 Gray and Watts (2017), for example, have scrutinised what is sometimes called the Supernatural Punishment Hypothesis. This is the hypothesis that belief in powerful gods, who inflict punishment on wrongdoers, tends to result in societies that are better able to harness the fruits of cooperation (see Norenzayan et al. 2016). Gray and Watts again caution that mere correlation between societies that believe in ‘moralising high gods’ and various measures of social complexity does not count strongly in favour of the Supernatural Punishment Hypothesis. We must also take into account the potentially confounding consequences of shared ancestry among the societies surveyed. Gray and Watts draw on Austronesian data to argue that belief in moralising high gods tends to be gained after, not before, the emergence of political complexity; so these data, they suggest, undermine the thought that moralising high gods drive this form of complexity. That said, they do find some support for a weaker supernatural punishment hypothesis based on belief in punishment interventions from natural spirits, ancestral spirits and mythical heroes, as well as from moralising high gods. In their view this type of belief facilitated, ‘the rise of political complexity’ without ‘helping sustain it’ (2017: 7848). Work such as this indicates the potential for cultural phylogenetics to inform broad-sweep hypotheses about not just the patterns, but also the causal processes, that have marked the cultural history of our species.