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Math  /  Data & Statistics

Question2. We wish to improve weaning weight (WW) in our cow herd. h2h^{2} for WW=.38W W=.38 herd mean for W W=587lbW \mathrm{~W}=587 \mathrm{lb} \% saved (males) = 1 \% saved (females) = 15 Standard deviation for WW = 23 lb Calculate: - Overall selection intensity - Response to selection - Generation interval for: - Males - Females o Overall - Generation interval - Response per year
Assume we keep our cows for 9 calf crops starting at 2 years of age and we use our bulls for 3 calf crops starting at 2 years of age.

Studdy Solution

STEP 1

What is this asking? We need to figure out how much we can improve the weight of our cows' calves by selecting the best ones to breed, and how quickly we can make these improvements over time. Watch out! Don't mix up the selection percentages for males and females, and remember that the generation interval is different for each!

STEP 2

1. Calculate selection intensity
2. Calculate response to selection
3. Determine generation intervals
4. Calculate response per year

STEP 3

First, let's **calculate the selection intensity** for males.
Since only 1%1\% of males are saved, we use the selection intensity value for 1%1\% from a standard table, which is approximately 2.6652.665.

STEP 4

Next, **calculate the selection intensity** for females.
For 15%15\% saved, the selection intensity is approximately 1.5541.554.

STEP 5

To find the **overall selection intensity**, we average the selection intensities for males and females, weighted by the number of each gender saved.
Since the percentage of males saved is much smaller, the male intensity has a greater impact.
The formula is:
Overall Selection Intensity=(2.665⋅0.01)+(1.554⋅0.15)0.01+0.15\text{Overall Selection Intensity} = \frac{(2.665 \cdot 0.01) + (1.554 \cdot 0.15)}{0.01 + 0.15}

STEP 6

Now, let's **calculate the response to selection** using the formula:
R=h2⋅Overall Selection Intensity⋅Standard DeviationR = h^2 \cdot \text{Overall Selection Intensity} \cdot \text{Standard Deviation}
where h2=0.38h^2 = 0.38 and the standard deviation is 23 lb23 \text{ lb}.

STEP 7

For **males**, the generation interval is the average age at which bulls are replaced.
Since bulls are used for 33 calf crops starting at age 22, the interval is:
Generation Interval (Males)=2+32=3.5 years\text{Generation Interval (Males)} = 2 + \frac{3}{2} = 3.5 \text{ years}

STEP 8

For **females**, the generation interval is the average age at which cows are replaced.
Cows are kept for 99 calf crops starting at age 22, so:
Generation Interval (Females)=2+92=6.5 years\text{Generation Interval (Females)} = 2 + \frac{9}{2} = 6.5 \text{ years}

STEP 9

To find the **overall generation interval**, we average the intervals for males and females, weighted by the number of each gender saved:
Overall Generation Interval=(3.5⋅0.01)+(6.5⋅0.15)0.01+0.15\text{Overall Generation Interval} = \frac{(3.5 \cdot 0.01) + (6.5 \cdot 0.15)}{0.01 + 0.15}

STEP 10

Finally, **calculate the response per year** by dividing the response to selection by the overall generation interval:
Response per Year=ROverall Generation Interval\text{Response per Year} = \frac{R}{\text{Overall Generation Interval}}

STEP 11

The **overall selection intensity** is approximately 1.6201.620.
The **response to selection** is approximately 14.15 lb14.15 \text{ lb}.
The **generation interval** for males is 3.5 years3.5 \text{ years}, for females is 6.5 years6.5 \text{ years}, and the **overall generation interval** is approximately 6.35 years6.35 \text{ years}.
The **response per year** is approximately 2.23 lb/year2.23 \text{ lb/year}.

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