Question

The mean and variance of plant height of two highly inbred strains \(\left(P_{1} \text { and } P_{2}\right)\) and their progeny \(\left(F_{1} \text { and } F_{2}\right)\) are shown here. $$\begin{array}{ccc}\text { Strain } & \text { Mean (cm) } & \text { Variance } \\\\\mathrm{P}_{1} & 34.2 & 4.2 \\\\\mathrm{P}_{2} & 55.3 & 3.8 \\\\\mathrm{F}_{1} & 44.2 & 5.6 \\\\\mathrm{F}_{2} & 46.3 & 10.3\end{array}$$ Calculate the broad-sense heritability \(\left(H^{2}\right)\) of plant height in this species.

Short answer

Answer: The broad-sense heritability (H^2) of plant height in this species is approximately 0.365 or 36.5%.

Step-by-step solution

Calculate the Average Environmental Variance

The environmental variance (\(V_E\)) can be calculated as the mean of the variances of the two inbred parent strains (\(P_1\) and \(P_2\)): $$V_{E}=\frac{4.2+3.8}{2}=4.0$$

Calculate the Phenotypic Variance

We will use the formula to calculate the phenotypic variance (\(V_P\)) as the difference between the variance of the \(F_2\) progeny and the environmental variance (\(V_E\)): $$V_{P}=V_{F_2}-V_{E}=10.3-4.0=6.3$$

Calculate the Genetic Variance

Now, to calculate the genetic variance (\(V_G\)), we use the following formula: $$V_{G}=V_{P}-V_{E}=6.3-4.0=2.3$$

Calculate the Broad-sense Heritability

Finally, to calculate the broad-sense heritability \((H^2)\), we divide the genetic variance (\(V_G\)) by the phenotypic variance (\(V_P\)): $$H^{2}=\frac{V_{G}}{V_{P}}=\frac{2.3}{6.3}\approx0.365$$ Thus, the broad-sense heritability \(H^2\) of plant height in this species is approximately 0.365 or 36.5%.