Genotype Frequencies and Allele Frequencies
The genotype frequency is a measure of the relative proportions of different genotypes within a population. Likewise, an allele frequency is simply a measure of the relative proportion of alleles within a population. Genotype frequencies are obtained by dividing the number of individuals with each genotype by the total number of individuals. For example, consider a hypothetical population of 200 people for the MN blood group system in which there are 98 people with genotype MM, 84 people with genotype MN, and 18 people with genotype NN. The genotype frequencies are therefore:
Frequency of MM = 98/200 = 0.49 Frequency of MN = 84/200 = 0.42 Frequency of NN = 18/200 = 0.09
Note that the total frequency of all genotypes adds up to 1 (0.49 + 0.42 + 0.09 = 1). These frequencies are proportions. If you find it easier to think about the frequencies in terms of percentages, then simply multiply the proportions by 100. Thus, we see that 0.49 X 100 = 49 percent of the population with genotype MM. Likewise, 42 percent have genotype MN, and 9 percent have genotype NN.
Allele frequencies are computed by counting the number of each allele and dividing that number by the total number of alleles. In the example here, the total number of alleles is 400 because there are 200 people, each with 2 alleles. To find out the number of M alleles for each genotype, count up the number of alleles for each genotype, and multiply that number by the number of people with that genotype. Finally, add up the number for all genotypes. In the example, 98 people have the MM genotype, and therefore 98 people have two M alleles. The total number of M alleles for people with the MM genotype is genotype is 98 X 2 = 196. For the MN genotype, 84 people have one M allele, giving a total of 84 X 1 = 84 M alleles. For the NN genotype, 18 people have no M alleles, for a total of 18 X 0 = 0 M alleles. Adding the number of M alleles for all genotypes gives a total of 196 + 84 + 0 = 280 M alleles. The frequency of the M allele is therefore 280/400 = 0.7. The frequency of the N allele can be computed in the same way, giving an allele frequency of 0.3. Note that the frequencies of all alleles must add up to 1.
Another example of allele frequency computation is given in Table.
The method of counting alleles to determine allele frequencies can be used only when the number of individuals with each genotype can be determined. If one of the alleles is dominant, this will not be possible, and we must use another method.
Example of Allele Frequency Computation
Imagine you have just collected information on MN genotypes for 250 humans in a given population. Your data are:
Number of MM genotype = 40
Number of MN genotype = 120 Number of NN genotype = 90
The allele frequencies are computed as follows:
Genotype Number of People
Total Number of Alleles
Number of M Alleles
Number of N Alleles
MM 40 80 80 0
MN 120 240 120 120
NN 90 180 0 180
Total 250 500 200 300
The relative frequency of the M allele is computed as the number of M alleles divided by the total number of alleles: 200/500 = 0.4. The relative frequency of the N allele is computed as the number of N alleles divided by the total number of alleles: 300/500 = 0.6.
As a check, note that the relative frequencies of the alleles must add up to 1.0 (0.4 + 0.6 = 1.0).
Hardy-Weinberg Equilibrium
Now that we have computed the allele frequencies for the MN blood group for our hypothetical population, we turn to the next question: What are the expected genotype frequencies in the next generation? If the population reproduces, what proportion of children in the next generation will have genotype MM ? What proportion will have MN, or NN ?
As shown in Chapter 2, we can easily answer this question for any specific pair of parents. For example, if a man with genotype MN mates with a woman with genotype MN, we expect that 25 percent of the offspring will have genotype MM, 50 percent will have genotype MN, and 25 percent will have genotype NN (see Figure 2.9). Extending this computation to the entire population means that we would need to consider all possible pairings (e.g., MM and MN, MM and NN, and so forth) and the number of each pairing (e.g., how many men with MN mate with women with MN, and so forth).
Reference: THE HUMAN SPECIES: An Introduction to Biological Anthropology; JOHN H.
RELETHFORD (Page: 44)
Although this might seem to be an overly complex question to answer, two scientists, G. H.
Hardy and W. Weinberg, independently arrived at a simple and elegant solution in 1908, known today as Hardy-Weinberg equilibrium. This is a mathematical statement that relates the allele frequencies in a population to the expected genotype frequencies in the next generation. It is best explained using a simple model of a single locus with two alleles, such as the MN blood group above. First, we need to know the allele frequencies, which were derived above as 0.7 for the frequency of the M allele and 0.3 for the frequency of the N allele. By convention, we use
the symbols p and q to refer to the allele frequencies, and in this case, p is shorthand for “the frequency of the M allele” and q is shorthand for “the frequency of the N allele.” Using these symbols, we say that p = 0.7 and q = 0.3.
The Hardy-Weinberg equilibrium model states that, given allele frequencies p and q, the expected genotype frequencies in the next generation are:
Frequency of the MM genotype = p2 Frequency of the MN genotype = 2 pq Frequency of the NN genotype = q2
For our hypothetical example (where p = 0.7 and q = 0.3), we can now predict the genotype frequencies in the next generation using these formulae:
Frequency of the MM genotype = p2 = (0.7)2 = 0.49
Frequency of the MN genotype = 2 pq = 2 x 0.7 x 0.3 = 0.42 Frequency of the N N genotype = q2 = (0.3)2 = 0.09
Thus, we expect that in the next generation, 49 percent of the offspring will have genotype MM, 42 percent will have genotype MN, and 9 percent will have genotype NN. You may have noticed something interesting about the above example. We started with a set of genotype frequencies for one generation, used them to compute the allele frequencies, and then used the allele frequencies to compute the genotype frequencies in the next generation. In this particular case, however, we wound up with the exact same genotype frequencies that we started with: MM _ 0.49, MN _ 0.42, NN _ 0.09. Nothing changed! If we started over and computed the allele frequencies for the next generation, we would still get the same results.
This shows an example of a subtle but important application of the Hardy-Weinberg model:
Given certain assumptions, the genotype and allele frequencies will remain the same from one generation to the next.
This may not appear to make a lot of sense because the model appears to predict no evolution!
After all, if we defi ne microevolution as a change in allele frequencies over time, and if Hardy- Weinberg predicts no change, then what relevance does this have? The relevance becomes clear when we go back and examine that critical phrase —given certain assumptions.
A population might not be in Hardy-Weinberg equilibrium for two basic reasons. Observed and expected genotype frequencies may differ because of the effects of evolutionary forces and/or nonrandom mating. Evolutionary forces are those mechanisms that can actually lead to a change in allele frequency over time. There are four evolutionary forces: mutation, natural selection, genetic drift, and gene flow (each is described in detail in the following section).
These four forces are the only mechanisms that can cause the frequency of an allele to change over time.
