If there are 4 possible alleles at a locus, how many possible genotypes exist?

To determine the number of possible genotypes at a locus with 4 different alleles, we can use the formula for calculating the number of combinations of genotypes that can occur in a given set of alleles.

For any given allele, it can be homozygous (where both alleles are the same) or heterozygous (where two different alleles are present). In the case of 4 alleles, let's denote them as A, B, C, and D.

1. Count Homozygous Genotypes: Each allele can form a homozygous genotype. Therefore, for 4 alleles, there are 4 homozygous genotypes: AA, BB, CC, DD.

2. Count Heterozygous Genotypes: For heterozygous combinations, you take pairs of different alleles. The formula for choosing 2 alleles from 4 is given by the combination formula ( \binom{n}{r} ), where ( n ) is the total number of alleles and ( r ) is the number of alleles chosen. Here, ( n = 4 ) and ( r = 2 ). Therefore, the calculation would