The Distribution Route from Ancestors to Descendants

We study the distribution of descendants of a known personality, or of anybody else, as it propagates along generations from father and mother through their children. We ask for the ratio of the descendants to the total population and construct a model for the route of Distribution from Ancestors to Descendants (DAD). The population ratio rn is found to be given by the recursive equation rn+1 = (2 − rn)rn , that provides the transition from the n−th to the (n + 1)th generation. r0 = 1/N0 and N0 is the total relevant population at the first generation. The number of generations it takes to make half the population descendants is log N0/ log 2 and additional ∼ 4 generations make everyone a descendent (=the full descendant spreading time). These results are independent of the population growth factor even if it changes along generations. As a running example we consider the offspring of King David. Assuming a population of N0 = 106 of Israelites at King David’s time (∼ 1000 BC), it took 24 generations (about 600 years, when taking 25 years for a generation) to make every Israelite a King David descendent. The conclusion is that practically every Israelite living today (and in fact already at 400 BC), and probably also many others beyond them, are descendants of King David. We note that we didn’t take into account here any geo-social-demographic factor. Nevertheless, along tens of generations, about 120 from King David’s time till today, the DAD route is likely to govern the distribution in communities that are not very isolated. We add a rather philosophical note. Even if mankind started with many Adams and Eves, it took relatively very short time to consider the whole founder group at any early era, as a Common Forefather – Super DAD – of all of us. ar X iv :0 90 4. 47 92 v2 [ qbi o. PE ] 3 0 A pr 2 00 9