mass burial dates: what to use? r_combine, combine, sum, phase, difference?

[Ronny Friedrich]

Dear all,

we have data from a couple of mass burial sites containing

about 15 individuals each. "Deposition" time of the bones is

thought to be same for each mass burial site

All C14 dates are from bones of different individuals in each site.

How would I treat those dates in OxCal beyond simple

calibration.

Colleagues suggested using R_Combine for each mass burial site.

## My questions:

What would R-Combine, Combine, Sum etc etc mean for bone

dates?

Bone does not date the year of death but rather something between

the bone growth-period an the year of death (depending on the age that the

individuals have reached by the time of their deaths).

Combining those dates wouldn't make sense to me since they

do not date the same event, so to say.

Is sum the better way to treat the individual mass burial sites?

How would I compare different mass burial sites to each other

in terms of whether or not they are contemporary (use

"difference" in OxCal?)?

THANKS A LOT

Ronny

[Rayfo...@aol.com]

Hello Ronny,

 

When merging data, R_Combine is used when the samples are from the same radiocarbon reservoir, e.g. two samples from the same body.  The merging is carried out on the radiocarbon determination, i.e. before calibration.  Since all your dates are from different individuals, R_Combine would not be appropriate.

 

Combine is the function that merges the PDF of dates after calibration, when they are thought to be co-eval or apply to the same event.

 

At the battle of Culloden, mass graves, each of a different clan, were dug where each clan fell.  The date of all the deaths can be set to a single day (near enough), so Combine would be appropriate.  A test is made to gauge if combine is appropriate:

 

Combine()
 X2-Test: df=2 T=2.203(5% 5.991)
  68.2% probability
    433AD (29.6%) 490AD
    532AD (38.6%) 595AD
  95.4% probability
    421AD (95.4%) 622AD
 Agreement n=3 Acomb= 86.0%(An= 40.8%)

The last line gives the Acomb=  index which, if acceptable, should be greater than the An= figure.

 

Alternatively a single bounded Phase would be used for each mass burial, the assumption being that all in a grave died and were buried at the same time.

 

If there was evidence that the deaths were not co-eval  with the deposition in the grave but interred sometime later (perhaps curation of the bones) then a bounded Phase would bracket the deaths but not the deposition.

 

Sum does not result in a PDF.

 

Difference can be used to compare the Boundaries of the phases of the two sites or the Order function, or, since you have a full set of dates, then First and Last in each mass grave may be used to compare.

 

It depends on the premises you make (and declare).  Change the premise and the model changes.

 

A further consideration in a mass death situation might be that some members came from further afield and may have a dietary difference requiring marine curve offsets.  Just a thought.

 

I hope this helps,

 

regards

 

Ray

 

 

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[Yannis Maniatis]

Dear Ray, and all,

There was a secondary question in Ronny’s e-mail which is also my question and this is why I intervene.

That is, if there is a way to treat with OxCal human bone dates which do not necessarily reflect the date of death but probably something between

the bone growth-period and the year of death, relating also to the age of each individual at death.

 

Any advice will be very welcome,

 

With many thanks,

 

Yannis  

[Rayfo...@aol.com]

Hello Yannis,

 

There must be some way of quantifying the claimed "dates which do not necessarily reflect the date of death but probably something between the bone growth period and the date of death" on an individual basis.

 

Although I've come across the concern, it is not my field and I'd welcome a link to the subject in more detail, in particular some indication of the magnitude of the effect.  If it is of major concern, perhaps some manipulation of the R_Date uncertainty might be the way to deal with it, though the experts will be better placed to comment.

 

Do you have in mind a chart of Age vs Radiocarbon offset?  That could be tricky. as providing age at death can be difficult depending on the sample and the circumstance.

 

I tried to cover it with my comment on premises.  You could have a model using the Radiocarbon determinations and one with whatever the basis of your offset(s) and check the sensitivity of the model to the different premises.

 

The Radiocarbon determination is not a date, increasing the uncertainty will increase the calibrated calendar date uncertainty.  If the offset is large it may render the exercise worthless as a calibrated date.  Much depends on the model you choose and how you defend it.  It is largely a heuristic exercise.

 

Best wishes

 

Ray

[Yannis Maniatis]

Hello Ray,

Thank you for your answer. I have not made much study of this effect myself but I have read some papers and the effect depending on the age at death could be from 10 to 30 years for ages between 30-60 years.

