Davidic Ancestry in the First Century? #general


I'm doing a personal research project to see if I can find a reasonable estimate for the number or percentage of Jews at the beginning of the first century who could trace their lineage to King David. Given that King David was born some 1,000 years prior to the first century, I would imagine that it would be a somewhat significant portion of the population at the time (speaking of, what is also a reasonable estimate of the total Jewish population around that time?). One relevant factor which I would think needs to be considered is that not every child born would survive to adulthood, but I'm not sure how to estimate how many childbearing people that would result in for each generation. Another relevant factor would be that it was much more common in ancient times for people to marry within their own family lines, such as to first or second cousins, so that would somewhat narrow the branching of the genealogy as opposed to each generation continually marrying outside of their family line, but again I'm not sure exactly how much that would narrow the numbers by.
I don't need specific names for any of this, just a general estimate if the information is accessible, or otherwise some advice for how I might go calculating the number on my own. Thanks!

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