Scientists are developing a statistical solution to the problem of dating archeology

Archaeologists have long had a dating problem. The analysis of radiocarbon normally used to reconstruct past human demographic changes is based on a method easily skewed by radiocarbon calibration curves and measurement uncertainty. And there has never been any statistical correction that worked, until now.

“No one has systematically explored the problem or shown how it can be treated statistically,” said Santa Fe archaeologist Michael Price, lead author of an article in Journal of Archaeological Sciences on a new method he developed to summarize sets of radiocarbon dates. “It’s really exciting how this work came together. We identified a fundamental problem and we solved it.”

In recent decades, archaeologists have increasingly relied on sets of radiocarbon dates to reconstruct the size of the past population using an approach called “dates as data”. The basic assumption is that the number of radiocarbon samples from a given period is proportional to the size of the population in the region at that time. Archaeologists have traditionally used “added probability densities” or SPDs, to summarize these sets of radiocarbon dates. “But there are a lot of problems inherent in SPDs,” says Julie Hoggarth, an archaeologist at Baylor University and co-author of the paper.

Radiocarbon dating measures the decay of carbon-14 into organic matter. But the amount of carbon-14 in the atmosphere fluctuates over time; it is not a constant baseline. Thus, the researchers create radiocarbon calibration curves that map carbon-14 values ​​to dates. However, a single carbon 14 value may correspond to different dates, a problem known as “equifinality,” which can naturally skew SPD curves. “This has been a major problem,” and an obstacle to demographic analysis, Hoggarth says. “How do you know the change you’re seeing is a real change in population size and not a change in the shape of the calibration curve?”

When he discussed the issue with Price several years ago, he told her he was not a fan of the SPDs either. He asked what the archaeologists had to do. Basically, he said, “Well, there’s no alternative.”

This realization led to a search of many years. Price has developed an approach to estimating 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 analysis to obtain a more accurate population estimate. He and his team applied the approach to the existing radiocarbon dates of the Mayan city of Tikal, which has extensive prior archaeological research. “It serves as a really good test case,” says Hoggarth, a Mayan scholar. For a long time, archaeologists debated two demographic reconstructions: the population of Tikal increased at the beginning of the Classical period and then reached the plateau, or increased at the end of the Classical period. When the team applied the new Bayesian algorithm, “it showed a really strong population increase associated with the last classic,” he says, “so it was a really wonderful confirmation for us.”

The authors produced an open source package that implements the new approach and the links and code of the website are included in their work. “The reason I’m excited about this,” Price says, “is that it points out a mistake that matters, fix it, and lay the groundwork for future work.”

This document is just the first step. Then, by “merging data,” the team will add old DNA and other data to the 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 the data approximates: a “bias problem” if and when radiocarbon dates are distinguished toward a specific time period, leading to inaccurate analyzes.

But this is a topic for another paper.