Tracing and quantifying inheritance over many generations

Question

Apologies if this is the wrong location for this question, and please feel free to point me in the right direction with appropriate Anglo-Saxon embellishments...

I'm after some ball-park numbers for the following questions (plus any hints how to calculate them for different params - e.g. less generations, larger starting pop.):

Given a starting population of 10,000, and given 2,500 generations, with an end population of 5,000,000,000

1. What are the chances of being a direct descendant of 1 individual of the original 10,000?
2. If you had a DNA sample of that individual, would you be able to tell if you were a direct descendant?
3. Would siblings of the original individual confuse things with regard to Q2?

Answer 1

Since it seems my comment helped, I've been suggested to post this as an answer...

I'd reccomend everyone interested in these sort of population genetics to have a look at 'The Ancestors Tale' by Richard Dawkins. In particular, chapter 0, which deals with human/hominid genetics. That should help answer questions. The relevant part of the book appears to be available online for free in GoogleBooks (https://books.google.co.uk/books/about/The_Ancestor_s_Tale.html?id=s86_CQAAQBAJ).

Below I'll note down the answers from the comments section, not because I wrote them but I figured it might help anyone who stumbled over this question afterwards:

1. The chances of being a direct descendant of 1 individual of the original 10,000 is 100%, assuming they have any descendants. - Tom Melly

2. If one had a DNA sample of that individual, one could use uniparental markers (either Y chromosome for men, or mtDNA for women) to infer whether they are a direct descendant. - 4galaxy7

(My guess is that it doesn't have to be uniparental markers. Other genes might work just as well. I'm thinking of Neanderthal/Denisovan work. But I might be wrong.)

Answer 2

Question 1

If I understand the question, then you are asking 'Given a starting population of 10 000 individuals and 2 500 generations, what is the probability that one of the 5 000 000 000 individuals descendend individuals is directly descended from one of the founders?'.

If we are assuming no migration in or out of the system, then the answer must be 1, since there are no ways to be descended from someone outside the system. Please let me know if I have misunderstood the question.

Question 2

For this, it's only possible to use uni-parental markers. This is because inferring exact genealogical relationships using autosomal markers beyond something like 3rd cousins is extremely difficult, owing to the stochastic way in which recombination breaks up segments. Beyond a few generations, only the uniparentally inherited mtDNA and non-recombining Y-chromosome can be informative about relatedness.

Uniparental markers don't recombine, so mutations aside, you expect to inherit an exact copy of your mothers mtDNA marker. If you know the number of generations which are likely to separate you and the putative ancestor, you can estimate the some kind of likelihood of being directly descended from the ancestor given the number of pairwise differences between the individual and the ancestor.

This is what they did when they wanted to identify the remains of Richard III. It's a good paper and easy to read / open access, so I'd recommend checking it out.

Question 3

Simply, no. The inference of being a direct descendent from one of the ancestors would be independent from any of the other potential descendants in the sample.