 

Can you explain please how we use in practice the premises.

 

Best wishes,

[Rayfo...@aol.com]

Hi Yannis

 

R_Date(2000,20)+N(10,5) would offset a radiocarbon determination by a Normal uncertainty with mean 10 years and sd 5 years.It would be for the modeller to defend the logic of the N(X,Y) offset and presumably this would be different for each death?  So on your figures it could be as much as N(30,10)Perhaps a mass death event would be mainly young warriors thus below age 30?.......Here is an example where I've put four R_dates, all the same, but added various offsets. Plot()
 {
  Sequence()
  {
   Boundary("Start 1");
   Phase("1")
   {
    R_Date("NoOffset", 3600, 25);
    R_Date("OffsetA", 3600, 25)+N(10,10);
    R_Date("OffsetB", 3600, 25)+N(20,10);
    R_Date("OffsetC", 3600, 25)+N(30,10);
   };
   Boundary("End 1");
  };
 };The resulting output when rounded to 10 years as often suggested, has little to no effect.  Even without rounding,  the dates vary by only a couple of years, probably lost in the MCMC noise.best wishesRay

[Yannis Maniatis]

Dear Ray,

That is clearly understood.

I will try it with some real dates to see the effect.

 

Thank you very much, I am much obliged!

[Ronny Friedrich]

Thanks everybody for pointing me into those directions.

Regarding the bone collagen dates...

There are a couple of nice papers describing the meaning

of bone dates and that they do not date the year of death.

Barta, 2007, Radiocarbon, Vol. 49

Betina Dinner did some work on bone collagen dates of modern bones

etc

I think it is intuitively clear that bones cannot date the year of death.

Bone growth happens in the first 19 years and this is when most of the

carbon is incorporated into the bone structure.

Thereafter, carbon exchanges with a rate of a few percent per year.

Basically, bone at the time of death has a lot of older carbon stored in it

from many years before.

With more and more precise AMS data available that offset is starting to

show.

I'm under the impression that this effect is almost unknown with archaeologist.

What is your experience?

[Rayfo...@aol.com]

Hi Ronny,

 

Thanks for the link to Barta.

 

On your query of:

"I'm under the impression that this effect is almost unknown with archaeologist.

What is your experience?"

 

Truth be known, for many, Bayesian modelling of archaeological data itself has a long way to go, so I suspect the question of Human Bone Collagen Offset will make the eyes roll even further.....

 

From the OxCal manual:

 

Delta_R([Name], Shift/Expression, [Uncertainty]);

• defines the shift that is to be applied to dates before calibration; applies to the current Curve; if required a non-Normal prior can be applied to this parameter using the expression but this will only have an effect on MCMC models, for straight calibrations the mean and standard deviation of the distribution will be used.

So the Delta R offset as suggested in the Barta Paper would not apply to straight calibrations.  In a MCMC model scenario each R_Date would need a unique Delta R expression.

 

I'm also not sure of the validity of comparing a 68.2% probability (model A) with a 95.4% probability (model B).  As far as I know a Normal distribution is a Normal distribution, specified by Mu and 1sd irrespective of whether you 'look at'  the 1sd range or  the 2sd range or the 3sd range.  If you sample a restricted range (model A) then little wonder it fails a test for normality.

 

But I need to read more.

 

best wishes

 

Ray

 

 

 

--

[MILLARD, ANDREW R.]

As others have said, R_combine is not appropriate unless the samples are of the same calendar age and reservoir.

An age offset can be used as a simple correction between mean age of formation and age-at-death in human bone collagen.

Alternatively, one can use the Reservoir command which accounts explicitly for bone turnover and the time averaging of the calibration curve produced by that. This is probably more appropriate for older adults where the bone is integrating over several decades with a turnover rate that does not vary very much.

You may also need a marine reservoir correction specific to each individual.

Having allowed for turnover or offset and marine corrections, it would then be appropriate to use Combine on the dates.

An alternative, and simpler, approach would be to use a phase with a Tau_Boundary. This allows for an exponential distribution of events leading up to the boundary. If the turnover rate of all the bones used is broadly comparable this will probably work just as well.

For our Scottish Soldiers project I used an age offset based on published data for the age of bone in adolescents of a specific age-at-death. See the page 5 of the chronology report linked at https://www.dur.ac.uk/archaeology/research/projects/europe/pg-skeletons/acadpapers/.

