Estimated Breed Values Example
BASICS OF EBVs
EBVs use information about the phenotypes of a dog and its relatives to predict genotype of a dog, its "breeding value" for a particular trait. As you looked at the pedigrees above, you were trying to deduce the genetic value of a particular dog for hips based on information about its littermates and other relatives, but as more information is added to the pedigree - which should allow you to make a better guess - it gets harder and harder to mash it all up in your mind to come up with some evaluation of the dog you're interested in. Plus, you might have some biases that interfere with making a completely objective evaluation, like how well you get along with another breeder, or what you know about temperaments of some of these dogs (which would be better to evaluate separately), and even your ability for abstract thinking.
We can eliminate bias and isolate the information about hips from potential environmental effects and anything else that could confound our ability to predict the genetics of a particular dog using EBVs. The EBV of a dog is the RELATIVE genetic value of a member of a breeding population, so if you add data to pedigrees the EBVs of the dogs will change, and hopefully become more accurate predictors of genotype. So EVBs calculated from one group of dogs will not necessarily be comparable to those from another group of dogs unless you have some way of comparing those populations with each other in a standard way (and there are ways to do that). But this is really no different from the evaluations you do in your head, which can only be based on information you have about the dogs.
Determining EBVs for a trait
Let's walk through a very simple pedigree and analysis to see how this works. This is based on the example in Eldin Leighton's paper about how the Seeing Eye has been using EBVs in the breeding of guide dogs. You can download a copy here.
Here is the pedigree for a group of 9 dogs (there are also a few unknown parents).
We can redraw this as a standard pedigree to make the relationships clearer.
We have information for four dogs about a trait we're interested in that was scored from 1 to 5, with higher scores being better; these numbers are in red.
We want to know which of the dogs, 6, 7, 8, or 9, has the highest breeding value (i.e, the best genotype) for our trait. We don't have trait information about any of the other dogs in the pedigree.
You might look at this and think that the only information you have to work with are the scores for those 4 dogs. But there is more than that. Those dogs are all related to each other - some are full sibs and all share a grandsire. So you know they all share genes from dog 1 that affect their breeding value for the trait we're interested in. We just need to figure out a way to to use the relationship information to make a prediction about genotype for each of our 4 dogs.
We're about to do some simple math. Don't let your eyes glaze over. These calculations are VERY simple and you'll never have to do them yourself. But it's useful to know where numbers come from, so don't sweat it; just follow along. Remember, these are actually the steps you might try to go through in your head when you evaluate a pedigree, but instead of making a wild guestimate we're going to see how we can do a tiny bit of simple math that will let us hang numbers on a tree that will allow you to compare dogs in a quantitative way.
Determining relatedness
The first thing we need to figure out is the level of relatedness of each of these dogs to each other. We know that progeny share half the genes of each parent. So the genetic relatedness of 6 and 7 to their parents 2 and 3 is 0.5; they have 50% of the genes of each parent.
We are going to collect this information in a table with 9 columns and 9 rows. We can color in these first comparisons in orange. Notice that we have to do this for both places where those pairs of animals appear in this matrix.
The other set of numbers we can fill in is the relationship of a dog to itself. So comparing 1 to 1 the relationship is 1.0, and 2 to 2 is 1.0, and 3 to 3 is 1.0, so you can fill in all those numbers, which will fall on the diagonal in the table.
Next, what is the genetic relatedness of 6 to his grandsire 1? Because a dog gets half the genes of its parent, with each generation the influence of an ancestor goes down by half. So 6 has half (0.5) the genes of 3, and 3 has half (0.5) the genes of 1. Therefore, 3 should have [(0.5)(0.5)], or 0.25 (25%) of the genes of its grandsire, dog 1. So in our table, we can put 0.25 in for the relationship of 6 to 1, and it is the same for the sibling 7 (in yellow).
Before we go further, we need to remind ourselves that although we know that a dog has exactly 50% of the genes of a parent, it doesn't necessarily have 25% of the genes of each grandparent. That's because the sample of genes it gets from a parent is random and might include more genes that came from one grandparent than the other. In fact, it is highly unlikely that a dog will get exactly 25% of its genes from each grandparent. So when we calculate relatedness of dogs related more distantly than parent and offspring, the number we get is just an estimate. Just like flipping a coin 20 times and getting 13 heads instead of 10, the sample of genes a dog gets from its parent won't necessarily be exactly half of the genes from a grandparent.
We see in this pedigree that we have two sets of siblings that share a common grandsire. We can figure out the relatedness of dog 8 with dog 3 by accounting for each step between them. If you've taken the ICB course about Coefficient of Inbreeding, you will remember this is exactly what we did when we traced paths to come up with a prediction of shared alleles. If you haven't taken the COI course, what we're going to do next might not immediately make sense to you, but we're not going to do a separate lesson on this step. It's enough if you understand the general principles, which are a) that each step in a pedigree represents a sampling of 50% of the alleles of the immediately related dog, and b) by counting up how many steps there are connecting one dog with another we can estimate their genetic relatedness.
