Developing Bayesian Tools for Archaeological Research

Bayesian inference is a statistical method for updating the probability of a hypothesis as additional evidence becomes available. Thus, it provides a natural framework for interdisciplinary approaches and the combination of diverse sources of evidence.

A relatively recent development in isotope-based studies has been the introduction of Bayesian mixing models. A common feature to different models is the incorporation as model parameters of consumer and food isotopic signals and of diet-to-consumer isotopic offsets. Under this approach quantified individual diets are expressed as posterior probability distributions. Different models have been made available including the model FRUITS (Food Reconstruction Using Isotopic Transferred Signals) which has been widely used for reconstructing diets in numerous historical and cultural contexts. The technical features that define FRUITS correspond to the need of addressing key aspects of archaeological, physiological, and isotopic research involved in the diet reconstruction process:

Incorporating multiple sources of uncertainty. The process of quantifying diets from isotopic data requires that uncertainties for all model parameters are taken into account. This includes uncertainties in isotopic values of potential food groups, diet-to-consumer isotopic offsets, and food concentration values. However, FRUITS is primarily aimed at individual diet reconstruction and such it also includes the uncertainty in individual consumers. This uncertainty is larger than instrumental uncertainties as results from mammal feeding experiments have demonstrated.

Combination of multiple isotopic proxies. To combine multiple isotopic proxies implies that the dietary routing mechanisms for each identified. In this respect, carbon and nitrogen stable isotopes are often combined under the assumption that both are derived from dietary protein. However, if there is a dietary contribution from other nutrients (carbohydrates or lipids) more complex models are required. In this respect, FRUITS implemented a weight parameter which can be used to assign, for example, to assign the contributions from protein, lipids, and carbohydrates towards the bone collagen carbon isotope signal. This approach also allows for the incorporation of several other isotopic proxies each with a specific dietary routing mechanism (e.g. ¹⁴C_Coll, ¹³C_AA, ¹⁵N_AA)
Expansion of dietary estimates. Traditional bone collagen carbon and nitrogen stable isotope analyses typically quantifies protein contributions. However, with the FRUITS model in addition to the traditional estimate of protein contribution also quantified are the total caloric contributions from each food group and the relative contribution from the different food nutrients (e.g. protein, carbohydrates, lipids, minerals, and vitamins). Macronutrient contributions can be estimates using calories as units allowing for their comparison with other dietary evidence.
Combining multiple sources of dietary evidence. Multiple sources of dietary evidence (e.g. written sources, archaeo-faunal or botanical studies, physical anthropology) can be combined to obtain more precise dietary estimates (see figure below).

FRUITS is being merged with IsotopeR, a Bayesian mixing model developed by John B. Hopkins III (Unity College, University of California) and Jake M. Ferguson (University of Minnesota). This merger will combine the features of both models and will be made available as an R package. There is also an ongoing collaboration with Prof. Christopher Bronk Ramsey (University of Oxford) to ensure compatibility between FRUITS and OxCal program employed to provide radiocarbon calibration and analysis of archaeological and environmental chronological information.

Comparison of dietary estimates generated using FRUITS for two archaeological case studies with and without added prior information. The circles mark independently known dietary intakes.

Comparison of dietary estimates generated using FRUITS for two archaeological case studies with and without added prior information. The circles mark independently known dietary intakes.

In addition to the work on FRUITS several other Bayesian tools are being developed to aid in the reconstruction of human mobility, quantifying human impacts (e.g. irrigation, manuring), and Big Data querying (R package for IsoMemo).

Related Publications

Wilkin, S., Miller, A. V., Miller, B. K., Spengler, R. N. III., Taylor, W. T., Fernandes, R., Hagan, R. W., Bleasdale, M., Zech, J., Ulziibayar, S., Myagmar, E. 2020. Economic Diversification Supported the Growth of Mongolia’s Nomadic Empires. Scientific Reports. 10:3916.

Cubas Morera, M., Lucquin, A. J. A., Robson, H. K., Colonese, A. C., Arias, P., Aubry, B., Billard, C., Jan, D., Diniz, M., Fernandes, R., Fábregas Valcarce, R. 2020. Latitudinal Gradient in Dairy Production with the Introduction of Farming in Atlantic Europe. Nature Communications. 11:2036.

Hendy, J., Colonese, A. C., Franz, I., Fernandes, R., Fischer, R., Orton, D., Lucquin, A., Spindler, L., Anvari, J., Stroud, E. and Biehl, P. F. 2018. Ancient Proteins From Ceramic Vessels at Çatalhöyük West Reveal the Hidden Cuisine of Early Farmers. Nature communications. 9:4064.

Fernandes, R., 2016. A simple(r) model to predict the source of dietary carbon in individual consumers. Archaeometry, 58(3), pp.500-512.

Fernandes, R., Grootes, P., Nadeau, M.J. and Nehlich, O., 2015. Quantitative diet reconstruction of a Neolithic population using a Bayesian mixing model (FRUITS): the case study of Ostorf (Germany). American journal of physical anthropology, 158(2), pp.325-340.

Fernandes, R., Millard, A.R., Brabec, M., Nadeau, M.J. and Grootes, P., 2014. Food reconstruction using isotopic transferred signals (FRUITS): a Bayesian model for diet reconstruction. PLoS One, 9(2), p.e87436.

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Ricardo Fernandes