# What is the AA genotype

## The Hardy-Weinberg equation

The Hardy-Weinberg equation can be used to calculate the allele frequency of a population (with two different alleles for a gene) in the following generations.

As an example, the Hardy-Weinberg equation is explained here using a rabbit population in which the alleles black (dominant, A) and white (recessive, a) occur for the gene “coat color”. Heterozygous carriers of the alleles, i.e. individuals with the genotype Aa, have gray fur. There are a total of 200 individuals in our sample population. 120 of them are black (AA), 50 are white (aa) and 30 are gray (Aa / aA). Using this information, it is now possible to count how many dominant (A) and how many recessive (a) alleles are present in the population

Tip: Always remember: Every individual has two alleles! 14,99€

Now the relative frequencies of both alleles to the totality of the alleles have to be calculated. To do this, divide the allele frequency A or a by all alleles:
\ begin {align *}
\ textbf {Allele A:} \ quad \ frac {270} {400} \ = \ {0.675} \ text {(= 67.5%)} \ quad \ textbf {or. Allele a:} \ quad \ frac {130} {400} \ = \ {0.325} \ text {(= 32.5%)}
\ end {align *}

Now the equation comes into play, with which the frequencies of the alleles for the next generation can be calculated:
\ begin {align *}
p ^ 2 \ + \ 2pq \ + \ q ^ 2 \ = \ 1
\ end {align *}

with p as the relative frequency (in%) of the allele A in the gene pool, q as the relative frequency (in%) of the allele a in the gene pool and 1 as the totality of the population, i.e. 100%.

This formula translated into words: homozygous (AA) + heterozygous (Aa / aA) + homozygous (aa) = 1

If you want to calculate the frequencies of the different alleles in the next generation, you have to calculate the probabilities for all three possible genotypes (AA, Aa, aa). This is done by plugging the relative frequencies calculated above into the formula. The result is a percentage of how many next-generation rabbits exist with this genotype.

\ begin {align *}
\ begin {array} {llll}
\ text {Genotype AA:} \ quad & p ^ 2 = p \ cdot p = 0 {,} 675 \ cdot 0 {,} 675 \ approx 0 {,} 455 & \ (\ approx 45 {,} 5 \% )
\\
\ text {Genotype aa:} \ quad & q ^ 2 = q \ cdot q = 0 {,} 325 \ cdot 0 {,} 325 \ approx 0 {,} 105 & \ (\ approx 10 {,} 5 \% )
\\
\ text {Genotype Aa / aA:} \ quad & 2 pq = 2 \ cdot 0.675 \ cdot 0 {,} 325 \ approx 0 {,} 438 & \ (\ approx 43 {,} 8 \%)
\ end {array}
\ end {align *}

The Hardy-Weinberg Law can only be used in ideal populations. These are characterized by the following:
• there are no mutations
• there is no migration between different populations
• there are no random effects
• there is panmixie (everyone mates with everyone)
• no genotype has selection disadvantages.

It is easy to see that these characteristics do not occur in the wild. Therefore, the application of the Hardy-Weinberg law is only limited to theoretical considerations and cannot be adopted one-to-one for real, natural populations.

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