Genes, Generations, and Bloodlines in Speculative Fiction

Last week, I read 12.21.12: The Vessel. One of its main characters was directly descended from Cleopatra. This plot development made me wonder how many genes someone would really share with a direct ancestor so many generations back. Cleopatra died in 30 B.C., over 2030 years ago. The typical length of a human generation is between 20-25 years; let's split the difference and call it 22.5 years. That gives me about 90 generations between Cleopatra and someone born today. Humans have about 20,000 genes that code for proteins (there are plenty of important regulatory sites as well, but for now, let's keep things simple.) If we assume half of the genes are lost each generation, then we can create a table like this:

Generation #     Number of Genes
0 (starting)           20,000
1                         10,000
2                         5,000
3                         2,500
4                         1,250
5                         625
6                         313 (rounded up)
7                         157 (rounded up)
8                         79  (rounded up)
9                         40 (rounded up)
10                       20
11                       10
12                       5
13                       2.5
14                       1.25
15                       0.625

So, obviously, after ninety generations, you would share much less than a single gene with an ancestor that far back. However, this is assuming no inbreeding. In practice, the number of ancestors would double with each generation you go back (two parents, four grandparents, eight great-grandparents), so you quickly reach a point where the number of direct ancestors exceeds the world population of people alive at that time. So we're all 50th cousins or something like that. I'm not sure how to apply that to our hypothetical descendant of Cleopatra. He or she would have a bit more in common with Cleopatra than this example suggests due to inbreeding, but I doubt it would be a significant amount. Perhaps Cleopatra has more descendants alive today than we realize--hundreds or thousands. Of course, one of my recent science links reported that Europeans have between 1-4% Neanderthal DNA, and this DNA might affect some of our traits today.

So, if you're writing a fantasy with a family who passes a magical trait down their bloodline, you might want to consider how many generations it will be before that trait gets washed out--or what the family will do to keep it strong. Maybe everyone will have to marry their cousins, or maybe anyone with a random mutation for this trait will be brought into the bloodline. Better yet, use a science fiction setting and bring in genetic engineering. That could cause all sorts of interesting plot developments!

Am I the only one who is nerdy enough to figure these things out? Do you think about these things when you read or write? If you have a Google account, you can comment below.

Edit to add: Two thingsI didn't discuss in my original post but should have are mitochondrial DNA and the Y chromosome. Mitochrondria are believed to be ancient bacteria that were assimilated into eukaryotic cells to serve as a site of energy generation. They still have their own DNA, and they are passed down exclusively by the mother. The Y chromosome carries a sex-determining region that makes men male. Both mitochondrial DNA and the Y chromosome are passed down without being combined with other DNA, so they could pass relatively unchanged (except for random mutations) through the generations as long as you have descendants of the right sex. Something else to think about when you're designing your magical family....