Question

A population of laboratory mice was weighed at the age of six weeks (full adult weight) and found to have a mean weight of 20 g. The narrow heritability of weight gain \(\left(h^{2}\right)\) is known to be 0.25 in this laboratory strain. If mice weighing 24 g are selected and mated at random, what is the expected mean weight of the next generation?

Short answer

Answer: The expected mean weight of the next generation of laboratory mice is 21 g.

Step-by-step solution

Identify Given Information and the Target Variable

We are given: 1. Mean weight of adult mice: 20 g 2. Narrow heritability (\(h^2\)): 0.25 3. Selected mice weight: 24 g Our goal is to find the expected mean weight of the next generation.

Calculate the Selection Differential

The selection differential (S) is the difference between the mean weight of the selected mice and the mean weight of the entire population. In our case: S = 24 g (selected mice) - 20 g (entire population) = 4 g

Apply the Narrow Heritability

The narrow heritability (\(h^2\)) represents the proportion of the phenotypic variance (in our case, weight) that is due to additive genetic factors. We can find the expected response to selection (R) using the formula: R = \(h^2\) × S Using the given values: R = 0.25 × 4 g = 1 g

Calculate the Expected Mean Weight of the Next Generation

Now we can find the expected mean weight of the next generation of mice by adding the response to selection (R) to the original mean weight of the population. Expected mean weight of the next generation = Current mean weight + R Expected mean weight of the next generation = 20 g (mean weight of the original population) + 1 g (Response to selection) = 21 g The expected mean weight of the next generation of mice is 21 g.

Key concepts

Response to Selection

When we select certain organisms with desired traits for reproduction, we cause a change in the overall genetic makeup of the population. This change is quantified as the 'response to selection' (R). It represents the degree to which a trait's average value in a population changes from one generation to the next as a result of selection.

In our exercise, we were looking at a population of laboratory mice, aiming to calculate the expected mean weight of their offspring after selecting heavier mice for breeding. Using the formula R = \(h^2\) \times S, we found that the response to selection was 1 g. This implies that, on average, the next generation will be heavier than the previous one by 1 g, solely due to the selective breeding of heavier mice.

Selection Differential

The selection differential (S) is the measure of how selective the breeding process is. Specifically, it is the difference between the mean trait value of the selected individuals and that of the general population.

In the given exercise, the selection differential was calculated as the difference in weight between the selected mice (24 g) and the population average (20 g), resulting in a 4 g difference. This 4 g selection differential quantifies the intensity of our selection for heavier mice, setting the stage for how much change we can anticipate in the population's weight as a result of our selective breeding practices.

Phenotypic Variance

Variation in traits like weight in a population is referred to as phenotypic variance. It encompasses differences due to both genetic factors and environmental influences. In the context of genetics, only a portion of this variance is heritable, meaning that it can be passed down from parents to offspring.

This heritable portion of the variance is captured by the heritability estimate (\(h^2\)), which in our mouse example was given as 0.25. The heritability tells us that 25% of the weight variance in these mice can be attributed to genetic differences that can respond to selection. Understanding phenotypic variance is crucial as it informs us about how much a trait can potentially change under selective breeding.

Genetic Factors in Weight

Genetic factors play a critical role in determining the weight of organisms, including our laboratory mice. In genetics, these factors are recognized by estimating the narrow heritability (\(h^2\)), which in our case is 0.25. This number indicates that a quarter of the variability observed in the mice's weight can be explained by the additive effect of genes passed on from the parents.

However, it's important to remember that weight is not solely determined by genetics. Environmental factors and their interaction with genetics also play a significant role. Thus, while we can predict an average increase in weight due to selective breeding for heavier mice, individual weights will still vary around this new average due to both genetic diversity and environmental factors.