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Chapter 18: Problem 8

In a population of mice, there are two alleles of the \(A\) locus \(\left(A_{1} \text { and } A_{2}\right) .\) Tests showed that, in this population, there are 384 mice of genotype \(A_{1} / A_{1}, 210\) of \(A_{1} / A_{2}\) and 260 of \(A_{2} / A_{2}\). What are the frequencies of the two alleles in the population?

Short Answer

Expert verified
The frequencies are 0.5725 for allele \(A_1\) and 0.4274 for allele \(A_2\).

Step by step solution

01

Understand the total number of mice

To find the frequency of each allele, first determine the total number of mice in the population. Add up the number of mice for each genotype: \(384 { (A_1/A_1)} + 210 { (A_1/A_2)} + 260 { (A_2/A_2)} = 854\).
02

Calculate allele frequency for A1

Calculate the frequency of allele \(A_1\). Each \(A_1/A_1\) mouse has 2 copies of \(A_1\), and each \(A_1/A_2\) mouse has 1 copy. Use the formula: \[\text{Number of } A_1 \text{ alleles} = 2 \times 384 + 1 \times 210 = 768 + 210 = 978\]. Then divide by the total number of allele copies, which is twice the number of mice (854): \(\text{Frequency of } A_1 = \frac{978}{1708} = 0.5725\).
03

Calculate allele frequency for A2

Calculate the frequency of allele \(A_2\). Each \(A_2/A_2\) mouse has 2 copies of \(A_2\), and each \(A_1/A_2\) mouse also has 1 copy. Use the formula: \[\text{Number of } A_2 \text{ alleles} = 2 \times 260 + 1 \times 210 = 520 + 210 = 730 \]. Then divide by the total number of allele copies, which is twice the number of mice (854): \(\text{Frequency of } A_2 = \frac{730}{1708} = 0.4274\).

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Key Concepts

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

Allele Frequency
Allele frequency is a key concept in understanding genetic variation within a population. It refers to how common a particular allele is among all the alleles for a given gene.
For example, consider a population of mice. Each mouse has two alleles at a genetic locus, one from each parent.
  • To calculate allele frequencies, you first need to determine how many of each allele there are in the population.
  • To do this, count the alleles for each genotype and add them up.
  • Each homozygous individual (like those with genotype \(A_1/A_1\) or \(A_2/A_2\)) contributes two alleles of the same type.
  • Heterozygous individuals (like \(A_1/A_2\)) contribute one allele of each type.
The total number of alleles is twice the number of individual organisms (since each has two alleles). In our case:
  • Total alleles = 2 \times 854 = 1708.
Once you know the contributions of each genotype, finding the allele frequencies involves dividing these numbers by the total number of alleles. This gives you a value between 0 and 1, representing the proportion of that allele in the population.
Genotype
Genotype refers to the genetic makeup of an organism in terms of its alleles. Each organism has a specific combination of alleles at a given gene locus, which determines its genotype.
In our mouse population, genotypes are the specific pairings of the alleles \(A_1\) and \(A_2\) at the locus under consideration.
  • There are homozygous genotypes like \(A_1/A_1\) and \(A_2/A_2\), which consist of identical alleles.
  • The heterozygous genotype \(A_1/A_2\) contains different alleles.
The genotypic composition of a population can affect allele frequencies and vice versa. The principle of how allele frequencies translate into genotype frequencies is fundamental to understanding Hardy-Weinberg equilibrium. This states that in the absence of disturbances such as selection, mutations, migration, or genetic drift, allele and genotype frequencies remain constant over generations, provided that the population is sufficiently large and mating is random.
Population Genetics
Population genetics is a branch of genetics that studies the distribution and changes of allele and genotype frequencies in populations. It forms a crucial part of evolutionary biology.
  • Population genetics uses mathematical models to predict the genetic makeup of populations over time.
  • These models assess factors such as natural selection, genetic drift, mutations, and gene flow.
One key tool in population genetics is the Hardy-Weinberg principle, which serves as a null hypothesis for the genetic structure of a population. According to this principle, if a population is not affected by evolutionary influences, allele and genotype frequencies will remain constant. Understanding these dynamics helps us make predictions about how populations may respond to changes in their environment, such as new selective pressures or changing mating habits. By monitoring allele and genotype frequencies, scientists can study how genetic traits are propagated, assess evolutionary relationships, and identify populations or species that could be at risk of decline due to genetic factors.

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Most popular questions from this chapter

Using pedigree diagrams, calculate the inbreeding coefficient ( \(F\) ) for the offspring of (a) parent-offspring matings; (b) first-cousin matings; (c) aunt-nephew or uncleniece matings; (d) self-fertilization of a hermaphrodite.

The sd gene causes a lethal disease of infancy in humans when homozygous. One in 100,000 newborns die each year of this disease. The mutation rate from \(S d\) to sd is \(2 \times 10^{-4}\). What must the fitness of the heterozygote be to explain the observed gene frequency in view of the mutation rate? Assign a relative fitness of 1.0 to \(S d / S d\) homozygotes. Assume that the population is at equilibrium with respect to the frequency of sd.

The recombination fraction \((r)\) between linked loci \(A\) and \(B\) is \(0.25 .\) In a population, we observe the following haplotypic frequencies: $$\begin{aligned}&0.49\\\&A B\\\&a B \quad 0.49\\\&A b \quad 0.00\\\&a b \quad 0.02\end{aligned}$$ a. What is the level of linkage disequilibrium as measured by \(D\) in the present generation? b. What will \(D\) be in the next generation? c. What is the expected frequency of the \(A b\) haplotype in the next generation?

A group of 50 men and 50 women establish a colony on a remote island. After 50 generations of random mating, how frequent would a recessive trait be if it were at a frequency of \(1 / 500\) back on the mainland? The population remains the same size over the 50 generations, and the trait has no effect on fitness.

In a population of a beetle species, you notice that there is a 3: 1 ratio of shiny to dull wing covers. Does this ratio prove that the shiny allele is dominant? (Assume that the two states are caused by two alleles of one gene.) If not, what does it prove? How would you elucidate the situation?
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