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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.
For a gene with two alleles A (dominant) and a (recessive), let:
Since every allele is either A or a:
p+q=1
If gametes combine randomly, the proportions of genotypes in the next generation are given by the binomial expansion of (p + q)²:
p2+2pq+q2=1
The equilibrium only holds if:
If any of these fails, allele frequencies change between generations — i.e. the population evolves.
Cystic fibrosis affects about 1 in 2500 people of European ancestry and is autosomal recessive. Use Hardy-Weinberg to find the frequency of carriers.
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.
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?
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. ✓
If the assumptions fail, allele frequencies shift. The four main causes of frequency change are:
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.
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:
Individuals moving between populations bring their alleles with them, making the populations more genetically similar and preventing divergence.
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