The study of cultural dispersals in lowland South America has a long history, tracing back to the 19th century and intensifying in the 20th century with the integration of linguistic, ethnographic, and archaeological evidence. Dispersals encompass various mechanisms, including migration, demic expansions, and cultural trait diffusion. While recent research has built upon existing models, incorporating ancient DNA evidence, this paper focuses on a different methodological approach: inferring dispersal dynamics based on geolocated pre-Columbian radiocarbon dates. The authors aim to bridge the gap between dispersal-focused research and quantitative analyses of chronometric data, proposing a new method to analyze pre-Columbian cultural dispersals by formally accounting for chronometric uncertainty in radiocarbon data and by assessing whether the datasets show statistically significant evidence for a dispersal process. This is crucial because it addresses the inherent qualities of archaeological datasets and provides a test of whether further analysis is warranted or if more data is needed. The method is broadly applicable beyond the South American context.

Archaeological studies of pre-Columbian cultural dispersals heavily rely on spatiotemporal datasets—georeferenced chronometric dates. Archaeology has seen rapid advancements in radiometric data analysis, including methods accounting for spatial and temporal aspects of dispersal processes. Quantitative approaches often search for spatiotemporal trends, such as decreasing age with increasing distance from a source. Linear regression, a common method, analyzes the relationship between the date of first appearance of a cultural entity and its distance from a presumed origin. However, this typically utilizes median calibrated dates, ignoring the inherent chronometric uncertainty. The authors build upon previous work highlighting the significant impact of this uncertainty on the determination of dispersal parameters, emphasizing that ignoring uncertainty risks inaccurate conclusions.

The study uses two datasets of radiocarbon determinations: one for the Tupiguarani expansion (375 dates from 234 sites) and one for the Arauquinoid expansion (178 dates from 47 sites). Only dates with verifiable georeferenced locations, publications, and lab codes (excluding those with errors exceeding ±200 ¹⁴C years) were included. The authors address the issue of using median dates in regression analysis, which fails to account for chronological uncertainty. They propose using quantile regression, which is more robust to non-normally distributed data and unequal variances. Specifically, they regress to the 99th percentile of the dataset, capturing the earliest dates without arbitrarily excluding outliers. This is tested with regressions to the 90th and 95th percentiles to ensure robustness. Monte Carlo simulations (1000 runs) were conducted to quantify uncertainty in regression parameters due to dating errors. A crucial innovation is the development of a significance test to determine if the results show statistically significant evidence against a null slope (instantaneous dispersal). The null model is created by randomly permuting the spatial and temporal components of the dataset, preserving characteristics like resolution and extent. Summed probability distributions (SPDs) are then used to calculate a 95% confidence envelope, allowing for p-value calculation using a two-tailed test. The method is validated using a well-established dataset on the spread of the Neolithic in Europe, comparing results with a randomized version of the dataset.

The analysis of the Arauquinoid dataset revealed regression lines close to horizontal, suggesting a near-zero slope. Both median date regression and regression incorporating full chronometric uncertainty yielded slopes close to zero, corresponding to extremely high dispersal speeds and even suggesting a counter-intuitive direction of spread. P-values indicated that the dataset did not provide enough evidence to reject the null hypothesis of no dispersal. The Tupiguarani dataset, despite its larger spatial extent, also showed a lack of statistical significance in both median date and full uncertainty regressions, failing to reject the null hypothesis. The analysis showed that the regression parameters fell within the confidence interval of the null hypothesis. Even when using a less robust approach (median dates), the p-value for the slope indicated a lack of significance.

The results confirm the necessity of significance testing in analyzing archaeological dispersal datasets. The lack of significance in both the Arauquinoid and Tupiguarani datasets, even the larger one, illustrates that data quality and resolution, not just spatial scale, are critical. The study highlights that simply observing a slope in a median-date regression is insufficient and emphasizes the importance of considering the full extent of chronometric uncertainty. The failure to detect statistically significant evidence for dispersals in these established cases raises questions about previous studies relying on similar datasets for inferring dispersal parameters and routes. The non-detection doesn't disprove the dispersals, but rather suggests they were too rapid to be resolved with the current data. The authors suggest revisiting demographic models of cultural expansion, advocating for consideration of alternative models (such as exchange and copying) and improved methods of analyzing large, complex datasets in cultural evolution. They advocate for integrating multiple datasets—archaeological, linguistic, and ethnographic—to obtain more robust results and advance our understanding of pre-Columbian cultural processes.

This study underscores the crucial role of considering chronological uncertainty when analyzing spatial radiometric datasets for archaeological dispersals. When uncertainty is comparable to the dispersal duration, datasets lack the resolution to detect dispersal signals. The authors' new significance test provides a means to assess data suitability before further analysis and modeling. Applying this methodology to the Arauquinoid and Tupiguarani datasets showed a lack of statistically significant evidence for dispersals, highlighting the need for more comprehensive data or alternative theoretical frameworks. Future research should focus on incorporating a wider range of data and more sophisticated analytical methods to refine our understanding of prehistoric cultural dynamics.

The methodology relies on choices like dispersal origin and distance metrics (geodesic distance used here). While these choices likely wouldn't significantly alter the conclusions, future studies could explore alternative approaches. The linear regression framework assumes spatial homogeneity and isotropy, a limitation shared by many dispersal studies. More complex models could address this but are beyond the current scope. The methodology doesn't differentiate between a few sites with many dates and many sites with single dates—a limitation common to many regression-based approaches that reduce complex spatial data to a single distance parameter.