We're going to trace a path like this:
8 ---> 4 --> 1 --> 3
At each of 3 steps, we have a factor of 0.5 to account for, so we estimate the relatedness of dog 8 to dog 3 as
(0.5)(0.5)(0.5) = 0.125
This will be the same for all of the pairs of dogs that are 3 steps from each other, so we can fill in those values in our table (green).
We have one more set of relationships to figure out, this time between dogs 6 and 7 with dogs 8 and 9. This is exactly like the one we just did but with one additional step, as here:
8 ---> 4 --> 1 --> 3 --> 7
Just like before, we count the steps between the first dog (8) and the last dog (4) in the path. There are 4 steps, so we multiply 0.5 by itself 4 times. So
(0.5)(0.5)(0.5)(0.5) = 0.0625
We can fill in those values in our matrix (pink).
Now we have a matrix with estimates of the relatedness of each of the dogs in our pedigree. And remember, you'll NEVER have to do these calculations yourself (!!!). You input your pedigree into the computer and it spits this matrix out in an instant.
Heritability
There's one more thing we have to consider when we evaluate the breeding value of a dog for a particular trait, and that's its heritability. If the heritability of the trait is zero, then we're done here; genetics don't matter. if it's 1, then we know that any dog that got the gene (or genes) will have the trait. But the heritability of most traits is somewhere between 0 and 1, and we need to take that into consideration when we try to estimate the breeding value for a trait.
You learned how heritability is calculated from your BugsVille simulation. Let's say that the heritability of the trait we're interested in here is 0.2, or 20%.
Computing the EBVs
Okay, here is where we give all of this information to the computer, the black box does some mystery math (called "matrix algebra") that is no fun to do by hand, and something else called BLUP (Best Linear Unbiased Prediction, also no fun to do yourself), and it spits out some numbers that tell us something about the breeding values of our 4 dogs. Remember, these are estimates - we can never know the true breeding value unless we know the actual genes involved, but this is a quantitative prediction, which will be far more accurate than what you would come up with by squinting at the a pile of pedigrees, testing the wind, and making your best guess.
So, the computer grinds away on these data and comes out with some numbers (males in blue, females in red).
The first thing you'll notice is that we got estimates of the genetic value of every animal in the pedigree except for the unknowns and dog #1, because he has no known ancestors. Then, notice that some of these numbers are positive and some are negative. This is because the EBV for a dog is relative to the population average for that trait. Our rating scale for evaluating the trait from 1 to 5, so a dog with a positive value is better than the average (numbers in green) and a negative value is worse than average (numbers in red).
These numbers tell us some interesting things. From the traits scores we recorded, we would have thought that dog 9 (score = 5) and dog 7 (score = 4) had the best potential to produce offspring with good scores. In fact, dogs 8 and 9 have the same breeding values (0.13), and dog 7 in fact has a negative score, as does her littermate dog 6. The actual test scores for these dogs would have led you astray in evaluating these dogs - you probably would have decided that dog 7 was more valuable to you genetically than dog 8, but in fact the genotype for 7 is worse than the population average for the trait you scored.
Remember - these EBV scores were based on three kinds of information: your scores for each of 4 dogs, how all of the dogs are related to each other, and the heritability of the trait in this population. The estimated breeding values you get might not be at all what you thought they were, but this technique has been used for decades in the breeding of domestic animals and plants and has been shown to be superior to any other method of improving the selection for particular traits.
Managing multiple traits
You can also use EBVs for multiple traits at a time. Say you are interested in selecting for 3 traits at the same time. One trait is of foremost importance (e.g., a potentially lethal disease), and the other two less so (e.g., litter size and temperament). You can weight the evaluations for each trait and compute an EBV that takes into consideration those weights. You want good litter sizes and great temperaments, but your foremost concern is minimizing the risk of producing puppies with a potentially lethal disease. Guide dog breeding programs might use 7 different traits in their calculations, including ones for health, size, temperament, coat, or whatever else that is important to them.
How can EBVs be used?
EBVs can be used for ANY trait that is heritable. They have been widely used for decades in the breeding of livestock for production, and although they are not widely used by the show dog breeder, they are starting to be used in dogs.
- Health, conformation, and behavior traits in guide dogs
- Hip dysplasia in dogs (e.g., in the UK, Finland, and US)
- Syringomyelia and Chiari Formation in Cavalier King Charles Spaniels
- Breeding programs to improve behavior
- Improvement of working abilty
EBVs in horses
You can get a better idea of their potential from the types of traits they are being used for in horses. Notice also that EBVs can be based on DNA information if the association between a trait and DNA is known.
Various traits relevant to show horses (conformation, movement, health)
Riding horses
Jumpers
Dressage
Racing
Sport
Temperament and draught work
...and many more.
NEXT: Learn how to use the Cornell EBV database for hips and elbows:
http://www.instituteofcaninebiology.org/ebv-examples.html