Natural Selection: Hardy-Weinberg Principle (Cambridge International A-Level Biology)

Spec point — use the Hardy–Weinberg principle to calculate allele and genotype frequencies in populations and state the conditions when this principle can be applied

Natural selection: the Hardy-Weinberg principle

• The Hardy-Weinberg principle can be used to predict allele frequencies in a population

• The principle can only be applied accurately to populations under certain conditions, e.g. in populations where:

  • **no natural selection **is taking place
  • there is no migration into or out of the population
  • mating is random
  • the population is** large**
  • no mutations are occurring

Hardy-Weinberg equations

• If the phenotype of a trait in a population is determined by a single gene with only two alleles (we will use B / b as examples throughout this section) then the population will consist of individuals with three possible genotypes:

  • Homozygous dominant (BB)
  • *Heterozygous (Bb)
  • Homozygous recessive (bb)

• When using the Hardy-Weinberg equation, frequencies are represented as proportions of the population; a proportion is a number out of 1

• The frequency of alleles can be represented; this is the proportion of all of the alleles in a population that are of a particular form

  • The letter p represents the frequency of the dominant allele (B)
  • The letter q represents the frequency of the recessive allele (b)
  • As there are only two alleles at a single gene locus for a phenotypic trait in the population:

p + q = 1

• E.g. in a population of 100 individuals there would be 200 alleles because every individual has two versions of each gene

  • If 120 of those alleles were the dominant allele then the frequency of the dominant allele would be 120/200
  • It could be said that p = 120 ÷ 200 = 0.6
  • If p = 0.6 then q = 1 - 0.6 = 0.4

• The frequency of genotypes can also be represented; this is the proportion of all of the individuals with a particular genotype

  • The frequency of homozygous dominant individuals is represented by p²
  • The frequency of heterozygous individuals is represented by 2pq **
  • The frequency of homozygous recessive individuals is represented by** q²
  • As these are all the possible genotypes of individuals in the population the following equation can be constructed:

p²+ q² + 2pq = 1

Worked Example In a population of birds 10 % of the individuals exhibit the recessive phenotype of white feathers.

Calculate the frequencies of all genotypes. Use F / f to represent dominant and recessive alleles for feather colour.

Answer

• Begin by working out:

  • the part of the Hardy-Weinberg equation that we have been given:

    • 10 % recessive white phenotype ****ff
    • 10 % = 0.1
    • q²** = 0.1**

  • the part of the Hardy-Weinberg equation that we need to work out:

    • Frequency of the heterozygous genotype = 2pq
    • Frequency of the homozygous dominant genotype = p²

Step 1: find q

q²* *= 0.1

q =* *$\sqrt{0.1}$

**q = 0.32

** Step 2: **find p (the frequency of the dominant allele F).

If q = 0.32, and p + q = 1

p + q = 1

p = 1 - 0.32

p = 0.68**

**Step 3: **Find p² (the frequency of the homozygous dominant genotype)

0.68² = 0.46

Final answer: p²** = 0.46**

Step 4: **Find 2*pq *(the frequency of the heterozygous genotype)

2 x (0.68) x (0.32) = 0.44

Final answer: 2pq = 0.44**

Exam Hint When you are using Hardy-Weinberg equations you must always start your calculations by determining which part of the equation you have been given, and which part you need to work out.

It is most common for questions to give the proportion of individuals that display the recessive phenotype; this is the only phenotype from which you can immediately work out its genotype as it will always be homozygous recessive.