In a population of tomato plants, mean fruit weight is \(60 \mathrm{g}\) and \(h^{2}\) is \(0.3 .\) Predict the mean weight of the progeny if tomato plants whose fruit averaged \(80 \mathrm{g}\) were selected from the original population and interbred.

Understanding the selection differential is essential when discussing evolutionary change or selective breeding in a population. It quantifies the strength of selection by measuring the difference between the average trait of the entire population and the average trait of the selected parents, or the breeding individuals.

For instance, if we consider the mean weight of fruits in a population of tomato plants, selection differential is calculated by subtracting the population mean from the mean weight of the selected plants. In our exercise, the selection differential (\( S \)) was found by simply taking the mean weight of the selected tomato plants (\( 80 \text{g} \) ) and subtracting the mean fruit weight of the original population (\( 60 \text{g} \) ), which equals to a 20g difference.

This differential is not just a numerical value; it reflects the potential for selection to cause a shift in the population's traits. If all other factors are equal, a higher selection differential suggests a greater potential for change.

The concept of heritability is foundational in genetics and breeding. It represents the proportion of variation in a trait that is attributable to genetic differences among individuals within a population. This value is often denoted as (\( h^{2} \) ) and is usually expressed as a value between 0 and 1.

Heritability plays a pivotal role in predicting whether and to what extent a trait will respond to selection. A high heritability implies that a large part of the variation seen in a trait, like fruit weight in tomato plants, is due to genetic differences. In our case, the heritability of fruit weight is (\( 0.3 \) ), meaning 30% of the variation is due to genetic factors.

It's crucial to grasp that heritability does not indicate the degree to which a trait is genetically determined; rather, it signifies how much of the variation in the trait can be passed on to the next generation. Traits with higher heritability are more easily modified by selective breeding since a larger proportion of the trait difference is due to genetic factors.

By integrating our understanding of selection differential and heritability, we can foresee changes in traits across generations. This process is commonly applied in agricultural breeding programs, such as the one depicted in our tomato plant example. The principle lies in combining the selection differential with the heritability to predict the response to selection, and thus, the mean trait value of the progeny.

When we predict progeny mean weight, we are essentially estimating the expected average trait of the offspring based on the selection we have applied. To determine this, we calculated the selection response (\( R \) ) by multiplying the heritability (\( h^{2} = 0.3 \) ) by the selection differential (\( S = 20 \text{g} \) ). The result gave us a 6g increase in mean fruit weight for the progeny. Finally, by adding the original population mean (\( 60 \text{g} \) ) to the selection response (\( R = 6 \text{g} \) ), we predict that the progeny will have an average fruit weight of 66g.

This prediction is an essential tool for breeders, as it helps set realistic expectations for the outcomes of their selective breeding programs and informs decisions about which individuals to select for breeding the next generation of plants or animals.