Hardy-Weinberg Equilibrium Theory

The Hardy-Weinberg Equilibrium Theory is a simple mathematical model for the modern definition of evolution  that can be used to track the changes in allele frequencies within a population from one generation to the next. It is based on the idea of that no evolution– genetic equilibrium–is statistically unlikely. However, the hypothetical instance of no evolution can serve as a baseline in order to estimate and predict instances of allele frequency changes (evolutionary change) in descendent populations solely based on the proportion of phenotypic variances within a population (Jurmain 2010:438).

The modern theory of evolution, called the Modern Synthesis, combines Darwin’s theory of trait inheritance and natural selection with population genetics. The modern scientific definition of evolution: a change in allele frequencies from one generation to the next in the gene pool of a population. Or, in other words, evolution is the sum total of the genetically inherited changes in individual members of a population. The effects of evolution are felt by individuals but it is only a population as a whole that actually evolves from one generation to the next.

What is genetic equilibrium?

There is genetic equilibrium (e.g. no evolution) in the gene pool of a population only if ALL of following seven factors are true:

  1. There is no genetic mutation occurring
  2. There is no natural selection acting on inherited traits, making some organisms in the gene pool reproductively more successful than others
  3. The population is infinitely large (genetic drift is not possible)
  4. All members of the population breed
  5. All mating is totally random–there is no nonrandom mating (e.g. sexual selection)
  6. Everyone in the population produces the same number of offspring
  7. There is no migration in or out of the population (no gene flow)

Since it is unlikely that there exists a population where any one of these things would be true, let alone all of them, evolution is believed to be inevitable. The Hardy-Weinberg Equilibrium Theory uses the concept of genetic equilibrium as a baseline to predict the probabilities of allele frequencies occurring in a descendent population based on the genetic frequencies of their parents.

How the Hardy-Weinberg Equilibrium Equation is used

The  Hardy-Weinberg Equilibrium Equation is used to discover the probable genotype frequencies in a population even if only the phenotypic frequencies are available. I can also be used to predict the genotypic frequencies in future generations of a population. The Hardy-Weinberg Equilibrium Equation was developed in the early 20th Century independently by Godfrey Hardy in England and Wilhelm Weinberg in Germany.

What prompted Hardy and Weinberg to independently come up with a theory of genetic equilibrium?

By the early 20th century, the simple Mendelian rules of dominance or recessiveness were understood. Geneticists used “Punnett squares” (see the image above) to show the probability of gene frequencies in offspring based on the known genotypes of their parents. The Hardy-Weinberg equation allowed geneticists to do the same thing for entire populations.

Hardy-Weinberg Equation: p2 + 2pq + q2 = 1

p = the probability of the frequency of the dominant allele for homozygous (AA) and half for heterozygous (1/2Aa)

q = the probability of the frequency of the recessive allele for homozygous (aa) and half for heterozygous (1/2Aa).

Because there are only two alleles, one from the mother and one from the father, both together must equal one: p + q = 1.

In this equation, is the predicted frequency of homozygous dominant (AA) people in a population, 2pq is the predicted frequency of heterozygous (Aa) people, and is the predicted frequency of homozygous recessive (aa) ones. 

“Despite the fact that evolution is a common occurrence in natural populations, allele frequencies will remain unaltered indefinitely unless evolutionary mechanisms such as mutation and natural selection cause them to change.  Before Hardy and Weinberg, it was thought that dominant alleles must, over time, inevitably swamp recessive alleles out of existence.  This incorrect theory was called “genophagy” (literally “gene eating”).  According to this wrong idea, dominant alleles always increase in frequency from generation to generation.  Hardy and Weinberg were able to demonstrate with their equation that dominant alleles can just as easily decrease in frequency.” (O’Neill 2011).

Resources

Darwin, Charles ( 2009 [1871]) The Descent of Man and Selection in Relation to Sex, Lawrence, KS: Neeland Media, LLC.

Jurmain, Robert, Lynn Kilgore, Wenda Trevanthan, Russell L. Ciochon (2010), Belmont, CA: Wadsworth CENAGE Learning, Inc.

O’Neill, Dennis (2011) “Hardy-Weinberg Equilibrium Model,” Palomar College, Retrieved from: http://anthro.palomar.edu/synthetic/synth_2.htm

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