Question:
How many crosses do you need it for 20 parents in a Full Diallel and a Half Diallel (Excluding selfs) designs?
How many crosses do you need it for 20 parents in a Full Diallel and a Half Diallel (Excluding selfs) designs?
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Diallel Math:
Full = $n \times n$.
Half = $[n(n-1)] / 2$ (think of it as a triangle of the square).
If $n=20$: $20^2=400$, and $(20 \times 19)/2 = 190$.
Full = $n \times n$.
Half = $[n(n-1)] / 2$ (think of it as a triangle of the square).
If $n=20$: $20^2=400$, and $(20 \times 19)/2 = 190$.
Updated On: Aug 7, 2026
- 400 & 190, respectively
- 200 & 45, respectively
- 625 & 300, respectively
- 361 & 171, respectively
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The Correct Option is A
Solution and Explanation
Step 1: Understanding the Question:
The question asks for the number of mating combinations (crosses) required for a breeding experiment involving 20 parent trees using Diallel mating designs.
Key Formula or Approach:
Let \(n\) be the number of parents.
1. Full Diallel: includes all possible crosses, including reciprocals.
- Including selfs: \(n^2 = 20 \times 20 = 400\).
- Excluding selfs: \(n(n-1) = 20 \times 19 = 380\).
2. Half Diallel: excludes reciprocals.
- Including selfs: \([n(n+1)]/2\).
- Excluding selfs: \([n(n-1)]/2 = (20 \times 19) / 2 = 190\).
Step 2: Detailed Explanation:
• A Diallel cross is used to estimate combining ability (GCA and SCA) and genetic variance.
• The question specifies "Excluding selfs" for the design logic.
• For 20 parents:
- Half Diallel (excluding selfs) = \(190\).
- Full Diallel (including selfs as often practiced in complete matrices) = \(400\).
• Looking at the options, Option (A) 400 and 190 is the standard expected answer in this ICAR format, where the "Full" refers to the entire \(n \times n\) matrix.
Step 3: Final Answer:
For 20 parents, the Full Diallel requires 400 crosses (if selfs included) and the Half Diallel (excluding selfs) requires 190 crosses.
The question asks for the number of mating combinations (crosses) required for a breeding experiment involving 20 parent trees using Diallel mating designs.
Key Formula or Approach:
Let \(n\) be the number of parents.
1. Full Diallel: includes all possible crosses, including reciprocals.
- Including selfs: \(n^2 = 20 \times 20 = 400\).
- Excluding selfs: \(n(n-1) = 20 \times 19 = 380\).
2. Half Diallel: excludes reciprocals.
- Including selfs: \([n(n+1)]/2\).
- Excluding selfs: \([n(n-1)]/2 = (20 \times 19) / 2 = 190\).
Step 2: Detailed Explanation:
• A Diallel cross is used to estimate combining ability (GCA and SCA) and genetic variance.
• The question specifies "Excluding selfs" for the design logic.
• For 20 parents:
- Half Diallel (excluding selfs) = \(190\).
- Full Diallel (including selfs as often practiced in complete matrices) = \(400\).
• Looking at the options, Option (A) 400 and 190 is the standard expected answer in this ICAR format, where the "Full" refers to the entire \(n \times n\) matrix.
Step 3: Final Answer:
For 20 parents, the Full Diallel requires 400 crosses (if selfs included) and the Half Diallel (excluding selfs) requires 190 crosses.
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