Question:
In a haplodiploid ant species, sons are haploid and produced from unfertilized eggs, while daughters are diploid and produced from fertilized eggs. A single queen establishes a colony after mating with three different unrelated males. The queen uses the sperm from all three males equally to produce her female offspring. The average genetic relatedness between two randomly selected female offspring in this colony will be:
In a haplodiploid ant species, sons are haploid and produced from unfertilized eggs, while daughters are diploid and produced from fertilized eggs. A single queen establishes a colony after mating with three different unrelated males. The queen uses the sperm from all three males equally to produce her female offspring. The average genetic relatedness between two randomly selected female offspring in this colony will be:
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A quick way to compute this is: $r = \frac{1}{4} + \frac{1}{2} P(\text{same father})$. Since $P(\text{same father}) = 1/k$ (where $k$ is the number of mates), $r = \frac{1}{4} + \frac{1}{2k}$. For $k=3$, $r = 0.25 + 0.167 = 0.417$.
Updated On: Sep 8, 2026
- 0.417
- 0.500
- 0.750
- 0.333
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The question asks for the average genetic relatedness between two randomly selected female offspring in a haplodiploid ant colony where the queen mated with three unrelated males.
Step 2: Key Formula or Approach:
In haplodiploid species, females are diploid (receive $50\%$ of their genome from the mother and $50\%$ from the father), while males are haploid (receive $100\%$ of their genome from the mother's unfertilized egg).
The genetic relatedness ($r$) between two female offspring can be calculated based on whether they share the same father (full sisters) or different fathers (half sisters).
Step 2: Detailed Explanation:
• Since the queen mates with three different unrelated males, and uses their sperm equally, any two randomly selected female offspring have a certain probability of being full sisters (sharing the same father) or half sisters (having different fathers).
• The probability that two randomly selected females share the same father is: \[ P(\text{same father}) = 3 \times \left(\frac{1}{3} \times \frac{1}{3}\right) = \frac{1}{3} \]
• The probability that they have different fathers is: \[ P(\text{different fathers}) = 1 - P(\text{same father}) = 1 - \frac{1}{3} = \frac{2}{3} \]
• Let us calculate the genetic relatedness ($r$) in both scenarios: 1. If they are full sisters (same father): itemize
• They share $50\%$ of their genes from the mother (relatedness via mother = $0.25$).
• Since the father is haploid, he passes $100\%$ of his genes to all of his daughters. Thus, they share $100\%$ of their paternal genes (relatedness via father = $0.5$).
• Therefore, the relatedness between full sisters is: \[ r_{\text{full}} = 0.25 + 0.5 = 0.75 \]
2. If they are half sisters (different fathers):
• They share $50\%$ of their genes from the mother (relatedness via mother = $0.25$).
• Since their fathers are different and unrelated, they share $0\%$ of their paternal genes (relatedness via father = $0$).
• Therefore, the relatedness between half sisters is: \[ r_{\text{half}} = 0.25 + 0 = 0.25 \]
The average genetic relatedness ($r$) is the weighted average of these two scenarios: \[ r = P(\text{same father}) \times r_{\text{full}} + P(\text{different fathers}) \times r_{\text{half}} \] \[ r = \left(\frac{1}{3} \times 0.75\right) + \left(\frac{2}{3} \times 0.25\right) \] \[ r = 0.25 + \frac{0.5}{3} = 0.25 + 0.1667 \approx 0.417 \]
itemize
Step 3: Final Answer:
Therefore, the average genetic relatedness between two randomly selected female offspring in this colony is 0.417.
The question asks for the average genetic relatedness between two randomly selected female offspring in a haplodiploid ant colony where the queen mated with three unrelated males.
Step 2: Key Formula or Approach:
In haplodiploid species, females are diploid (receive $50\%$ of their genome from the mother and $50\%$ from the father), while males are haploid (receive $100\%$ of their genome from the mother's unfertilized egg).
The genetic relatedness ($r$) between two female offspring can be calculated based on whether they share the same father (full sisters) or different fathers (half sisters).
Step 2: Detailed Explanation:
• Since the queen mates with three different unrelated males, and uses their sperm equally, any two randomly selected female offspring have a certain probability of being full sisters (sharing the same father) or half sisters (having different fathers).
• The probability that two randomly selected females share the same father is: \[ P(\text{same father}) = 3 \times \left(\frac{1}{3} \times \frac{1}{3}\right) = \frac{1}{3} \]
• The probability that they have different fathers is: \[ P(\text{different fathers}) = 1 - P(\text{same father}) = 1 - \frac{1}{3} = \frac{2}{3} \]
• Let us calculate the genetic relatedness ($r$) in both scenarios: 1. If they are full sisters (same father): itemize
• They share $50\%$ of their genes from the mother (relatedness via mother = $0.25$).
• Since the father is haploid, he passes $100\%$ of his genes to all of his daughters. Thus, they share $100\%$ of their paternal genes (relatedness via father = $0.5$).
• Therefore, the relatedness between full sisters is: \[ r_{\text{full}} = 0.25 + 0.5 = 0.75 \]
2. If they are half sisters (different fathers):
• They share $50\%$ of their genes from the mother (relatedness via mother = $0.25$).
• Since their fathers are different and unrelated, they share $0\%$ of their paternal genes (relatedness via father = $0$).
• Therefore, the relatedness between half sisters is: \[ r_{\text{half}} = 0.25 + 0 = 0.25 \]
The average genetic relatedness ($r$) is the weighted average of these two scenarios: \[ r = P(\text{same father}) \times r_{\text{full}} + P(\text{different fathers}) \times r_{\text{half}} \] \[ r = \left(\frac{1}{3} \times 0.75\right) + \left(\frac{2}{3} \times 0.25\right) \] \[ r = 0.25 + \frac{0.5}{3} = 0.25 + 0.1667 \approx 0.417 \]
itemize
Step 3: Final Answer:
Therefore, the average genetic relatedness between two randomly selected female offspring in this colony is 0.417.
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