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Questions 186-188 of the GRE Biology Practice Test are prefaced with this genetic pedigree:

Questions 186-188 refer to the following pedigree for the inheritance of a very rare human disease over three generations.

Genetic Pedigree

It looks like the allele that caused the "affected" phenotype was dominant because Generation II showed a 3/4 probability of having the phenotype, and it looks like it was autosomal because it affected males and females roughly equally. This is confirmed by the answer to Question 186 ("Which of the following is the most likely mode of inheritance for the disease trait?") which is "(D) Autosomal dominant".

However, why don't the offspring 1, 2, 3, 4, and 5 in Generation III show a similar rate of expression?

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    $\begingroup$ Don't pay attention to probability in pedigree analysis. The number of offspring is too small. Just look for things that can't happen and use that to rule out modes of inheritance $\endgroup$
    – De Novo
    Oct 13, 2018 at 23:55
  • $\begingroup$ @DeNovo I guess that makes sense, but questions 187 and 188 (see link in the question) talk about probability, so how do i go about answering them? $\endgroup$
    – freeradical
    Oct 14, 2018 at 2:18
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    $\begingroup$ I don't see those questions quoted here, but that's usually a two part question. Part one may require you to determine an inheritance mode, or most likely inheritance mode from a pedigree. Part two may then require you to demonstrate some additional knowledge about that inheritance mode (e.g. what is the probability that the offspring from this individual and that individual will express some trait). $\endgroup$
    – De Novo
    Oct 14, 2018 at 2:32

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Why don't the offspring 1, 2, 3, 4, and 5 in Generation III show a similar rate of expression?

Because there are only 5 individuals in that list. The entire generation III involves 8 individuals (all the offspring of one affected and one unaffected parent). The entire pedigree involves 12 offspring of an affected and unaffected parent.

When you look at III 1-5, you see 1/5 affected (0.20).

When you look at III 1-8, you see 3/8 affected (0.375).

When you look at all offspring of an affected and unaffected parent, you see 6/12 affected (0.50).

As you increase the number of offspring you consider, the proportion affected gets closer to the expected value of 0.5. Given a very rare autosomal dominant condition (i.e., I-2 is most likely heterozygous), this is exactly what would be expected. You may have to look at fruit flies, or some other prolific organism, to see it quite so clearly. Mendel looked at tens of thousands of pea plants, if I recall.

Generally, you shouldn't use the proportion of offspring that show a trait to rule out any particular mode of inheritance, especially if you're looking at a small number of offspring. You can state the probability of a particular child expressing a mendelian trait. That doesn't mean a small sample won't deviate from that probability.

You can read more about this in chapter 7 of Thompson & Thompson Genetics in Medicine.

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