# An Example

In an open-pollinated variety, a farmer selects 100 ears from 100 plants to provide the seed for the next generation. The mean grain weight of the selected plants is 200 grams per plant. The mean grain weight of all the ears that were measured is 150 grams per plant. Assuming a narrow-sense heritability of 15%, what is the expected genetic gain? The answer of 7.50 grams per plant that is obtained by multiplying the heritability of 15% (=0.15) by the superiority of the selected plants for grain weight of (200 – 150 = 50) is not correct. Do you know why?

The reason this answer is incorrect is because the lack of pollen control has not been considered. The selection differential of the female parents is, in fact, given by (200 – 150). But assuming that the pollen that pollinated the ears of the selected plants was a random sample of the pollen from the entire population, then the selection differential of the male parents is 0. Because the male and female parents contribute the same number of genes to the next generation, the overall selection differential is the average of the selection differentials of the male and female parents. Hence, the expected genetic gain is

Using the breeders’ equation assumes that the heritability is known. Often this will not be true. But, the breeders’ equation can be used to estimate the heritability. Assume that a farmer evaluates both the original and the improved generation in the same environment. He measures a difference of 3.75 grams of grain per plant. He knows that his selection differential was 150 grams per plant. Then the heritability can be estimated as

To estimate the genetic gain, both generations must be evaluated in the same environment so that environmental effects do not cause a bias. Measuring both generations in the same environment requires keeping a remnant sample of the first generation. This can be done either by not planting all the seed used to plant this generation or by harvesting a random sample of the ears from this generation. That random sample should contain at least 100 ears and care must be taken to ensure that the sample is indeed random. Random means that every plant in the population has an equal chance of being included in the sample. Often, so little change will occur from one generation of selection that estimating heritability from a single generation of selection will be quite imprecise. The same formula can be used to estimate heritability after several generations of selection have been completed. The only difference is that the estimated genetic gain must be divided by the number of generations of selection so that the genetic gain is the average gain per generation of selection. Likewise, the value of the selection differential is the average value across the multiple generations of selection.