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I agree Greg, a simple linear relationship does not work. Human
osteologists have long known this of course. For zooarchaeological examples
see the work of Foss Leach and his colleagues on New Zealand fish species,
e.g.,

http://www.tepapa.govt.nz/ResearchAtTePapa/ResearchAndMuseumPapers/Pages/Tuhinga3.aspx

http://www.tepapa.govt.nz/ResearchAtTePapa/ResearchAndMuseumPapers/Pages/Tuhinga12.aspx

http://www.tepapa.govt.nz/ResearchAtTePapa/ResearchAndMuseumPapers/Pages/Tuhinga6.aspx

http://www.tepapa.govt.nz/ResearchAtTePapa/ResearchAndMuseumPapers/Pages/Tuhinga7.aspx



and for an application of their method ,e.g.,

International Journal of Osteoarchaeology 11:150-162



The problem then becomes one of regional variation., I have measured
snapper maxilla from further north than the population sampled by Leach and
found that a  significant proportion have a bony spur on one of the
measurement points of the maxilla.

A similar problem will arise for different breeds of cattle, as an example.

Nothing is ever simple, that’s why it’s fun

Mat





*From:* Analysis of animal remains from archaeological sites [mailto:
[log in to unmask]] *On Behalf Of *GREG CAMPBELL
*Sent:* Friday, 1 November 2013 12:08 a.m.
*To:* [log in to unmask]
*Subject:* [ZOOARCH] Size prediction formulae



Predicting original sizes of animals from the parts that survive
archaeologically is a daily task for archaeozoologists.  It’s not
inherently bad that most of the formulae we use are three, four or five
generations old.  What can be bad about the formulae is that they assume
shape is constant regardless of size.  For example, if you calculate
shoulder height by multiplying humerus length by some number, you  are
assuming that number (the proportion of shoulder height to humerus length)
is constant for all shoulder heights.  This is bad because that proportions
is almost never constant; we all know from experience that animal shape is
not constant, it varies with size (the calf is not the same build as the
cow, the foal is not the same build as the horse, etc.).  So most animals
change shape as they change size: they exhibit allometric growth.  So
insisting on simple proportions won't work well.

Also, there are large numbers of dimensions that can be measured on
an animal's bones, or even on a particular bone, so it is difficult to know
which dimension is the best predictor of size, and whether using more than
one dimension would give better predictions.

This has been a concern of mine for over a decade.  I have recently
published a paper on how to derive accurate size reconstruction formulae
from surviving dimensions in an archaeologically important but
badly-preserved animal:

Campbell, G.E. (2013): Size prediction in archaeomalacology: the Common
Mussel, *Mytilus edulis* L., as an example.  *Archaeological and
Anthropological Sciences*. doi: 10.1007/s12520-013-0155-2

The technique incorporates the most common form of allometric growth, it
uses standard statistical software, and it weeds out the dimensions that
are not good predictors, leaving the ones that are. It does deal with a
marine shell, and it is rude to recommend one’s own paper, but I feel the
technique should be applied more widely, or at least debated by the wider
zooarch community.

I look forward to your comments.

Greg Campbell

The Naïve Chemist



PS: despite my previous rants about lack of open-access, the editors at AAS
did work hard to produce the paper, and therefore I will not be handing out
free .pdf copies, at least not until a decent interval has passed.