Grand Randomness

First cousins, all 25% Puerto Rican in theory.

Given that this vacation in the North Carolina Outer Banks may be the biggest confluence of my family ever, I have been thinking a lot about family and how it forms us individually. It's amazing to see all of the parts of the great machine in motion together over an extended period of time.

One thought I had concerns genetic inheritance from grandparents. We know that half of our DNA comes from each of our parents, and their DNA comes equally from their parents. It might seem reasonable to assume that we therefore get exactly a quarter of our makeup from each of our four grandparents, but I realized that assumption is not quite accurate.

The reason is that our DNA is grouped into chromosomes, 23 each from our mother and our father. This quantization prevents uniform inheritance. Right off the bat since we receive an odd number of chromosomes from each parent, we cannot receive an even number from each of our parents' parents. If I have 12 chromosomes from my mother's father, I have 11 from my mother's mother, and the split cannot be made even.

Moreover, there is nothing guaranteeing an even split. Whether or not each chromosome from our mother comes from her mother or her father is essentially a coin flip, and like coin flips the selection for each chromosome is independent. So, the fact that the chromosome 8 my mom passes on to me might come from her mother has no bearing on whether or not chromosome 9 does. That means it is theoretically possible for her to pass on only her mother's chromosomes or only her father's, though that is only as likely as flipping 23 heads or 23 tails in a row (about one in four million). Such children are genetically equivalent to children of one grandparent, and genetically unrelated to the other!

Therefore consider first cousins. There is good reason to expect they could take after their shared grandparents to differing degrees because they will inherit different proportions of their grandparents' DNA (to say nothing of the fact that they are inheriting from different subsets of that code due to having different parents).

How significant is this variation? Well, if my calculations are correct a full 32% of people inherit the most equitable 11/12 split from a given pair of grandparents, and 91% are no worse than an 8/15 split. So most people are relatively even combinations of their grandparents. But the flip side of that conclusion is that about one in eleven inheritances gets twice as much of one grandparent as the other. Since we inherit from two sets of grandparents, it is almost double that probability that we have at least one lopsided inheritance.

If these assumptions hold (and I don't expect they are changed by higher order effects), 18% of people, almost one in five, has received a lopsided amount of DNA from one grandparent.The effects of that randomness only multiply through subsequent generations, meaning it's even more likely inheritance from great grandparents isn't equitable. After all, we all have 64 great great great great grandparents, but only 46 chromosomes total. Someone (or 18 people) is going to be squeezed out, save for other effects like crossing over.

For me there are two takeaways of this reasoning. The first is that it is indeed possible to take after a particular grandparent more than the others, as far as genetics go anyway. The second is that it would be really fun to get everyone in my family's genomes sequenced so that all of this movement could be charted through the family tree rather than merely speculated on.