Breeding Value Accuracy

Paul L Charteris
Institute of Veterinary, Animal and Biomedical Sciences,
Massey University, Palmerston North, New Zealand

In the long-term breeders must supply their bull buyers with animals of desired genetic merit accompanied by a high level of customer support. Two important aspects impact on the provision of animals of desired genetic merit. First, you must define attributes that impact the desirability of an animal. This is the basis of a selection objective. Second, you must achieve progress in moving the average merit of successive generations of animals in the direction defined by your objective. This involves ranking animals (using Estimated Breeding Values, EBV’s) for the traits in the objective and selecting the highest ranked individuals. This issue of "Beef Breeding Matters" will cover aspects of EBV accuracy, defining different measures of accuracy, confidence intervals for EBV’s and determinants of EBV accuracy. Accuracy To make genetic progress for any trait or combination of traits, we wish to select animals having the highest genetic merit (or true breeding value, true BV) out of all the animals available for selection. As much as we would like to, we never know the true breeding value of an animal. Most financially important traits, such as carcass weight are influenced by many genes (tens to thousands) each of which add together to comprise the true breeding value of that animal. Identifying the true breeding value of a bull for carcass weight would require locating and quantifying the size of all the genes possessed by this bull influencing carcass weight. Given the number of possible genes influencing carcass weight, such an exercise would be very costly and time consuming. In practice breeders predict the true breeding value of animals using measured performance, within New Zealand’s beef industry these predictions are called Estimated Breeding Values (EBV’s).

The difference between the true BV of an animal and the EBV of the same animal is known as the error of estimation. Ideally these errors would be very small so that animals chosen with the highest EBV’s are in fact the animals with the highest genetic merit (true BV’s). One measure of the relationship between true BV and EBV is given by the correlation (r) between these values. The correlation will lie between 0 and 1.0, with a correlation of 0 implying that the EBV is a totally inaccurate estimate of true BV and 1.0 implying the true BV is known exactly. The relationship between true BV and EBV at different levels of r are shown in Figure One.

Figure One Relationship between true BV and EBV for three accuracy values, r= 0.8, 0.5 & 0.3



Measures of accuracy

The accuracy of Group Breedplan EBV’s is the correlation between the true BV and the EBV. In practice, r is multiplied by 100 to express it as a percentage. For a given trait the accuracy depends on the amount of information available on the individual and its relatives in relation to contemporary groups. In the case of a bull evaluated from a progeny test, accuracy is a direct reflection of the number of progeny. For a trait with a heritability of 0.25, r can be calculated according to [1] where n is the number of progeny per bull.

[1]

This accuracy measure quickly attains high values progeny numbers exceed 20. In dairy progeny testing schemes, 80 or more daughters are typically obtained from each bull, thus r = 0.92 [2]. The N.Z. dairy industry uses r² to reflect EBV quality, known as reliability. For an r value of 0.92, r²becomes 0.84. This r² value allows a greater distinction between high accuracy EBV’s, such as for bulls having tens of thousands of daughters where the apparent accuracy using r would be little better than for bulls with 80 daughters. The U.S. beef industry uses accuracy standards dictated by the Beef Improvement Federation (BIF). The BIF accuracy scale is based on minimising Prediction Error Variance (PEV is a measure of the magnitude of errors in predicting breeding values) rather than maximising r. BIF accuracies are determined by equation [3]. It is important that breeders considering trait information from different sources (e.g. Group Breedplan, beef bulls marketed through the dairy industry and U.S. catalogues), recognise these EBV accuracies which are related are expressed on a different basis.

[3]

For any given measurement on the animal, the reported accuracy will be higher in Group Breedplan than would appear for a U.S. evaluation. This does not imply Group Breedplan EBV’s are more accurate, rather for the same amount of information on an animal, Group Breedplan prefer to publish a higher accuracy value. Table One shows the number of progeny required to achieve Group Breedplan accuracies for two different trait heritabilities (0.1 and 0.3) and equivalent EBV accuracies for the U.S. beef and NZ dairy evaluations

Convert from U.S. (US) to Group Breedplan (GBP) accuracy:

Step1. Divide U.S. accuracy by 100 (accuracy will be between 0 and 1)
Step 2.Group Breedplan accuracy =

Note: This will allow conversion of accuracies from the U.S. scale to Group Breedplan only. Since Group Breedplan and U.S. evaluations have different records on each animal evaluated and use different genetic bases (different base years and different animals within each base year) from which EBV’s are derived you cannot directly compare EBV’s or accuracies between these evaluations.

Table One Accuracy of EBV’s from Group Breedplan, (and progeny required), U.S. Beef Improvement Federation and New Zealand dairy cattle genetic evaluation (Livestock Improvement Corporation)

Confidence intervals

These accuracy values can be used to assess the extent to which true BV may differ from the EBV. For any accuracy, the average EBVs of a group of animals will accurately reflect the true BV of the group. Some individual bulls in the group will have better true BVs than their EBV suggest whereas some will be poorer than their EBV’s. Sometimes a breeder may want to know how close the EBV is to the true BV of the animal. This cannot be answered directly, however a similar question is, what is the range within which we can be 80% sure to include the true BV for a given EBV? This is the confidence range for the EBV. The confidence range depends on:
1. The EBV which predicts the true BV
2. The accuracy of prediction (r²)
3. The amount of genetic variation for that trait
4. A desired confidence percentage, which will correspond to a t value, a breeder may choose 90%.
The lower and upper limit of an EBV will depend on:

Lower limit = [Eq 4]

Upper limit = [Eq 5]

Now lets suppose we have a bull in a catalogue with a 600-Day weight EBV of +56 kg and accuracy of 70%. We want to know the range of EBV’s for this bull that is 90% sure to include the true BV for 600-Day weight.

