In a cross of two pure-breeding lines of tomatoes producing different fruit sizes, the variance in grams (g) of fruit weight in the F₁ is 2.25 g and the variance among the F₂ is 5.40 g. Determine the genetic and environmental variance (VG and VE) for the trait and the broad sense heritability of the trait.
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1
Understand the problem: The goal is to calculate the genetic variance (VG), environmental variance (VE), and broad-sense heritability (H²) for the trait of fruit weight in tomatoes. The variance in the F₁ generation (2.25 g) represents the environmental variance (VE), and the total variance in the F₂ generation (5.40 g) includes both genetic and environmental components.
Step 1: Recall the formula for total variance in the F₂ generation: Total Variance (VF₂) = Genetic Variance (VG) + Environmental Variance (VE). Here, VF₂ = 5.40 g and VE = 2.25 g. Rearrange the formula to solve for VG: VG = VF₂ - VE.
Step 2: Calculate the broad-sense heritability (H²) using the formula: H² = VG / VF₂. This formula expresses the proportion of the total variance that is due to genetic variance.
Step 3: Substitute the values of VG (calculated in Step 1) and VF₂ (5.40 g) into the formula for H². Ensure that the units are consistent throughout the calculation.
Step 4: Interpret the results. The genetic variance (VG) represents the contribution of genetic factors to the observed variation in fruit weight, while the environmental variance (VE) represents the contribution of non-genetic factors. The broad-sense heritability (H²) indicates the proportion of the total variance that is attributable to genetic factors.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Genetic Variance (VG)
Genetic variance (VG) refers to the portion of phenotypic variance in a trait that can be attributed to genetic differences among individuals. It encompasses additive genetic variance, dominance variance, and interaction variance. Understanding VG is crucial for determining how much of the trait's variation is inherited and can be passed on to future generations.
Environmental variance (VE) is the component of phenotypic variance that arises from environmental factors affecting individuals, such as nutrition, climate, and other external conditions. It highlights how the environment can influence the expression of a trait, independent of genetic factors. This concept is essential for understanding the total variability in a trait and its heritability.
Broad-sense heritability (H²) is a measure of the proportion of total phenotypic variance in a trait that is attributable to genetic variance. It is calculated as the ratio of genetic variance (VG) to the total phenotypic variance (VP), which includes both genetic and environmental variance. H² provides insight into the potential for a trait to respond to selection and is important for breeding and conservation efforts.