Calculating estimated breeding values

An estimated breeding value (EBV) is simply the value of an animal's additive genetic effects. It is the value of the genes which the animal may transfer to its offspring. Animal's BV is half of the BV of it's parent, or twice the value of the BV of it's offspring. Note that BVs are always only estimates - even if they are referred shortly as "breeding values".

The most important concepts related to EBV are shortly described below.

• Heritability, h2: The part of the difference between animals which is due to difference in breeding values. It's always between 0 and 1. h2 = Var(A)/Var(P) = σ_A² / σ_P²
• Â_i denotes the animal's EBV
• Accuracy r_TI: is the level of confidence we have for a given EBV. Accuracy is calculated as correlation between A and Â, where A is the actual BV. Accuracy increases as the amount of results (=number of offspring) and/or the heritability increase.
• Error of estimation, ε : The difference between the real and estimated BV. ε = Â - A. Usually it is 0, because we don't know A, so A = Â. The variance of ε is called PEV and calculated as Var(ε) = (1– r_TI²)Var(A) = Var(A) - Var(Â)
• BLUP: Best Linear Unbiased Prediction, currently the most used and reliable method of calculating EBVs. BLUP has three models:

• Animal model: Concerns all animals in the population, linked by their relations
• Sire model: Calculates EBVs based on the male relatives of the animal's sire
• Sire - Dam of sire -model: Corrects the EBV of the other parent by using the parent's sire's information.

A parent's EBV is two times
the EBV of its offspring.
(c) Linda Lester / betterphoto.com

EBV is calculated using one of three possible methods. First, an individual estimation considers only the animal's own results for one or several traits. Second, an estimation based on relatives considers results from the animal's relatives for one or several traits. Results are weighed based on how close a relative they're from. Factors affecting the weight are genetic relationships, genetic parameters of the trait and availability of other records. Finally, a combination uses both the animal's and its relative's information. The combination gives the most reliable EBVs, because it combines information from many sources, increasing accuracy. An excellent example of this is the international bull comparison index INTERBULL.

EBV formulas

The formula for calculating EBV varies depending on the method of estimation used. EBV based on animal's own results is calculated as

(Â_i - A) = b * (P_i - P)

and EBV for animal's relatives' results as

I = 2 b (P_i - P)
where b = (n * h²) / ((n-1) * h² + 4)

Â_i : EBV for the animal
A: Actual breeding value
b: correlation efficient
P_i: Average result of the animal's offspring
P: Average result of the comparison group
h²: heritability for the trait
n: number of offspring.

Estimating BV for a trait x using results from another, linked trait y:

 âix = b (y-μy)

where b = cov(a_x,_y) / var(y)

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In this case, accuracy depends on genetic correlation and heritability of the measured trait y:

rax,ay = cov(a_x, _y)/ σ_axσ_y = r_axy h_y