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Genetics Unit 10: Population Genetics and Hardy-Weinberg

Population genetics follows allele frequencies across generations. The Hardy-Weinberg principle gives a baseline, and departures from it reveal mutation, migration, drift, selection and nonrandom mating.

Covers: Allele and genotype frequencies, The Hardy-Weinberg principle and its assumptions, Carrier and X-linked frequency calculations, Testing for equilibrium with chi-square, Mutation and migration, Genetic drift, bottlenecks and founder effects, Natural selection and inbreeding

Study guide

Population genetics studies a gene pool, the set of alleles in a population. Allele frequencies are found by counting alleles: for a gene with alleles A and a in N diploid individuals, p = (2 × AA + Aa)/2N and q = 1 − p. Genotype frequencies are the fractions of individuals with each genotype. Evolution, at its simplest, is a change in allele frequencies over generations. Keep allele and genotype frequencies separate: a population can change genotype frequencies (through inbreeding, for example) without any change in allele frequencies.

The Hardy-Weinberg principle states that in a large, randomly mating population with no mutation, migration or selection, allele frequencies stay constant, and genotype frequencies after one generation of random mating are p², 2pq and q². These follow from combining gametes at random: an A egg meets an A sperm with probability p², and so on. This lets us estimate carrier frequencies. If a recessive disease affects 1 in 10,000, q = 0.01 and carriers are 2pq ≈ 0.02, or about 1 in 50. For X-linked genes, male phenotype frequencies equal the allele frequency, while affected females occur at q².

To test whether a population is in equilibrium, compute p and q from observed genotypes, calculate expected counts as p²N, 2pqN and q²N, and run a chi-square test. Because p is estimated from the data, df = 3 genotype classes − 2 alleles = 1. A heterozygote deficit suggests inbreeding, population structure or selection against heterozygotes; an excess suggests heterozygote advantage or recent mixing. Inbreeding changes genotype frequencies, raising homozygotes to q² + Fpq and lowering heterozygotes to 2pq(1 − F).

Several forces change allele frequencies. Mutation creates new alleles but changes frequencies slowly because rates are low. Migration (gene flow) moves alleles between populations: q' = (1 − m)q + m q_m, making populations more similar. Genetic drift is random change from sampling in finite populations; it is strongest when the effective population size is small, as after bottlenecks or in founder populations. A new neutral allele is fixed with probability 1/(2N), and heterozygosity is lost at about 1/(2N) per generation. Skewed sex ratios reduce effective size: Ne = 4NmNf/(Nm + Nf).

Natural selection changes allele frequencies through differences in fitness, the relative survival and reproduction of genotypes. Selection against a recessive allele is slow once it is rare, because most copies hide in heterozygotes; for a recessive lethal, q_t = q₀/(1 + t q₀). Heterozygote advantage, as with sickle-cell alleles in malaria regions, keeps both alleles at an equilibrium q = s/(s + t). Harmful alleles can persist through mutation-selection balance, with q ≈ √(u/s) for recessives. Real populations reflect a mix of these forces acting together.

Key ideas

• Allele frequencies are found by counting alleles, not individuals.
• Hardy-Weinberg predicts p², 2pq and q² after one generation of random mating with no evolutionary forces.
• Carriers of rare recessive alleles are far more common than affected individuals.
• For X-linked genes, males show q and females show q².
• A Hardy-Weinberg chi-square test with two alleles has 1 degree of freedom.
• Drift is strongest in small populations and causes loss of variation and divergence.
• Inbreeding raises homozygosity without changing allele frequencies; heterozygote advantage maintains both alleles.

Formulas and rules

Common mistakes

• Using the recessive phenotype frequency as q instead of taking its square root.
• Computing allele frequency by dividing by N instead of 2N.
• Using 2 degrees of freedom for a two-allele Hardy-Weinberg chi-square.
• Thinking inbreeding changes allele frequencies.
• Expecting selection to quickly remove a rare recessive allele.

Before the test, make sure you can

• Calculate allele and genotype frequencies from genotype counts.
• State the Hardy-Weinberg assumptions and expected genotype frequencies.
• Calculate carrier frequencies from disease incidence, including X-linked cases.
• Test a population for Hardy-Weinberg equilibrium with chi-square and 1 df.
• Calculate the effects of migration, inbreeding and selection on frequencies.
• Explain drift, bottlenecks and founder effects and calculate Ne.
• Calculate equilibrium frequencies for heterozygote advantage and mutation-selection balance.

Words to know

Gene pool

All alleles of all genes in a population.

Allele frequency

The proportion of all copies of a gene that are a particular allele.

Hardy-Weinberg equilibrium

Stable allele and genotype frequencies (p², 2pq, q²) when no evolutionary forces act.

Gene flow

Movement of alleles between populations by migration.

Genetic drift

Random change in allele frequencies from chance sampling.

Bottleneck

A sharp reduction in population size that increases drift.

Founder effect

Drift that occurs when a few individuals start a new population.

Effective population size

The size of an ideal population that would show the same amount of drift.

Fixation

When an allele reaches a frequency of 1.

Fitness

The relative survival and reproduction of a genotype.

Selection coefficient

The reduction in fitness of a genotype, s = 1 − w.

Heterozygote advantage

Higher fitness of heterozygotes than of either homozygote.

Mutation-selection balance

Equilibrium where new mutations replace alleles removed by selection.

Inbreeding

Mating between relatives, which increases homozygosity.

Assortative mating

Mating with partners of similar phenotype more often than by chance.

Sample practice questions

30 more questions like these, from level 1 to 5, are in the practice set.