Question

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

Short answer

Answer: The predicted mean weight of the progeny is 66g.

Step-by-step solution

Identify the formula for the response to selection

The formula for the response to selection is: $$R=h^2\times S$$ Here, $R$ is the response to selection, $h^2$ is the heritability, and $S$ is the selection differential.

Calculate the selection differential

To find the selection differential, we first need to determine the difference between the mean fruit weight of the selected plants and the mean fruit weight of the original population. The selection differential is given as: $$S=\text{Selected Mean Fruit Weight}-\text{Original Mean Fruit Weight}$$ Using the provided values, we have: $$S=80\mathrm{g}-60\mathrm{g}=20\mathrm{g}$$

Substitute values to find the response to selection

Now, we have all the information needed to find the response to selection by substituting the values of heritability and selection differential in the formula: $$R=h^2\times S=0.3\times 20\mathrm{g}$$ Calculating the value, we get: $$R=6\mathrm{g}$$

Predict the mean weight of the progeny

The response to selection tells us the expected change in the mean fruit weight. To find the mean weight of the progeny, we need to add this change to the original mean fruit weight: $$\text{Mean Weight of Progeny}=\text{Original Mean Fruit Weight}+R$$ Plugging in the values, we have: $$\text{Mean Weight of Progeny}=60\mathrm{g}+6\mathrm{g}=66\mathrm{g}$$ Thus, the predicted mean weight of the progeny is $66\mathrm{g}$.

Key concepts

Heritability

Heritability is a core concept in plant genetics and tells us how much of the variation in a trait can be attributed to genetic factors. It is denoted by the symbol $h^2$. Heritability values range from 0 to 1, where 0 indicates no genetic influence and 1 indicates complete genetic determination. In practical terms, it helps breeders determine the potential success of a selection program. The higher the heritability, the more likely it is that the desired traits will be passed on to the next generation. In our exercise example, we have a heritability of $0.3$. This means that 30% of the variation in fruit weight among the tomato plants is due to their genetic makeup. It gives us insight into how much of the selection differential we might expect to "see through" to the progeny. This is crucial for predicting whether selecting for a specific trait will lead to significant changes in the offspring.

Selection Differential

The selection differential $S$ is a measure of how much the selected group differs from the original average population. It quantifies the intensity of selection that is being applied. A greater selection differential means that the chosen traits in the selected individuals differ more significantly from the average population traits. To calculate $S$, you subtract the original mean trait (in this case, mean fruit weight) from the mean trait value of the selected group. So, if selected tomato plants have a mean fruit weight of $80\mathrm{g}$ and the original population's mean is $60\mathrm{g}$, the selection differential $S$ would be $20\mathrm{g}$.The selection differential gives breeders an idea of the extent to which they are applying directional selection pressure, which, when combined with heritability, helps predict potential changes in the progeny.

Response to Selection

The response to selection $R$ is the predicted change in a trait from one generation to the next, as a result of selection. It informs breeders of the expected success of their selection efforts in the offspring. The response to selection can be calculated using the formula: $$R=h^2\times S$$In our example, where heritability $h^2$ is $0.3$ and the selection differential $S$ is $20\mathrm{g}$, the response to selection is $6\mathrm{g}$. This result predicts that the mean fruit weight of the progeny will be $6\mathrm{g}$ higher than the original population's mean. Understanding the response to selection helps breeders anticipate the effectiveness of their breeding program. By using heritability and the selection differential together, they can make informed selections and strategically enhance desired traits in future plant generations.