Having said all that, the exact place on the calibration curve and the precision of your radiocarbon determinations will also be critical in determining whether the corrections make any difference whatsoever. In some places on the curve you may simply not be able to resolve the date better than a century or two.

Having calculated dates for the two events, then Difference is the way to examine contemporaneity.

Best wishes

Andrew
--
 Dr. Andrew Millard 
e: A.R.M...@durham.ac.uk | t: +44 191 334 1147
 w: https://www.dur.ac.uk/archaeology/staff/?id=160
https://www.dur.ac.uk/imems/
Director of the Institute of Medieval &
Early Modern Studies, and
 Senior Lecturer in Archaeology,
Durham University, UK

> -----Original Message-----
> From: ox...@googlegroups.com [mailto:ox...@googlegroups.com] On Behalf
> Of Ronny Friedrich
> Sent: 31 January 2017 08:26
> To: OxCal <ox...@googlegroups.com>
> Subject: mass burial dates: what to use? r_combine, combine, sum,
> phase, difference?
>

[Rayfo...@aol.com]

Hello Andrew,

 

Thanks for putting that link to the Scottish Soldiers Project.  I found the various models are a very useful example of the alternative considerations that can be applied.

 

I have one question, if you will indulge me?

 

When you include the SK9 and SK16 dates in the D Sequence, how do you decide that they follow all the other dates sequentially?  They both end with poor Individual indices (I do understand that this can be ignored in the outlier models).

 

I tried instead to deal with the offsets by adding N(5,2) and N(4,2) to the R_Dates and moving them to the start of the D_Sequence without gaps.  Perhaps they should ,in that scenario, be outside the D_Sequence.

 

However the upshot gives date of deaths:

 

 

The Amodel index for Model 1A is 112.

 

The code I used is below, only as an illustration of my question

 

 Options()
 {
  Resolution=1;
  kIterations=200;
 };
 Plot()
 {
  Curve("IntCal13","IntCal13.14c");
  Curve("Marine13","Marine13.14c");
  // Delta_R for the eastern coast of Scotland of -62+/-53 (Russell et al., 2011, J Arch Sci 38:1008 1015).
  Delta_R("LocalMarine",-62,53);
  sequence( )
  {
   c_date(1612);
   Date("deaths");
   c_date(1754);
  };
  D_Sequence("PGL13")
  {
   Mix_Curves("Mix SK9","IntCal13","LocalMarine",7.0,10);
   R_Date("SK9", 389, 30)+N(5,2);
   Mix_Curves("Mix SK16","IntCal13","LocalMarine",4.7,10);
   R_Date("SK16", 397, 30)+N(4,2);
   Mix_Curves("Mix SK21 LRM1","IntCal13","LocalMarine",9.3,10);
   R_Date("SK21 LRM1 formed age 5", 298, 30);
   Gap(2);
   Mix_Curves("Mix SK12 LLM1","IntCal13","LocalMarine",11.6,10);
   R_Date("SK12 LLM1 formed age 5", 358, 30);
   Gap(8);
   Mix_Curves("Mix SK21 LRM3","IntCal13","LocalMarine",11.6,10);
   R_Date("SK21 LRM3 formed age 15", 292, 27);
   Gap(2);
   Mix_Curves("Mix SK12 LLM3","IntCal13","LocalMarine",17.3,10);
   R_Date("SK12 LLM3 formed age 15", 358, 28);
   Gap(1);
   Date("=deaths");
  };
 };

Best wishes

 

Ray

[Bayliss, Alex]

Hi Ronny,

Generally, I think there are several factors confounding accuracy here.

1) You need to assess diet so you can construct a mixture model of the different reservoirs in each individuals. I tend to do this using a FRUITS model of the stable isotopes, and then the Mix_Curves function of OxCal. Andrew's example gives a helpful look at the code. But doing this three-way if you have freshwater, marine, & terrestrial food sources is complicated (I think if you looked back, Chris, provided advice on how to work this out and program it in OxCal a couple of years ago). And, of course, you need to know the radiocarbon age of the reservoirs (which are often very poorly known).

2) Then there is collagen turnover. The best data I know of for this is Hedges et al. 2007, American Journal of
Physical Anthropology 133, 808–16. I thought about this in the Saxons project (see attached pp58-9), but didn't do anything to incorporate it in the model. I think either of the methods suggested by Ray or Andrew would work. But don't forget that archaeological methods of aging adult individuals are in need of improvement! Is the work by Betina Dinner published?

