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Hardy-Weinberg Equilibrium: Definition, Equation & Evolutionary Agents

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  • 0:00 Population Genetics Background
  • 0:37 The Hardy-Weinberg Equilibrium
  • 1:45 The Hardy-Weinberg Equation
  • 6:08 Different Evolutionary Agents
  • 7:24 Lesson Summary
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Lesson Transcript
Instructor: Angela Hartsock

Angela has taught college Microbiology and has a doctoral degree in Microbiology.

In this lesson we will define Hardy-Weinberg equilibrium and break down the Hardy-Weinberg equation to figure out if a population of hypothetical beetles is evolving.

Population Genetics Background

Let's say we're studying a large group of beetles, 86% of which are green, 14% are brown. What will the percentage be in future generations? Why? Now we're thinking in terms of population genetics. Population genetics is the study of the allelic, genotypic, and phenotypic variation in a population. It tells us something about how populations are evolving and can help us make predictions about what's driving evolution.

The Hardy-Weinberg Equilibrium

The Hardy-Weinberg equilibrium gives us a tool to observe how populations evolve (or don't). It states that the frequencies of alleles and genotypes will stay the same through the generations as long as there are no evolutionary influences. In other words, our beetles will stay 86% green over time as long as the following requirements are met:

  1. Mating must be random
  2. Population size must be large, so one individual isn't accounting for a significant portion of the gene pool
  3. No migration, meaning individuals can't be entering or leaving the population
  4. No random mutations in the genes being studied
  5. No natural selection on the genes being studied

As long as our beetles follow these tenets, they will be in a Hardy-Weinberg equilibrium. You can imagine that on our unpredictable planet this kind of stability isn't the norm. So what good is this concept? Well, it gives us a sort of baseline. If the population deviates from the equilibrium, we'll know something is up in terms of evolution.

The Hardy-Weinberg Equation

The Hardy-Weinberg equation allows us to calculate and predict genotype frequencies in large populations satisfying the equilibrium requirements. The Hardy-Weinberg equation is:

The Hardy-Weinberg equation
hardy-weinberg equation

For a gene with two possible alleles, p and q represent the allelic frequency. Since we're dealing with frequencies and probabilities, the equation adds up to 1.

Let's use a diagram to see how this equation works with our beetles. There are only two alleles controlling the green and brown phenotype: 'A,' the dominant green allele, and 'a,' the recessive brown allele. We have 1,000 beetles in our parent population: 360 are green with the genotype AA, 480 are green with the genotype Aa, and 160 are brown with the genotype aa. So we can calculate the frequency of each genotype by dividing the number of each genotype by 1,000, giving us 0.36, 0.48, and 0.16.

A hypothetical beetle population to illustrate Hardy-Weinberg equilibrium.
Image of equilibrium in a hypothetical population

But what's the frequency of each allele? Remember, each genotype includes the two inherited alleles. For the AA and aa genotypes, every individual has two identical alleles, so the allelic frequency for those members can just be carried over from the genotype frequencies (0.36 and 0.16). For the Aa genotype, half the alleles will be A and half will be a, so we will split that frequency (0.48) in half for each allele and add it to the frequencies from our AA and aa individuals.

The frequency of 'A:' 0.24 + 0.36 = 0.6

The frequency of 'a:' 0.24 + 0.16 = 0.4

Now we can say that the frequency of 'A' is 0.6 and the frequency of 'a' is 0.4. If we randomly pick a beetle from our population, there is a 60% chance it carries an 'A' allele and a 40% chance it carries an 'a' allele.

The power of the Hardy-Weinberg equation comes when our population starts producing offspring. Now we can look at our offspring to see if the allele frequencies match the parent generation. We can use the Hardy-Weinberg equation to predict what our allele frequencies would be in the absence of evolutionary pressure on our allele of interest. Every mother and father in our parent generation has a 60% chance of passing on an 'A' allele (assigned as p in our equation) and a 40% chance of passing on an 'a' allele (assigned as q in our equation).

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