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 \(66 \mathrm{g}\).