How to Find the Coefficient of Relatedness Between Any Two Members in a Pedigree
The coefficient of relatedness (r) is the percent of variable genetic material that two individuals have in common with one another. This information is especially useful for Hamilton’s rule problems (article linked).
For human pedigrees, there are two methods to calculating r. For more straightforward cases, you can just convert the relationship shown on the pedigree to a common relationship, and answer with a memorized r value for that relationship. For example, look at the pedigree and decide how individuals G and E are related:
Colloquially, G and E are niece and uncle. Memorize the chart below, and you can use it to determine the r value for various other relationships:
For relationships not covered on this chart, or more complicated pedigrees, we need to start thinking a bit. The most straightforward way to find r is by following these steps:
1) Identify the most recent common ancestral couple.
2) Count the number of generations above each individual to each member of the couple.
3) For each individual, raise 0.5 to the number found in step (2).
4) Add these two quantities. That results in your r value!
Here’s a straightforward example of this workflow between siblings:
Try to derive the rest of the chart of r values on your own using this method.
USABO usually throws one of two curveballs on this approach: they can either introduce half-siblings, or incest. These factors complicate the workflow.
For half-siblings, you need to look at the most recent common ancestor, as the second member of this couple is different for each individual. To generalize the aforementioned workflow to include cases with half-siblings, we can revise step 1 as follows: Identify the most recent common ancestor(s) of the two individuals. Step 2 becomes: Count the number of generations above each individual to each identified ancestor. Steps 3 and 4 remain the same.
Incest makes things complicated in more ways than one. In our lovely timed MCQs, before embarking on a frustrating path, we should pretend the incest doesn’t exist, and find r. Eliminate all the answer choices with an r value below what you calculated, as incest in prior matings can only increase the r value. Since there are infinite combos of incestuous relationship questions, I’ll guide you through an example calculation, from which you can derive a method to solve more complex problems. To find the coefficient of relatedness between two offspring produced from the union of siblings, you need to use the typical relatedness (0.5) between siblings and the increased relation due to their parents’ incest (r of parents/2). Adding these terms (0.5 + 0.5/2) gives the total amount of shared DNA between the offspring. So r=0.75.
Hope that was helpful. Here’s some stuff.
https://www.youtube.com/watch?v=5kOGq8c4qao - overview of concepts in this article.
https://www.youtube.com/watch?v=ve9XUbvuYvA - bee relatedness.
