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#### What’s the probability that two children share one whole copy of the X Chromosome without sharing a father?

I’ve made an X Chromosome model that predicts shared X DNA percentages and ranges for various ancestors, but I haven’t yet calculated ranges for siblings or any other relatives. Anyway, this is a simple probability question.

Sometimes people get a certain axiom reversed and it isn’t necessarily true anymore. The correct axiom is that two sisters who don’t share one full X Chromosomes (out of two copies each) cannot share a father, i.e. they must be half-sisters who share a mother. The way to get it backwards is to say that, if two sisters share one full half of an X Chromosome, that they must share a father. Now, I don’t know what the probability is of an exception occurring to the incorrectly-stated axiom, but I know it isn’t zero, and we can probably get a good approximation of the percentage.

14% of the time the X chromosome doesn’t recombine in mothers. This means, if we’re assuming that events are independent, the chances that any two siblings will have X Chromosomes that weren’t recombined is 1.96%. But half of the time that that happens, they will share none of that X, and the other half of the time, they’ll share the whole X from their mother.

So, still assuming independent events, any two siblings who share a mother should share no X DNA on one X Chromosome 0.98% of the time. Likewise, they should share a full, un-recombined, X Chromosome 0.98% of the time. Some people say that it’s more like 3% of the time that siblings will share a full X Chromosome. That may be, although I don’t know where that information comes from.

I find it quite plausible that certain women are more likely to pass an X Chromosome un-recombined, and others are less likely to do so. My own mother has passed more of her father’s DNA than her mother’s DNA six out of six times, so it seems that recombination events are not necessarily independent as I assumed above.

In that case, probably more than 1% of the time two siblings who share a mother will share no DNA on one X Chromosome, and likewise more than 1% of the time we’ll see the case of them sharing a whole X Chromosome copy, possibly being mistaken for half-siblings who share a father.

Feel free to ask me about modeling & simulation, genetic genealogy, or genealogical research. To see my articles on Medium, click here. And check out my nifty that’s based on the first of my three genetic models. It lets you find the amount of an ancestor’s DNA you have when combined with various relatives.