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Narrow-sense heritability is a concept that tells us how much of the variation in a trait among a population is due to genetic differences, specifically additive genetic variance. Additive genetic variance refers to the total genetic effects in which alleles contribute to a phenotype proportionally without interactions between alleles, capturing the predictable genetic transmission from parents to offspring. This concept is mathematically expressed as:

• \( h^2 = \frac{V_A}{V_P} \)

where \( V_A \) is the additive genetic variance and \( V_P \) represents the total phenotypic variance. When looking at heritability, it reflects the expected response to selection or breeding. If environmental conditions are uniform among individuals, a trait with high narrow-sense heritability is largely influenced by genetic differences. However, as environmental variance or dominance variance increases, while \( V_A \) remains unchanged, the overall phenotypic variance \( V_P \) increases thus reducing \( h^2 \), reflecting less genetic control over the trait.

Broad-sense heritability takes a more complete view of genetic influence, by accounting for the total genetic variance. This means it considers not only the additive genetic variance, but also dominance variance and interaction (or epistatic) variance between genes. Broad-sense heritability is denoted as:

• \( H^2 = \frac{V_G}{V_P} \)

Here, \( V_G \) is the total genetic variance which includes all genetic factors (additive, dominance, and interaction), and \( V_P \) is again the total phenotypic variance. Because broad-sense heritability captures multiple genetic components, it can reveal the overall potential for genetic improvement in a population. If dominance variance increases, \( V_G \) increases, and since \( V_P \) also increases, broad-sense heritability may increase or stay about the same depending on the balance between genetic variance components and total phenotypic variance. However, unlike narrow-sense heritability, broad-sense is less commonly used in predicting selection response due to its comprehensive nature.

Genetic variance describes how much of the phenotypic variation can be attributed to differing genetic factors among individuals in a population. It's an essential part of understanding heritability, divided into:

• Additive variance (\( V_A \)): This captures the direct genetic influence on the trait, where each allele adds a specific amount to the trait value.
• Dominance variance (\( V_D \)): Occurs when interactions between alleles at a locus affect the trait; not additive and may change the effect due to dominance relationships.
• Epistatic variance (\( V_I \)): Results from interactions between different genes, complicating the direct transmission from parent to offspring.

To sum up, genetic variance provides the portion of phenotypic diversity due to genetics and helps in predicting potential responses to selection. Changes in any component of genetic variance can influence heritability calculations, impacting conservation and breeding strategies in populations.

Environmental variance refers to the portion of phenotypic variance that arises not from genetics, but from environmental factors. These factors can include a variety of influences:

• Nutritional availability: Differences in diet can lead to variations in physical development and size.
• Climate conditions: Temperature variations can affect metabolic rates and growth patterns.
• Social interactions: The presence of siblings or other social partners can alter behaviors or stress levels.

When environmental variance increases and all else remains the same, it enlarges the total phenotypic variance (\( V_P \)). As a result, both narrow-sense and broad-sense heritability decrease because they are calculated as proportions of \( V_P \). Understanding environmental variance is crucial in separating environmental effects from genetic effects, helping scientists and breeders make informed decisions for managing populations and enhancing genetic potential.