Mass selection is the most elementary type of selection: based on observed phenotypes. The variation among animals is represented by the phenotypic variation. The selection differential S would be the difference in average performance of the population and the selected parents. We are interested in the genetic response, so we need to translate the difference in phenotype to difference in genotype. To achieve this, we can scale the result with the heritability, because the heritability indicates what proportion of the phenotypic variance can be attributed to genetic variance. The result of this scaling would give the expected genetic response to selection in the offspring generation. In formula this looks like:
Response to selection given a selection strategy causes a shift in genetic potential, also called genetic gain, indicated with . For mass selection response to selection is equal to genetic gain. The equation thus becomes:
Note that this formula is very similar to that of estimating the EBV using mass selection:
In fact, estimating genetic gain is the same as estimating the average EBV of the parents, as that is how much better than the average of the parental generation you would expect the offspring generation to perform.
How does this work in practice? For example, you are managing a goat population and you want to increase their adult body weight. Your average adult goat weighs 50 kg. You have selected a number of males and females that on average weigh 55 kg (ignore for now the fact that males are heavier than females). The heritability of adult body weight in your population of goats is 0.42. You want to know, given your current breeding decision, what your average goat will weigh in the next generation. If we do the calculations: S = 55 – 50 = 5 kg, and your ΔG = 5 * 0.42 = 2.1 kg. So you expect your next generation to be 2.1 kg heavier than the current generation: They will weigh on average 50 + 2.1 = 52.1 kg.
An important assumption in evaluating predicted genetic gain, is that the environmental influences will not change from generation to generation. Following the goat example: the next generation is expected to weigh 52.1 kg, provided that the environmental influences will remain the same. Of course this may not be true, but because we have no accurate idea about the environmental influences in the next generation. Therefore we assume they do not change.
Thus: important assumption in evaluating predictions of genetic gain: environmental influences remain constant across generations