The question of when and why societies have transitioned away from matriliny to other types of kinship systems-and when and why they transition towards matriliny-has a long history in anthropology, one that is heavily engaged with both evolutionary theory and cross-cultural research methods. This article presents tabulations from a new coding of ethnographic documents from the Standard Cross-Cultural Sample (SCCS), tallying claims of transitions in kinship systems both away from and to matriliny using various levels of stringency. We then use our counts as the outcome variables in a set of Bayesian analyses that simultaneously estimate the probability of a transition occurring given societal covariates alongside the conditional probability of detecting a transition given the volume of ethnographic data available to code. Our goal is to estimate the cross-cultural and comparative frequency of transitions away from and to matriliny, as well as to explore potential causes underlying these patterns. We find that transitions away from matriliny have been significantly more common than 'reverse transitions' to matriliny. Our evidence suggests that both rates may be, in part, an artefact of the colonial and globalizing period during which the data comprising much of the current ethnographic record were recorded. Analyses of the correlates of transitions away from matriliny are consistent with several of the key causal arguments made by anthropologists over the past century, especially with respect to subsistence transition (to pastoralism, intensive agriculture and market economies), social complexity and colonialism, highlighting the importance of ecological factors in such transitions. This article is part of the theme issue 'The evolution of female-biased kinship in humans and other mammals'.