Hardy-Weinberg Principle

• The Hardy-Weinberg principle states that if certain conditions are met, the?allele frequencies of a gene within a population will not change from one generation to the next
• There are several?conditions or assumptions?that must be met for the Hardy-Weinberg principle to hold true:
  • Mating?must be?random?between individuals
  • The population is?infinitely large
  • There is?no migration, mutation?or?natural selection
• The Hardy-Weinberg?equation?allows for the?calculation of allele and genotype frequencies?within populations
• It also allows for predictions to be made about how these frequencies will change in future generations
• If the allele frequencies in a population?change over time, then it means that migration, mutation or natural selection has happened

Hardy-Weinberg calculations

• 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, the?frequency of a genotype?is represented as a?proportion?of the population
  • For example, the?BB?genotype could be 0.40
  • Whole population = 1
  • 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 this phenotypic trait in the population:

p + q?= 1

• The chance of an individual being homozygous dominant is?p2
  • In this instance, the offspring would inherit dominant alleles from both parents (?p?x?p?=?p2?)
• ?The chance of an individual being heterozygous is?2pq
  • Offspring could inherit a dominant allele from the father and a recessive allele from the mother (?p?x?q?)?or?offspring could inherit a dominant allele from the mother and a recessive allele from the father (?p?x?q?) =?2pq
• The chance of an individual being homozygous recessive is?q2
  • ?In this instance, the offspring would inherit recessive alleles from both parents (?q?x?q?=?q2?)
• As these are all the possible genotypes of individuals in the population, the following equation can be constructed:

p2?+?q2?+ 2pq?= 1

Solution:

• • We will use?F / f?to represent dominant and recessive alleles for feather colour
  • Those with the recessive phenotype must have the homozygous recessive genotype,?ff
  • Therefore?q2?= 0.10?(as 10% of the individuals have the recessive phenotype and?q2?represents this)

To calculate the frequencies of the homozygous dominant (?p2?) and heterozygous (?2pq?):

Step 1: Find q

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 homozygous dominant genotype)

0.682?= 0.46

p2?= 0.46

Step 4: Find 2pq =?2 x (p) x (q)

2 x (0.68) x (0.32)

= 0.44

Step 5: Check calculations by substituting the values for the three frequencies into the equation; they should add up to 1

p2?+?2pq?+?q2?= 1

0.46 + 0.44 + 0.10 = 1

In summary:

• • Allele frequencies:
    • p?=?F?= 0.68
    • q?=?f?= 0.32

     

  • Genotype frequencies:
    • p2?=?FF?= 0.46
    • q2?=?ff?= 0.10
    • 2pq?=?Ff?= 0.44