The Distribution Route from Ancestors to Descendants

Details The Distribution Route from Ancestors to Descendants The Distribution Route from Ancestors to Descendants

2009-04-30

arxiv.org/abs/0904.4792v3

Biology

Quantitative Biology

Populations and Evolution

16 pages, 2 figures

Scientific paper

We study the distribution of descendants of a known personality, or of anybody else, as it propagates along generations from father or mother through any of 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 $r_n$ is found to be given by the recursive equation $ r_{n+1} \approx (2-r_n) r_n ,$ that provides the transition from the $n-$th to the $(n+1)$th generation. $ r_0 =1/N_0$ and $N_0$ is the total relevant population at the first generation. The number of generations it takes to make half the population descendants is $\log N_0/\log 2$ and additional $\sim 4$ 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 between $N_0 = 10^6$ and $5 \cdot 10^6$ of Israelites at King David's time ($\sim 1000$ BC), it took 24 to 26 generations (about 600-650 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 350-400 BC), and probably also many others beyond them, are descendants of King David. We note that this work doesn't deal with any genetical aspect. We also 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.

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