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A breeder is trying to decrease the maturation time in a population of sunflowers. In this population, the mean time to flowering is 100 days. Plants with a mean flowering time of only 90 days were used to produce the next generation. If the narrow-sense heritability for flowering time is 0.2, what will the average time to flowering be in the next generation

Sagot :

marianaegarciaperedo

Answer:

The next generation average time to flowering will be 98 days.

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 narrow-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 or lost 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 = X₀ - X₁

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

Available data:  

  • trying to decrease the maturation time in a population of sunflowers.
  • the population mean time to flower is 100 days → X₀
  • Chosen parental Plants mean flowering time is 90 days → Xs
  • the narrow-sense heritability for flowering time is 0.2 → h²

According to what we sow previously, we need to find out the value of X₁, which reflects the next generation average time to flowering.

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

X₁ = R + X₀

We already know that X₀ = 100 days,  

Now we need to calculate R.  

  • R = h²SD

We know that h² = 0.2,  

Now we need to calculate SD

  • SD = Xs - X₀

Xs = 90 days → Parentals media flowering time

X₀ = 100 → Population media flowering time

SD = Xs - X₀  

SD = 90 - 100  

SD = - 10 days

Knowing this, we can calculate R

  • R = h²SD

o h² = 0.2  

o SD = - 10

R = 0.2 x (-10)

R = - 2

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

X₁ = R + X₀

X₁ = - 2 + 100

X₁ = 98

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