Question

You are hired by Murphey Farms to decrease the backfat in their hogs. The current hog population has a mean backfat content of 20.2mm. You selected the hogs with the smallest amount of backfat, mated them and obtained the progeny generation. The selected hogs had a mean backfat content of 9.5mm. You know that the heritability for percent backfat in hogs is 0.47.
1. What is the selection differential? Round your values properly to 2 decimal digits.
2. What is the expected response to selection? Round your values properly to 2 decimal digits.
3. What is the expected mean of the progeny generation? Round your values properly to 2 decimal digits.

Answer 1

Answer:

1. SD = -10.7
2. R = -5.3
3. X₁ = 14.9 ≅ 15mm

Explanation:

Before answering the question, we need to know a few concepts.

Artificial selection is the selecting practice of a specific group of organisms in a population -that carry the traits of interest- to be the parents of the following generations.  

Parental individuals carrying phenotypic values of interest are selected from the whole population. These parents interbreed, and a new generation is produced.  

The selection differential, SD, is the difference between the mean value of the trait in the population (X₀) and the mean value of the parents, (Xs). So,  

SD = Xs - X₀    

Heritability in the strict sense, h², is the genetic component measure to which additive genetic variance contributes. The heritability might be used to determine how the population will respond to the selection done, R.  

h² = R/SD

The response to selection (R) refers to the metric value gained from the cross between the selected parents. R can be calculated by multiplying the heritability h², with the selection differential, SD.  

R = h²SD  

R also equals the difference between the new generation phenotypic value (X₁) and the original population phenotypic value (X₀),  

R = X₁ - X₀  

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Now that we know these concepts and how to calculate them, we can solve the proposed problem.

Available data:  

• You are decreasing the backfat in the hogs.

• The hog population mean backfat content = 20.2mm → X₀

• The selected hogs had a mean backfat content of 9.5mm → Xs  

• Heritability is 0.47 → h²

According to what we sow previously, we need to find out the value of X₁, which reflects how tall the new generation of corn will grow.  

• We know that R = X₁ - X₀, so we need to clear this formula to calculate X₁

X₁ = R + X₀  

We already know that X₀ = 20.2mm  

Now we need to calculate R.  

• R = h²SD  

We know that h² = 0.47,  

Now we need to calculate SD

• SD =  Xs - X₀  

Xs = 9.5mm → Parentals media height

X₀ = 20.2mm → Population media Height

SD = Xs - X₀  

SD = 9.5 - 20.2

SD = -10.7  

Knowing this, we can calculate R

R = h²SD

• h² = 0.47  

• SD = -10.7

R = 0.47 x -10.72

R = -5.3

Finally, once we know the R-value we can calculate the X₁ value

X₁ = R + X₀

X₁ = -5.3 + 20.2

X₁ = 14.9 ≅ 15mm