Biology 2 · Mechanisms of Evolution
Population Genetics and Hardy-Weinberg Equilibrium
On this page 5 sections
The college version
Core Explanation
Population Interbreeding group of individuals of the same species in the same area genetics integrates Mendelian genetics with Darwinian evolution by studying how allele and genotype frequencies change (or remain stable) in populations over time. It provides the mathematical framework for understanding evolution.
Key Definitions
- Population: A group of individuals of the same species living in the same area and interbreeding.
- Gene pool All alleles at all loci in a population: The total collection of all alleles at all loci in a population.
- Allele frequency Proportion of a specific allele at a locus (p + q = 1): The proportion of a specific allele among all alleles at a given locus in the population.
- For a gene with two alleles (A and a): p = frequency of A, q = frequency of a
- p + q = 1 (all allele frequencies at a locus sum to 1)
- Genotype frequency Proportion of individuals with a specific genotype (p² + 2pq + q² = 1): The proportion of individuals in a population with a specific genotype (AA, Aa, or aa).
The Hardy-Weinberg Principle
The Hardy-Weinberg principle, independently derived by G.H. Hardy (mathematician) and Wilhelm Weinberg (physician) in 1908, states that allele and genotype frequencies in a population will remain constant from generation to generation in the absence of other evolutionary influences.
For a gene with two alleles:
p² + 2pq + q² = 1
Where:
- p² = frequency of homozygous dominant genotype (AA)
- 2pq = frequency of heterozygous genotype (Aa)
- q² = frequency of homozygous recessive genotype (aa)
- p + q = 1
The Five Assumptions
Hardy-Weinberg equilibrium Null model where allele/genotype frequencies remain constant across generations requires that ALL of the following conditions are met:
| Assumption | What it means | What happens if violated |
|---|---|---|
| 1. No mutation | No new alleles are created | Mutation introduces new alleles → change in allele frequencies |
| 2. Random mating | Individuals pair by chance, not by genotype | Nonrandom mating (inbreeding, assortative mating) shifts genotype frequencies |
| 3. No natural selection | All genotypes have equal survival and reproduction | Selection changes allele frequencies systematically |
| 4. Extremely large population size | No genetic drift | Small populations experience random frequency changes (drift) |
| 5. No gene flow | No migration of individuals between populations | Gene flow introduces or removes alleles |
Critical insight: These assumptions are virtually NEVER all met in real populations. Hardy-Weinberg equilibrium is therefore a Null model Baseline expectation assuming no evolution; deviations indicate evolutionary forces at work — a baseline expectation of what would happen if evolution were NOT occurring. When observed genotype frequencies deviate from Hardy-Weinberg expectations, we have evidence that one or more evolutionary mechanisms are operating.
How It Works — Calculations
Calculating Allele Frequencies from Genotype Counts
In a population of 100 individuals at a locus with two alleles (A and a):
- 36 are AA
- 48 are Aa
- 16 are aa
Total alleles = 200 (each diploid individual carries 2 alleles)
Frequency of A (p): Count A alleles: 36(AA)×2 + 48(Aa)×1 = 72 + 48 = 120 p = 120/200 = 0.6
Frequency of a (q): Count a alleles: 16(aa)×2 + 48(Aa)×1 = 32 + 48 = 80 q = 80/200 = 0.4 (Or simply: q = 1 − p = 1 − 0.6 = 0.4)
Testing for Hardy-Weinberg Equilibrium
Using the same population, calculate expected genotype frequencies IF the population is in equilibrium:
Expected genotype frequencies:
- AA: p² = (0.6)² = 0.36
- Aa: 2pq = 2(0.6)(0.4) = 0.48
- aa: q² = (0.4)² = 0.16
Expected counts (×100 individuals):
- AA: 36, Aa: 48, aa: 16
Observed = Expected → The population IS in Hardy-Weinberg equilibrium at this locus.
Worked Example — Detecting Evolution
A population of 500 individuals is genotyped for a disease locus:
| Genotype | Count |
|---|---|
| TT | 200 |
| Tt | 200 |
| tt | 100 |
Step 1: Calculate allele frequencies Total alleles = 500 × 2 = 1,000 T alleles: 200(TT)×2 + 200(Tt)×1 = 600 → p = 600/1000 = 0.6 t alleles: 100(tt)×2 + 200(Tt)×1 = 400 → q = 400/1000 = 0.4
Step 2: Expected Hardy-Weinberg genotype frequencies TT: p² = (0.6)² = 0.36 → expected count = 0.36 × 500 = 180 Tt: 2pq = 2(0.6)(0.4) = 0.48 → expected count = 0.48 × 500 = 240 tt: q² = (0.4)² = 0.16 → expected count = 0.16 × 500 = 80
Step 3: Compare observed vs expected Observed: 200 (TT), 200 (Tt), 100 (tt) Expected: 180, 240, 80
There is a deviation — the population is NOT in Hardy-Weinberg equilibrium. There are more homozygotes (TT and tt) and fewer heterozygotes than expected. This pattern suggests inbreeding or population subdivision — both of which violate the random-mating assumption. Evolution is occurring at this locus.
Hardy-Weinberg for Sex-Linked Loci
For X-linked genes, allele frequencies are calculated differently because males are hemizygous (carry only one allele):
- In females: genotype frequencies follow p² + 2pq + q²
- In males: genotype frequencies equal allele frequencies (p and q)
- At equilibrium, allele frequencies are the same in both sexes, and the male phenotype frequency for an X-linked recessive trait equals q (the allele frequency), while the female frequency equals q².
