I totally agree with Jeff. Besides the high probability that there has never been a King David, at least in the form described in our "Tanach", there is a vast literature on Branching processes starting with "the rate of extinction of surnames along the generations" by Galton and Watson, 1875. It has been further shown that for a generation duration of around 25 years, and given a certain "David", after 500-800 years the whole population will be his descendants. Even if we consider "Assortative mating" (Endogamy), common to very many Jewish communities, this process of disseminating the "Davidic" traits is only moderately delayed.
We used this modelling to understand the spreading of mutations typical for the Jewish population, and gave an example of the spreading of the genetic disease FMF (Familial Mediterranean Fever). See: Levi and Gath, Effects of mating patterns on genealogical trees: Assessment of the high carrier rate of Familial Mediterranean Fever in rural Israeli districts, Journal of Theoretical Biology, 443 (2018) 92–99.
Prof. Isak Gath MD, DIC, DSc
Faculty of Biomedical Engineering Tel. Office #972-4-8294115
Technion Israel Institute of Technology Home #972-4-9835704
32000 Haifa, Israel