Allelic Frequencies

Alleles are genes that occur at a specific location on the chromosome. Alleles can come in pairs or multiples; either way, they control the same trait. For example, in one of Mendel's pea plant experiments, the alleles were purple (PP) and white (pp). Alleles are usually either dominant or recessive.

• Dominant alleles only need one copy to show up in an individual. In this case, the dominant allele is purple (P).

• Recessive alleles only show up if an individual has two copies of it.

In Mendel's experiment, the recessive allele is white (p). Mendel's experiment confirmed this by crossing purple (PP) and white (pp) to get purple (Pp) heterozygous flowers, as illustrated in Figure 1.

• Heterozygous individuals are individuals with two different alleles, such as Pp, in this case.

• Homozygous individuals are individuals with identical two alleles or PP and pp in this case.

The definition of allele frequency is shown below. Allele frequencies tell us how common an allele is relative to the population we are interested in.

Allelic frequencies are usually written in percentage or fractional form. We can also think of allelic frequencies as the number of chromosomes within the population that carry a specific allele compared to the total Population Size of our sample.

Allele frequencies differ from phenotypic ratios. Phenotypic ratios only deal with phenotypes or the physically visible characteristics of organisms. In contrast, we need to consider heterozygous individuals for allele frequencies. This is because heterozygous individuals can mask recessive alleles. For instance, Pp is a heterozygous flower, but it's still purple like PP, the homozygous dominant flower.

Figure 1: Mendel's pea plant experiment illustrated. Daniela Lin, Study Smarter Originals.

Allelic Frequencies in a Population

Now that we understand what allelic frequencies are, we need to go over how allelic frequencies relate to a population.

Allelic frequencies relate to population because the calculations result in fractions or percentages that demonstrate how common an allele is within a population.

The Genotype is a set of alleles that decides a living organism's Phenotype. In the case of Mendel's pea plant experiments, the genotypes are PP, Pp, and pp. The corresponding phenotypes, respectively, are purple, purple, and white.

A genotypic population deals with a combination of allelic or gene frequencies for all the genes within the specific population we are interested in. The reason this is important to know is that without allelic frequency shifts, evolution could not occur.

Evolutions don't occur in individuals; they occur in Populations! An individual can't evolve. Instead, evolution involves gene frequencies changing within the population or gene pool.

Allelic and Genotypic Frequencies

After understanding how alleles and genes relate to Populations, we must emphasize the difference between allelic and genotypic frequencies.

Genotypic frequencies deal with all the genotypes in the population or gene pool. In comparison, allele frequencies deal with all the alleles in the population or gene pool.

For example, if we had a population with AA, Aa, and aa individuals, the genotypic frequencies would be AA or homozygous dominant, Aa or heterozygous, and aa or homozygous recessive individuals. In contrast, the allelic frequencies are the dominant A allele and the recessive a allele.

The genotypic frequency can be found by taking the number of individuals with a particular Genotype over all the individuals within a population or gene pool.

We can figure out each genotype's frequency by dividing a particular genotype by the total individuals found in the population we are studying.

We can use the Hardy-Weinberg equation to calculate genotypic frequencies. The Hardy-Weinberg equation is a formula used to determine a population's genetic variation. The Hardy-Weinberg equation can be represented by \(p^2+2pq+q^2=1\). We will expand on this equation in the following sections.

Hardy-Weinberg can also help us figure out if a population is evolving or not.

The factors that keep a population at HWE are random mating, no mutations, infinite Population Size, no Natural Selection, and no Gene Flow.

• Random mating occurs in populations that can randomly choose their mates.

• Gene Flow is the transfer or exchange of genes from one population to another.

• Mutations are usually changes in the DNA of a living organism.

• Natural Selection usually refers to the process in which specific individuals with better traits survive and reproduce over others.

• Infinite population sizes are needed to stop the effects of Genetic Drift. Genetic Drift is the change of gene frequency in a population because of random chance. Genetic drift occurs in smaller populations because they have less variation in individuals leading to less adaptation.

Allele Frequency Example

Above, we went over the basics surrounding genotypic and allele frequencies. Now we'll go over an example of how to calculate allele frequencies.

We can calculate the allele frequencies of the dominant A allele by considering that homozygous dominant individuals AA make up 0.36 of the total population.

In contrast, the heterozygous individual's Aa makes up 0.48 of the total population. The dominant A allele is "100% present" in AA individuals and "50% present" in Aa individuals; therefore, the frequency of the A allele in the population is 0.36 + 0.24 = 0.6, as shown in figure 2. We get 0.24 by dividing 0.48/2.

For the recessive a allele, it's the same as how we calculated the dominant A allele, except homozygous recessive individuals aa make up 0.16 of the total population. Therefore, it's 0.16 + 0.24 =0.4 as shown in Figure 2.

Figure 2: Genotypic and allelic frequencies related to the HWE equation. Wikimedia.

Once we've found the frequency of each genotype and the frequency of each allele in the population, we can consider the offspring of the parent generation (mother and father) by using a Punnett square.

The offspring receive one allele from their father and another from their mother. Figure 2 demonstrates that then the genotypic frequencies of the offspring are as follows: \(p^2 =0.36\) for AA, \(pq =\) 0.24 + 0.24 or 0.48 for Aa, and \(q^2 =0.16\) for aa.

Allele frequency formula

The formula for genotypic frequencies is \(p^2+2pq+q^2=1\) where \( p^2\) is the homozygous dominant frequency, the \( q^2\) means the homozygous recessive frequency, and the 2pq value represents the heterozygous frequency.

The formula for our allele frequencies is p+q=1, meaning that the combined two alleles, p and q, equal 1. In other words, when added up in a population, the two alleles result in a frequency of 100%. To find either p or q, we take the square root of \( p^2\) and \( q^2\), respectively.

To find p, we can also subtract q by one as p+q=1 when solved for q is p= 1-q. We usually don't calculate p first because dominant alleles can mask or hide recessive alleles in heterozygous individuals. Thus, instead of calculating p by just looking at the population, we should try to find q first and use q to calculate p.

After understanding what allele frequencies are, how they relate to populations and genotypic frequencies, and how to calculate them, we need to realize that allelic frequencies don't necessarily correlate with the fitness of an allele. For example, non-beneficial or deleterious recessive mutations can be masked in heterozygous individuals making it seem like the allele is rarer than it is in a population.

In biology, fitness refers to the reproductive success of an individual, organism, etc. The higher the fitness, the higher the reproductive success.