This explains why X-linked recessive disorders (e.g., red-green color blindness, hemophilia A) are far more common in males: a male needs only ONE copy of the recessive allele (probability = q), while a female needs TWO copies (probability = q²).
Common Misconceptions and Exam Traps
- Exam trap: "p² = frequency of the dominant phenotype." p² is the frequency of the homozygous dominant GENOTYPE (AA). The dominant phenotype includes both AA (p²) and Aa (2pq).
- Misconception: "If a population is at Hardy-Weinberg equilibrium, evolution has stopped." Hardy-Weinberg equilibrium is locus-specific. A population can be at equilibrium at one locus while evolving at another. Also, violations may exist but be too small to detect with the available sample size.
- Exam trap: Using p + q = 1 to directly calculate genotype frequencies. You MUST first square/combine: p² + 2pq + q² = 1. p and q are allele frequencies; p², 2pq, and q² are genotype frequencies.
- Misconception: "Hardy-Weinberg describes most real populations." It describes almost NO real populations — that's the point. It's a null model, not a description of nature.
- Exam trap: Forgetting that Hardy-Weinberg applies to a LOCUS, not an organism. A population can be at equilibrium for one gene and not another.
Eli explains
The same idea, in plain words
Explain it like I’m 10
Imagine a huge jar filled with colored marbles — blue ones (allele A) and red ones (allele a). If you randomly pull out two marbles at a time, you can predict exactly how many pairs will be blue-blue, blue-red, or red-red, just from knowing how many of each color are in the jar. The Hardy-Weinberg principle is that mathematical prediction, but for genes. If the actual pairs in a real population DON'T match the prediction, it means something interesting is going on — maybe certain combinations survive better, or maybe the population is too small and randomness is taking over. Hardy-Weinberg is the "nothing unusual happening" baseline that helps scientists spot when something IS happening.
Key takeaways
- p + q = 1 (allele frequencies); p² + 2pq + q² = 1 (genotype frequencies at Hardy-Weinberg equilibrium)
- Hardy-Weinberg = null model: if observed ≠ expected, evolution is occurring (or nonrandom mating)
- Five assumptions: no mutation, random mating, no selection, large population, no gene flow
- ALL five assumptions are rarely met — Hardy-Weinberg is a tool for DETECTING evolution, not describing it
- Calculate p and q from genotype counts FIRST, then calculate expected frequencies
- X-linked recessive traits: males affected at frequency q; females at frequency q²
- Allele frequencies: p + q = 1
- Genotype frequencies at H-W equilibrium: p² + 2pq + q² = 1
- Five assumptions: no mutation, random mating, no selection, large population, no gene flow
- H-W is a null model — deviations indicate evolutionary forces at work
- Calculate observed allele frequencies FIRST, then compute expected genotype frequencies
- For X-linked recessive traits: male affected rate = q; female affected rate = q²
- In a population of 1,000 individuals, 160 have the recessive phenotype (aa). Assuming Hardy-Weinberg equilibrium, what are the frequencies of the A and a alleles?
- A population has genotype counts: AA=90, Aa=420, aa=490. Is this population in Hardy-Weinberg equilibrium? Show your work.
- Why is the frequency of X-linked color blindness much higher in males (~8%) than in females (~0.64%)?
- If 160/1000 have the recessive phenotype (aa), then q² = 0.16. Taking the square root: q = 0.4. Then p = 1 − q = 1 − 0.4 = 0.6. The frequency of A (p) is 0.6 and a (q) is 0.4. (Genotype frequencies at equilibrium: AA = 0.36 = 360 individuals; Aa = 0.48 = 480; aa = 0.16 = 160.)
- Total = 1000 individuals, 2000 alleles. p = (90×2 + 420)/2000 = 600/2000 = 0.3; q = 1 − 0.3 = 0.7. Expected H-W counts: AA = (0.3)²×1000 = 90; Aa = 2(0.3)(0.7)×1000 = 420; aa = (0.7)²×1000 = 490. Observed = Expected exactly. Yes, this population IS in Hardy-Weinberg equilibrium at this locus.
- For an X-linked recessive trait with allele frequency q = 0.08: Males have only one X chromosome, so the probability a male is affected equals q = 0.08 (8%). Females have two X chromosomes and need TWO copies of the recessive allele to express the trait: q² = (0.08)² = 0.0064 (0.64%). The ~12.5-fold difference (q vs. q²) is characteristic of X-linked recessive inheritance.
Study tools & related lessonsYou’ll learn to · Key vocabulary · Related
You’ll learn to
- Define population, gene pool, allele frequency, and genotype frequency
- State the Hardy-Weinberg principle and its five assumptions
- Calculate allele and genotype frequencies using the Hardy-Weinberg equations
- Explain why Hardy-Weinberg equilibrium functions as a null model for detecting evolution
- Determine whether a population is evolving at a given locus
Key vocabulary
- Population
- Interbreeding group of individuals of the same species in the same area
- Gene pool
- All alleles at all loci in a population
- Allele frequency
- Proportion of a specific allele at a locus (p + q = 1)
- Genotype frequency
- Proportion of individuals with a specific genotype (p² + 2pq + q² = 1)
- Hardy-Weinberg equilibrium
- Null model where allele/genotype frequencies remain constant across generations
- Null model
- Baseline expectation assuming no evolution; deviations indicate evolutionary forces at work
- Genetic drift
- Random changes in allele frequencies due to finite population size
Sources & references
This lesson was adapted from the open educational references above; their licenses and attributions are preserved. See Copyright & Licensing.
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