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I'm reading a recent book about DNA and human migration, and it raised an interesting point: many of your ancestors didn't contribute DNA to you. This can be seen by first simplifying: imagine that crossing-over didn't happen, so that each of your chromosome came unaltered from one of your parents. You have 46 chromosomes, they each have 46 chromosomes, obviously half of the parental set got lost. But consider: after one generation you have two parents, after two generations you have four grandparents... after six generations you have 64 great^4-grandparents... and only 46 chromosomes. So at least 18 ancestors from back then failed to get any chromosomes into you: there's just not enough chromosome to be mapped to all of your ancestors!
In reality crossing-over does happen, but the book says that just means a linear increase in the number of splices, so that after 10 generations you have about 700 ancestral DNA segments but 1024 ancestors -- once again, 30% of them are left out of you.
In the extreme case, you have 30,000 genes, so ignoring splices inside genes, at 16 generations (only 320-640 years!) you have 65,536 ancestors and most ancestors than genes for them to contribute.
Of course, as you go back you start having nth-cousin ancestors and thus a smaller number of unrelated ancestors in a generation, but the principle still holds.
In reality crossing-over does happen, but the book says that just means a linear increase in the number of splices, so that after 10 generations you have about 700 ancestral DNA segments but 1024 ancestors -- once again, 30% of them are left out of you.
In the extreme case, you have 30,000 genes, so ignoring splices inside genes, at 16 generations (only 320-640 years!) you have 65,536 ancestors and most ancestors than genes for them to contribute.
Of course, as you go back you start having nth-cousin ancestors and thus a smaller number of unrelated ancestors in a generation, but the principle still holds.