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 formula for broad-sense heritability: H^2 = \frac{V_G}{V_P}, where V_G is the genetic variance and V_P is the phenotypic variance.
2. Determine the phenotypic variance (V_P) from the F2 generation, which is given as 10.3.
3. Calculate the genetic variance (V_G) using the formula V_G = V_P - V_E, where V_E is the environmental variance.
4. Estimate the environmental variance (V_E) by averaging the variances of the parental strains P1 and P2: V_E = \frac{4.2 + 3.8}{2}.
5. Substitute the values of V_G and V_P into the heritability formula to find H^2.

Key Concepts

Broad-Sense Heritability (H²)

Broad-sense heritability (H²) is a measure of the proportion of phenotypic variance in a trait that can be attributed to genetic variance among individuals in a population. It encompasses all genetic contributions, including additive, dominance, and interaction effects. H² is calculated using the formula H² = VG/VP, where VG is the genetic variance and VP is the total phenotypic variance. Understanding H² is crucial for predicting how traits may respond to selection.

Phenotypic Variance (VP)

Phenotypic variance (VP) refers to the total variance observed in a trait within a population, resulting from both genetic and environmental factors. It can be partitioned into genetic variance (VG) and environmental variance (VE). In the context of the question, calculating VP involves summing the variances of the parental strains and their progeny, which helps in understanding the overall variability in plant height.

Genetic Variance (VG)

Genetic variance (VG) is the portion of phenotypic variance that is attributable to genetic differences among individuals. It can be further divided into additive genetic variance (the cumulative effect of individual alleles) and non-additive genetic variance (due to interactions between alleles). In calculating broad-sense heritability, accurately estimating VG is essential, as it directly influences the heritability of traits like plant height.