If there are five alleles at a locus, how many genotypes can there be at this locus? How many different kinds of homozygotes can there be? How many genotypes and homozygotes can there be with eight alleles at a locus?
The Correct Answer and Explanation is:
Answer:
- For 5 alleles at a locus:
- Genotypes: The number of possible genotypes can be calculated using the formula for combinations with repetition:
[
\text{Number of genotypes} = \binom{n + 1}{2} + n
]
Where (n) is the number of alleles. In this case, (n = 5), so:
[
\binom{5 + 1}{2} + 5 = \binom{6}{2} + 5 = 15 + 5 = 20 \text{ genotypes.}
] - Homozygotes: The number of different homozygotes is simply equal to the number of alleles. For 5 alleles, there are 5 homozygotes.
- For 8 alleles at a locus:
- Genotypes: Using the same formula, where (n = 8):
[
\binom{8 + 1}{2} + 8 = \binom{9}{2} + 8 = 36 + 8 = 44 \text{ genotypes.}
] - Homozygotes: The number of homozygotes remains equal to the number of alleles. Therefore, for 8 alleles, there are 8 homozygotes.
Explanation:
The number of genotypes at a locus can be derived from how alleles pair up. Genotypes consist of two alleles: one inherited from each parent. If there are (n) alleles, a genotype can either consist of two identical alleles (homozygote) or two different alleles (heterozygote).
To calculate the total number of genotypes:
- Homozygotes: These occur when both alleles in the genotype are the same. For (n) alleles, there are (n) possible homozygotes because there is one homozygote for each allele (e.g., for 5 alleles, there are 5 homozygotes: AA, BB, CC, DD, EE).
- Heterozygotes: These occur when the two alleles in the genotype are different. For (n) alleles, the number of heterozygotes is given by the number of ways to choose 2 alleles from (n), which is represented by the combination formula ( \binom{n}{2} ). This gives us the number of ways to select 2 different alleles out of (n), which is (\frac{n(n – 1)}{2}).
Thus, the total number of genotypes is the sum of homozygotes and heterozygotes:
[
\text{Total genotypes} = \binom{n}{2} + n
]
For homozygotes, there are always exactly (n) different homozygotes.
By applying this formula for both 5 and 8 alleles, we arrive at the answers provided above.