Population Genetics

Hardy-Weinberg Theory and Population Genetics

Evolution may be expressed as a change in gene frequency from one generation to the next in a population. Gene frequency is the frequency of an allele at a given locus in a population. Changes in gene frequency may be brought about by:

Consider an allele (A) at a given locus, with an alternate allele (a) located at the same locus. Let the proportion of the (A) allele in the population be p and the proportion of the (a) allele be q. Let us assume that this is not a multiple allelic series and that chromosomes with (A) plus all chromosomes with (a) will constitute the entire set of chromosomes in the population with respect to (A) and (a). Then: p + q = 1.

Observe the above population of individuals. Each individual has two copies of the A gene. The big A allele or the little a allele.

An individual in a diploid population which reproduces sexually is the result of one male gamete plus one female gamete being combined to form a zygote. If the mating is random, the proportions of genes in the gametes will determine the proportion of genotypes in the population. Therefore, genotype proportions in our simple 2 allele situation should be expressed by squaring the sum of the allele proportions in a simple binomial as follows:

(p + q)2 = p2 + 2 pq + q2 = 1

AA individuals = p2

Aa individuals = 2 pq

aa individuals = q2

What are five assumptions which must be made for genetic equilibrium to occur between successive generations?

Natural selection is one of the main factors, resulting in changes in gene proportions. Natural selection may take many different degrees from completely lethal to very slight. Ordinarily, however, natural selection is probably rather subtle in its action, being recognized as one population having a very slight reproductive advantage over another. The effects of selection are often illustrated by using an extreme example such as a completely lethal recessive. This situation represents complete selection against a certain genotype.

It is possible to calculate the effects of complete selection against the homozygous recessive genotype using a modification of the basic Hardy-Weinberg equation. Without going into the derivation of this formula, it may be expressed as follows:

qn = proportion of recessive allele after n generations of selection

qo = original frequency of the recessive allele

 

Note: This modified expression derived from the Hardy-Weinberg may only be used in situations where the homozygous recessive individuals do not reproduce.

- Define p.
- Define q.
- Define p2; 2pq; q2.
- In what ways do the above definitions differ?

Demonstration of the Hardy-Weinberg Equilibrium

The following exercise, if carried out and understood, will provide you with an understanding of the basic Hardy-Weinberg equilibrium and at the same time illustrate the effects of several kinds of selection on this equilibrium.

Set up a population (generation 0) made up of 100 diploid individuals. The genotype of any one of these individuals may be represented using two beans, in various combinations, as follows:

Genotype
White beans
Red beans
homozygous dominant AA
2
0
heterozygous Aa
1
1
homozygous recessive aa
0
2

The population of 100 individuals will therefore be made up of 200 alleles (beans). Let the proportion of genotypes in these 100 individuals (200 beans) be 25% AA, 50% Aa and 25% aa. Make up the 200 beans in the appropriate proportions.

25 AA individuals
50 white beans
  
50 Aa individuals
50 white beans
50 red beans
25 aa individual
  
50 red beans
100 Individuals
100 white beans
100 red beans

Questions:

  1. In terms of population genetics, what do the beans in this beaker represent?
  2. What is the value of p (proportion of dominant allele) in the population?
  3. What is the value of q (proportion of recessive allele)?
  4. In generation one, according to the Hardy-Weinberg equation, what will be the proportion of homozygous dominant, heterozygous and homozygous recessive individuals?
  5. Are the proportions of these three genotypes the same in generation one as in generation 0?
  6. Is this always the case (consider a population at generation 0 made up of 30% AA, 67% Aa, 3% aa, or a population made up of 0% AA, 100% Aa, 0% aa).
  7. How many generations does it take for a population to reach a state of Hardy-Weinberg equilibrium if it is not already in equilibrium? -
  8. What assumptions do you make concerning mating, selection, mutation, emigration and immigration for this equilibrium to hold true?
  9. What is the evolutionary significance of this equilibrium?

Answers to the above:

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