Because the allele and genotype frequencies are proportions

Because the allele and genotype frequencies are proportions they always sum to 1.0. But why?

Why do p and q always add up to 1?Explain why once you set the frequency for A and a, you can’t also set the frequency for Aa.

Solution

Answer) This is because the allele and genotypic frequencies are proportional. Which means that if sum of frequencies of allele is 1, then the sum of genotypic frequencies (which are sum of all possible combinations from given alleles) will always be 1.

It can be understood easily;

Let’s say we are dealing with a gene which has a single allele denoted as “A”. So, to be clear we will always denote that 100 % of alleles for this gene are “A”.

In terms of probability for this allele, P_A = 1, this probability is also called as frequency of allele A.

Now, if there is a mutation from allele A to a. then the certain percentage of alleles for this gene will be a type.

But we know that the probability can either be 0 or 1.

So, P_A + P_a = 1

Or it can be rewritten as p + q = 1, P_A = p and P_a = q

After setting up the frequency for A and a, frequency of genotypes can also be set up using multiplication rule.

Frequency of genotype Aa = frequency of A x frequency of a.

Or P_Aa = P_A x P_a

This explain why the allele and genotype frequencies are proportions they always sum to 1.0