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(a) Calculate the observed genotypic and allelic frequencies for this population.

(b) Calculate the numbers of genotypes expected if this population were in Hardy-Weinberg equilibrium.

(c) Using a chi-square test, determine whether the population is in Hardy-Weinberg equilibrium.

(a) The observed genotypic and allelic frequencies are calculated by using Equations 23.1 and 23.3:

(b) If the population is in Hardy-Weinberg equilibrium, the expected numbers of genotypes are:

(c) The observed and expected numbers of the genotypes are:

Genotype Number observed Number expected

HH 40 28.57

Hh 45 67.07

hh 50 39.37

These numbers can be compared by using a chi-square test:

The degrees of freedom associated with this chi-square value are n — 2, where n equals the number of expected genotypes, or 3 — 2 = 1. By examining Table 3.4, we see that the probability associated with this chi-square and the degrees of freedom is P < .001, which means that the difference between the observed and expected values is unlikely to be due to chance. Thus, there is a significant difference between the observed numbers of genotypes and the numbers that we would expect if the population were in Hardy-Weinberg equilibrium. We conclude that the population is not in equilibrium.

2. A recessive allele for red hair (r) has a frequency of .2 in population I and a frequency of .01 in population II. A famine in population I causes a number of people in population I to migrate to population II, where they reproduce randomly with the members of population II. Geneticists estimate that, after migration, 15% of the people in population II consist of people who migrated from population I. What will be the frequency of red hair in population II after the migration?

From Equation 23.16, the allelic frequency in a population after migration (qii) is qn = qi(m) + qn(1 — m)

where qI and qII are the allelic frequencies in population I (migrants) and population II (residents), respectively, and m is the proportion of population II that consist of migrants. In this problem, the frequency of red hair is .2 in population I and .01 in population II. Because 15% of population II consists of migrants, m = .15. Substituting these values into Equation 23.16, we obtain:

q'n = .2(.15) + (.01)(1 — .15) = .03 + .0085 = .0385

This is the expected frequency of the allele for red hair in population II after migration. Red hair is a recessive trait; if mating is random for hair color, the frequency of red hair in population II after migration will be:

3. Two populations have the following numbers of breeding adults:

Population A: 60 males, 40 females Population B: 5 males, 95 females

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