Hardy-Weinberg Theorem and Genotype Frequencies

Hardy-Weinberg Theorem

• The Hardy-Weinberg Theorem is a formula that explains evolution using genotype and allele frequency concepts.
• The formula is: p²+2pq+q² = 1
• This formula states that the sum of the frequencies of the three different genotypes for a gene with two alleles (AA, Aa, and aa, for example) totals to 1.
• Genotype frequencies calculated: the frequencies of the homozygotes for either allele are the square of the frequencies of the allele itself, and the frequency of the heterozygotes is the frequency of the two alleles multiplied by each other, and then multiplied by two.
  • f(AA) = p²
  • f(Aa) = 2pq
  • f(aa) = q²
• This holds true only if each gene copy in a population can pair randomly with any other gene copy.
• Imagine a gene pool as a hat filled with marbles, where blue marbles represent the A allele and red marbles represent the a allele; random mating allows simulating matings by randomly pulling two marbles.
• If mating is random the chance of an offspring having the genotype AA, requires pulling out two blue marbles where the chance of pulling out a blue marble is p, therefore the chance of pulling two blue marbles is p².
• This explains the chance of getting offspring homozygous for the a allele, where the frequency is q, so the frequency of the homozygous genotype is q².

Heterozygotes

• To get heterozygotes, a blue and a red marble must be drawn, the chance of drawing a blue marble is p, and a red marble is q.
• Combinations such as blue then red, with probability p x q, or red then blue, with probability q x p (equal to p x q), can occur.
• The two combinations cannot occur at the same time, they are dependent events; so add them together: (p x q) + (p x q), or 2pq.
• The Hardy-Weinberg Theorem is valid only with completely random mating, a necessary assumption.

Hardy-Weinberg Equilibrium

• Hardy-Weinberg predicts that despite initial genotype frequencies, one generation of random mating results in Hardy-Weinberg Theorem frequencies.
• A population with these genotypic frequencies is said to be in Hardy-Weinberg equilibrium (HWE).

Assumptions of Hardy-Weinberg

• Mating must be random.
• The population must be infinite in size due to sampling error a statistical phenomenon that occurs when expected results are applied to a finite sample.

Additional Assumptions & Predictions

• There is no mutation which is defined as one allele changing to another because this changes allele and genotype frequencies.
• There cannot be any migration or individuals leaving or entering because this also changes the frequencies
• Everyone has to survive and reproduce equally because otherwise they will put their alleles into the gene pool hat more often, and that shifts the HW frequencies.
• If mating is random, the genotype frequencies will be in HWE after one generation.
• If all the assumptions of Hardy-Weinberg are true, the population will not evolve, and allele frequencies will not change.

Use of the Theorem

• It serves a a model of an imaginary population that is simple to understand
• Natural populations and their evolution are often extremely complex, and would difficult, if not impossible, to study with much precision.
• Necessary assumptions such as no evolution means the opposite of the assumptions cause evolution.
• Creating a simplified model with no evolution, at the same defining the assumptions necessary to avoid evolution, we define the forces that cause evolution.
• Each force can be added back into calculations to dissect how populations evolve, form hypotheses, and evolve a testable theory for studying life's evolution.

Explore the Hardy-Weinberg Theorem, a formula explaining evolution through genotype and allele frequencies. Understand how the equation p²+2pq+q² = 1 calculates genotype frequencies, assuming random gene pairing within a population. Learn how this principle helps model genetic equilibrium in evolving populations, and calculate allele frequencies.