Anthropologists often recorded the typical amount of kinship altruism – that is, the altruism between individuals who identify one another as kin -- they observed in what they referred to as tribal or traditional societies (e.g., Murdock 1949; Keesing 1975; Fortes 1969; Evans-Pritchard 1940). This altruism, they noted, was extended to very distant kin. This altruism toward distant kin, as several scholars have pointed out (E. O. Wilson, D.S. Wilson), is fundamentally inconsistent with the predictions of kin selection. In this paper, we present a possible solution to this puzzle, and one that does not reply on group selection. To do this we introduce a new evolutionary concept called “ancestor-descendant conflict” and the mathematical formula upon which it is based. The concept of “ancestor-descendant conflict” is a multi-generational diachronic extension of Trivers’ concept of “parent-offspring conflict.” It leads to an extension and revision of Hamilton’s rule “C