11.3 Population Genetics and Hardy-Weinberg Equilibrium

Genetic Composition of Populations

Population genetics tracks how allele frequencies shift across generations within a group of interbreeding organisms. The Hardy-Weinberg principle gives you a mathematical baseline: if nothing is driving evolution, allele frequencies stay put. Any deviation from that baseline tells you evolution is happening. This section covers the key vocabulary, the math behind Hardy-Weinberg, and the forces that push populations away from equilibrium.

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Gene Pools and Allele Frequencies

A gene pool is the complete set of alleles at every gene locus across all individuals in a population. It captures the total genetic diversity available for inheritance.

Allele frequency is the proportion of one specific allele relative to all alleles at that locus in the population. You calculate it like this:

$p = \frac{\text{number of copies of a specific allele}}{\text{total number of alleles at that locus}}$

For a diploid organism, every individual carries two alleles per locus, so a population of 500 individuals has 1,000 total alleles at any given locus. If 350 of those are the dominant allele A, then:

$p = \frac{350}{1000} = 0.35$

Allele frequencies can shift over time whenever evolutionary forces act on the population. Those forces include mutation, natural selection, genetic drift, and gene flow.

Hardy-Weinberg Equilibrium and Principle

The Hardy-Weinberg principle states that allele and genotype frequencies in a population will remain constant from generation to generation if no evolutionary forces are acting on it. A population meeting this condition is said to be in Hardy-Weinberg equilibrium, meaning it is not evolving.

Five conditions must all be met simultaneously for equilibrium to hold:

1. No mutation at the locus in question
2. Random mating with respect to the trait
3. No natural selection (all genotypes are equally fit)
4. No gene flow (no migration into or out of the population)
5. Infinitely large population size (no genetic drift)

No real population satisfies all five conditions perfectly. That's the point: Hardy-Weinberg equilibrium is a null model. You compare real data against it to detect whether (and how) a population is evolving.

The Hardy-Weinberg Equations

For a gene with two alleles, let $p$ = frequency of the dominant allele and $q$ = frequency of the recessive allele.

$p + q = 1$

This simply means the two allele frequencies must add up to 100% of the alleles at that locus.

The genotype frequencies are predicted by expanding $(p + q)^2$:

$p^2 + 2pq + q^2 = 1$

• $p^2$ = frequency of homozygous dominant individuals
• $2pq$ = frequency of heterozygous individuals
• $q^2$ = frequency of homozygous recessive individuals

Applying Hardy-Weinberg: A Worked Example

Suppose 16% of a population shows the recessive phenotype for a trait. Find the allele and genotype frequencies.

1. The recessive phenotype corresponds to genotype $aa$, so $q^2 = 0.16$.

2. Solve for $q$: $q = \sqrt{0.16} = 0.4$.

3. Since $p + q = 1$, then $p = 1 - 0.4 = 0.6$.

4. Homozygous dominant ($AA$): $p^2 = (0.6)^2 = 0.36$ (36%).

5. Heterozygous ($Aa$): $2pq = 2(0.6)(0.4) = 0.48$ (48%).

6. Homozygous recessive ($aa$): $q^2 = 0.16$ (16%).

Notice that nearly half the population carries the recessive allele without showing it. This is a common exam insight: heterozygous carriers are often the largest genotype class.

Factors Affecting Allele Frequencies

Any violation of the five Hardy-Weinberg conditions introduces a force that can change allele frequencies. These are the mechanisms of microevolution.

Genetic Drift and Its Effects

Genetic drift is a random change in allele frequencies caused by chance alone, not by any selective advantage. It has the strongest effect in small populations, where a few random events can dramatically shift allele proportions.

Two classic scenarios illustrate genetic drift:

• Bottleneck effect: A catastrophic event (wildfire, disease outbreak, habitat destruction) drastically reduces population size. The surviving individuals carry only a fraction of the original gene pool's diversity. For example, northern elephant seals were hunted down to roughly 20 individuals in the 1890s. Even though the population has since recovered to over 100,000, their genetic diversity remains extremely low.
• Founder effect: A small group of individuals colonizes a new area and establishes a separate population. The allele frequencies in this new group may differ significantly from the source population simply because of the small sample. The high frequency of Ellis-van Creveld syndrome among the Old Order Amish traces back to a small number of founding families who happened to carry the allele.

Both scenarios lead to reduced genetic variation and can cause alleles to become fixed (reaching 100% frequency) or lost (dropping to 0%) purely by chance.

Gene Flow, Mutation, and Non-random Mating

Gene flow is the movement of alleles between populations, typically through migration or interbreeding. It has two major effects:

• It can introduce new alleles into a population that previously lacked them.
• It tends to equalize allele frequencies between connected populations, making them more genetically similar over time.

Mutation is any heritable change in the DNA sequence. Mutations can create entirely new alleles or alter existing ones. On their own, mutations change allele frequencies very slowly because they're rare events. However, mutation is the ultimate source of all new genetic variation. Without it, the other evolutionary forces would have no raw material to act on.

Non-random mating occurs when individuals choose mates based on phenotype or relatedness rather than at random. Two common forms:

• Assortative mating: Individuals preferentially mate with others who share (or differ in) a particular trait. This shifts genotype frequencies without directly changing allele frequencies.
• Inbreeding: Mating between close relatives increases the proportion of homozygotes in the population and decreases heterozygosity. This doesn't change allele frequencies by itself, but it does change genotype frequencies and can expose harmful recessive alleles.