What are the chances that two children of the same couple will have the same genes without being identical twins?

If I randomly select half the chromosomes of the male and female eventually I will select the same exact half for both a second time. How often does this occur? Is this considered a twin if it is born at a different time as in years apart?

• Just because the poster might not have an intuition for why this is obviously very low doesn't make this a bad question. In fact, this is interesting. Commented Feb 10 at 17:53

The chances are effectively zero.

Even in the absence of recombination, this calculation involves choosing the correct member of a pair from each of the 23 chromosomes, from both the father and the mother.

223 × 223 = 246 = 70,368,744,177,664

So, less than a 1 in 70-trillion chance. For some context, only about 117 billion humans have ever been born in history.

A more accurate calculation would include recombination, which occurs on all chromosomes (except the XY in males). Incorporating this would require knowledge of the recombination profile and number of genes for each chromosome. It would make the above probability many, many orders of magnitude less likely. (Like, it's very possible there are more potential combinations of two parents' chromosomes than there are atoms in the universe.)

If this were to occur, I personally wouldn't call them twins. That term is consistently used to reference a single pregnancy, regardless of whether the children are genetically identical.

There is a one in 1/(0.5)^46 = 70 trillion chance of this happening in theory without accounting for recombination. However, there is a 6% chance of this happening when there are 4 chromosomes, which is applicable to real plant and animal species! With real human data, which takes into account recombination, hotspots, etc., there is a one in 4.771 * 10^39 chance of this happening. This is one in a 5 thousand billion billion billion billion chance, and only 100 billion humans have ever lived.

Extra information:

Theoretically, there is a one in 17.59 trillion chance of independent assortment happening so that the exact autosome combination is the same (0.5^44).

There are chromosomes A and B. Uppercase: from mom. Lowercase: from dad

Mother: A1 A2 B1 B2

Father: a1 a2 b1 b2

1st step: assort chromosome A. 4 options. (A1 a1, A2 a1, A1 a2, A2 a2) 2nd step: assort chromosome B. 4 options. (B1 b1, B2 b1, B1 b2, B2 b2) Now, there are 16 options for the child for 2 chromosomes. Imagine a pairwise matrix of these options; the top left to bottom right diagonal represents the pairs in which two children have the same chromosome combination. This is 16 children out of a total 16*16, or 0.0625 = ~6% chance of happening. This means this must happen regularly for some animal species! https://en.wikipedia.org/wiki/List_of_organisms_by_chromosome_count

If we increase the chromosome count to 22, there are 4 options for each chromosome, so there is a one in 1/(0.25)^22 or 1/(0.5)^44 or one in 17.59 trillion chance.

Different-sex siblings can never be 100% genetically identical.

For men, the Y-chromosome will always be the same and brothers will have a 1/2 chance of having the same X chromosome. For women, the X chromosome from the father will always be the same and there is a 1/2 chance of getting the same X chromosome from the mother. Since they have to be both the same sex (50% chance) and get the same X chromosome, this increases the odds by 4 to (1/(0.5)^44)*4 = 70 trillion. This is why the sex chromosome acts like an autosome.

For full siblings, there is an observed mean of 0.50146 relatedness with an SD of 0.03761 (from the supplementary table). To get this halfway to twins, we would need 0.25/0.03761 = 6.6471683063 SDs above the mean. This occurs, on average, once in (1 / (1 - norm.cdf(6.6471683063))) = 66,937,665,852 events. To go the rest of the way to full twins, we will need to be (1-0.50146)/0.03761 = 13.2555171497 SDs above the mean, which is one in 4.771 * 10^39 events!

Since about 100 billion humans have ever lived, and a “chance” half-twin half-sibling occurs once every 67 billion humans, this has probably happened before. Interestingly, this 75% genetically related sibling pair, derived from empirical data, has about the same probability of about 75% of the chromosomes happening to assort the same way.

More extra information:

Darlingtonia's answer is good. However, there is recombination, which makes it extremely more unlikely than it already is. The existence of inbreeding helps with this a bit, as sequences might be exactly the same between mother and father already.

Let's look at some data.

This paper used real allele frequencies to generate a relatedness distribution for full siblings. https://academic.oup.com/beheco/article/20/2/410/219031 Another paper looked at relatedness of full siblings had has standard errors available. https://academic.oup.com/beheco/article/29/2/468/4819097

But this isn't fine grained enough. Let's make a simulation. Also, let's assume the siblings will both be women or both be men. Since this only happens half the time, the real odds are halved. We will also ignore recombination hotspots, discussed here: http://adamauton.com/adam_auton_thesis.pdf

23*2 chromosomes. 1.6 recombinations per chromosome (we are ignoring variation between different chromosomes): https://book.bionumbers.org/what-is-the-rate-of-recombination/.

Length of the average chromosome: 6.3 Giga-base-pairs divided by 46 = 136,956,522. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6391780/

136,956,522 base pairs make up each of the 46 chromosomes. Recombination happens 1.6 times on each chromosome.

137 base pairs make up each of the 46 chromosomes. Recombination happens 1.6 times on each chromosome. Allow two parents to produce 10 offspring in this way. Then, calculate the average relatedness coefficient between the children.

We could use the infinite allele model but adjusted for the baseline relatedness we’d expect due to chance, which, for four alleles, is 0.25. However, this would incorrectly classify genetic twins as only 75% related.

Therefore, we could use chunks. The length of shared chunks can be used to estimate genetic relatedness. We would also need to use SNPs, not total base pairs, as most base pairs will be the same for all mammals.

At this point, we are making way too many assumptions for this simulation estimate to be realistic.

Instead, let’s look at real data:

“IBD sharing between pairs of full siblings in the SAMAFS and Hemani20k data, which have mean IBD proportions of 0.501 and 0.502” https://journals.plos.org/plosgenetics/article?id=10.1371/journal.pgen.1007979

We want both homologous chromosomes in one individual to be identical by descent to make “twins.”

For full siblings, there is an observed mean of 0.50146 relatedness with an SD of 0.03761 (from the supplementary table). To get this halfway to twins, we would need 0.25/0.03761 = 6.6471683063 SDs above the mean. This occurs, on average, once in (1 / (1 - norm.cdf(6.6471683063))) = 66,937,665,852 events. To go the rest of the way to full twins, we will need to be (1-0.50146)/0.03761 = 13.2555171497 SDs above the mean, which is one in 4.771 * 10^39 events!

Since about 100 billion humans have ever lived, and a “chance” half-twin half-sibling occurs once every 67 billion humans, this has probably happened before.