Hardy-Weinberg Equation

Hardy-Weinberg Principle

Allele Frequencies

• Population: a group of individuals of the same species that breed together
• Gene pool: all copies of every allele in the population
• All genetic diversity of the entire population
• Homozygous: having two of the same alleles at a locus
• Fixed allele: all individuals in the population are homozygous at this locus
• Heterozygous: having two different alleles at a locus
• Polymorphism: Individuals in the population can be either Homozygous or Heterozygous at this locus
• Allele Frequency: the relative number of a specific allele at a locus
• Expressed as a proportion or a percentage Example: Imagine a population of flowers that have a polymorphism at a specific locus. If there are 200 "r" alleles and 400 "R" alleles, then the frequency of "r" is 200/600 = 0.33 (33%)

Hardy-Weinberg Principle

• Calculate what the allele frequencies should be if the population is not evolving
• Null hypothesis
• If the real world is different, then population may be evolving
• Hardy-Weinberg Equilibrium (HWE): allele frequencies in a population should remain constant
• No change with each new generation
• We think about all possible crosses between individuals in a population
• Consider all alleles floating around in gene pool
• Each generation we take a random scoop from that pool, and that becomes the next generation
• Probability of getting one specific allele = allele frequency
• $P(r) = f(r)$
• Assumptions of Hardy-Weinberg
• No mutations
• Random mating
• No natural selection
• Large population size
• No gene flow

Hardy-Weinberg Equation

Hardy-Weinberg Equation

• Use Hardy-Weinberg equation to estimate the frequency of each genotype
• So for a locus with alleles $R$ and $r$ where $P(R) = p$ and $P(r) = q$
• $P(RR) = P(R) * P(R)$ $P(RR) = p*p$ $\colorFour{P(RR) = p^2}$
• Two ways to get a Heterozygote
• $P(Rr) = P(R) * P(r)$ $P(Rr) = p * q$ $P(Rr) = pq$
• $P(rR) = P(r) * P(R)$ $P(rR) = q * p$ $P(rR) = qp$
• $P(Rr) + P(rR) = pq + qp$ $\colorFour{P(Het) = 2pq}$
• $P(rr) = P(r) * P(r)$ $P(rr) = q*q$ $\colorFour{P(rr) = q^2}$
• The allele frequencies and probabilities must all = 1
• $f(R) + f(r) = 1$
• $P(R) + P(r) = 1$
• $P(RR) + P(Het) + P(rr) = 1$
• $\colorFour{\boxed{p^2+2pq\ +\ q^2\ =\ 1}}$

Applying the Hardy-Weinberg Equation

• Compare the actual distribution of homozygotes and heterozygotes in a population to the predicted HWE
• If they do not match, there may be selection or evolution
• If we assume the population is in HWE
• If we know the frequency of one allele (p or q) we can calculate the rest
• If we know the frequency of any homozygous genotype we can calculate the rest

Example: Applying HWE During Experimentation