While dismissing the nineteenth century theory of matrilineal priority as an evolutionary scenario, George Murdock (1937) finds that the theory would seem to have validity, provided that one assumes (and he does not) evolutionary stages in prehistory. However, his rejection of the theory appears to arise from a study of social formations across the ethnographic landscape, from hunter-gatherers to agriculturalists and pastoralists; whereas, the issue of matrilineal priority should be addressed entirely in the context \r\nof variations among the social formations of hunter-gatherers, since only hunter-gatherers existed during the period for which the question has relevance.\r\nMatriliny is not an abstract system of descent; it exists as a real social form only when it functions as a system of in-heritance. And there are at most two social resources among hunter-gatherers which are available for intergenerational distribution; birthrights to territorial resources and birthrights to human fertility. The consequences of these resources for social organization have not been recognized in cultural anthropology. However, \r\nI shall show that these two dynamically interpenetrating resources are fundamental to socio-economic processes among hunter-gatherers and are definitive in the choice of matriliny versus patriliny versus alineality. \r\nAlternative social formations among hunter-gatherers derive from four conditions: (a) If territory and fertility are both positively valued at the margin, then the society must be matrilineal (in the absence of cattle). (b) If territory and fertility are positively valued at the margin and cattle are available, then the system must be patrilineal. (c) In the exceptional case of demographic expansion into new territories, the marginal value of new territory would be nearly zero and the marginal valuation of fertility would be high, so that the system would be matrilineal. And finally (d) if the marginal social valuation of territory were positive or zero and the marginal so-\r\ncial valuation of fertility is zero, due to social or ecological circumscription, then the society would be either matrilineal, patrilineal or alineal, as a function of its particular history and context.\r\nAs the earliest modern humans struggled to emerge and survive as a new species in the challenging, competitive, environments of the Late Pleistocene, they would have required dynamically expanding social formations, featuring positive valuations of fertility and territory. This category of societies was central to the peopling of the world; and they would have been matrilineal. Other social formations would also emerge, but they would tend to suffer demographic decline or stagnation and become lost to social history in the wake of the more dynamic. It is in this sense that matriliny had priority.\r\n\r\nhttps://www.socionauki.ru/journal/articles/1213777/