It seems obvious at first: your child shares half your genes, your child’s child share half of your child’s genes, 1/2 * 1/2 = 1/4, so clearly your grandchildren share 1/4 of your genes, simple!
But it seems to me that this isn’t accurate, correct me if I’m making any obvious mistakes:
When a gamete (i.e. sperm or egg) forms, it one half of your chromosomes, or one for each chromosomal pair. However, all that is guaranteed is that there is one for each pair*, not which one it is. Meaning you’re in no way guaranteed that any given gamete has exactly half your genes (which is, in fact, impossible given that a gamete has 23 chromosomes anyway, but the statement holds even if there were an even number).
So… this seems like a binomial distribution to me, assuming each chromosome in a pair is equally likely, it’s the chance that we get 11 or 12 (ceiling and floor of 23/2) “successes” from your genes out of 23 events. Which means a given grandchild only has about a .322 probability of sharing 1/4 your chromosomes (assuming no incest was involved). Though I am assuming each event is independent, which may be a problem? We’re also, obviously, ignoring things like chromosomal mutations that muddy things up by making the gamete not have precisely your or your spouse’s chromosome. Maybe that influences the 1/4 statement?
Is saying that a grandchild “shares 1/4 of your genes” just a simplifying statement since the mean is centered around your child’s gamete having 1/2 of your chromosomes, or is there an actual factor that causes a given grandchild to have ~1/4 your DNA with either near certainty or much better odds than .322? Obviously I simplified a lot, maybe taking out those simplifications narrow the odds?
Okay okay, you’re not guaranteed there’s exactly one of each pair either, but I don’t want to calculate this even further. Feel free to mention why if it’s actually directly relevant to the question though.
I phrased that really poorly, I realize. Obviously when your gamete forms it’s guaranteed to half have your genes, given that they’re your genes. What I meant was that your child’s gametes aren’t guaranteed to have half your genes because which chromosome in a pair that ends up in a given gamete is random.
Your question amounts to the following. Throw a fair coin 23,000 times (approximately the number of genes). Will heads come up exactly or approximately 11,500 times. Obviously the latter. But the more you deviate from 11,500, the less likely it is. On the other hand, exactly 11,500 is also very unlikely. It is very likely that the number will lie within 105 (approximately the square root of 11,500) of 11,500. This ignores the possibility of mutation.
So what you’re saying is that across the population, it’s very very close to 25% from each grandparent, but that in any one person, it may vary somewhat- for example one person may have 23.5% from one grandparent, and 26.5% from another?
I think the OP question is well stated except for the one misspoken bit that got fixed. I have wondered the same thing. I DON’T think we get our genes randomly, I think we get our chromosomes randomly. That is, getting a particular gene from your father is a VERY strong predictor that you got another gene on the same chromosome from your father.
However I am not sure. More significantly, I have tried to ask the question several times over the years and have never gotten a straight answer.
One more point. I think I have heard hints that there can be some mixing of genes within a chromosome, by some other mechanism, so the prediction I describe is strong but not absolute. Overall, though, it has been weirdly difficult to get an answer to what seems a simple enough question.
There’s “crossing over”, so you don’t get one or the other of the chromosomes, but generally a mix of them. So each chromosome gives some fraction from each of the two grandparents, and it’s not like tossing [del]a coin[/del] 23 coins. Still, the answer is “around 25%”.
However, when your reproductive cell forms with half of your genes, I thought that it more or less went through each and every one of your pairs and more or less selected your mom’s gene or you dad’s gene by random and didn’t guarantee that half of the genes selected would be your mom’s. So you could have a sperm cell that is 67% your mom and 33% your dad. A child formed from this sperm cell would therefore share more genes with grandma than grandpa, assuming you didn’t up and do your sister or something.
First a couple broad statements which probably are not quite what the OP was thinking…
Most DNA is nuclear and is inherited from both parents. A small fraction is mitochondrial DNA (mtDNA) and is not within the cell nucleus. The mtDNA contains a few genes and is inherited from your mother but not your father. In that sense you inherit slightly more genes from your mother than your father. Following that back another generation and you inherit this mtDNA from your maternal grandmother and not the other grandparents.
