But 1 in 10 billion was a wild overestimate. The chance would be much less than that even if, counterfactually, there was a 70+% chance that independent crossover events would be identical. Is there a “disorder” in which chromosome crossover doesn’t occur, or occurs only with low probability? If not, the chance asked for by OP is much less than 1 in 10 billion. Sorry if the approximation Zero isn’t close enough for you.
The followup question (chance that siblings are as genetically distant as first cousins) might be more interesting. Again, the possibility of a reproductive anomaly may be greater than that due to chance pair-splitting.
This is actually the technical definition of relatedness (which is basically the same as the folk one). When geneticists speak of relatedness, they are speaking about what percentage of genes (alleles) are identical by descent from a common ancestor, not just that they are coincidentally the same.
Crossing over isn’t entirely random. For one, there are mechanisms to guarantee at least one crossover per chromosome. Then there are mechanisms that prevent crossovers from happening too close to each other, which also limits the total number of crossovers. There are also “hotspots” where crossovers occur at much higher than the rate expected from purely random site selection.
In any case the statistical model is still “select n crossover points from 150 million possible positions on each chromosome”. The naive model might pick assume n has some simple distribution, and the crossover points are distributed uniformly. A more sophisticated model greatly restricts the probabilities, by accounting for the true distribution of crossover frequencies across each chromosome, and how each selected crossover reduces the nearby frequencies.
Even accounting for all of the non-randomness in crossing over still makes the OP’s situation damn near impossible. If there are, say, a mere 10 crossover hotspots per chromosome, each selected by coin flip with p = .2, the probability of any particular configuration is 1 in 10 million (which is a gross overestimate). Then, accounting for crossovers in this very simplistic way, the probability of any particular crossover/reassortment is (.2^10)^22*(1/2)^22 = 4 chances in 10^161. And that figure, far larger than the number of particles in the universe, is still many orders of magnitude too high. I think that number is close enough to zero for me…
From above -
Crossover happens 2 to 4 times per chromosome;
23 chromosomes in a sperm or egg.
so for simplicity, about 100 “pieces” and A and B would have to be complementary.
That’s 1 in 2x(2^100)
Then it has to happen the same for the other spouse.
This of course assumes the crossover process “splits” at the same location on the chromosome every time, which I assume is not necessarily the case?
Then you have to figure the odds of this happening to a egg and a sperm that happen to meet and create a viable blastocyte which grows to term with no problems.
Twice…
To the same couple…
I think the general consensus answer is correct - “odds are, not likely in the age of the universe”. (let alone in the time since humans have been human).
Besides, if it did happen, who would know?
What are the odds you’d flip a coin a few hundred times and have it always be heads? Four times? In a row?
Noted in passing: “The Tale of the Twins Who Weren’t” is a relatively long subsection of Heinlein’s SF novel Time Enough for Love. The point to them is the old man whose memoirs the novel purports to be having encountred a boy/gjrl pair who were from the same parents, but meiotic complements of each other – the precise half of each parent’s genes discarded in meiosis to produce the gametes for one child having been saved by advanced future genetics and used to produce the gametes for the other, so that despite being legally full siblings they were genetically no more closely related than any two random human beings are.
In the story, the non-related twins thing was done on purpose, as an experiment; some experimenter separated and recombined the halves of the chromosomes by hand somehow. So that gets around the problem of how extremely unlikely it is.
No winner.. The bit being mentioned as cross-over. One chromosome pair, Mm or Ff does not stay intact. Parts of M and m with break off and cross over, so a chomosome that started as
MMMMMMMMMMMMMMMMMMM and
mmmmmmmmmmmmmmmmm pair may end up as:
MMMmmMMmmmMMmMMMmM and
mmmMMmmMMMmmMmmmMm
After a cell split.
So 1 in 70 trillion is the absolute minimum odds.
Again, also consider the odds that those particular pairs match up when an egg is fertilized, by one of a few billion sperm cells… Twice…
So the odds are not zero, but considering how many lives of universes you would have to wait out before seeing an occurrance, might as well be.
OK, I think everyone’s basically on the right track here…let me see if I can simplify it all.
Let’s start by pretending there’s no such thing as crossovers. Mom and Dad have Son and Daughter. Let’s also ignore sex chromosomes, and just focus on the 22 pairs of autosomes. Now, Mom and Dad each have two homologues they can choose to pass on for each of the 22 pairs. Son is born with 22 chromosomes from Mon and 22 from Dad. Now, when Daughter is born, what are the odds that all 44 of her chromosomes are the “other” chromosomes from what Son got? In other words, let’s say that Son got all of Mom’s paternal chromsomes (ie the ones Mom got from her dad) and also all of Dad’s paternal chromosomes. Then Daughter would need to get only maternal chromosomes from each parent. Therefore, for 44 chromosomes, she would have a 1/2 chance of getting the “right” one (the “right” one being defined as the one Son didn’t get). That’s 0.5^44, which is roughly 2*10^-13. Already, the odds are astronomically low.
