Promiscuity and female descent.
The instinct of exogamy first developed in the totem-clan when it was migratory and lived by hunting, at least among the Australians and probably the American Indians.
The first condition of the clan was one of sexual promiscuity, and in _Totemism and Exogamy_ Sir J.G.Frazer has adduced many instances of periodical promiscuous debauchery which probably recall this state of things.

[159] The evil results which would accrue from in-breeding in the condition of promiscuity may have been modified by such incidents as the expulsion of the young males through the spasmodic jealousy of the older ones, the voluntary segregation of the old males, fights and quarrels leading to the rearrangement of groups, and the frequent partial destruction of a group, when the survivors might attach themselves to a new group.

Primitive peoples attached the utmost importance to the rule of exogamy, and the punishments for the breach of it were generally more severe than those for the violation of the laws of affinity in civilised countries.

The Australians say that the good spirit or the wise men prescribed to them the rule that the members of each totem-clan should not marry with each other.

[160] Similarly the Gonds say that their divine hero, Lingo, introduced the rule of exogamy and the division into clans before he went to the gods.
At first, however, the exogamous clan was not constituted by descent through males, but through females.