AS 332 Calculating Breeding Values Notes PDF

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Calculating Estimated Breeding Values (EBVs) AS 332 Livestock Breeding & Genetics Estimated Breeding Values (EBVs) are an estimate of the genetic merit of an individual for a trait. The EBVs are predicted from phenotypes: an individual’s own phenotypic record(s), pedigree records, and progeny records. Essentially, EBVs are predicted from phenotypic records by regression as follows. EBV b P

where b = regression coefficient, and P = average of phenotypic records for a trait, where the phenotypes can be records on an individual’s own performance, pedigree, or progeny. After calculating the EBV, you can derive expected progeny differences, or EPDs, by multiplying the EBV by one-half. The EBVs and EPDs can be predicted by 2 methodologies: 1) selection index, and 2) best linear unbiased prediction or BLUP. Practically, all breed associations use BLUP to estimate progeny differences. For EPD prediction, BLUP has several advantages over the selection index, the largest being that BLUP can use phenotypes from animals in different contemporary groups to calculate an individual’s EPD. However, BLUP is computationally intensive, involving the use of mixed linear modeling and matrix algebra, all of which are beyond the scope of a survey course in animal breeding. Therefore, to demonstrate how EPDs are calculated, we will use the less computationally intensive selection index method. In its simplest form, the selection index is simply a regression equation as described above, where we are using phenotypic information to predict EBVs by multiplying the phenotypic trait value by a regression coefficient. After predicting the EBV, you can transform the EBV into an EPD by multiplying the EBV by one-half. The simplest selection index equation uses a single phenotypic trait record to calculate an EBV as follows. EBV h 2 P

where P = an animal’s own performance for a trait and h2 = heritability. For example, an individual’s weaning weight EBV, as estimated from its own weaning weight, is simply the calf’s weaning weight multiplied by the heritability for weaning weight. In this equation, the regression coefficient is simply the heritability of the trait. The regression coefficient in the selection index accounts for the confidence we have that the available phenotypic information accurately predicts genetic merit. If we have less confidence in the phenotypes as a prediction of genetic merit, we expect that the breeding value won’t change much when the phenotype changes. Therefore, the phenotype(s) poorly predicts genetic merit and the EBV is regressed closer to the mean. If we have more confidence in the phenotypes as a prediction of genetic merit, we expect that the breeding value will change more when the phenotype changes. In this case, the phenotype(s) is a better predictor of genetic merit and the EBV is not regressed as much towards the mean. The regression coefficient accounts for the amount of information available to estimate genetic merit.

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For example, when we have only a single phenotypic record, the regression coefficient is the trait heritability. If heritability is high (h2~0.45), we won’t regress the phenotype towards the mean as much as if the heritability is low (h2~0.05). We have more confidence that the single performance record from the highly heritable trait is a better predictor of genetic merit than a single performance record from the lowly heritable trait. We can also estimate heritabilities from phenotypic averages; for example, we can estimate heritabilities from the average of repeated trait records, half-sib records, or progeny records. We use the following selection index to calculate the EBV from the average of repeated trait records for an individual. EBV 

nh 2 P 1  (n  1)r

where r = repeatability and P = average of repeated trait records for an individual. If, however, we wanted to calculate an EBV based on the average of an individual’s progeny records, then we would use the following equation. 2

EBV 

2 ph P 4  ( p  1)h 2

where p = number of progeny of this individual that have phenotypes and P = average of records for an individual’s progeny. For a complete list of equations that relate phenotypic performance records to EBVs, see page 231 Bourdon. For all of these prediction equations, once you calculate the EBV, you can subsequently calculate the EPD by multiplying the EBV by onehalf. Although you can calculate EBVs and EPDs from phenotypic records derived from multiple sources (for example, own performance, half-sibs, and progeny) with the selection index, you will need to use matrix algebra. For an introductory animal breeding course, you can capture the essence of how EBVs and EPDs are calculated by using the selection index equations for a single source, or type, of phenotypic record as we have done above. Graduate level courses in animal breeding discuss matrix algebra, EPD prediction, and BLUP more in-depth than what is needed in an undergraduate animal breeding course. As mentioned earlier, BLUP is used by breed associations to calculate EPDs, not the selection index. Accuracy of EBVs and EPDs Although the accuracy of the EBV is accounted for when the EBV is calculated, it is often helpful to know the accuracy of an EBV so you can judge how much selection risk you will be taking for a trait if you select that animal. Accuracies are provided on page 231 Bourdon for a large number of EBV calculations based on only a single source of phenotypic information. Each EBV has an associated accuracy, so if you use an equation on page 231 to calculate an EBV, you should notice that an equation to calculate the accuracy of the EBV is also available in 2

this table. In most cases, the accuracy is simply the square root of the regression coefficient, but accuracy is not always the square root of the regression coefficient. Be very careful that you are using the correct accuracy equation. A list of accuracy equations when calculating EBVs from own performance and progeny data can be found below. Table 1. Accuracy equations when calculating EBVs from 3 different types of phenotypes. Type of phenotypic record

