Genetics and Evolution HL: Allele Frequencies

Understanding how the genetic makeup of a population changes—or stays the same—is the very heart of evolutionary biology. The mathematical framework of Hardy-Weinberg equilibrium provides a powerful null hypothesis, a baseline against which you can measure evolutionary change. By mastering allele frequency calculations, you can quantify the forces of evolution, turning abstract concepts like natural selection into tangible, analyzable data.

The Language of Populations: Genes, Alleles, and Frequencies

Before diving into calculations, you must understand the core vocabulary. A gene pool is the complete set of alleles present in a reproducing population at a given time. An allele is a specific variant of a gene. Allele frequency is the proportion of a specific allele among all alleles for that gene in the pool, typically expressed as a decimal or percentage. For example, if 40 out of 100 alleles for a gene in a population are the dominant allele A, the frequency of A (denoted as p) is 0.4. Similarly, genotype frequency is the proportion of individuals in a population with a specific genetic combination (e.g., AA, Aa, aa). These frequencies are the raw data for tracking evolution, which is formally defined as a change in allele frequencies in a gene pool over generations.

The Hardy-Weinberg Principle: A Model for Genetic Equilibrium

The Hardy-Weinberg principle states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of evolutionary influences. This stability is called Hardy-Weinberg equilibrium. It’s a model, not a reality—like a frictionless surface in physics—but it is incredibly useful for identifying when and how evolution is occurring.

The principle is expressed with a simple equation. For a gene with two alleles, a dominant allele A (frequency = p) and a recessive allele a (frequency = q), the following must be true: $$p+q=1$$ This simply states that the frequencies of all alleles for a gene must add up to 100%.

The genotype frequencies are given by the Hardy-Weinberg equation: $$p^2+2pq+q^2=1$$ Here:

• $p^2$ represents the frequency of homozygous dominant genotype (AA).
• $2pq$ represents the frequency of heterozygous genotype (Aa).
• $q^2$ represents the frequency of homozygous recessive genotype (aa).

This equation is derived from the basic rules of probability: the chance of an offspring getting two A alleles is $p\ast p=p^2$, and so on.

Applying the Equation: A Worked Calculation

Imagine a population of 1000 flowers where the color is controlled by a single gene with incomplete dominance: RR (red), Rr (pink), rr (white). A survey finds 490 red, 420 pink, and 90 white flowers.

Step 1: Calculate observed genotype frequencies.

• Frequency of RR ($p^2$) = 490/1000 = 0.49
• Frequency of Rr ($2pq$) = 420/1000 = 0.42
• Frequency of rr ($q^2$) = 90/1000 = 0.09

Step 2: Calculate allele frequencies from observed data. You can find the frequency of the recessive allele r ($q$) directly from the homozygous recessive genotype frequency.

• $q^2=0.09$, therefore $q=\sqrt{0.09}=0.3$
• Since $p+q=1$, $p=1-0.3=0.7$

Step 3: Use allele frequencies to calculate expected Hardy-Weinberg genotype frequencies.

• Expected $p^2$ (RR) = $(0.7{)}^2=0.49$
• Expected $2pq$ (Rr) = $2\ast 0.7\ast 0.3=0.42$
• Expected $q^2$ (*rr$)=$(0.3)^2 = 0.09$

Step 4: Compare observed vs. expected. In this case, observed (0.49, 0.42, 0.09) match expected (0.49, 0.42, 0.09) perfectly. This population appears to be in Hardy-Weinberg equilibrium for this gene. If they did not match, it would be evidence that an evolutionary force is at work.

The Five Conditions for Genetic Equilibrium

For the Hardy-Weinberg model to hold true, a population must meet five strict conditions. Deviation from any one of these conditions is a mechanism of evolutionary change.

