There is one important calculation rule that you have to keep in mind when working with probabilities: if this AND that are both supposed to happen you should multiply the probabilities. Think about the situation where the same allele is passed on to the offspring AND to the grand-offspring. If this OR that is supposed to happen you should add the probabilities up. Think about the situation where allele 1 OR allele 2 of a gene is passed on to the offspring. It will become more clear with an example.
The additive genetic relationship (indicated with an ‘a’) between two individuals depends on the number of common ancestors and on the number of generations to each common ancestor. We will go through the steps to calculate the additive genetic relationship between two animals. Consider pedigree 2 in figure 6.
Question: What is the additive genetic relationship between animals J and K?
Answer in four steps:
Step 1: find the common ancestors.
The common ancestors of J and K are F and G.
Step 2: how many generations (meiosis) are there to each of the common ancestors?
Ancestor 1: F. The number of generations from J to F is 2, and from K to F is also 2.
Ancestor 2: G. The number of generations from J to G is 2, and from K to G is also 2.
Step 3: calculate the additive genetic relationship between the animals.
Through common ancestor 1: The probability that J and K have alleles in common that originate from common ancestor F is equal to the probability that the same alleles are passed on from F to H and from H to J and from F to I and from I to K. So we need to multiply these probabilities that are each equal to ½, resulting in ½ * ½ * ½ * ½ = ½4 = 0.0625
These same can be done for common ancestor 2: the probability that J and K have alleles in common that originate from common ancestor G is also equal to ½4 = 0.0625 .
These two probabilities can be added up because the animals are related because they share alleles from common ancestor 1 and/or from common ancestor 2. Both probabilities are independent of each other. The additive genetic relationship between J and K thus becomes 0.0625 + 0.0625 = 0.125 or aJ,K = 0.125.
These steps for determining the additive genetic relationship can be described in a formula as:
Where X and Y are the animals that we want to know the additive genetic relationship of, m is the number of common ancestors, and for each common ancestor n is the number of generations from animal X to the common ancestor, and p the number generations between animal Y and the common ancestor. You see that per common ancestor the probabilities of sharing alleles are multiplied across generations, because all need to happen, and the probabilities are accumulated across common ancestors, because they are independent of each other.