Question

When do I use p+q vs p2+2pq+q2 ? For example for this question, I had to use the latter equation but I am wondering why I couldnt have used the first.

White flowers are caused by a recessive allele at a single locus with two alleles (red & white). In a population of 100 plants at HWE you observe that 36 of them are white. What are the HWE frequencies for each of the three genotypes?

Answer 1

When the population is in Hardy-Weinberg equilibrium, we can use two formulas.

1: p+q = 1 [where p = frequency of dominant allele and q= frequency of recessive allele]

2: p²+2pq+q² = 1 [where p² = frequency of homozygous dominant, 2pq = frequency of heterozygous, and q² = frequency of homozygous recessive]

Homozygous dominant represents a genotype that contains two same dominant alleles.

Heterozygous represents a genotype that contains two different alleles.

Homozygous recessive represents a genotype that contains two same recessive alleles.

Therefore, we should use the formula, p+q = 1, for the calculation of allele frequency while we should use the formula, p²+2pq+q² = 1,​ for the calculation of genotype frequency.

Here white flowers are caused by a recessive allele, that means white flowers represents the genotype homozygous recessive.

In a population of 100 plants at HWE, you observe that 36 of them are white.

So, the frequency of homozygous recessive = q² = (36/100) =0.36

So, q = the frequency of recessive allele = = 0.6

As we know that, p+q = 1

So, p = (1-q) = (1-0.6) = 0.4

Therefore the frequency of dominant allele = p = 0.4

So, the frequency of homozygous dominant = p² = (0.4)² = 0.16

Therefore the frequency of heterozygous = 2pq = (2 $\times$ 0.4 $\times$ 0.6) = 0.48

The HWE frequencies for each of the three genotypes​:

The frequency of homozygous dominant = p² = 0.16

The frequency of heterozygous = 2pq = 0.48

The frequency of homozygous recessive = q² = 0.36