# How to determine the chances of inheriting an autosomal recessive disease if the carrier status of parents is unknown?

My question is about determining the carrier chances of an autosomal recessive disease without actually testing for it and to validate my understanding about autosomal recessive disorders.

In order to clarify my question I've drawn the following example scenario:

In this example the carrier status of only one of the family members is confirmed (child 1) as that child is confirmed to be affected by a autosomal recessive disease. To my understanding that makes it 100% certain that both parents have been carriers.

With the understanding that both parents are carriers, child 2 has naturally a 25% chance of being affected, 50% of being not affected but being a carrier and 25% of not being a carrier at all. As we can exclude child 2 from being affected in this example, there are three options left for child 2. To my understanding: a 66% chance of child 2 being a carrier and a 33% change of not being a carrier.

The three grandchildren (children of child 2) are all unaffected but their carrier status is unknown too. The carrier status of partner 1 and partner 2 of child 2 are also unknown. Let's say that the families of partner 1 and partner 2 have no history of similar autosomal recessive disorders and we can therefor assume but not exclude (by natural mutation chance) they are not a carrier.

Is it correct to therefor assume the following about the grandchildren:

• If child 2 is a carrier (66% chance): The chances of the grandchildren being a carrier are 50%.
• If child 2 is not a carrier (33% chance): The chances of the grandchildren being a carrier is still 33% as they are not affected but the carrier status of the partners is unknown.

So, what are the overall chances for the grandchildren to be carrier? 50%? Is my understanding and are my assumptions correct in this example?

Let's say that the families of partner 1 and partner 2 have no history of similar autosomal recessive disorders and we can therefor assume but not exclude (by natural mutation chance) they are not a carrier.

is inconsistent with:

The chances of the grandchildren being a carrier is still 33% as they are not affected but the carrier status of the partners is unknown.

If you're assuming this is a rare enough condition that it's reasonable to assume that partners with no family history are not carriers, you should be consistent with that assumption. In that case, if child 2 is not a carrier there is no way their offspring can inherit the carrier status from them.

So, 0.66 * .50 + 0.33 * 0 = 33% chance that they are carriers.

You may want to consider de novo mutation or that partner 1/2 are carriers depending on expected frequencies of those events, and not all genetic conditions are quite so perfectly Mendelian so that may also affect estimates a bit.

• De novo mutations are an interesting exception. But yes, it's very rare. The family history is mostly unknown. The only known factors are `child 1` is affected and `child 2` isn't affected. So my assumption is that father and mother (blue) are 100% carriers and therefor `child 2` still has 66% chance of being a carrier? While the chances of the grandchildren carrying (assuming it's rare and therefore partner 1 and 2 aren't affected, is 33% like you calculated? As in: `child2(0.66 * .5) + partner(0.33 * 0) = 33%`. Obviously if child 2 isn't a carrier grandchildren cannot be a carrier. Jan 9, 2023 at 9:24
• @BobOrtiz Yes, that's correct. Jan 9, 2023 at 21:59