Accuracy equation

A single performance record on an individual

h

Average of repeated records for an individual

nh 2 1  (n  1)r

Average of an individual’s progeny records

ph 2 4  ( p  1) h 2

Accuracies of EBVs and EPDs depend on 3 factors: 1) trait heritability, 2) type of record used to estimate EBVs and EPDs, and 3) number of records available. As heritability increases, phenotypes are better predictors of genetic merit. A single phenotypic record for a highly heritable trait is a more accurate predictor of genetic merit than a single phenotypic record for a lowly heritable trait. The type of records used to for genetic estimation also affects accuracy. Generally, the progeny records on an individual will provide the highest accuracies, followed by an individual’s own performance records and finally pedigree records. To obtain highly accurate (~1.0) genetic estimates, you need to have progeny records. An individual’s own phenotype can be influenced by the environment. However, the average of many progeny records dilute out environmental effects. We would assume that some of an individual’s progeny would be exposed to a better than average environment and some of the progeny would be exposed to a worse than average environment. When you average phenotypes for a large number of an individual’s progeny, these environmental effects (both positive and negative) tend to cancel themselves out. The mean of a large number of progeny records therefore is less subject to environmental influences and you can estimate genetic merit very accurately. EBVs and EPDs are unbiased estimators Because accuracy (amount of information available for estimating genetic merit) is accounted for when calculating EBVs, EBVs and EPDs are unbiased. There is an equal probability that the EBV will increase and decrease. When an EBV has a low accuracy, we would expect that as more “information” (own performance and progeny records) is included in the genetic analysis, the EBV will change considerably. Individuals with low accuracy EBVs have higher selection risks. The animal’s true breeding value is possibly quite different from its EBV. Still, because EBVs and EPDs are unbiased, the estimate is equally likely to change in a favorable and an unfavorable direction.

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I liken selecting animals with lowly accurate EPDs to buying junk bonds. In finances, a junk bond is a risky investment because of the higher rates of default relative to other bonds. To compensate for the higher default rates, junk bonds pay higher yields. When you select an animal based on a lowly accurate EPD, you often are selecting an animal that is cheaper than a proven animal with a highly accurate EPD. For example, yearling bulls have low accuracy EPDs and are often cheaper than a proven bull. Unfortunately, the yearling bull has higher selection risk. The yearling bull’s EPD may change considerably as we learn more about the genetic merit of this bull. You may end up using a bull that is only “middle of the pack” for the trait you are interested in improving, or worse. However, the bull may also truly be genetically valuable, in which case you have bought a valuable animal for the fraction of the cost of a proven bull. Best Linear Unbiased Prediction (BLUP) As stated earlier, BLUP is the method of choice for estimating genetic merit. All breed associations that estimate breeding values use BLUP instead of the selection index. Why is BLUP more popular for estimating genetic merit? 1. You can estimate genetic merit using individuals across contemporary groups. When using selection index methodology, you are limited to only animals raised within a single contemporary group. Hence, BLUP is able to calculate across-herd EPDs and EBVs. 2. BLUP can account for genetic trends in a breed. 3. BLUP can use all information available to estimate genetic merit, including distant relatives. The selection index is limited to only using close relatives (parents, grandparents, and siblings). 4. BLUP accounts for non-random mating and the merit of an individuals’ mates. 5. BLUP can account for bias caused by culling for poor performance. Poor producing animals are often culled from a herd early. Let’s examine 2 dairy bulls: “Roscoe” has a high breeding value for milk yield and “Get Down Tonight Bear” has a low breeding value for milk yield. On average, you would expect G.D.T. Bear’s female progeny to produce less milk and thus be culled earlier. For the most part, the cows sired by G.D.T. Bear that remain productive will have higher than average milk yields. If I was to compare the average milk yield from cows sired by “Roscoe” and “G.D.T. Bear”, G.D.T. Bear’s progeny might be comparable to Roscoe’s progeny for milk yield. Because the poor producing progeny from G.D.T. Bear were culled earlier, his progeny average looks better. BLUP can account for this bias, but the selection index cannot. 6. BLUP can separate out direct and maternal effects. Both direct and maternal effects are genetic effects. Direct effects are alleles that affect trait expression by being expressed in the individual. For example, the sum of all of a calf’s alleles that affect weaning weight is this calf’s direct effect on weaning weight.

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Maternal effects are alleles that affect trait expression by being expressed in the dam (mother) of an individual. For example, a cow’s mothering ability and milk yield has an effect on her calf’s weaning weight. The sum of all of the cow’s alleles that affect mothering ability and milk is the calf’s maternal effect for weaning weight. Paternal effects can also exist. Paternal effects are alleles that affect trait expression by being expressed in the sire (father) of an individual. In agriculture, very few examples of paternal traits exist. Once the sire passes his alleles onto his progeny, the sire rarely has an effect on an individual’s performance. However, some examples in nature do exist, such as with Empire Penguins, where the sire actually cares for the egg.

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