Our model accounted for the often large measurement errors and accounts for both the presence and absence of the technology to maximise the available information. The results strongly reject the idea of a single origin and provide the strongest support for a triple origin model.

For example, we found no evidence of millet in the residues from Japanese ceramics, in stark contrast to those from Korea (see image below; the brown-coloured dots indicate vessels with millet biomarkers, the blue ones are aquatic biomarkers).

The diffusion of rice and millet in this region has an interesting story - Millet arrived in the Korean peninsula towards the end of the 5k BCE, but it was not transmitted to the Japanese islands until the 1k BCE, soon after the introduction of rice in Korea and the resulting demographic expansion.

I cover methods that are becoming increasingly common, such as hierarchical models, but also slightly more obscure approaches, such as error-in-variables models and generative inference.

This paper looked at methodological aspects, exploring different measures of aggregation, within, between, and across residential communities. Our analyses show that single measures such as the Gini coefficient fail to capture how the inequality can be organised beyond the scale of individual sites.