Sum things are not what they seem: Problems with the interpretation and analysis of radiocarbon-date proxies

Radiocarbon-date proxies are widely used in studies exploring long-term variation in human and environmental phenomena. Examined phenomena include, for example, variation in past human population levels and climate-change-driven sea level fluctuations. These processes are thought to have affected the amount of organic carbon deposited into the archaeological and/or palaeoenvironmental record at a given time. Time-series representing through-time fluctuations in the frequency of dated radiocarbon samples are, therefore, often used as proxies for such processes. However, there are important problems with radiocarbon-date proxies that have so far gone underappreciated in the scientific literature. The primary problem is that the proxies are easily misinterpreted, and this has serious implications for downstream analyses. Here we report the results of a two-part study. In the first part, we investigated the most accurate interpretation of radiocarbon-date proxies produced with each of the two established methods, widely-used summed probability density functions and a new kernel density estimation approach. In the second part, we performed a simulated regression experiment to determine whether the proxies could be used to quantitatively investigate the processes they are often thought to represent. Our analyses unfortunately reveal that the proxies do not reflect what they are generally thought to---i.e., through-time variation in processes correlated with radiocarbon sample frequency. Rather, they represent a combination of through-time variation in sample frequency and chronological uncertainty. More importantly, though, our regression experiment demonstrated that the proxies can produce very misleading results. While the proxies may be useful under certain conditions for addressing certain kinds of research questions, they are not generally suitable as representations of through-time processes. A major implication of this finding is that a significant number of high-profile published studies may be reporting false results based on misinterpretations of core data. Another major implication is that the proxies should be avoided in future research when the goal is to understand through-time variation in a given process.