for the last equation:

(1 - (1 - 0.5^x)^50,000) = 0.5 (I didn’t put this 0.5 on the right side of the equation). That 0.5 is the “reasonable chance” that I mention. If there is a 50/50 chance you have no genes from your ancestor, then that is a “reasonable chance”, I figure.

** The question is not how many of the genes are SHARED between you & an ancestor, but how many you ACTUALLY INHERITED. ** The difference might seem subtle, but we cannot assume that our parents have entirely complementary gene sets.

OK, moving from that point, it is a probability issue:

chance to pass on a gene: 50%

# of genes: 50,000 (just taken from story, I don’t know)

“reasonable chance” you have no genes from an ancestor: 50% (I am choosing this for simplicity, after seeing the calculation it should make sense)

solve: “number of generations till reasonable chance no genes from ancestor”: call it “x”

——————

“chance a gene does NOT make it through all ancestors”: (1 - [chance to pass on gene]^[number of generations]) = (1 - 0.5^x)

“chance NO GENES make it through all ancestors”: (1 - [chance a gene does not make it]^[number of genes]) = (1 - (1-0.5^x)^50,000)

Solving for x, this gives ~ 16 generations. So it takes ~ 16 generations for someone to share NOT EVEN ONE GENE with an ancestor.
Note that it is POSSIBLE for this to occur much sooner. E.g., if you look back “only” 13 generations, the chance is 0.2%.

Mike

Crossing over certainly complicates the situation, but even if you take it to the limit, and suppose that all three billion base pairs in the human genome are inherited independently — even then you can only go about 31 generations back before you run out of ancestors.

As for the spam screening: Unfortunately, it hasn’t been quite stringent enough to stop all the spammers.

But the main reason I wrote this comment was just to point out that your spam screening requires a certain fairly high level of intelligence; it’s not only spam-screening but uninformed-person-screening.

I’d say “at least” instead of “roughly.” Modulo all the usual caveats about in-breeding, X-chromosomes, etc., a good way to look at how many ancestors passed genes along to you is by working backwards, progressively (or is it regressively?) divvying up your genes between your parents, grandparents, great-grandparents, and so on, but keeping in mind there is a bit of a crapshoot at each step. That is, while it’s true (by assumption) that *exactly* half your genes come from your mother and half from your father, it’s not true that *exactly* a quarter come from each grandparent. The quarter each is only approximate, with a bit of binomial drift. Let me explain by simplifying the genome to consist of exactly 8 genes, which we want to trace back three generations.

By assumption, your 8 genes come 4 from your father and 4 from your mother. But to go the next generation back, you need to consider the genes your parents *didn’t* pass along to you from their 8-gene genome. Of the 70 (=8-choose-4) ways each of your parents can divvy his/her genome, only 36 ways give 2 of your genes to each grandparent. The other 34 ways are a 3-1 split or (rarely) a 4-0 split. So it’s reasonably likely that your 8 genes come in something like a (2,2,3,1) split among your grandparents. The 1 is significant because it means that, in this scenario, at least one great-grandparent gets left out of the “you” lottery. It’s also reasonably likely that at least of the 2’s will fail to split 1-1 at the great-grandparent level, so you may only be related to 6 of your 8 great-grandparents. Thus your 8-gene family tree may look something like this (pardon the crude typesetting):

8 you
/ \
/ \
4 4 parents
/ \ / \
2 2 3 1 grandparents
/ \ /\ /\ /\
1 1 2 0 1 2 1 0 great-grandparents

A more careful analysis and/or simulation, which I don’t have time to do correctly, could give a precise answer for the expected number of ancestors who “exherit” your genes. In the 8-gene case, my guess is it’ll be between 6 and 7 when going back 3 generations. For 50,000 genes going back 16 generations, I would expect the expected number to be at least a few thousand shy of 50,000. That’s just a semi-educated guess though.

The popular perception of genetics is complete bullshit anyway; genes matter in our makeup far less than most people think they do.