

The author thinks so. He claims the results cast doubt on the Bayesian approach. Bayesian calibration supposedly has a “younging effect” when imprecise age estimates are used as data.

Count

What effect did the ²³⁰Th age estimates have on the model results?

Zarian

That’s what has me confused. I should have thought the Bayesian model would be augmented with the ²³⁰Th age estimates. Instead, the authors present the ²³⁰Th and ¹⁴C results separately and compare them. In their view, the ¹⁴C results suffer in the comparison because many of them are less precise than many of the ²³⁰Th age estimates.

Count

Ah, then you want my help with a new calibration that includes ¹⁴C and ²³⁰Th age estimates?

Zarian

Yes, that would be splendid. Did you get OxCal running again?

Count

I did. The new NodeServer.js interface to Firefox works a charm. Is the Taŋatatau model available digitally?

Zarian

I don’t think so. The Bayesian calibration reported in the book was carried out with BCal, which works without a user-accessible input file.

Count

Then how shall we model the calibration?

Zarian

(Flipping through the book again) Ah, here it is. Figure 5.5 is described as a “[s]chematic representation of the Bayesian calibration model for radiocarbon dates from the main excavation block.” Will that suffice?

Count

I believe we can make that work. I see the author has established ten phases, each labeled with a code prefixed with “SZ”. The phases are in two lines, a long one that runs from SZ-1A to SZ-15, and a short one that runs from SZ-9 to SZ-17. Are you satisfied with the phasing of all those thin deposits?

Zarian

To be honest, I’m a bit confused by the phasing. The excavations at Taŋatatau might have been the first in the Pacific to use the Harris Matrix, albeit in modified form.

Count

What is SZ then?

Zarian

It’s an acronym for “stratigraphic zone”.

Count

My dear Zarian, the word “zone” doesn’t appear in the “Glossary of terms used in archaeological stratigraphy” in Harris’ wonderful little book Principles of Archaeological Stratigraphy. I would have expected either “period” or “phase.”

Zarian

If I understand correctly, each stratigraphic zone comprises one or more “beds.”

Count

“Beds,” you say? Hmm, another term absent from Harris’ glossary. Were these “beds” the collection units used by the excavators?

Zarian

No, the collection units were the “levels” of each 1 m² excavation unit.

Count

(exasperated) Are the contexts identified anywhere? Surely, one can’t have a Harris Matrix without the units of stratification archaeologists typically call contexts?

Zarian

It says here on page 45 that “the term level thus approximates what some users of the Harris Matrix recording system refer to as an ‘excavation context’ …” and that “one or more levels in a unit typically correspond to the beds recorded in the stratigraphic sections.”

Count

I can see why you’re confused. The Harris Matrix was designed, in part, to ameliorate problems indicated by vague words like “typically” and “approximates.” We’d best not go down this rabbit hole.

Zarian

Agreed. Can we also agree that the stratigraphic zones represent an experienced excavator’s impression of the stratification and proceed on that basis?

Count

By all means, let’s take the excavator’s word as an hypothesis susceptible to testing. Before we start the calibration, though, you must promise me you’ll help with data entry. I don’t have the energy to input 71 ¹⁴C and 25 ²³⁰Th dates.

Zarian

I’m happy to help with data entry. I’m even happier to report that there are 38 ¹⁴C dates to enter, not 71.

Count

Why only 38 ¹⁴C dates?

Zarian

The author practices “chronometric hygiene.” ¹⁴C dates processed early in the dating program didn’t identify the wood charcoal and many of the standard errors are large, so the author chose to exclude them. He also excluded two recent high-precision age estimates on nutshells that appear to be residual outliers.

Count

Well-meaning mistakes, I’m certain. Nevertheless, the lack of wood charcoal identifications merely raises the potential for old wood, it doesn’t guarantee the unidentified charcoal is from old wood. Many of the excluded ¹⁴C dates might carry information about the Taŋatatau sequence.

Zarian

But the chronometric hygiene protocol tags the unidentified wood charcoal for exclusion!

Count

You might think of that as “the nuclear option,” my dear Zarian. Nowadays, the modeling facilities implemented by OxCal are up to the task of handling the potential for old wood. Best practice identifies outliers during a calibration, which BCal and Oxcal will do quite happily.

Zarian

My dear Count, you make the model sound magical. I’d much rather ignore obviously bad data, than have it dog an analysis through to the end.

Count

Perhaps I can convince you otherwise. Shall we calibrate?

Zarian

Have it your way. You’ll forgive me for being skeptical.

