### Grandpa’s genes

Are you genetically related to your grandfather?

I know I am. I’m male, so my Y-chromosome came from my dad (left). And he’s male too, so his Y-chromosome came from his dad (right).

But I’m getting worried about my sister. I know she got an X from dad, which was grandma’s to start. There were 22 other chromosomes in the lucky spermatozoon which fertilized the egg which became her first cell. Each of those were picked at random–a 50% chance it came from grandma and a 50% chance it came from grandpa. Could they all have come from grandma? Could she have missed all 22 chances at inheriting grandpa’s genes? It’s not super likely–the probability is $1/2^{22}$, or about one in four million.

But there are ~160 million women in America–could it be that 40 of them are unrelated to their biological grandfather?

I thought so, until I remembered chromosomal crossover–the dance where your genes do-si-do. Before the climactic moment of meiosis, when all of my dad’s chromosome pairs lined up, then got yanked into two bunches (one of which begat my sister), before that, both sets of grandparental chromosomes were hanging out together. On occasion, they would swap pieces (when called to do so by recombinase proteins).

Hoping to preserve the idea that there might be these 40 pseudo-granddaughters wandering around, I checked out just how often. According to a genetical study of a few hundred icelandic families, between generations there is a one percent chance of a crossover in each stretch of a million DNA base pairs. There are about 3 billion base pairs in the genome, so this makes a no-crossover generation pretty unlikely; one in a trillion zone. So maybe this has happened to an ant, but never to a human.

Takeaway: for better or worse, you are related to your relatives.