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Chapter 22: 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: 18%

Step by step solution

01

Understand Hardy-Weinberg equilibrium equation

The Hardy-Weinberg equilibrium equation is given by the formula: \(p^2 + 2pq + q^2 = 1\), where p is the frequency of the dominant allele, q is the frequency of the recessive allele, \(p^2\) represents the frequency of homozygous dominant individuals, \(2pq\) represents the frequency of heterozygous individuals, and \(q^2\) represents the frequency of homozygous recessive individuals in a population.
02

Calculate frequency of homozygous recessive individuals

We are given that \(81 \%\) of the population are homozygous recessive individuals. To get the frequency, we need to convert this percentage into a decimal. So, \(q^2 = 0.81\).
03

Calculate frequency of recessive allele

To find the frequency of the recessive allele (q), take the square root of the frequency of homozygous recessive individuals: \(q = \sqrt{q^2} = \sqrt{0.81} = 0.9\).
04

Calculate frequency of dominant allele

Since there are only two types of alleles for a locus in the Hardy-Weinberg equilibrium, we can calculate the frequency of the dominant allele (p) using the formula: \(p = 1 - q\). So, \(p = 1 - 0.9 = 0.1\).
05

Calculate frequency of heterozygous individuals

Now, we can use the Hardy-Weinberg equilibrium equation to find the frequency of heterozygous individuals (2pq): \(2pq = 2 \times 0.1 \times 0.9 = 0.18\).
06

Convert frequency into percentage

Finally, to express the frequency of heterozygous individuals as a percentage, multiply the frequency by 100: \(0.18 \times 100 = 18 \%\). So, we would expect \(18 \%\) of the individuals in the next generation to be heterozygous for this locus.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Homozygous Recessive Individuals
Homozygous recessive individuals are key to understanding genetic variations in a population. These are individuals who carry two copies of the same recessive allele for a specific gene. When considering the Hardy-Weinberg equilibrium, which serves as a model for genetic distribution in a population, homozygous recessive individuals are represented by the term \(q^2\) in the equation. This model assumes no evolution is occurring—that is, the frequencies of alleles (gene variants) do not change over time.

In practical terms, if 81% of a population are homozygous recessive, this tells us the frequency of this genetic trait within that group. It's quite straightforward to evaluate the presence of this trait in future generations by using the Hardy-Weinberg equation, which in turn helps predict genetic diversity and potential for genetic diseases linked to recessive alleles.
Allele Frequency
Allele frequency is the cornerstone of population genetics. It measures how common a particular allele—or version of a gene—is in a population. Two frequencies are at play: one for the dominant allele (represented by \(p\)) and one for the recessive allele (\(q\)). These frequencies are crucial because they determine the genetic variability and potential evolutionary changes in a group of organisms.

The Hardy-Weinberg equation, \(p^2 + 2pq + q^2 = 1\), hinges on the fact that the sum of these probabilities (p and q) is 1, or 100 percent. When the allele frequencies are known, as in our exercise where \(q\) was calculated to be 0.9, scientists can gauge the genetic makeup of the next generation—helping to predict prevalence of diseases, response to selection pressures, or even how a population might adapt to environmental changes.
Heterozygous Individuals
Heterozygous individuals possess two different alleles for a given gene, one from each parent. In terms of the Hardy-Weinberg equilibrium, these individuals are significant because their genetic makeup includes both dominant and recessive alleles, represented by \(2pq\) in the formula. This heterozygosity is essential for maintaining genetic diversity within a population, contributing to the ability of a species to adapt and survive in changing environments.

Knowing the percentage of heterozygous individuals, like the 18% calculated in the exercise, provides insight into the genetic structure of a population. This balance between homozygosity and heterozygosity shapes the overall genetic health and resilience against potential threats, such as diseases or changes in habitat.

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Most popular questions from this chapter

Review the Chapter Concepts on page \(457 .\) 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.

In a recent study of cichlid fish inhabiting Lake Victoria in Africa, Nagl et al. (1998. Proc. Natl. Acad. Sci. IUSA/ 95: \(14,238-14,243\) ) examined suspected neutral sequence polymorphisms in noncoding genomic loci in 12 species and their putative river-living ancestors. At all loci, the same polymorphism was found in nearly all of the tested species from Lake Victoria, both lacustrine and riverine. Different polymorphisms at these loci were found in cichlids at other African lakes. (a) Why would you suspect neutral sequences to be located in noncoding genomic regions? (b) What conclusions can be drawn from these polymorphism data in terms of cichlid ancestry in these lakes?

The genetic difference between two Drosophila species, \(D\). heteroneura and \(D .\) sylvestris, as measured by nucleotide diversity, is about 1.8 percent. The difference between chimpanzees (P. troglodytes) and humans (H. sapiens) is about the same, yet the latter species are classified in different genera. In your opinion, is this valid? Explain why.

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 Hardy-Weinberg 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?

Achondroplasia is a dominant trait that causes a characteristic form of dwarfism. In a survey of 50,000 births, five infants with achondroplasia were identified. Three of the affected infants had affected parents, while two had normal parents. Calculate the mutation rate for achondroplasia and express the rate as the number of mutant genes per given number of gametes.
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