Well, what you say is correct. But when we say “do two individuals share DNA” in the context above, it’s implicit that we’'re only considering the parts of the genome where any polymorphism* exists at all in the human population. Obviously at the bases where every human is identical, any pair of humans is identical regardless of ancestry.
*And, in fact, if we’re considering inbreeding, we may only be considering the subset of human polymorphism that is not neutral, that has a phenotype, which will be far less than the total polymorphism.
Mathematically, the odds are that any siblings share about 50% same DNA. The risk is that if one parent has a defective or weak gene, normally the OK version from the other parent will compensate. The danger in close relatives is that they may carry the same bad gene as one of their genes, and the child will get two copies of the bad gene and no good gene.
I guess the point is that unless there is a demonstrated problem, a family history of genetic problems -odds are there are very few genetic problems anyway. Many states and countries allow first cousins to marry, they have about 1/8 similar genes, so their child should only have about 1/16 “matched up” genes. Some studies show only about a 2% to 3% higher risk of genetic diseases for paired first cousins’ offspring.
we have 46 chromosomes, so 23 from each parent. Ignoring the shuffling that happens, simple math, the odds are 1 in 2^46. Consider 2^10 is approx. 10^3 (it’s actually 1024, so close enough…) that’s odds of almost 10^13, which is a big number, considering earth’s total population is 7x10^9. Toss in crossovers and that adds an even bigger pile of zeroes at the end of those odds.
Even discounting crossing over, the probability of “normal” chromosome assortment being identical twice is so small, that the real answer to this question is a much higher probability. The question is: what is the most plausible way that normal inheritance might mutate in a fashion that produced two siblings (which we can reasonably define as two people whose DNA comes entirely from the eggs & sperm of the same 2 parents) whose DNA is exactly complementary, and what is the probability of that. We certainly can’t answer the question definitively, but mutations to meiosis that might have this effect seem plausible at a level many orders of magnitude below (1/2)^23.
One of us is misunderstanding the math, and I realize that it might be me.
My reasoning:ignoring crossing over, the chromosome chosen from each pair can be considered the same as a flip of a coin, or 23 choices between a “heads” chromosome and a “tails” chromosome. This would give 2^23 possible combinations of “flips”, only one of which is “no duplicates”, so 1/8,388,608.
So, the first child can be any combination at all - odds are 1. The second child must pick a specific combination to complement whatever the first child “picked”. Each child has 92 chromosomes to “choose” from, 46 from each parent, 23 pairs each, and must pick 46 - i.e. from the first parent, pick A1 not A2 of the pair- and so on until they have 46. So like flipping a coin 46 times. For the “A” set (or whatever they’re called) Whether you pick A1 or A2 from dear old dad does not affect whether you pick A3 or A4 of the matching pair from mommie dearest. One pair, two coin tosses. The first child, any pair will do. The second child has no choices, they must pick the opposite, and that’s where the odds come in.
There is a real biological way that we can remove the additional requirement for unlikely probability of exactly the same crossing over happening twice on every chromosome.
In meiosis, the DNA a of a haploid (2N) cell is first duplicated to make a 4N cell where all 4 chromosomes align for crossing over. After crossing over, there is a first nuclear division 4N>2N. One of those cells gets one product of crossing over, the other gets the exact complement. The cells are still 2N, so there are two different chromosomes in each cell, each of which is complementary (with respect to crossing over) with one of the two different chromosomes in the other 2N cell. There is then a second division 2N>1N, in which the chromosomes assort randomly. So we still need the random assortment to occur identically in each 2N cell when it goes 2N>1N, but that is “only” a probability (1/2)^23.
The scenario above would only apply to fraternal twins, but we are now asking: what is the probability that, in fraternal twins, both sperm are products of the same meiosis, and both eggs are from the same meiosis? The sperm number would usually be very large of course (many sperm in one ejaculate), but we can envision spermatogenesis completing with two sperm somehow stuck together. I’d hazard a guess that maybe this is less unlikely than the probability that crossing-over happens twice identically in two different meioses.
So we’re left with the (1/2)^23 factor for chromosome assortment, the probability of fraternal twins, and the probability that the two eggs and the two sperm that create the fraternal twins are the products of the same meioses.
Some googling shows that some scientists/researchers/whoever believe that human polar bodies could in theory be rarely fertilized, but that there is no known example (or even a way of testing for it.) It is called “polar body twinning” or “half-identical twins.”
No, it only has to happen once. It does not matter what the first child is, just that the second one has to specifically pick 46 chromosomes that complement.
I.e. I flip a coin 46 times and record the sequence, whatever it is - HHTHTHHTT… Now I have to flip another 46 times, and get exactly the opposite… TTHTHTTHH… 2^46
(again, ignoring crossovers).
I vaguely remember the twins in Heinlein, I just didn’t see any great significance to it. I remember when I read it, may moons ago, my reaction was “who the heck would possibly care?” Especially when you need a DNA analysis lab (tech did not exist at the time of writing?) to verify it.
