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How to Calculate the Coefficient of Inbreeding

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  • 0:01 An Inbred Pedigree
  • 1:29 Inbreeding Coefficient (F)
  • 4:28 Solving the Equation
  • 6:09 Lesson Summary
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Lesson Transcript
Instructor: Katy Metzler

Katy teaches biology at the college level and did her Ph.D. work on infectious diseases and immunology.

So, you know what inbreeding is and what effects it can have on a population. In this lesson, we'll walk you through the next step: how to calculate just how inbred an individual is.

An Inbred Pedigree

By now you've learned that inbreeding is mating between genetically related individuals and that it causes an increased proportion of homozygous individuals in a population. Now that we understand what inbreeding is and what effects it can have, we need to learn how to calculate just how inbred a particular individual is. We do this by looking at the individual's pedigree, which is basically their family tree, and by using a special equation.

Before we look at the equation, let's look at an inbred pedigree. Remember that in pedigrees the females are represented by circles and the males are represented by squares. A line connecting a male and a female symbolizes that they've gotten married, and any people that branch off of that line are their kids.

A pedigree can show instances of inbreeding
Pedigree chart

Okay, at first glance, you might notice that there is something unusual about this family tree. It has a closed loop. Uh oh, that's not supposed to happen. A closed loop in the family tree means that some close relatives have had kids together. Sounds like inbreeding!

Individual A in this pedigree is inbred because she is the child of two parents, B and C, that have relatives in common. Which relatives do they have in common? D and E, who are A's great grandparents. All right. We get that A is inbred, but since we're population geneticists, we really like to use equations, and we want to find out just how inbred A actually is.

Inbreeding Coefficient (F)

To do that, we will use an equation to calculate the inbreeding coefficient (F). The inbreeding coefficient tells us the probability that an individual has two identical alleles for a given gene. Let's back up a little and remember that alleles are just alternative forms of the same gene.

Since we have two copies of each of our chromosomes (except Y in males), we can have two different alleles for each of our genes. There are lots of different alleles in a population, and people often inherit different ones from each parent. This inbred individual, however, would have two exact same alleles for some of her genes because they ultimately came from the same relative in her family tree.

Here's the equation for the inbreeding coefficient: F = the sum of [(1/2)^n * (1 + F sub A)] for all inbreeding paths. F is the inbreeding coefficient, which is what we're trying to calculate. 1/2 is just 1/2, so that's good. The exponent n is the number of individuals in the inbreeding path, which I'm about to show you. We will have to do this equation for each inbreeding path, then add up all the answers, which is why the equation starts with the phrase 'the sum of' (usually indicated by the Greek capital letter sigma). Finally, F sub A is the inbreeding coefficient for the relative that the inbred individual's parents have in common. Whew! This will make a lot more sense if we go through an example.

Okay, let's calculate the inbreeding coefficient for individual A. First, we need to draw inbreeding paths, which are basically lines connecting A's parents and the relatives they have in common. We said that the couple D and E are the relatives that A's parents, B and C, have in common.

So, first we draw a path starting from A's mother B, then to B's mother, and then to D, who's A's great grandfather. We're not done yet, though: we need to keep drawing the path until it comes back to A's father. Back down through A's grandfather on her father's side, and finally to C, who is A's father.

Trace inbreeding paths to identify n
Pedigree with breeding paths

Now, take a look at that path. How many people are in it, not counting A? 1, 2, 3, 4, 5 people in the path. That is our first n! Awesome!

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