Answer:
The value of X₁, which is how tall the new generation of corn will grow equals 5.6 feet.
Explanation:
Before answering the question, we need to know a few concepts.
<u>Artificial selection</u> 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 <u>selection differential, SD,</u> <em>is the difference between the </em><u><em>mean value of the trait in the population (X₀)</em></u><em> and the </em><u><em>mean value of the parents, (Xₙ)</em></u><em>.</em> So,
SD = X₀ - Xₙ
<u>Heritability in the strict sense, h²</u>, is the <em>genetic component measure to which additive genetic variance contributes</em>. The heritability might be used to determine how the population will respond to the selection done, R.
h² = R/SD
The <u>response to selection (R)</u> refers to the metric value gained from the cross between the selected parents. <em>R can be calculated by multiplying the heritability h², with the selection differential, SD. </em>
R = h²SD
<em>R also equals the difference between </em><u><em>the new generation phenotypic value (X₁)</em></u><em> and the original population phenotypic value (X₀), </em>
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:
- You are selecting taller corn plants.
- The population of corn has a mean height of 4 feet → X₀
- Parental selected plants of 6 feet → Xₙ
- Heritability of corn height is 0.8 → 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 = 4 feet,
Now we need to calculate R.
We know that h² = 0.8,
Now we need to calculate SD
Xₙ = 6 → Parentals media height
X₀ = 4 → Population media Height
SD = X₀ - Xₙ
SD = 4 - 6
SD = -2 feet.
Knowing this, we can calculate R
R = h²SD
- h² = 0.8
- SD = 2
R = 0.8 x 2
R = 1.6
Finally, once we know the R-value we can calculate the X₁ value
X₁ = R + X₀
X₁ = 4 + 1.6
X₁ = 5.6