Mechanisms of Evolution

Hardy-Weinberg Equilibrium

The Hardy-Weinberg principle states that in the absence of evolution, allele and genotype frequencies will remain constant.
The Hardy-Weinberg principle, named after the scholars who introduced the idea, states that if a population is not evolving, the allele and genotype frequencies will not change between generations. An allele is a version of a gene, and a genotype is the genetic makeup of an individual. The mechanisms of evolution all have one thing in common: They all change the frequency of at least one gene within a population (interbreeding group). As long as the frequency of one gene has changed between generations, evolution has occurred. In the case that no evolution is occurring, which is rare in natural populations, a population is said to have reached Hardy-Weinberg equilibrium. Formally defined, Hardy-Weinberg equilibrium is the state of a population in which allele and genotype frequencies do not change between generations because evolution is not occurring.

In addition, if a population is in Hardy-Weinberg equilibrium, the genotype frequencies are predictable based on the allele frequencies. Because the frequency of genes does not change between generations, knowing the frequencies in one generation allows for accurate calculations of the frequencies in each successive generation as long as the population stays in equilibrium. This is significant because the Hardy-Weinberg principle can be applied and the values compared with genotype frequencies of a real population to answer the question, "is this population evolving?"

Conditions of Hardy-Weinberg Equilibrium

In order for the Hardy-Weinberg equilibrium to occur, there needs to be no mutation, no natural selection, random mating, no genetic drift, and no gene flow within the population.
Hardy-Weinberg equilibrium requires the complete absence of evolution (genetic change between generations). This would indicate that none of the forces of microevolution, such as natural selection, gene flow, genetic drift, and mutation (direct change in DNA sequence), are operational. A population is considered to be in Hardy-Weinberg equilibrium if, for a gene or locus (location on a chromosome) of interest, there is no change in genotype or allele frequency. An allele is a version of a gene, and a genotype is the genetic makeup of an individual. The frequencies are the proportion of occurrences of a particular allele or genotype within a population. From the perspective of a whole genome, a population would never be in Hardy-Weinberg equilibrium. Hardy-Weinberg equilibrium requires the following:
  • No mutation
  • No natural selection
  • Random mating
  • No genetic drift (very large populations are less affected by random events)
  • No gene flow

These requirements are very difficult to meet in natural populations. However, the Hardy-Weinberg principle is a useful tool for determining whether a population is evolving at a particular site.

Allele Frequencies and Using Hardy-Weinberg

An allele frequency is how often certain genes appear in the population. This is used to calculate whether or not the alleles are changing.
To know whether evolution is occurring at a particular on a chromosome, one must know whether alleles or genotype frequencies are changing. An allele is a version of a gene, and a genotype is the genetic makeup of an individual. Genotype frequency is the proportion of individuals in the population that have a particular genotype. The first step is to calculate the current genotype and allele frequencies. Then, that information can be used to predict what the genotype frequencies should be in Hardy-Weinberg equilibrium (the state in which allele and genotype frequencies do not change). If the predicted genotype frequencies match the actual genotype frequencies of a population, then evolution is not occurring at that locus. For example, a butterfly population might have some butterflies that are blue (BB), some that are purple (Bb), and some that are pink (bb).
Calculating genotype frequencies (the proportion of individuals in the population with a particular genotype) involves counting the number of individuals of a genotype and dividing by the total population.
To calculate the genotype frequencies, count the number of individuals with each genotype and divide by the total number of individuals. In this example population, the genotype frequencies are:
BB=1/10=0.1or10%Bb=3/10=0.3or30%bb=6/10=0.6or60%\begin{array}{l}\mathrm{BB}\;=\;1/10\;=\;0.1\;\mathrm{or}\;10\%\;\\\mathrm{Bb}\;=\;3/10\;=\;0.3\;\mathrm{or}\;30\%\;\\\mathrm{bb}\;=\;6/10\;=\;0.6\;\mathrm{or}\;60\%\end{array}
To calculate the allele frequencies, look at the alleles B and b individually. Each locus has two spots for alleles, so calculate the proportion of all available spots that are filled by a particular allele. In this case, it is 20 spots. BB individuals have two spots and both are filled with a B, so they get counted twice for the B allele. Each Bb butterfly has one spot filled with a B, so they get counted once. The same logic applies for b. In this example population, the allele frequencies are as follows:
B=((2×1)+(1×3))/20=0.25or25%b=((2×6)+(1×3))/20=0.75or75%\begin{array}{l}\mathrm B\;=\;((2\times1)+(1\times3))/20\;=\;0.25\;\mathrm{or}\;25\%\;\\\mathrm b\;=\;((2\times6)+(1\times3))/20\;=\;0.75\;\mathrm{or}\;75\%\end{array}
The genotype frequencies always add up to 1, or 100%. This is because they are proportions of the whole population. The same is true for allele frequencies.

