16. Two inbred lines of beans were intercrossed. In F1 the variance in bean length was measured as 2.0. The F1 was selfed to obtain F2 and the variance in bean length in F2 was 7.0. The broad heritability of bean length in the F2 population will be:
(1) 0.75 (2) 9.0
(3) 5.0 (4) 0.71
Understanding Broad-Sense Heritability in F2 Populations
Broad-sense heritability (H²) measures the proportion of total phenotypic variance attributable to genetic variance. It includes all genetic factors like additive, dominance, and epistatic effects. In the context of F1 and F2 populations from inbred lines, environmental variance is estimated from the genetically identical F1 generation, while the F2 generation variance encompasses both environmental and genetic variances. This approach provides a clearer distinction between genetic and non-genetic effects.
Calculation Example
- Environmental variance (Ve) = Variance in F1 = 2.0
- Total phenotypic variance in F2 (Vp) = 7.0
- Genetic variance (Vg) = Vp (F2) – Ve (F1) = 7.0 – 2.0 = 5.0
Thus, broad-sense heritability,
H² = Vg / Vp = 5.0 / 7.0 = 0.71
Explanation of Options
- 0.75 – Close but slightly higher than the correct value.
- 9.0 – Illogical as heritability is a proportion and must be ≤1.
- 5.0 – Incorrect, this is genetic variance, not heritability.
- 0.71 – Correct broad-sense heritability value.
Formula and Significance in Plant Breeding
The formula to compute broad-sense heritability is:
H² = Vg / Vp
where Vg is genetic variance and Vp is phenotypic variance. Heritability values range from 0 to 1; values closer to 1 indicate that traits are largely controlled by genetics, enabling effective selection in breeding programs. This metric helps breeders understand how well traits like bean length will respond to selection in subsequent generations.
This detailed explanation will help students and researchers accurately estimate heritability and understand the importance of genetic variance in plant breeding.
References: The environmental variance is estimated from the F1 variance (2.0), genetic variance is the difference between F2 and F1 variance, and the broad-sense heritability is the genetic variance divided by the total F2 variance, which equals 0.71.
