Question

According to early studies (performed by Wright) on guinea pig coat color, the total variance in a randomly mating strain was \(0.573\). The variance in an inbred strain was \(0.340\). From correlations between relatives in the randomly mating population the heritability (gene effect) was determined to be 38 percent of the total variance. Find the following: (a) variance due to gene effect; (b) variance due to epistasis and dominance.

Short answer

(a) The variance due to gene effect is 0.21754. (b) The variance due to epistasis and dominance is 0.35546.

Step-by-step solution

Calculate the variance due to gene effect (additive variance)

To determine the variance due to the gene effect, we will use the given heritability percentage (38%) and the total variance in the randomly mating strain (0.573). The formula to calculate additive variance (V_A) is: \[V_A = h^2 × V_T\] Where: - \(V_A\) is the additive variance (variance due to gene effect), - \(h^2\) is the heritability (expressed as a decimal), - \(V_T\) is the total variance. Now, let's plug in the given values: \[V_A = (0.38) × (0.573)\] \[V_A = 0.21754\] The variance due to gene effect (additive variance) is 0.21754 (rounded to 5 decimal places).

Calculate the variance due to epistasis and dominance (non-additive variance)

To find the variance due to epistasis and dominance, we have to subtract the variance due to gene effect (additive variance) found in Step 1 from the total variance in the randomly mating strain. The formula to calculate non-additive variance (V_D) is: \[V_D = V_T - V_A\] Using the values found in step 1: \[V_D = 0.573 - 0.21754\] \[V_D = 0.35546\] The variance due to epistasis and dominance (non-additive variance) is 0.35546 (rounded to 5 decimal places). So, the answers to the exercise questions are: (a) Variance due to gene effect: 0.21754. (b) Variance due to epistasis and dominance: 0.35546.

Key concepts

Additive Variance

Additive variance, often denoted as \( V_A \), represents the portion of genetic variance that is attributed directly to the additive effects of individual genes. In simpler terms, it is the kind of variance we can "add up" based on the effects of individual genetic variants contributing directly to the trait. This additive effect is crucial because it is the variance most easily and directly selected upon in evolutionary processes and breeding programs.

To calculate additive variance, we use heritability \( h^2 \) of a trait, which quantifies the proportion of total phenotypic variance attributable to genetic factors. Heritability is estimated as a decimal; if heritability is said to be 38%, it would be used as 0.38 in calculations. The formula to find the additive variance is:

\[ V_A = h^2 \times V_T \]

Where \( V_T \) is the total phenotypic variance. In our given example, the total variance \( V_T \) is 0.573, and heritability \( h^2 \) is 0.38. This gives us an additive variance of \( V_A = 0.21754 \), meaning this is the portion of the total variance directly attributable to genes being passed from parents to offspring.

Non-Additive Variance

Non-additive variance, noted as \( V_D \), refers to components of genetic variance that do not directly add up in the way additive variance does. It includes more complex interactions such as dominance and epistasis.

- **Dominance:** Involves interactions between alleles at a single gene locus, where one allele may mask the expression of another.- **Epistasis:** Refers to interactions between genes at different loci, where the effect of one gene is modified by one or several other genes.

These forms of genetic interactions make up the non-additive genetic variance. To calculate it, we subtract the additive variance from the total phenotypic variance:

\[ V_D = V_T - V_A \]

Using the values provided, with a total variance \( V_T \) of 0.573 and an additive variance \( V_A \) of 0.21754, the non-additive variance \( V_D \) is 0.35546. This calculation tells us how much of the total variance is due to complex interactions between genes.

Genetic Variance Calculation

Calculating genetic variance involves determining how much of the trait variability in a population can be attributed to genetic differences among individuals. We split this genetic variance into additive and non-additive components, as they each represent different genetic scenarios and implications for traits' heritability.

- **Additive variance** is often a primary focus because it indicates the potential success of selection in breeding programs or natural selection in populations.- **Non-additive variance** reflects genetic interactions that complicate the prediction of offspring traits based on parentage, but still play a significant role in the phenotypic outcomes of organisms.

These components align with the equation:

\[ V_G = V_A + V_D \]

Where \( V_G \) is the total genetic variance. In our exercise, the genetic variance is determined as part of the phenotypic variance \( V_T = 0.573 \), and is split into its additive \( V_A = 0.21754 \) and non-additive \( V_D = 0.35546 \) components. This breakdown helps in understanding the underlying genetic architecture of complex traits and estimating how they might change or be improved through selection.