The Hardy–Weinberg principle provides a mathematical model, which predicts…

The idea

The Hardy-Weinberg principle is a mathematical model, not a law of nature. It predicts that in a population meeting a set of conditions the allele frequencies stay the same from one generation to the next, so no evolution takes place. Two equations carry it: p + q = 1 for the frequencies of a dominant and a recessive allele, and p squared + 2pq + q squared = 1 for the genotype frequencies, where p squared is the homozygous dominant, 2pq the heterozygous and q squared the homozygous recessive. Because only the homozygous recessive phenotype reveals its own genotype, almost every calculation begins by setting q squared equal to the proportion showing the recessive characteristic, taking the square root to find q, then finding p as 1 - q. Its real value is as a null model.

What earns the marks

• Stating that allele frequencies remain constant from generation to generation when the conditions of the model are met.
• Using q squared as the frequency of the homozygous recessive phenotype to find q, then p = 1 - q.
• Calculating 2pq as the frequency of heterozygotes from p and q rather than measuring it directly.
• Explaining that the principle does not hold when any of its conditions is broken, for example when individuals carrying an allele are selected against, so allele frequency changes.
• Listing the conditions required for the principle to hold: large population, random mating, no migration, no mutation and no selection.

Common mistakes and how to put them right

• Giving q when the question asks for q squared.

  Put it right: Check the symbol and the units requested.

• Forgetting to take the square root, or taking the square root of the wrong quantity.

  Put it right: q squared is the homozygous recessive frequency, so take the square root to find q.

• Treating everyone showing the dominant characteristic as p squared, when that group also contains the heterozygotes, 2pq.

  Put it right: p squared is only the homozygous dominant.

• Giving the frequency of carriers as pq rather than 2pq.

  Put it right: Heterozygotes are represented by 2pq.

• Saying the principle is simply wrong for a real population instead of naming the condition that has been broken.

  Put it right: Identify which condition, such as selection or non-random mating, is violated.

Exam tips

• Write down which value the question has given you, and which symbol it belongs to, before you calculate anything.
• When asked whether the principle would hold, answer yes or no and then justify your answer by referring to the relevant conditions of the model.
• Keep frequencies as decimals to at least three places until the final answer, then round as the question instructs.