### HARDY-WEINBERG PRINCIPLE

In studying evolution, one needs to look at changes in allelic frequencies over time. Let's consider a population of peppered moths that has 1000 individuals composed of 700 AA and 200 Aa dark-winged moths, and 100 aa light-winged moths. We will still assume that wing color is determined by a gene at a single locus and that there are only two possible alleles. The genotypes and phenotypes of all the individuals in this population are shown below:  We are interested in what happens in subsequent generations. But first, let's calculate the frequencies of the AA, Aa, and aa genotypes (denoted as P, Q, and R, respectively) and the allelic frequencies of A and a (denoted p and q, respectively) in the current generation.

Frequency of AA = 700/1000 = 0.7
Frequency of Aa = 200/1000 = 0.2
Frequency of aa = 100/1000 = 0.1

Notice Freq AA + Freq Aa + Freq aa = 1 Because the moths are diploid organisms, there are 1000 x 2 = 2000 alleles.

Out of 2000 alleles:

AA contributes 700 x 2 = 1400 A alleles
Aa contributes 200 x 1 = 200 a alleles and 200 x 1 = 200 A alleles
aa contributes 100 x 2 = 200 a alleles

Therefore:

Frequency of allele A: p = (1400+200)/2000 = 0.8
Frequency of allele a: q = (200+200)/2000 = 0.2

Notice that p + q = 1