Adjusting Genotype Probabilities

This page covers something that arises frequently in genetics and is worth becoming very familiar with so that you can recognize it instantly. If a cross of two heterozygotes (Dd x Dd) yields a progeny that has the dominant phenotype this progeny could be either DD or Dd since either genotype is possible from the cross. However, you cannot determine the progeny genotype based solely on phenotype. We often designate individuals with a dominant phenotype but unknown genotype as D_.

In such situations you may want to know whether or not the individual is a carrier (heterozygote) or homozygous dominant. You can answer the question by performing a test cross, which is a cross with a homozygous recessive individual:

D_ x dd

If you get any dd progeny from the test cross, then you know you had a carrier. In these cases you should get 1/2 dominant phenotype and 1/2 recessive phenotype (make sure you see why this is the case). If you get only dominant phenotype progeny then the individual is DD.

The important point that we want to cover here is that you can determine the probability of the individual being a carrier in advance of doing a test cross. This is quite important since we will often have to deal with questions about this individual and we are unable to do a test cross to determine the actual genotype. Therefore, we need to know the probability of each possible genotype so that we can deal with these questions (as covered elsewhere).

To see how we can determine the probabilities of the possible genotypes, let's start with the original cross mentioned above - the one with two heterozygotes. As you know:

Dd x Dd  -> ¼ DD, ½ Dd, ¼ dd

As shown, you can predict the frequency of each genotype and phenotype in advance of the cross. However, in the case discussed above you take a progeny with the dominant phenotype and want to know what is the probability that this individual is Dd (as opposed to DD)?

Looking at the cross you might think that the answer is ½. This is not true, however. The reason that it isn't true is that the expected frequencies given are a prediction BEFORE the cross, but you know after the fact that the individual is NOT dd. Therefore, you have to adjust the probabilities to account for this knowledge: what you really need to know is, what is the probability of Dd given that it is either DD or Dd but NOT dd?

When dealing with a situation like this, what you do is "adjust" the original probabilities. What follows here is a simple way to calculate the adjusted probabilities:

• Take all of the genotypes that the individual could be. In our example these are DD and Dd.
• Express the prior probabilities of these with a common denominator, in this case these are ¼ and 2/4 for DD and Dd.
• Add the nominators: 1 + 2 = 3.
• Recalculate the probabilities using the original nominators and this sum as the new denominator:
• DD becomes 1/3, Dd becomes 2/3

These are the adjusted probabilities. Therefore, in our question the probability that the individual is a carrier given that the individual is D_ is 2/3.

This "adjustment", or “correction”, is very common so make sure you that you understand how to apply it and when you would apply it. The example dealt with here is probably the most common situation you will see, but other situations can arise. What they will share is that you are dealing with an individual who can only be one of a limited number of the genotypes that were originally possible (from a cross).