3) Then there is the fact that generally you will be working with a calibration curve that is interpolated at 5 years from data that is measured on decadal or even bi-decadal samples (unless you are working after AD 1542). So, all this sophistication is probably in danger of out running the basic science that underpins everything.

Elephant traps at every stage... Good luck!!

Alex





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[Rayfo...@aol.com]

Hello,

 

having now read the Barta 2007 and the Geyh 2001 papers I think I was wrong to suggest the offset method of

 

    R_Date("OffsetA", 3600, 25)+N(10,10);

The above papers are clear that the offset is in the 14C domain so require the use of Delta_R offsets e.g.

 

  Delta_R("M2B", 27, 4);
  R_Date("Hd11855M2B", 3600, 25);

 

This would be more appropriate when following the Barta method.

 

Here is a calibration using a wiggle free curve that shows the offset in the 14C domain.  Using the offset in the calendar domain produces a different result that depends on the slope of the curve at that point. For example the offsets in the 14C domain for the curve shown requires the corresponding Calendar offsets to achieve the same result.  This relationship changes with the slope of the curve.

 

Offsets in 14C and Calendar domains to give the same result: (changes depending on the slope)

 

14C domain	Calendar
0	0
6	4
14	10
21	16
27	20
33	25

 

Having said that, Alex and Andrew rightly point out the many pitfalls.  I just wonder what happens when it comes to comparing models that include the offsets and those that don't, or models that have some dates with offsets and others without.

 

By the way, if anyone would like the wiggle free curve StraightLineMod2.14c file, let me know.  I find it useful when toying with scenarios.

 

regards

 

Ray

 

In a message dated 01/02/2017 15:38:42 GMT Standard Time, y.man...@inn.demokritos.gr writes:

Dear Ray,

That is clearly understood.

Best wishes

 

Ray

 

In a message dated 01/02/2017 12:37:28 GMT Standard Time, y.man...@inn.demokritos.gr writes:

Ray

[MILLARD, ANDREW R.]

> From: Rayfoskidd via OxCal [mailto:ox...@googlegroups.com]

> Sent: 06 February 2017 17:48

> To: ox...@googlegroups.com
> Subject: Re: mass burial dates: what to use? r_combine, combine, sum,
> phase, difference?
>

> having now read the Barta 2007 and the Geyh 2001 papers I think I was
> wrong to suggest the offset method of
>
> R_Date("OffsetA", 3600, 25)+N(10,10);
>
> The above papers are clear that the offset is in the 14C domain so
> require the use of Delta_R offsets e.g.
>
> Delta_R("M2B", 27, 4);
> R_Date("Hd11855M2B", 3600, 25);

I've revisited these papers and I think they are wrong to advocate a 14C domain correction.

First, I see no reason how a biological turnover process can give a specific change in 14C content, independent of the calibration curve. The amount of 14C available to be incorporated in the bone is the key thing, and in a terrestrial situation that is atmospheric 14C which we know varies with age-since-birth differently for individuals born in different years. Geyh's Figure 1 exemplifies this by effectively calculating a different calibration curve for different birth years, based on a turnover model. If the offset was in the 14C scale this would be unnecessary because only the atmospheric 14C at the date of death, the age-at-death, and the 14C content of his samples would be relevant to construct Figure 2.

Second, although Geyh 2001 calculates the correction in calendar years, he then inexplicably describes it in the text as a correction to conventional 14C ages. Note how the units of the x- and y-axes in his figure 2 are "yr" - which is correct because he calculated the calendar offset between age-at-death and the mean age of bone formation and compared it with age-at-death. But when that figure is reproduced as Barta's Figure 1 the y-axis units have become "14C years", which is incorrect.

[Rayfo...@aol.com]

Hello Andrew,

 

A puzzle to be sure! And well above my pay grade!  (zero per annum).  However, I am keen as always to learn.