Count

I’ve named the first calibration tangatatau_1. It has 14 phases, 63 ¹⁴C age estimates, and 25 ²³⁰Th age estimates.

Zarian

Why so many phases? The model in the book has ten.

Count

The four additional phases represent contexts whose dated events were scrubbed away by the hygienist and not re-dated. When we added the age estimates from the unidentified charcoal, we had to add phases to accommodate them.

Zarian

What do the results look like? Are they closer to the Bayesian results from the book or the ²³⁰Th dates from the recent paper?

Count

Neither. There is an absolute lack of fit between the model and the data. Two OxCal measures of this fit are A_model and A_overall. The OxCal manual recommends values of both A statistics greater than 60% for a good fit. The values of the A statistics for tangatatau_1 are both 0%.

Zarian

This isn’t doing much to cure my skepticism.

Count

Stay with me. OxCal has flagged five age determinations as outliers. The second calibration, tangatatau_2, removes them from the model, leaving 58 ¹⁴C age determinations.

Zarian

Hopefully, this improves matters.

Count

Not yet. The values for the A statistics yielded by tangatatau_2 are still 0%.

Zarian

My dear Count, all those bad data are dogging you unmercifully!

Count

Perhaps you’re right. The third calibration, tangatatau_3, removes the seven age estimates on bad corals, those identified in the recent paper as having a ²³⁰Th/²³²Th ratio < 10. This is justified because the dating program was experimental and the bad corals yielded systematically older dates than the good corals, which suggests there was a problem determining their ages.

Zarian

Is your best practice making any progress?

Count

I’m afraid not. The values of the A statistics appear stuck on 0%.

Zarian

Now, Count, you know I’m a man who seeks out best practice and strives to implement it at every turn. Please, while the evening is still young, let’s see what happens when we add the good coral dates to the model from the book. Starting from a solid base might help us find success.

Count

As you wish. First, we’ll measure the solid base. The fourth calibration, tangatatau_4, attempts to replicate in OxCal the model published in Tangatatau Rockshelter, which was calibrated with BCal. The model and data fit quite nicely. The values of the A statistics are both greater than 70%. The results match nicely with the published results in the lower part of the sequence, but there are some differences near the top that suggest our model constraints might not match the constraints of the published model.

Zarian

The base seems solid enough, don’t you think?

Count

Yes, it is nice to see the A statistics get up off the floor. Nevertheless, I’m concerned we had to ignore so many age determinations to get here. The tangatatau_4 calibration succeeds because it leaves 33 age determinations and 4 phases on the sidelines.

Zarian

Why won’t you acknowledge that data might be bad and leave it at that?

Count

(sighing) Now you are suggesting that I find peace of mind by treating the model as if it were not a fallible product of our own minds. Let’s see if our solid base supports the ²³⁰Th age estimates for the good coral artifacts, shall we?

Zarian

Yes, at last!

Count

My dear Zarian, look at the results of the tangatatau_5 calibration. The A statistics have fallen to percentages in the mid twenties, well below the recommended threshold of 60%. The base has crumbled under the weight of the new observations.

Zarian

There must be some bad data among the ²³⁰Th age determinations.

Count

OxCal has flagged five of the ²³⁰Th age determinations as outliers. More than a quarter of the ²³⁰Th age determinations don’t fit the model.

Zarian

Are we faced with the choice of rejecting ²³⁰Th dates until the A statistics top 60%, or rejecting all of the ¹⁴C evidence as the recent paper appears to suggest?

Count

Only if you are unwilling to question the model. Another possibility treats the model as an hypothesis susceptible to testing. If we take that approach, then the lack of fit between model and data suggests the hypothesis isn’t true.

Zarian

But aren’t all models false in some sense?

Count

Why, yes they are. Perhaps a better way to think about it is the bad fit indicates the model isn’t particularly useful because it fails to explain so many observations.

Zarian

So, we should be looking for a model that explains as many of our observations as possible?

Count

That would be my preference. Are you ready to take another look at the model?

Zarian

Yes.

Count

May I have the book, please? Here, take a look at Table 5.6 on p. 88. The table presents elapsed time estimates for each of the model’s ten phases. Do you see a pattern?

Zarian

Yes, I do. The phases at the top of the sequence, from SZ-3 on up to SZ-17, might have no duration whatsoever. The low range of each estimate is 0.

Count

The top of the sequence is where the thin deposits remind one of filo pastry. Correct?

Zarian

Yes, that’s right. It makes sense that those thin deposits represent short intervals.