Step 1. EBV = +56 kg

Step 2. r² = 70% = 0.72 = 0.49

Step 3. Chance EBV is in range = 90%, from Table Two the corresponding t value is 1.65.

Step 4. From Table Three, genetic variation for final weight (600-Day wt) is 400 kg.

Step 5. Include numbers into Equations 4 and 5.

From these calculations we are 90% confident that the EBV range 32 to 80 kg will include the true BV of this bull for 600-Day weight. There is a 10% chance that the true BV of this bull will be outside this range. Group Breedplan sire summaries publish these confidence intervals. You can apply equations 4 and 5 using EBV’s and accuracies from your own herd.

Table Two Values of t for different confidence ranges for the EBV

Determinants of EBV accuracy
EBV accuracies are determined by a number of factors, including the heritability of the trait, the number of records on the animal and its relatives and the number of records on genetically correlated traits. Breeders can only influence accuracy of EBV’s through improving the number or quality of records made, heritability remains a biological constant and cannot be affected by breeder management.

Figure Two Accuracy of EBV’s when one record is made on the individual. Accuracy = square root of heritability,r= 0.8, 0.5 & 0.3

The influence of trait heritability on accuracy of EBV’s is shown in Figure Two for the instance where only one measurement is made on the animal. Under these circumstances, the highest accuracy is the square-root of the heritability of that trait. Most beef cattle traits of importance have a heritability range of 0.1 to 0.5, within that range accuracy is from 0.32 to 0.71 if only one record is made on the animal. EBV accuracy increases as trait heritability increases. For highly heritable traits, little improvement in EBV accuracy results from additional information from relatives; for traits of low heritability, a greater increase in EBV accuracy is obtained from using records on relatives.Maximum EBV accuracy achievable will depend upon the source of records used. For a trait with a heritability of 0.25, the maximum possible EBV accuracy obtained from one record made on the animal would be 0.5; using one record on each parent alone would result in an accuracy of 0.35. Enough progeny can provide a high EBV accuracy, 140 progeny will provide an accuracy of 95%.

Figure Three Accuracy of predicting breeding values from progeny records depends on trait heritability and number of progeny evaluatedE

BV accuracy improves as trait heritability and number of progeny evaluated increases (Figure Three). Little increase in accuracy is achieved with more than 50 progeny per bull. The increase in accuracy with number of progeny records depends on whether the progeny added is the fifth or the fiftieth, for example, going from 5 to 10 progeny increases accuracy much more than going from 50 to 55 progeny. For a trait with a heritability of 0.25, evaluating 6 offspring will be just as reliable as one record made on the sire, progeny testing with few offspring is of little use.

When comparing between bulls in a catalogue or in different catalogues, we are really interested in comparing their true breeding values. EBV differences between two bulls reflect the true BV differences between bulls, however the accuracy of difference in EBV’s between bulls depend on the level of genetic linkage between them. Two high accuracy EBV bulls which have been progeny tested in different herds can have a low accuracy between them since they have no progeny managed in common herds. The accuracy of EBV’s between bulls can be improved by evaluating their progeny in the same herd or in different herds using a link sire. Ideally, we would have catalogues with accuracies of EBV differences for every bull with every other bull.

EBV bias is different from accuracy. EBV’s can be biased due to inaccurate recording of measurements or management of animals. Bias may arise if contemporary groups are not accurately reported (for example if show animals are not recorded as being managed in a separate group) or if measurements made on the animal are wrong due to faulty equipment or poor note taking. In some industries, unscrupulous breeders preferentially feed progeny of certain sires to bias his EBV’s upwards, but their exploits are usually exposed once the bull is in widespread use and his EBV’s fall.

In practice, consideration of EBV accuracy may have little effect on the annual rate of herd genetic progress. Breeders restricting themselves to purchasing only high accuracy EBV bulls may have a lower rate of genetic progress than breeders willing to accept moderate accuracy levels since selection intensity will be decreased if selection decisions are restricted to only a small subset of potential sires. Secondly, high accuracy EBV sires have usually had progeny evaluated resulting in time delays. If the herd of origin of this sire is making genetic progress it is likely that sons or grandsons of this sire would have higher genetic merit than the bull evaluated, although their accuracies will be lower.

Selecting only high accuracy animals reduces the variability of selection response. The rate of genetic progress per year may be similar to that for a herd with low accuracy EBV’s. In the latter case, in any one year the average EBV’s of the herd will be more variable than for a herd only selecting high accuracy animals. The amount of attention paid to EBV accuracy will depend on the level of risk commercial farmers or breeders are willing to incur when making selection decisions.