Secondly, the X chromosome contains more genes than the Y chromosome. Generally females have two X chromosomes and no Y chromosomes; males have one X and one Y chromosome. We all inherit an X chromosome from our mothers. Males thus receive slightly more nuclear DNA from the mother than from the father. Tracing that back a generation for a male and both grandmothers thus contribute slightly more nuclear DNA and the paternal grandfather slightly less.
More directly to the OP’s query
Setting aside the issue of sex chromosomes, the OP is really asking about whether meiosis guarantees precisely 50% assortment of nuclear somatic (somatic = not sex chromosome) DNA. And the answer is no.
ZenBeam mentioned crossing over (aka recombination) that occurs during gamete formation. This does shuffle your parent’s chromosomes so you are not receiving a chromosome that is identical to your grandparent’s chromosome. Genes that are physically close together on the chromosome (said to be linked, or in linkage disequilibrium) do tend to stay together as Napier mentioned.
Each chromosome has many recombination “hot spot” points where crossing over is more likely. The odds that there is a crossing over at any particular hot spot is low, but by sheer numbers each chromosome ends up with some cross overs. But there is no guarantee that the resulting recombinant chromosome is precisely 50/50 from each parent.
On average it is certainly true that we share 25% of our (somatic nuclear) DNA with each grandparent. But it is not necessarily exactly 25%. Given the number of cross overs during gamete formation there is not likely to be much deviation from the mean of 25%.
Exactly how many cross overs occur is not uniform. In fact it seems to be partially genetic with at least six identified gene loci cited as being responsible for the variation in number of recombination events. There is even a variation between males and females in the average number of recombination events. Females have about 1.6 times as many recombination events during egg formation as males have during sperm formation.
The same study cited:
Not to get too technical, but the manner in which they identified a recombination event leaves it open that the true number of recombinations is higher.
Crud. I hate it when I know something I type was off a bit but I can’t see the problem within the edit window. Substitute autosomal for somatic in my prior post.
Well, possible, yes. Hypothetically. But incredibly unlikely.
As a practical matter it would not happen (even leaving out mutations and such) - the odds are just too stacked against it.
In the normal process of meiosis sperm are made in such a way that sperm A and sperm B have mutually exclusive DNA.
It is not quite so simple in egg formation. As meiosis proceeds one parent cell gives rise to one egg and three non-viable cells.
In order to have siblings not share any DNA it would be easiest, theoretically, to have sperm A and sperm B (as described above) each fertilize separate eggs. Those eggs would come from separate meiotic processes and have beaten the odds to have recombination events exactly alike.
Ignoring DNA that’s common to all humans and only focusing on the DNA that we care about when we talk about person X sharing Y% of person Z’s genes, is there an answer to the following question: what percent of genes on average do siblings share. And furthermore, if it’s possible to answer, what percentage of DNA would a niece or nephew share with their aunt, on average of course.
For example, if my sister and my boyfriend had a kid together, could you say what percent his genes would be the same as mine (X% mine?) and the same as my boyfriend’s (approximately 50% his), on average?
Just to corroborate, because of how meiosis and crossing over work, it is possible for you and your sibling to share anywhere from 0% to 100% of your DNA just by random chance. If you do the numbers, however, the odds are very very very very good that the true figure is very very very very close to 50%. The probability of having two gametes that share all of the same chromosomes is 1:2^23, which is about 8.4 million. And that’s ignoring recombination, which shoots that 8 million figure up by lots of orders of magnitude.
So, while it’s possible that your grandchild could share anywhere from 0 to 50% of your genes, it’s very likely that it’s actually very close to 25%
Similar calculations apply to aunt/nephew and other similar calculations. You can do the math as if every cross is a 50/50 split and feel reasonably confident that your answer is very close to the truth, but there’s always the understanding that it could be slightly off.