Count

It makes less sense when you consider that a stratigraphic zone near the top takes in several thin deposits. But that’s not the the line of argument I wish to take. Instead, I’d like to propose that the stratigraphic zones that might have no duration are indicating where the model is implausible.

Zarian

How’s that?

Count

Take another look at the multiplot of the tangatatau_1 calibration, which includes all of the age determinations. Look especially at the spread of age determinations within each of the stratigraphic zones from SZ-3 on up.

Zarian

Why, with small variations, they are virtually identical to one another!

Count

That’s right. It’s almost as if they were interchangeable. Yet, the chronological model insists it is possible to discriminate among several zones and to order them by time. Perhaps the age determinations are trying to tell us a different story?

Zarian

What story might that be?

Count

That many of the thin deposits near the top of the sequence are secondary deposits of materials that originated elsewhere in the sequence. Is there evidence for pit features and the like that might plausibly account for so many secondary deposits?

Zarian

Why, maybe so. The author indicates that 59 pits were designated as features F1 through F59.

Count

Were the 59 pit features identified during excavation and collected separately?

Zarian

Maybe not. Fifteen “principal features” of the fifty nine show up on the Figure 4.20 sequence diagram on page 69. These are the same features that appear in the Appendix of collection units.

Count

Presumably, the other 44 features were not collected separately, but their materials were collected with other materials at the same depth. If so, this would be a recipe for collecting mixed materials.

Zarian

The book refers me to an online database for that information, but the link is broken. I queried the webmaster and received a nice response that I would be notified when the link was fixed.

Count

That’s not much help to us now. Perhaps the other features show up on section drawings?

Zarian

I can find eight of them on the section drawings, which also show pit features identified as postholes, but which don’t have F numbers.

Count

Wait a second. Can you turn back to Figure 4.12 on page 58, please? Yes, that’s it. Look at SZ-4A. The profile of grid units F30 and G30 shows SZ-4A cutting through at least 3 beds, and completely through SZ-3 and well into SZ-1B. In grid unit D30, SZ-4A again cuts through SZ-3 and into SZ-1B. Much the same thing is shown for grid unit C30.

Zarian

Yes, I see that. On this profile drawing, SZ-4A looks for all the world like three separate large pits. Harris would likely call the edges of these pits vertical feature interfaces. The glossary in his book defines a vertical feature interface like this: “[u]sually referred to as a feature, this unit marks a distinct event, such as the digging of a pit, and results in the destruction of pre-existing stratification.”

Count

To which one might add “and distribution of the excavated sediments on the surface around the pit.”

Zarian

Given these observations, your “secondary deposits” model seems plausible. I don’t recall any information that would disqualify it.

Count

Let’s take a look then. The three phase model used by the tangatatau_6 calibration is capable of handling the great majority of ¹⁴C and ²³⁰Th age estimates because it places the upper portion of the sequence in a single phase. Phase I comprises the pre-human deposit, SZ-1A; Phase II comprises the early cultural deposits SZ-1B and -2; and Phase III comprises the rest of the later cultural deposits, including SZ-3, -4a, -5, -6 and 7, -8, -9, -13, -15, and -17, along with Features F5 and F37. The A statistics reported by OxCal are quite good; A_model is 89.2% and A_overall is 85%. In addition, OxCal doesn’t flag any outliers.

Zarian

The model makes a big difference!

Count

Yes it does. Our results so far indicate that the “younging effect” broached in the recent paper was produced by an over-determined model, one that attempted to impose order on a well-mixed deposit. Given the choice between narrowing observations to a small set that supports a complex model, or simplifying the model to accommodate observed variability, an experienced model builder most often turns to the latter.

Zarian

Finding a model capable of accommodating most of the observations does bring peace of mind, but it seems to require a lot of thought and a bit of intuition.

Count

Experience building models is one way to develop what you call intuition. Alex Bayliss in Great Britain has probably built more chronological models than any other archaeologist, living or dead. She recently published a paper that sets out some best practices. Another paper, by Caitlin Buck and Bo Meson, suggests that good Bayesians develop several models for each calibration to determine whether or not model components are misbehaving.

Zarian

As with other habits, modeling practice appears to make the master.

Count

I’m afraid so. But I’m curious about the larger issue: Has our chronological modeling and calibration changed your ideas about how and why declining social organization led to terror on Maŋaia?

Zarian

I’m not sure what to make of that now, although the three phase model does make sense of the difficulty analysts have had finding consistent trends over time at Taŋatatau. Trends would be obscured by the mixed stratification our analyses seem to indicate, don’t you think?

Count

That, my dear Zarian, is a topic for another day. Right now, let’s enjoy our new-found peace of mind.