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Chapter 25: Problem 34

In German cockroaches, curved wing \((c v)\) is recessive to normal wing \(\left(c v^{+}\right) .\) Bill, who is raising cockroaches in his dorm room, finds that the frequency of the gene for curved wings in his cockroach population is \(0.6 .\) In his friend Joe's apartment, the frequency of the gene for curved wings is \(0.2 .\) One day Joe visits Bill in his dorm room, and several cockroaches jump out of Joe's hair and join the population in Bill's room. Bill estimates that now, \(10 \%\) of the cockroaches in his dorm room are individual roaches that jumped out of Joe's hair. What is the new frequency of curved wings among cockroaches in Bill's room?

Short Answer

Expert verified
The new frequency of curved wings in Bill's cockroach population is 0.56.

Step by step solution

01

Understand Initial Conditions

To solve this, first understand that in Bill's population, the initial frequency of the gene for curved wings is 0.6, and in Joe's population it is 0.2. After cockroaches from Joe's population join Bill's, 10% of the new population is made up of cockroaches from Joe's population.
02

Calculate Contribution from Joe's Population

The contribution of Joe's population to the new gene frequency is given by their proportion in the total and their gene frequency. Since 10% of the new population are from Joe's, this contribution is \(0.1 \times 0.2 = 0.02\).
03

Calculate Contribution from Bill's Initial Population

The remaining 90% of the population is from Bill's original population with a frequency of 0.6. Hence, their contribution to the new gene frequency is \(0.9 \times 0.6 = 0.54\).
04

Sum the Contributions

The new frequency of the gene for curved wings is the sum of the contributions from both populations: \(0.02 + 0.54 = 0.56\).

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Key Concepts

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

Allele Frequency
Allele frequency refers to how common an allele is in a population. It tells us the proportion of all copies of a particular gene in a population that are one specific variant, or allele, of that gene. To grasp this better, imagine a bowl filled with marbles of different colors, representing different alleles. The frequency of each color (or allele) shows how often they appear in the bowl.
  • For example, if allele 'A' is present in 60% of the bowl's marbles, the frequency of allele 'A' is 0.6.
  • This concept was used to find how often the curved wing allele appeared among cockroaches in Bill's and Joe's populations.
Understanding allele frequency helps geneticists predict how likely an inherited trait might be in a population. Changes in these frequencies can indicate evolutionary changes.
Population Genetics
Population genetics is a field of biology that studies the genetic composition of populations, and how it changes over time. It looks at the distribution and changes of allele frequency, due to factors like mutation, natural selection, genetic drift, and gene flow.

One practical application of population genetics is figuring out how different factors affect the genetic diversity of a species. Imagine looking at all the genes in a large group of organisms as if examining a complex puzzle.
  • Each different piece represents different genes and alleles in that population.
  • When external influences, like cockroaches jumping from Joe's head to Bill's population, occur, they can affect which pieces (or alleles) become more prevalent or disappear over time.
This area of genetics helps scientists understand real-world phenomena, such as why certain species are more susceptible to diseases or how they adapt to changes in their environment.
Gene Flow
Gene flow, also called gene migration, is the transfer of genetic material from one population to another. It introduces new genes into a population, which can increase genetic diversity and potentially affect allele frequencies.

In the example of Bill and Joe's cockroaches, gene flow occurred when the roaches jumped out of Joe's hair, introducing new genetic material into Bill's population.
  • This caused a new allele frequency because the new cockroaches mixed and reproduced with Bill's.
  • Bill's new probability of the curved wing trait ( ) thus considered the proportion from Joe's population in the calculation.
Gene flow is essential for evolution and adaptation, as it allows for the exchange of genetic traits that may help populations survive changes in their environment. It can prevent populations from becoming genetically distinct and isolated.

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Most popular questions from this chapter

What assumptions must be met for a population to be in Hardy-Weinberg equilibrium?

The frequency of allele \(A\) in a population is 0.8 , and the frequency of allele \(a\) is \(0.2 .\) If the population mates randomly with respect to this locus, give all the possible matings among the genotypes at this locus and the expected proportion of each type of mating.

Compare and contrast the effects of mutation, migration, genetic drift, and natural selection on genetic variation within populations and on genetic divergence between populations.

Color blindness in humans is an X-linked recessive trait. Approximately \(10 \%\) of the men in a particular population are color blind. a. If mating is random with respect to the color-blindness locus, what is the frequency of the color-blindness allele in this population? b. What proportion of the women in this population are expected to be color blind? c. What proportion of the women in this population are expected to be heterozygous carriers of the color-blindness allele?

A certain form of congenital glaucoma is caused by an autosomal recessive allele. Assume that the mutation rate is \(10^{-5}\) and that people with this condition produce, on the average, only about \(80 \%\) of the offspring produced by people who do not have glaucoma. a. At equilibrium between mutation and selection, what will the frequency of the gene for congenital glaucoma be? b. What will the frequency of the disease be in a randomly mating population that is at equilibrium?
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