1. No Natural Selection: All genotypes must have an equal chance of survival and reproduction. If one genotype is more "fit," allele frequencies will shift.
2. No Genetic Drift: The population must be infinitely large to prevent random, chance fluctuations in allele frequencies. In reality, genetic drift has a major impact on small populations, such as through a founder effect (new population established by few individuals) or a bottleneck effect (population size drastically reduced).
3. No Gene Flow: There must be no migration of individuals (and their alleles) into or out of the population. Gene flow introduces new alleles or changes proportions between connected populations.
4. No Mutation: The allele themselves must not change into new forms. While mutation is the original source of all genetic variation and is typically very slow, it directly alters allele frequencies by converting one allele into another.
5. Random Mating: Individuals must choose mates without regard to genotype. Non-random mating, like assortative mating (choosing mates similar to oneself), does not change allele frequencies directly but alters genotype frequencies by increasing homozygosity.

Analyzing Deviations from Equilibrium: The Forces of Evolution

When you calculate Hardy-Weinberg expected frequencies and find a mismatch with real population data, your next task is to hypothesize which force is responsible.

• Natural Selection: This is the non-random differential survival and reproduction of individuals. If you observe that individuals with a certain genotype (e.g., $q^2$) are under-represented in the adult breeding population compared to Hardy-Weinberg expectations, it is strong evidence for selection against that genotype. You can use allele frequency data over multiple generations to calculate the strength of selection.
• Genetic Drift: Look for large changes in allele frequencies, especially for neutral alleles (those not under selection), in small, isolated populations. The hallmark of drift is unpredictability—the changes are random and not adaptive.
• Gene Flow: If a population's allele frequencies become more similar to those of a neighboring population, gene flow is the likely cause. For example, if an isolated population with a high frequency of a rare allele suddenly shows a lower frequency after a period of known migration, gene flow diluted the allele.
• Non-Random Mating: This force is detectable by examining genotype frequencies alone. It causes a deviation from expected genotype frequencies (specifically, a deficit of heterozygotes and an excess of homozygotes) without changing the underlying allele frequencies ($p$ and $q$ remain constant). This is a key distinction from the other four forces.

Common Pitfalls

1. Misidentifying $q^2$: The value $q^2$ in the equation represents the frequency of the homozygous recessive genotype only. You cannot use the frequency of the recessive phenotype as $q^2$ if dominance is incomplete or co-dominant, as all genotypes have distinct phenotypes. Always ensure you are working with genotype counts.
2. Assuming Equilibrium to Find Alleles: A common question gives you the frequency of a dominant phenotype and asks for the frequency of the recessive allele. You must remember that the dominant phenotype includes both $p^2$ and $2pq$. Therefore, the frequency of the recessive phenotype is $q^2$. If 16% of a population shows the recessive phenotype, then $q^2=0.16$, and $q=0.4$. Do not mistakenly subtract the dominant phenotype frequency from 1 to get $q$.
3. Confusing Conditions with Outcomes: Remember, the five conditions (no selection, no drift, etc.) are the requirements for equilibrium. Natural selection, genetic drift, etc., are the mechanisms that cause evolution when those conditions are violated. They are two sides of the same coin.
4. Overlooking the "Large Population" Assumption: When analyzing data from a small, isolated population (e.g., island species, captive breeding programs), genetic drift should be your primary hypothesis for allele frequency changes, even over short timescales, unless strong selective pressure is evident.

Summary

• The Hardy-Weinberg principle ($p^2+2pq+q^2=1$) provides a mathematical model to test if a population is evolving by comparing observed and expected genotype frequencies.
• A population is in Hardy-Weinberg equilibrium only if five conditions are met: no natural selection, no genetic drift (infinitely large population), no gene flow, no mutation, and random mating.
• Violation of any condition is a mechanism of evolution: natural selection (adaptive changes), genetic drift (random changes in small populations), gene flow (migration), mutation (source of new alleles), and non-random mating (shifts genotype frequencies only).
• When solving problems, correctly identify $q^2$ as the homozygous recessive genotype frequency, and use the square root to find the recessive allele frequency $q$.
• Real population data rarely fits the equilibrium model perfectly, and analyzing the deviations is the key to understanding which evolutionary forces are shaping the gene pool.