Question

In a herd of dairy cows the narrow-sense heritability for milk protein content is \(0.76,\) and for milk butterfat it is \(0.82 .\) The cor relation coefficient between milk protein content and butterfat is \(0.91 .\) If the farmer selects for cows producing more butterfat in their milk, what will be the most likely effect on milk protein content in the next generation?

Short answer

Answer: The most likely effect on milk protein content in the next generation if the farmer selects for cows producing more butterfat in their milk is an increase in milk protein content. This is because the two traits are positively correlated, and selecting for more butterfat will likely result in a higher milk protein content.

Step-by-step solution

Understand the given values and variables

In this problem, we have three given values: - Narrow-sense heritability for milk protein content (h_p^2): 0.76 - Narrow-sense heritability for milk butterfat (h_b^2): 0.82 - Correlation coefficient between milk protein content and butterfat (r): 0.91 These values will help us find the most likely effect on milk protein content in the next generation.

Selection differential

The selection differential (S) is the difference between the mean of the selected parents and the mean of the entire population. In this case, the selection differential is related to milk butterfat. Since we are not given the specific values for the selection differential, we will represent it as a variable: S_b.

Calculate the response to selection for milk protein content

The response to selection (R) is the change in a population's mean value for a trait after one generation of selection. In this case, we want to find the response to selection for milk protein content. We can use the formula: R_p = h_p^2 * r * S_b / sqrt(h_b^2) Where: - R_p is the response to selection for milk protein content - h_p^2 is the narrow-sense heritability for milk protein content - h_b^2 is the narrow-sense heritability for milk butterfat - r is the correlation coefficient between milk protein content and butterfat - S_b is the selection differential for milk butterfat

Substitute the given values into the formula

We will plug in the given values into the formula: R_p = 0.76 * 0.91 * S_b / sqrt(0.82) Since we do not have a specific value for S_b, we can only analyze the result qualitatively.

Analyze the result qualitatively

From the formula, we can see that the response to selection for milk protein content (R_p) is positive, as all the values are positive. This means that selecting for cows producing more butterfat in their milk will likely result in an increase in milk protein content in the next generation. Since the correlation coefficient (r) is quite high (0.91), the two traits are positively correlated, indicating that an increase in one trait is generally associated with an increase in the other.

Key concepts

Narrow-Sense Heritability

Understanding narrow-sense heritability is crucial when predicting how much a phenotype will respond to selection in genetics. It is formally defined as the proportion of phenotypic variance in a population that is attributable to additive genetic variances. This is denoted as h² and can range from 0 to 1, where a higher value indicates a greater likelihood that offspring will resemble their parents for that specific trait.

For example, considering the high narrow-sense heritability values for milk protein content \(0.76\) and milk butterfat \(0.82\) in dairy cows, it suggests that selective breeding for these traits could effectively produce offspring that exhibit desired levels of these traits, as a significant portion of variation is due to additive genetic factors.

Correlation Coefficient

The correlation coefficient, often denoted as 'r', measures the strength and direction of a linear relationship between two variables. Its value ranges between -1 and 1 where -1 indicates a perfect negative correlation, 1 indicates a perfect positive correlation, and 0 implies no correlation at all.

In the context of genetics, a high correlation coefficient, like the \(0.91\) value for the relationship between milk protein content and butterfat, suggests that these two traits tend to increase or decrease together. This close relationship can inform breeders that selecting for one trait will likely impact the other, which is essential for making informed breeding decisions.

Selection Differential

The concept of selection differential (represented often as S) plays a pivotal role in selective breeding. It refers to the average difference between selected individuals for breeding and the general population's average. In practical terms, it helps breeders understand how much a selected trait deviates from the norm and guides the intended breeding direction.

Our case doesn't give an explicit value for the selection differential for milk butterfat (S_b). However, even without the exact number, we presume this differential is positive when the farmer selects for cows with higher butterfat; this is because selection, by definition, favors individuals above the general average for the characteristic of interest.

Response to Selection

The response to selection, denoted as R, estimates the expected change in a trait's average value in the next generation due to selection. The formula that relates response to selection with narrow-sense heritability and the selection differential is expressed as R = h² * S.

In the exercise, the response to selection for milk protein content \(R_p\) is calculated using the formula R_p = h_p² * r * S_b / sqrt(h_b²). Extrapolating from this formula, one can conclude that because all involved parameters (h², r, S) are positive, with a high correlation coefficient, the response to selection will most likely lead to an increase in milk protein content when selecting for increased milk butterfat. This indicates that both milk protein and butterfat content are expected to rise concurrently in the selected cows' offspring.