The mean and variance of plant height of two highly inbred strains (P₁ and P₂) and their progeny (F₁ and F₂) are shown here.


  Strain  Mean (cm)  Variance 
   P₁     34.2        4.2
   P₂     55.3        3.8
   F₁     44.2        5.6
   F₂     46.3       10.3


Calculate the broad-sense heritability (H²) of plant height in this species.

Verified step by step guidance

1. Identify the components needed to calculate broad-sense heritability (H²). Broad-sense heritability is defined as the proportion of total phenotypic variance that is due to genetic variance. Mathematically, it is expressed as \(H^{2} = \frac{V_{G}}{V_{P}}\), where \(V_{G}\) is the genetic variance and \(V_{P}\) is the total phenotypic variance.
2. Estimate the environmental variance (\(V_{E}\)) using the variance of the parental strains (P₁ and P₂). Since these strains are highly inbred and genetically uniform, their variance mainly reflects environmental variance. Calculate \(V_{E}\) as the average of the variances of P₁ and P₂: \(V_{E} = \frac{4.2 + 3.8}{2}\).
3. Determine the total phenotypic variance (\(V_{P}\)) in the F₂ generation, which is given as 10.3. This variance includes both genetic and environmental components.
4. Calculate the genetic variance (\(V_{G}\)) in the F₂ generation by subtracting the environmental variance from the total phenotypic variance: \(V_{G} = V_{P} - V_{E}\).
5. Finally, compute the broad-sense heritability using the formula \(H^{2} = \frac{V_{G}}{V_{P}}\) by substituting the values of \(V_{G}\) and \(V_{P}\) obtained in the previous steps.

Key Concepts

Broad-Sense Heritability (H²)

Broad-sense heritability (H²) measures the proportion of total phenotypic variance in a trait that is due to genetic variance. It is calculated as the ratio of genetic variance to total phenotypic variance, indicating how much of the observed variation is inherited. H² helps predict the response to selection in breeding programs.

Phenotypic Variance and Genetic Variance

Phenotypic variance (Vp) is the total variation observed in a trait, arising from both genetic and environmental factors. Genetic variance (Vg) is the portion of phenotypic variance attributable to genetic differences among individuals. In inbred strains, environmental variance can be estimated from within-strain variance, aiding in separating genetic effects.

Use of Inbred Strains and Progeny Variance in Heritability Estimation

Highly inbred parental strains have minimal genetic variation within themselves, so their variance mainly reflects environmental effects. The increased variance in F₂ progeny compared to parents reflects genetic segregation and recombination. Comparing variances of parents and progeny allows estimation of genetic variance and thus broad-sense heritability.