Knowing the phenotypic variance and the selected proportion allows us to determine the superiority of the selected parents (how much better than average the selected parent are) on forehandbeforehand. This is based on the variance and the selected proportion only, so before the actual animals have been identified. This is very convenient! We can use this information to predict the genetic response to selection, given a certain proportion. This response can then be evaluated, and, if desired, compared to predicted selection results when using a larger or smaller selected proportion. The selection intensity is an important tool in the decision making process.
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If we consider the components of the formula for genetic gain, it actually makes sense. The S/ σp indicates the genetic superiority of the parents, expressed in σp. The σa/ σp translates σp into σa, so into genetics. The final σa translates the result in units of the trait under selection (e.g. kg milk, or ride ability score). Once again: advantage of working with selected proportions (and thus with selection intensity) is that results can be predicted prior to the actual selection decision. From now on we will only consider ΔG = i * rIH * σa as that is generally applicable, and not only for mass selection. Note that the order of the components of the formula does not matter.
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