What is the probability that a couple has no common defective gene?

If a couple has no common defective gene, they can produce a big healthy population from just two people, right?

What is the probability that a human couple (especially of different races) has no common severly (minor defects like a gap in teeth that is a small health threat don't count) defective gene?

Present a calculation.

• One's definition of "common" and "defective" are quite important for a question like this. For example, different genes that affect different stages of a metabolic pathway might be considered "common". A sickle-cell hemoglobin gene might be considered severely defective if it produces sickle-cell anemia, but not defective if it lessens the severity of malaria infection. Jun 15 at 23:51
• Your starting assumption is wrong. They can make a healthy first-generation population, but recessive defects can start pairing up in the second generation.
– Mark
Jun 16 at 22:56
• @Mark I did count all 4 variants of pairing. So your critique is wrong. Jun 17 at 2:23
• @porton I don't understand what you mean by "I did count all 4 variants of pairing." Could you clarify? Jun 17 at 15:02
• @Armand each parent has 2 genes, so there are 2x2=4 variants of pairing and I did take this into account. Jun 17 at 16:28

"If a couple has no common defective gene, they can produce a big healthy population from just two people, right?"

No. As described in the review "The genetic basis of disease" Essays Biochem. 2018 Dec 3; 62(5): 643–723. Published online 2018 Dec 3. doi: 10.1042/EBC20170053 "we now know that, on average, each individual has several hundred variants that are either known, or predicted, to be damaging to gene function, including roughly 85 variants that lead to truncated (incomplete) protein products."

Since a given 2nd generation offspring of a founding couple might have both their copies of a given gene be the exact same version from one grandparent, if that version is defective, both the offspring's copies will thus be defective. This is the consequence of inbreeding and is why for example conservation biologists try to preserve as many different individuals as possible as founders in a captive breeding program.

Genetically determined metabolic disorders are rare conditions that affect about one in 2000 newborn babies. These conditions can cause serious illness, and may cause death.

The size of human genome is 30000 genes.

This means that the probability y of no common defects (due to no better data I could find, I calculate under the wrong assumption that all the fetuses in the study survive at least till birth) is calculated as 1-y = (1-p4)30000 where p is the probability of a defect in a single gene, because there are 4 recombinations (I assume for simplicity the same probability for all genes and the same for men and women, I assume all people are from the same uniformly "intermixed" ethnos, and maximum one defect per gene).

Probability (under the same assumptions) of a baby to have a defect is 1/2000 = 1 - (1-p2)30000.

It remains to do math. Sage code:

``````var('p y')
p = find_root(1/2000==1-((1-p^2)**30000), 0, 1); p
find_root(1-y==(1-(p^4))**30000, 0, 1)
``````

We have p = 0.00012911558610889591, y = 10-11 that is almost impossible.

• Calculations corrected. Jun 15 at 15:02
• Please present improved calculations Jun 15 at 15:06
• This is all arithmetic and no genetics. I don't think your question can be answered with arithmetic. Jun 15 at 22:52
• I simply don't think you can make the sweeping assumptions you're making and arrive at a reasonably accurate answer to your question. Genetics matters and it changes your assumptions, but you're not accounting for genetics. You're just doing math. Jun 16 at 3:39
• @porton Genetically determined metabolic disorders are only a subset of all genetically determined disorders. Genes involved in metabolism are only a subset of all genes. Your other assumptions are wrong as well. In particular, you are forgetting that 2nd generation and later offspring of a couple can inherit both copies of a given gene from one of the 2 founders, so each of the 2 founders must have no defective gene copies at all in order to prevent this. Thus, the answer to your first sentence question is "no". Jun 16 at 6:55