There is no doubt about the matrilineal aspects of the cultural matrix through which these narratives descended before being written down in the form available to us today, and at least some of the matrilineal aspects of those narratives have been recognized for over a century.  The Fourth Branch of the Mabinogi begins with a traditional fertility scene in which a traditional lord cannot live (and presumably the land will not be fertile and prosper) without a maiden to be his footholder and ends with a companionless patrilineal lord ruling prosperously.  Ultimately, Gwydion is the pivotal figure about whom his society changes from matrilineal inheritance to patrilineal inheritance as he makes his nephew his son and his son his successor.  Lleu's position is the stronger for being able to claim lordship in both traditions, but the absence of women (and Lleu's prosperous rule) at the end of the Fourth Branch symbolizes both Gwydion's victory and the establishment of patrilineal lordship in Gwynnedd. . . .  Moreover, a patrilineal triumph to the Four Branches, which began with Rhiannon's telling Pwyll how to court her, how to wed her, and how to win her back from Gwawl and ended with a male ruler alone, is compatible with what we know of the cultural change from matrilineality to patrilineality which took place as the post-Celtic Indo-Europeans moved westward across Europe.