**R – Xi'an's Og**, and kindly contributed to R-bloggers)

**A** paper in Nature this week that uses reversible-jump MCMC, phylogenetic trees, and Bayes factors. And that looks at institutionalised or ritual murders in Austronesian cultures. How better can it get?!

“by applying Bayesian phylogenetic methods (…) we find strong support for models in which human sacrifice stabilizes social stratification once stratification has arisen, and promotes a shift to strictly inherited class systems.” Joseph Watts et al.

The aim of the paper is to establish that societies with human sacrifices are more likely to have become stratified and stable than societies without such niceties. The hypothesis to be tested is then about the *evolution* towards more stratified societies rather the *existence* of a high level of stratification.

“The social control hypothesis predicts that human sacrifice (i) co-evolves with social stratification, (ii) increases the chance of a culture gaining social stratification, and (iii) reduces the chance of a culture losing social stratification once stratification has arisen.” Joseph Watts et al.

The methodological question is then how can this be tested when considering those are extinct societies about which little is known. Grouping together moderate and high stratification societies against egalitarian societies, the authors tested independence of both traits versus dependence, with a resulting Bayes factor of 3.78 in favour of the latest. Other hypotheses of a similar flavour led to Bayes factors in the same range. Which is thus not overwhelming. Actually, given that the models are quite simplistic, I do not agree that those Bayes factors prove anything of the magnitude of such anthropological conjectures. Even if the presence/absence of human sacrifices is confirmed in all of the 93 societies, and if the stratification of the cultures is free from uncertainties, the evolutionary part is rather involved, from my neophyte point of view: the evolutionary structure (reproduced above) is based on a sample of 4,200 trees based on Bayesian analysis of Austronesian basic vocabulary items, followed by a call to the BayesTrait software to infer about evolution patterns between stratification levels, concluding (with p-values!) at a phylogenetic structure of the data. BayesTrait was also instrumental in deriving MLEs for the various transition rates, “in order to inform our choice of priors” (!). BayesTrait has an MCMC function used by the authors “to test for correlated evolution between traits” and derive the above Bayes factors. Using a stepping-stone method I am unaware of. And 10⁹ iterations (repeated 3 times for checking consistency)… Reversible jump is apparently used to move between constrained and unconstrained models, leading to the pie charts at the inner nodes of the above picture. Again a by-product of BayesTrait. The trees on the left and the right are completely identical, the difference being in the inference about stratification evolution (*right*) and sacrifice evolution (*left*). While the overall hypothesis makes sense at my layman level (as a culture has to be stratified enough to impose sacrifices from its members), I am not convinced that this involved statistical analysis brings that strong a support. (But it would make a fantastic topic for an undergraduate or a Master thesis!)

Filed under: Books, pictures, R, Statistics, University life Tagged: Austronesian cultures, Bayes factors, Bayesian hypothesis testing, BayesTrait, evolution, MCMC, Nature, phylogenetic tree, reversible jump MCMC

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