Now, let’s factor in recombination. As has been explained, we don’t pass on chromosomes as intact bodies. We pass them on in chunks that can be mixed and matched. So instead of passing 44 intact chromosomes, Mom and Dad are actually passing on some n>44 of intact “chunks”. Now, calculating n is going to be basically impossible. We need to know how many recombination events occur per chromosome, where the crossover happens, how far apart they are, etc, etc. The point, though, is that n will in practice be much, much larger than 44, so the odds of our “unrelated” siblings go down that much further. Adding in the sex chromosomes will make it even less likely.
So, in summary, your upper bound is around 2*10^-13. In reality, that’s a huge overestimate, and the actual odds, while not able to be precisely calculated, are orders of magnitude lower.
OK, one can go through all of the math, which gives migraines, but is worthwhile nonetheless.
Let’s consider founder effect, which is highly well documented.
Let’s consider genetic defects in certain royal families and certain wealthy families that insisted upon inbreeding to retain the family wealth.
THEN, consider inbreeding due to geography, of which Iceland is notable as a reference.
It’s NEARLY random, but the precise “formula” doesn’t exist, but inbreeding tends towards harmful, as any undesired trait would be passed along and potentially, reinforced in future generations.
ONE generation does not a “broken” genome make. MULTIPLE generations DOES, potentially make the risk of defect become a reality.
In fact, the closer the parents are genetically, the more likely they (a) both carry a “broken” gene and (b) they would have offspring where they both conribute that broken gene.
In a different thread, the discussion was that for first cousins, only about 3% of their genetic material was from the common source great-grandparents. However, if you are talking about 1 particular gene, that’s a different story. The odds of receiving a particular gene from a parent are 1 in 2; that 2 siblings get the same one, 1 in 4. Thus the odds of 2 cousins having it - 1 in 16, 2 second cousins, 1 in 64. Their offspring - odds of getting a particular pair of bad genes from parents who each have only 1 bad, one good; If parents are Aa and Aa, odds of aa are 1 in 4. So odds of a child of siblings getting both bad genes - 1 in 16. Odds of a pair of cousins giving their child a pair of bad genes - 1 in 64.
Plus, broken genes arise spontaneously quite often. The general belief is that the hemophilia gene was ikely a spontaneous mutation for Queen Victoria or her mother, since it does not seem to manifest before that. It is unusual in that it is male-dominant, female recessive usually being only on the X chromosome, IIRC.
The general risk is if a bad gene becomes prevalent in a community so that the odds of getting it from two realtively unrealted parents is significant. Howevr, since the odds of a couple with the one bad gene each - 1 in 4 of their children will have the problem, so if that means the child will not live and reproduce, a 75% survival rate (vs. 100% for a couple without the pair) suggests that over time bad genes will work their way out of the population.
the risk in inbred monarchial family trees is that there may be multiple bad genes and inbreeding means multiple inheritance chains to retain those bad genes; so odds like 1 in 64 are underestimates.
OTOH, a bad gene like Huntingdon’s, which manifests long after most childbearing is done, will likely not have a significant effect on it’s distribution in the population since there would be no selection presures. One article I read suggested that an occurence in Colombia can likely be traced back to one source who arrived (or a sailor who left his mark) hundreds of years ago. However, now that the mechanism is understood and can be tested for, some people are exercising evolutionary pressure by choosing not to have children, or by prenatal testing.
I don’t know, but it’s easy to get cousins that look like siblings…just have two brothers marry two sisters. All the kids are 1/4 of the four grandparents.
I realize that’s infinitesimally small still, but I think you’re over-counting things. You don’t have to get a specific combination twice; the first one can be any combination. The second child is the only one that has to be a certain thing.
Secondly, it doesn’t matter that there are a few billion sperm cells, as the only important one is the one that makes the second child. If you want to say “out of a few billion sperm cells,” then you also have to give the father the benefit of “a few billion” trials to generate the right sperm. Those odds cancel out and you’re left with just the lucky sperm that fertilizes the egg. So what you need is just the odds that a single sperm cell will be the duplicate partner of its successful brother.
Ergo, all you need to know is the number of possible combinations of sperm (X), and then the father’s chances of doing his part are 1 in X.
Then you need to calculate the mother’s chance of doing the same, which I bet is just the same number X.
So then it’s just X^2. Now someone calculate X and we’ll have our answer.
Oh, and I should point out that large families help the odds a lot. For a single child family, the chances are zero, obviously. But the second kid must match her brother. Then the third kid can match their opposite-sex sibling, but then the fourth kid can potentially match two opposite-sex siblings which are exclusive, so they’ve got double the chance…
If you sum this up over a dozen kids, “the savings are substantial.”
This reminds of a reason why the chance is much smaller than the already-small chance estimated above.
A sperm has only 23 chromosomes to help it develop, yet needs to win a race against millions of its fellows. (While admittedly the traits required for a sperm to swim quickly and with purpose may not have a close relation to the traits required for an adult to have a successful career, does not the sperms’ race contribute to evolutionary selection?) If such an ensemble of 23 chromosomes does have race-winning traits, it seems especially unlikely that its exact opposite will also be a race-winner.
On a separate matter, prestigious genealogist William Addams Reitwiesner believes Victoria inherited a hemophilia allele from her mother, writing “I think you haven’t looked at the entries in the parish registers and in the Hausarchives for what is said in the death records of the brothers of Queen Victoria’s maternal grandmother.” (But I haven’t looked in those records either. )
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