We all have 23 pairs of chromosomes - 22 pairs of non-sex chromosomes called autosomes and one pair of sex chromosomes (XX = female, XY = male). We inherit one copy of each autosome from our mother and one copy from our father - likewise each parent contributes one sex chromosome as well. So half of your DNA came from your mother and half from your father*. Typically most people assume that you inherit exactly half of your maternal DNA from her father and half from her mother - or 25% from each grandparent - and the same for your father's family. But that isn't necessarily true.
The reason why this isn't true is that during sex cell formation, chromosomes of the same type find each other, get tangled up and can swap segments. This is called recombination. It creates chromosomes that contain DNA from both grandparents. It's a random process so the relative amount of DNA from each grandparent in a single chromosome can vary a lot. As the sex cell continues to mature, the chromosomes need to separate so that the cell ends up with half the number of normal chromosomes. This process is also random. It is possible for more genetic material from one grandparent to end up in the mature sex cell that is used for fertilization than the other grandparent. In fact, it's been calculated that there is a 1 in4 million chance of all 50% of a parent's DNA contribution coming from only one of their parents!
Since each sex cell has experienced both chromosome recombination and random assortment independently, even full siblings can inherit markedly different quantities of DNA from their grandparents. Saying you have 25% of DNA in common with each grandparent is just an average estimate. Great grandparents you might expect 12.5% of DNA in common, great great grandparents only 6.25% and so on and so forth. But the reality is that it's possible to be quite a bit less (or sometimes more) than that, depending on how recombination and assortment occurred.
This is why it's possible to share no DNA in common with a significant chunk of 3rd cousins and beyond - even with a verified paper trail of ancestry. Your siblings might match with a distant cousin and you do not - not necessarily because of a non-parental event (NPE), but simply due to normal cellular processes. To help with visualizing how chromosomes might pass from generation to generation, I've drawn a pedigree with one pair of chromosomes. For simplicity's sake, I started with non-recombinant chromosomes in the first generation of ancestors. In the 4th generation, the second cousins do not happen to share DNA from the same great grandparent, although they are descendant from the same couple.
Hopefully this clears up some confusion and convinces you that you need more relatives to spit in tubes to really get at the migration of your family. 🤣
(*Turns out there is a really rare chance that you can inherit more DNA from one parent than the other - check out uniparental disomy.)
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