# After how many generations descendant is not more related to ancestor, than to a random individual in an ancestral population?

Descendant of n generation has on average 1/2n DNA of ancestor. (For example children have 1/2 DNA of parents and 1/4 DNA of Grandparents, After 10 Generation 1/1024 DNA and after 100 Generations 1/2100 DNA).

Is there a point (value of n) when descendant is no more related to ancestor and is similarly related to random individual from an ancestral population.

• Welcome to Biology.SE. Your question sounds like a Coalescent theory question. Do you assume that no mutations and no selection in your model? The answer will very likely depend on the population size. Jan 26, 2015 at 7:33
• Thank you. Answer will likely depend on effective population size. logically mutations will decrease value of n and selection will increase or decrease depending how it favors certain DNA. I just did not thought about this and wanted to know if this is even possible, that descendant is no more related to ancestor than to random individual from an ancestral population. Jan 26, 2015 at 8:13

As indicated in the comments, the answer will depend on the specifics of the population structure, including its size. But a first stab can be taken in this way: you had 2 ancestors one generation back, 4 two generations back, ..., $2^n$ (not necessarily distinct) $n$ generations back. So you certainly cannot be descended from everyone in the ancestral population if less than $\log_2 N$ generations have passed. ($N$ = population size, which for simplicity I assume to be stable.) In a freely mixing population under the very simplest assumptions, you will eventually decay exponentially towards complete coverage with a half-time of one generation.
So, in summary, it's complicated. It takes only a fairly small number of generations ($O(\log_2 N)$) before you're potentially related to most of the ancestral population. But over longer times ($O(N)$ generations) your relationship to the ancestral population actually goes down.