This is not a full answer, but I post it as one because the reasoning is too long to post it as a comment.
You can make a rough estimation using a few assumptions.
1) Let's say 1 generation = 25 years, so 1000 years are 40 generations.
2) Let's say that half of the population is able to leave offspring, so the probability of one individual having descendants = 0.5
3) Supposing that the average number of siblings is 3.
After the 3rd generation, it becomes a combinatorial problem that is too hard for me. I can tell that the probability of not having offsprings, giving that it already has, is going to 0 because of the number of offspring > 2
If this approach appears useful, I suggest you ask for a more complete solution on https://math.stackexchange.com/