Population genetics studies the distribution and dynamics of genetic variation within and between groups of organisms. Scientists use mathematical approaches to quantify this variation, which helps explain patterns of inheritance and evolution. A primary task is determining the proportion of different gene versions, known as alleles, present in a population. This article details the straightforward methodology for converting observed frequencies of individual genetic makeup (genotypes) into allele frequencies.
Defining Allele and Genotype Frequencies
The distinction between genotype frequency and allele frequency is central to population genetics. Genotype frequency refers to the proportion of individuals in a population that possess a specific combination of alleles for a particular gene. For a gene with two alleles, typically denoted as \(A\) and \(a\), the three possible genotypes are homozygous dominant (\(AA\)), heterozygous (\(Aa\)), and homozygous recessive (\(aa\)). The frequency of each genotype is calculated by dividing the count of individuals with that genotype by the total number of individuals.
Allele frequency describes the proportion of a specific allele among all copies of that gene in the population’s gene pool. Since diploid organisms carry two copies of the gene, one from each parent, the calculation must account for all alleles carried by the individuals. Therefore, the counts of \(AA\), \(Aa\), and \(aa\) individuals are used to tally the total number of \(A\) and \(a\) alleles.
The Direct Calculation Method
Calculating allele frequencies directly from observed genotype counts does not rely on assumptions about the population’s evolutionary state. Since diploid organisms carry two alleles for every gene, the total number of alleles in the gene pool is always twice the total number of individuals. This total figure serves as the denominator for the frequency calculation.
To determine the frequency of the dominant allele, often represented by \(p\), you must sum all instances of that allele found across the population. Every individual with the homozygous dominant genotype (\(AA\)) contributes two copies of the allele, while individuals with the heterozygous genotype (\(Aa\)) contribute one copy.
The formula for calculating the frequency of allele \(A\) (\(p\)) based on counts is: \(p = \frac{(2 \times N_{AA}) + N_{Aa}}{2 \times N_{Total}}\). Here, \(N_{AA}\) is the count of \(AA\) individuals, \(N_{Aa}\) is the count of \(Aa\) individuals, and \(N_{Total}\) is the total number of individuals in the population. The numerator sums all \(A\) alleles (two from homozygotes, one from heterozygotes). The denominator, \(2 \times N_{Total}\), represents the total number of alleles in the sample.
Similarly, the frequency of the recessive allele (\(q\)) is determined by summing all instances of the \(a\) allele. Homozygous recessive individuals (\(aa\)) contribute two copies of the \(a\) allele, and heterozygous individuals (\(Aa\)) contribute one copy. The formula for \(q\) is: \(q = \frac{(2 \times N_{aa}) + N_{Aa}}{2 \times N_{Total}}\). Since these two alleles represent the entire gene pool for that locus, the sum of the two allele frequencies must always equal one (\(p + q = 1\)).
Step-by-Step Numerical Example
Consider a hypothetical population of 500 individuals examining a single gene with two alleles, \(R\) (dominant) and \(r\) (recessive). The observed genotype counts are \(N_{RR} = 150\), \(N_{Rr} = 250\), and \(N_{rr} = 100\). The first step is confirming the total count: \(150 + 250 + 100 = 500\), so \(N_{Total} = 500\).
The total number of alleles in this population is \(2 \times 500 = 1000\), which serves as the denominator for both frequency calculations. To find the frequency of the dominant allele \(R\) (denoted as \(p\)), we must count all \(R\) alleles.
The \(RR\) individuals contribute \(2 \times 150 = 300\) \(R\) alleles, and the \(Rr\) individuals contribute 250 \(R\) alleles. The total number of \(R\) alleles is \(300 + 250 = 550\). Applying the formula, \(p\) is calculated as \(550 / 1000 = 0.55\).
Next, we calculate the frequency of the recessive allele \(r\) (denoted as \(q\)) by counting all \(r\) alleles. The \(rr\) individuals contribute \(2 \times 100 = 200\) \(r\) alleles, and the \(Rr\) individuals contribute 250 \(r\) alleles. The total number of \(r\) alleles is \(200 + 250 = 450\).
The frequency \(q\) is calculated as \(450 / 1000 = 0.45\). The final step involves verifying the result by ensuring \(p + q = 1\). In this example, \(0.55 + 0.45 = 1.00\), confirming the calculations are correct.