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Chapter 25: Problem 9

In a population that meets the Hardy-Weinberg equilibrium assumptions, \(81 \%\) of the individuals are homozygous for a recessive allele. What percentage of the individuals would be expected to be heterozygous for this locus in the next generation?

Short Answer

Expert verified
Answer: In the next generation, 18% of individuals are expected to be heterozygous.

Step by step solution

01

Determine the frequency of homozygous recessive individuals (\(q^2\))

We are given that 81% of the population are homozygous recessive. To express this as a decimal we divide by 100: \(q^2 = \frac{81}{100} = 0.81\)
02

Find the frequency of the recessive allele (\(q\))

To find the frequency of the recessive allele (\(q\)), we need to take the square root of the frequency of homozygous recessive individuals (\(q^2\)): \(q = \sqrt{q^2} = \sqrt{0.81} = 0.9\)
03

Calculate the frequency of the dominant allele (\(p\))

Since there are only two alleles in this case (dominant and recessive), the frequency of the dominant allele (\(p\)) is equal to 1 minus the frequency of the recessive allele (\(q\)): \(p = 1 - q = 1 - 0.9 = 0.1\)
04

Calculate the frequency of heterozygous individuals (\(2pq\))

Now that we have the frequencies of the dominant (\(p\)) and recessive (\(q\)) alleles, we can use the Hardy-Weinberg equilibrium equation to find the frequency of heterozygous individuals (\(2pq\)): \(2pq = 2 \times 0.1 \times 0.9 = 0.18\)
05

Convert the frequency of heterozygous individuals to a percentage

To find the percentage of heterozygous individuals, we need to multiply the frequency of heterozygous individuals (\(2pq\)) by 100: Heterozygous percentage = \(0.18 \times 100 = 18\%\) The expected percentage of individuals that would be heterozygous for this locus in the next generation is 18%.

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Most popular questions from this chapter

Shown below are two homologous lengths of the alpha and beta chains of human hemoglobin. Consult a genetic code dictionary (Figure 13.7 ) and determine how many amino acid substitutions may have occurred as a result of a single nucleotide substitution. For any that cannot occur as a result of a single change, determine the minimal mutational distance.

A form of dwarfism known as Ellis-van Creveld syndrome was first discovered in the late 1930 s, when Richard Ellis and Simon van Creveld shared a train compartment on the way to a pediatrics meeting. In the course of conversation, they discovered that they each had a patient with this syndrome. They published a description of the syndrome in \(1940 .\) Affected individuals have a short-limbed form of dwarfism and often have defects of the lips and teeth, and polydactyly (extra fingers. The largest pedigree for the condition was reported in an Old Order Amish population in eastern Pennsylvania by Victor McKusick and his colleagues (1964). In that community, about 5 per 1000 births are affected, and in the population of \(8000,\) the observed frequency is 2 per \(1000 .\) All affected individuals have unaffected parents, and all affected cases can trace their ancestry to Samuel King and his wife, who arrived in the area in \(1774 .\) It is known that neither King nor his wife was affected with the disorder. There are no cases of the disorder in other Amish communities, such as those in Ohio or Indiana. (a) From the information provided, derive the most likely mode of inheritance of this disorder. Using the HardyWeinberg law, calculate the frequency of the mutant allele in the population and the frequency of heterozygotes, assuming Hardy-Weinberg conditions. (b) What is the most likely explanation for the high frequency of the disorder in the Pennsylvania Amish community and its absence in other Amish communities?

In a population of cattle, the following color distribution was noted: \(36 \%\) red \((R R), 48 \%\) roan \((R r),\) and \(16 \%\) white \((r r) .\) Is this population in a Hardy-Weinberg equilibrium? What will be the distribution of genotypes in the next generation if the Hardy-Weinberg assumptions are met?

List the barriers that prevent interbreeding and give an example of each.

Read the Chapter Concepts list on page \(681 .\) All these pertain to the principles of population genetics and the evolution of species. Write a short essay describing the roles of mutation, migration, and selection in bringing about speciation.
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