I highly recommend Marvin Harris' Cannibals and Kings (or, indeed, any of his other books) for the real low-down on the story of the human race.
Certainly, the idea of the alpha-male monkey-man with a big stick, fighting and controlling access to females, has its place in the story of the rise of chiefs in tribal societies; but it is a much too American, competitive and aggressive, slant on human culture. The carrot was at least as big as the stick!
Nothing is more symptomatic of the difference between reciprocity and redistribution than the acceptance of boastfulness as an attribute of leadership. In flagrant violation of prescriptions for modesty in reciprocal exchanges, redistributive exchange involves public proclamations that the redistributor is a generous person and a great provider.
The slide (or ascent?) toward social stratification gained momentum wherever extra food, produced by the inspired diligence of redistributors, could be stored while awaiting Bigman feasts, potlatches, and other occasions of redistribution. The more concentrated and abundant, and the less perishable, the crop, the greater its potential for endowing Bigmen with power over people. While others would possess some stored-up foods of their own, the redistributors' stores would be the largest. In times of scarcity, people would come to him, expecting to be fed, and, in return, he would call upon those who had special skills to make cloth, pots, canoes, or a fine house for his own use. Eventually, the redistributor no longer needed to work in the fields to gain and surpass Bigman status. Management of the harvest surpluses, a portion of which continued to be given to him for use in communal feasts and other communal projects such as trading expeditions and warfare, was sufficient to validate his status. And increasingly, people viewed this status as an office, a sacred trust, passed on from one generation to the next according to rules of hereditary succession. The Bigman had become a chief; his dominion was no longer a single small, autonomous village, but a large political community, a chiefdom.
The early chiefs were, at least, as much Tammany Hall as Mississippi River alligator-man!