Archaeologists have long had a problem with dating. The radiocarbon analysis typically used to reconstruct past human demographic changes relies on a method easily skewed by radiocarbon calibration curves and measurement uncertainty. And there has never been a statistical solution that works – until now.
“No one has systematically explored the problem, or shown how you can treat it statistically,” says Michael Price, applied complexity researcher at SFI, lead author of an article in the Journal of Archaeological Sciences about a new method he developed to summarize sets of radiocarbon dates. “It’s really exciting to see how this work came to be. We identified a fundamental problem and solved it.
In recent decades, archaeologists have increasingly relied on sets of radiocarbon dates to reconstruct past population size through an approach called “dates as data”. The basic assumption is that the number of radiocarbon samples in a given time period is proportional to the size of the region’s population at that time. Archaeologists have traditionally used “summed probability densities,” or SPDs, to summarize these sets of radiocarbon dates. “But there are a lot of inherent problems with DBPs,” says Julie Hoggarth, Baylor University archaeologist and co-author of the article.
Radiocarbon dating measures the decay of carbon-14 in organic matter. But the amount of carbon-14 in the atmosphere fluctuates over time; it is not a constant baseline. So researchers create radiocarbon calibration curves that map carbon-14 values to dates. Yet the same carbon-14 value can correspond to different dates – a problem known as “equifinality”, which can naturally skew SPD curves. “This has been a major problem,” and a hindrance for demographic analyzes, says Hoggarth. “How do you know that the change you are observing is an actual change in the size of the population and not a change in the shape of the calibration curve? “
When she discussed the issue with Price several years ago, he told her he wasn’t a fan of SPDs either. She asked what the archaeologists should do instead. “Basically he said, ‘Well, there is no alternative.’”
This awareness led to a multi-year quest. Price developed an approach to estimate prehistoric populations that uses Bayesian reasoning and a flexible probability model that allows researchers to overcome the problem of equifinality. The approach also allows them to combine additional archaeological information with radiocarbon analyzes to obtain a more accurate estimate of the population. He and his team applied the approach to existing radiocarbon dating of the Mayan city of Tikal, which carried out extensive prior archaeological research. “It serves as a very good test case,” says Hoggarth, a Mayan scholar.
For a long time, archaeologists have debated two demographic reconstructions: the population of Tikal increased at the beginning of the Classical period and then reached a plateau, or it increased at the end of the Classical period. When the team applied the new Bayesian algorithm, “it showed a very large population increase associated with the end of the Classic,” she says, “so that was a really wonderful confirmation for us.”
The authors have produced an open source package that implements the new approach, and links and website code are included in their article. “The reason I’m excited about this,” Price says, “is that it’s about pointing out a mistake that matters, correcting it, and laying the groundwork for future work. “
This document is only the first step. Then, thanks to “data fusion”, the team will add old DNA and other data at radiocarbon dates for even more reliable demographic reconstructions. “That’s the long-term plan,” Price says. And it could help solve a second problem with dates as an approach to data: a “bias problem” if and when radiocarbon dates are skewed towards a particular time period, leading to inaccurate analyzes.
But that’s a topic for another article.
Reference: “End-to-end Bayesian analysis for summarizing sets of radiocarbon dates” by Michael Holton Price, José M. Capriles, Julie A. Hoggarth, R. Kyle Bocinsky, Claire E. Ebert and James Holland Jones, September 15, 2021, Journal of Archaeological Sciences.
DOI: 10.1016 / j.jas.2021.105473