ABO_population

p, q, & r: Population Genetic Ratios with three alleles / locus

      ABO blood groups
          Isoagglutinin locus (I) on Chromosome 9 has three alleles: I^A, I^B , I^O
                A & B alleles are co-dominant: both are expressed in the blood group phenotype
                A & B alleles are dominant to O : AA, AO & BB, BO indistinguishable
                    Matings ("marriages") between males & females produce

**Genetics of ABO phenotypes**
	I^A	I^B	I^O
I^A	A	AB	A
I^B	AB	B	B
I^O	A	B	O

six genotypes (AA, AO, BB, BO, AB, & OO) & four phenotypes (A, B, AB, O)

How common are these alleles, genotypes, & phenotypes in the human population?

For the human ABO blood group locus with three alleles, we know:

**Frequency of I - locus alleles**
Allele	I^A	I^B	I^O
Frequency	0.4	0.1	0.5
Formula	p	q	r

**Frequency of ABO blood types**
Phenotype	A	B	AB	O
Genotypes	I^AI^A & I^AI^O	I^BI^B & I^BI^O	I^AI^B	I^OI^O
Formula	p² + 2pr	q² + 2qr	2pq	r²
Frequency	0.56	0.11	0.08	0.25

    For a locus with three alleles
          Since     p + q + r = 1
          The trinomial expansion gives     (p + q + r)²= p² + 2pq + q² + 2qr + r² + 2pr = 1
         H_e = 2pq + 2pr + 2qr = 1 - (p² + q² + r²)
    In general, for a locus with multiple alleles
                      n
       H_e = 1 - (q_i)²      for n alleles
                     i=1
        where q_i = freq. of i th allele of n alleles at a locus
                In the ABO case:   H_e = 1 - (0.4² + 0.1² + 0.5²) = 0.42