5.1 Population Genetics & Change

Why Population Genetics Matters on the Diploma

Unit D is about 15% of the Biology 30 diploma exam, and Hardy-Weinberg calculations are a reliable source of numerical-response questions. The exam expects you to move beyond single crosses (Unit C) and reason about whole populations — all the interbreeding members of a species in one area. This section gives you the equations and the conditions you must be able to apply quickly and correctly.

Gene Pools and Allele Frequencies

A gene pool is the total collection of all alleles for all genes in a population. For a gene with two alleles, we track two frequencies:

• p = frequency of the dominant allele (e.g. A)
• q = frequency of the recessive allele (e.g. a)

Because every allele copy in the population is either A or a, the two frequencies must sum to one:

p + q = 1

This is the foundation for everything that follows. If you know one allele frequency, you immediately know the other.

The Hardy-Weinberg Equation

When alleles combine randomly into diploid genotypes, the genotype frequencies follow:

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

The key shortcut: the only phenotype you can usually count directly is the recessive one (aa), because dominant phenotypes mask heterozygotes. So you almost always start from q^2 — the observed recessive frequency.

Worked Calculation

In a population of 1000 plants, 160 show the recessive white flower (aa). Find p, q, and the number of heterozygotes.

1. q^2 = 160 / 1000 = 0.16
2. q = √0.16 = 0.4
3. p = 1 − q = 1 − 0.4 = 0.6
4. p^2 (AA) = 0.6^2 = 0.36 → 360 plants
5. 2pq (Aa) = 2(0.6)(0.4) = 0.48 → 480 heterozygotes

Check: 0.36 + 0.48 + 0.16 = 1.00. ✔ Always take the square root of q^2 first; do not square-root the p^2 term you are trying to find.

Carrier Frequency and a Second Example

A classic numerical-response setup gives a recessive disorder frequency and asks for carriers (Aa). Suppose 1 in 2500 people has a recessive condition.

1. q^2 = 1 / 2500 = 0.0004
2. q = √0.0004 = 0.02
3. p = 1 − 0.02 = 0.98
4. Carrier frequency 2pq = 2(0.98)(0.02) = 0.0392 ≈ 3.9%

Notice that even when the disorder is rare, carriers are far more common than affected individuals, because recessive alleles are mostly hidden in heterozygotes. Round only at the final step, and watch the units the question asks for — a proportion, a percent, or a head count.

Five Conditions for Genetic Equilibrium

A population in Hardy-Weinberg equilibrium is NOT evolving — allele frequencies stay constant generation to generation. This requires all five conditions:

1. Very large population (no sampling error / drift)
2. No mutation (alleles are not converted to new forms)
3. No gene flow (no migration in or out)
4. Random mating (no mate choice for the trait)
5. No natural selection (all genotypes survive and reproduce equally)

Real populations rarely meet all five, so the principle is best used as a null model: deviation from p^2 + 2pq + q^2 is evidence that microevolution is occurring.

Mechanisms of Microevolution

Microevolution is a change in allele frequencies within a population. Four mechanisms break Hardy-Weinberg equilibrium:

• Mutation — the ultimate source of new alleles; slow on its own.
• Gene flow — migration of individuals/gametes moves alleles between populations, tending to make them more similar.
• Genetic drift — random change in allele frequencies, strongest in small populations. The founder effect (a few individuals start a new population) and the bottleneck effect (a crash drastically reduces the population) both reduce genetic variation.
• Natural selection — non-random, differential survival and reproduction; the only mechanism that consistently produces adaptation.

Types of Natural Selection

Selection reshapes the distribution of a phenotype:

• Stabilizing selection favours the average phenotype and removes extremes (e.g. human birth weight). Variation decreases.
• Directional selection favours one extreme, shifting the mean (e.g. antibiotic resistance, peppered moths darkening with pollution).
• Disruptive (diversifying) selection favours both extremes against the middle, and can split one population into two.

A related driver is sexual selection, where traits that improve mating success (bright plumage, antlers) spread even if they reduce survival.

Speciation

When reproductive isolation prevents gene flow long enough, two diverging gene pools can no longer interbreed and become separate species. The exam distinguishes two modes:

• Allopatric speciation — a geographic barrier (mountain, river, ocean) physically separates populations, which then diverge through independent selection and drift.
• Sympatric speciation — populations diverge without geographic separation, through behavioural, temporal, or polyploidy-based isolation.

Speciation is the link between microevolution (allele-frequency change within a population) and macroevolution (the origin of new species and larger-scale change across geological time). Accumulated small changes, sorted by selection and isolated by barriers, produce biodiversity.

Common Hardy-Weinberg Traps

Watch for these exam mistakes:

• Mixing allele and genotype frequencies. p and q are allele frequencies; p^2, 2pq, q^2 are genotype frequencies. The answer 0.6 is an allele frequency, not a count of carriers.
• Forgetting the 2 in 2pq. Heterozygotes can form two ways (A from mother / a from father, or the reverse), so their frequency is 2pq, not pq.
• Dominant phenotype ≠ p^2. The dominant phenotype includes both AA and Aa, so its frequency is p^2 + 2pq, or simply 1 − q^2.
• Square-rooting the wrong term. Start from the observed recessive frequency q^2; never square-root p^2 to find p directly when you do not yet know p.