Next, to predict what the genotype frequencies should be if the population was in Hardy-Weinberg equilibrium, consider the entire gene pool (set of genes of the population).

Assuming random mating, there is a 25% chance that a sperm from this population will be B and a 75% chance that a sperm will be b. The same probabilities apply to eggs from this population. Use a diagram similar to a Punnett square to calculate the expected genotype frequencies of the next generation. A Punnett square is used to calculate the expected genotype frequencies of offspring from two parents. These same principles can apply to an entire gene pool.
Applying the principles behind a Punnett square allows the prediction of genotype frequencies (proportions of individuals with a certain genotype) for the entire gene pool under Hardy-Weinberg equilibrium. The genotype frequencies are calculated for the population and applied individually to each allele in the Punnett square (0.25 for B, 0.75 for b).
The expected genotype frequencies are as follows:
BB=(allelefrequencyofB)×(allelefrequencyofB)=(0.25)2=0.06Bb=((allelefrequencyofB)×(allelefrequencyofb))×2=2(0.25)(0.75)=0.38bb=(allelefrequencyofb)×(allelefrequencyofb)=(0.75)2=0.56\begin{array}{l}\mathrm{BB}\;=\;(\mathrm{allele}\;\mathrm{frequency}\;\mathrm{of}\;\mathrm B)\;\times\;(\mathrm{allele}\;\mathrm{frequency}\;\mathrm{of}\;\mathrm B)\;=\;(0.25)^2\;=\;0.06\;\\\mathrm{Bb}\;=\;((\mathrm{allele}\;\mathrm{frequency}\;\mathrm{of}\;\mathrm B)\;\times\;(\mathrm{allele}\;\mathrm{frequency}\;\mathrm{of}\;\mathrm b))\;\times\;2\;=\;2(0.25)(0.75)\;=\;0.38\;\\\mathrm{bb}\;=\;(\mathrm{allele}\;\mathrm{frequency}\;\mathrm{of}\;\mathrm b)\;\times\;(\mathrm{allele}\;\mathrm{frequency}\;\mathrm{of}\;\mathrm b)\;=\;(0.75)^2\;=\;0.56\end{array}
Traditionally, Hardy-Weinberg formulas use the letters p and q to represent the dominant and recessive allele frequencies, respectively. So, the expected genotype frequencies of the population are as follows:
BB=p2=0.06Bb=2pq=0.38bb=q2=0.56\begin{array}{l}\mathrm{BB}\;=\;\mathrm p^2\;=\;0.06\;\\\mathrm{Bb}\;=\;2\mathrm{pq}\;=\;0.38\;\\\mathrm{bb}\;=\;\mathrm q^2\;=\;0.56\end{array}
Because these values are proportions, they must equal 1. At this point, it is evident where the values in the Hardy-Weinberg formula for genotype frequencies come from: p2+2pq+q2=1\mathrm p^2\;+\;2\mathrm{pq}\;+\;\mathrm q^2\;=\;1 . The formula for allele frequencies must also always equal 1: p+q=1\mathrm p+\mathrm q=1 . Last, compare the observed genotype frequencies with the calculated expected frequencies. The values are close but not the same. From this, it is possible to conclude that some evolution is happening at this locus.

Observed vs. Expected Hardy-Weinberg Frequencies

Observed Genotype Frequencies Expected Under H-W Equilibrium
BB 0.10 0.06
Bb 0.30 0.38
bb 0.60 0.56

The frequencies of each allele are observed, and then a Punnett square is used to calculate the expected frequencies under Hardy-Weinberg (H-W) equilibrium. The observed frequencies in the butterfly population are close to the expected frequencies calculated under Hardy-Weinberg equilibrium but not exactly the same. Therefore, this locus is undergoing evolution.