 

I agree that Geyh's figure 1 has (yr) in both axes.  However the caption of fig 2. has:

 

Correction term E

"

corr

for conventional

14

C ages of human bone collagen as a function of the age

t at death of the individual and different carbon exchange rates. The most common one is 1.5%

Correction term Ecorr for conventional 14C ages of human bone collagen as a function of the age ' t ' at death of the individual and different carbon exchange rates.  The most common on is 1.5%"

 

Then from the body of the text:(included in case others are following the discussion)

 

"Implications for the common 14C dating of Human Bone Collagen

 

"

Implications for the Common

14

C Dating of Human Bone Collagen

The confirmation that the main uptake of carbon in bone collagen ceases at 19 years and the subse-

quent carbon exchange occurs at a low rate of about 1.5% affects the conventional

14

C dating of bone

collagen. Any conventional

14

C age t of human bone collagen has to be corrected to take into

account the fact that the main

14

C uptake ceases in the adult human. The correction term E

corr

depends on the age t

life

of the individual at death. The real

14

C age t

real

is obtained from t

real

= t −

E

corr

. This correction is important for dating historic events related to dated bones. Figure 2 shows,

for example, that 32 years have to be subtracted from the

14

C age of bone collagen of an individual

The confirmation that the main uptake of carbon in bone collagen ceases at 19 years and the subsequent carbon exchange occurs at a low rate of about 1.5% affects the conventional 14C dating of bone collagen.  Any conventional 14C age 't' of human bone collagen has to be corrected to take into account the fact that the main 14C uptake ceases in the adult human.  The correction term 'Ecorr' depends on the age 'tlife' of the individual at death.  The real 14C age 'treal' is obtained from 'treal' = 't'  -  'Ecorr'.  This correction is important for dating historic events related to dated bones.  Fig 2 shows, for example, that 32 years have to be subtracted from the 14C age of bone collagen of an individual who was 65 years old at the time of death."

 

My reading of that, is that the correction is in the 14C domain. i.e. 't',  Ecorr, 'treal' all pertain to the 14C age.  I think that Geyh's error was in the y axis of fig 2 where he used the term correction E(yr) when he should have made clear it was 14C yr as made explicit in his caption and the following text and as followed by Barta 2007 fig 1 and 2.

 

In Barta 2007 (Abstract) he says "The eventual impact of the HBCO correction on archaeological chronology depends on the portion of the calibration curve through which the HBCO-corrected date is calibrated.  At a certain level of 14C measurement precision, the difference between the HBCO-corrected and non corrected calendar dates can be considerable."

 

I read this as meaning the 14C determination (R_Date) and the HBCO correction are applied prior to calibration.

 

However, as I said, it is well above my pay grade.

 

I also wonder about the applicability of an analysis of Bomb period data being extrapolated to times of less 14C intensity.  Is there a paper that addresses this or is it somehow expected to hold?

 

Best wishes

 

Ray

 

[Rayfo...@aol.com]

Hi,

 

Perhaps we need clarification from the originators of the Correction Ecorr charts to determine if it was intended as a 14C yr correction or a calendar year correction.

 

However, irrespective of the outcome, should the offset not also include the uncertainty created from the  different exchange rates displayed in the chart?.

 

Geyh and Barta show that the uncertainty of the age at death (assumed Gaussian) results in a distorted offset in the Ecorr  axis.  However this distortion is only a result of the shape of the exchange rate curve which is assumed to be 'most common' of 1.5%

 

There is a further uncertainty implicit in the family of curves 0%,1%,1.5%, 2%, 3%, of the exchange rate.

 

Below I've added to the Geyh chart fig 2 offsets that would result from a single age of 65 years with no uncertainty in the calendar scale. 

 

On the 1.5% curve 65 yr maps to offset Ecorr 34yr.

 

On the 1%-2% curves 65yr maps to Ecorr 30 to 47 yr.

 

On the 0%-3% curves 65 yr maps to Ecorr 24 to 46 yr.

 

This would be added to the uncertainty in the age at death uncertainty.

 

If the age at death uncertainty at 1 standard deviation (sd) was say 2.5 years, the Ecorr uncertainty from the  2sd  spread of 60 to 70 years could be as much as 20 to 50 years using the 0% to 3% C exchange rate curves.

 

Is there not a case in this example for using the Uniform uncertainty to avoid over precision, e.g.

 

 Delta_R (U(20,50)); R_Date (xyz)

 

or R_Date (xyz,) +U(20,50)

 

 depending on whether the correct offset is in the 14C domain or calendar domain.

 

It is not clear in the papers when the term Standard Error is used, that Standard deviation is meant.

 

regards

 

Ray