Hardy-Weinberg and Speciation

We now leave individual families behind and look at genetics on the scale of whole populations. The Hardy-Weinberg principle gives a mathematical description of how allele and genotype frequencies behave in a non-evolving population, and lets us calculate how many carriers of a recessive disease there are even when we only know the frequency of affected individuals. At the other end of the story, speciation — the splitting of one species into two — is the ultimate outcome of evolutionary change, and it comes in two main flavours depending on how the populations become isolated. OCR A-Level Biology A specification module 6.1.2(h)–(j) requires you to apply the Hardy-Weinberg equations, describe genetic drift and the mechanisms that cause populations to deviate from equilibrium, and distinguish allopatric and sympatric speciation.

Key Definitions:

• Gene pool — the total collection of alleles in a breeding population at a given time.
• Allele frequency — the proportion of one allele among all copies of that gene in a population.
• Hardy-Weinberg principle — in an idealised population, allele and genotype frequencies remain constant from one generation to the next.
• Genetic drift — random changes in allele frequencies due to chance events, most powerful in small populations.
• Speciation — the formation of a new species from an ancestral population.
• Allopatric speciation — speciation caused by geographical isolation.
• Sympatric speciation — speciation within a single geographical area, caused by reproductive isolation without physical separation.

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Allele Frequencies in a Population

For a gene with two alleles A (dominant) and a (recessive), let:

• p = frequency of A (a number between 0 and 1).
• q = frequency of a.

Since every allele is either A or a:

$p + q = 1$p+q=1

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The Hardy-Weinberg Equation

If gametes combine randomly, the proportions of genotypes in the next generation are given by the binomial expansion of (p + q)²:

$p^2 + 2pq + q^2 = 1$p2+2pq+q2=1

• p² = frequency of homozygous dominant (AA).
• 2pq = frequency of heterozygous (Aa).
• q² = frequency of homozygous recessive (aa).

The five Hardy-Weinberg assumptions

The equilibrium only holds if:

1. No mutation at the locus of interest.
2. No natural selection — all genotypes equally fit.
3. No migration in or out of the population.
4. Random mating — no preference for particular genotypes.
5. Large population — so random fluctuations average out.

If any of these fails, allele frequencies change between generations — i.e. the population evolves.

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Worked Example 1: Cystic Fibrosis Carriers

Cystic fibrosis affects about 1 in 2500 people of European ancestry and is autosomal recessive. Use Hardy-Weinberg to find the frequency of carriers.

• q² = 1/2500 = 0.0004
• q = √0.0004 = 0.02
• p = 1 − 0.02 = 0.98
• Carrier frequency 2pq = 2 × 0.98 × 0.02 = 0.0392 ≈ 1 in 25.

So about 4% of the European population are carriers of cystic fibrosis, even though only 0.04% are affected. This kind of calculation is essential for genetic counselling — carriers vastly outnumber sufferers for any recessive disease.

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Worked Example 2: PTC Tasting

The ability to taste phenylthiocarbamide (PTC) is dominant; non-tasters are homozygous recessive. In a sample of 1000 people, 160 are non-tasters. What fraction of the population are heterozygous?

• q² = 160/1000 = 0.16
• q = 0.4
• p = 0.6
• 2pq = 2 × 0.6 × 0.4 = 0.48

So 48% of the population are heterozygous tasters — nearly half. And p² = 0.36 (36% homozygous tasters), q² = 0.16 (16% non-tasters). Check: 0.36 + 0.48 + 0.16 = 1.00. ✓

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When Hardy-Weinberg Fails: Mechanisms of Evolution

If the assumptions fail, allele frequencies shift. The four main causes of frequency change are:

1. Natural selection

Genotypes with higher fitness (more offspring) become more common. Classic example: the peppered moth (Biston betularia) — during the Industrial Revolution, dark (melanic) morphs were favoured on sooty tree trunks because they were camouflaged from bird predators, so the frequency of the dark allele rose sharply.

2. Genetic drift

In small populations, chance events can dramatically change allele frequencies. If only a handful of organisms reproduce in a given generation, the allele frequencies in their offspring may look very different from those of the parent generation, just by sampling error. Two special cases of strong drift are:

• Founder effect — a small group colonises a new area, carrying only a subset of the original gene pool. The frequencies in the new colony reflect which alleles the founders happened to bring. Example: the Amish communities of Pennsylvania, descended from ~200 founders, have high frequencies of certain genetic conditions (e.g. Ellis-van Creveld syndrome) that are rare in the general European population.
• Bottleneck — a population crashes to a small size (by disease, disaster, hunting) and subsequently recovers, but has lost much of its genetic variation. Example: cheetahs show remarkably low genetic diversity because of an ancient bottleneck.

3. Migration (gene flow)

Individuals moving between populations bring their alleles with them, making the populations more genetically similar and preventing divergence.

4. Mutation