Chapter 8, Problem 1PDT

a.

Summary Introduction

To calculate: The frequency of A₁ in generation 1 and 2, if the frequency in generation 0 is 0.4 and the frequency of 10 percent migrant population is 0.6.

Introduction: The movement of genetic variation from one population to another population is known as gene flow. Gene flow plays two important roles in evolution that equalizes allele frequencies to remove genetic differences between populations. It makes two populations more similar. The second effect of gene flow is to establish new alleles into a population from a different population. Dispersal is the movement of individual or gametes and results in gene flow.

Explanation of Solution

The given values are as follows:

• Suppose in generation 0, the number of armadillos is 100.
• The frequency of allele A₁ in a population of armadillos is 0.4.
• The frequency of allele A₁ of the migrant is 0.6.
• Migration rate is the fraction of migrant individual to the total number of native population.

Therefore,

$\left[\text{m}=\frac{\text{10}}{\text{100}}=\text{0}\text{.1}\right]$

The difference in allele’s frequency is given by the equation,

$\left[\text{Δp}={\text{m(p}}_{\text{m}}-\text{p)}\right]$

By substituting the given values in above formula:

$\left[\begin{array}{l}\text{Δp}={\text{m(p}}_{\text{m}}-\text{p)}\\ \text{Δp}=\text{0}\text{.1(0}\text{.6}-\text{0}\text{.4)}\\ \text{Δp}=\text{0}\text{.02}\end{array}\right]$

Thus, in generation 1, the frequency of allele A₁ will be:

$0.4+0.02=0.42$

The frequency of allele A1 in generation 1 is 0.42.

In generation 2:

The given values are as follows:

• The number of armadillos is 110.
• The frequency of allele A₁ in a population of armadillos is 0.42.
• The frequency of allele A₁ of the migrant is 0.6.

Therefore, the migration rate is:

$\left[\text{m}=\frac{\text{10}}{\text{110}}=\text{0}\text{.09}\right]$

The difference in allele frequency is given by the equation:

$\left[\text{Δp}={\text{m(p}}_{\text{m}}-\text{p)}\right]$

Therefore, by putting the given values:

$\left[\begin{array}{l}\text{Δp}={\text{m(p}}_{\text{m}}-\text{p)}\\ \text{Δp}=\text{0}\text{.09(0}\text{.6}-\text{0}\text{.42)}\\ \text{Δp}=\text{0}\text{.016}\end{array}\right]$

Thus, in generation 2, the frequency of allele will be:

$0.42+0.016=0.436$

The frequency of allele A1 in generation 2 is 0.436.

b.

Summary Introduction

To explain: Whether the change in allele frequency in generation 1 is greater than, less than, or equal to the change in generation 2.

Introduction: The movement of genetic variation from one population to another population is known as gene flow. Gene flow plays two important roles in evolution that are; it equalizes allele frequencies to remove genetic differences between populations. It makes two populations more similar. The second effect of gene flow is to establish new alleles into a population from a different population. Dispersal is the movement of individual or gametes and results in gene flow.

Explanation of Solution

In generation 1,

The given values are as follows:

• Suppose in generation 0, the number of armadillos is 100.
• The frequency of allele A₁ in a population of armadillos is 0.4.
• The frequency of allele A₁ of the migrant is 0.6.
• The difference in allele frequency ${\text{(p}}_{\text{m}}-\text{p)}$ is 0.2.
• Migration rate is the fraction of migrant individual to the total number of native population.

Therefore,

$\left[\text{m}=\frac{\text{10}}{\text{100}}=\text{0}\text{.1}\right]$

The change in allele’s frequency is given by the equation,

$\left[\text{Δp}={\text{m(p}}_{\text{m}}-\text{p)}\right]$

By substituting the given values in above formula:

$\left[\begin{array}{l}\text{Δp}={\text{m(p}}_{\text{m}}-\text{p)}\\ \text{Δp}=\text{0}\text{.1(0}\text{.6}-\text{0}\text{.4)}\\ \text{Δp}=\text{0}\text{.02}\end{array}\right]$

Thus, in generation 1, the change in allele frequency is 0.02.

In generation 2:

The given values are as follows:

• The number of armadillos is 110.
• The frequency of allele A₁ in a population of armadillos is 0.42.
• The frequency of allele A₁ of the migrant is 0.6.
• The difference in allele frequency ${\text{(p}}_{\text{m}}-\text{p)}$ is 0.18.

Therefore the migration rate is:

$\left[\text{m}=\frac{\text{10}}{\text{110}}=\text{0}\text{.09}\right]$

The change in allele frequency is given by the equation:

$\left[\text{Δp}={\text{m(p}}_{\text{m}}-\text{p)}\right]$

Therefore, by putting the given values:

$\left[\begin{array}{l}\text{Δp}={\text{m(p}}_{\text{m}}-\text{p)}\\ \text{Δp}=\text{0}\text{.09(0}\text{.6}-\text{0}\text{.42)}\\ \text{Δp}=\text{0}\text{.016}\end{array}\right]$

Thus, in generation 2, the change in allele frequency is 0.016.

Therefore the change in allele frequency in generation 1 is greater than generation 2.

The change in allele frequency of a population is directly proportional to the migration rate (m) and the difference in allele frequencies between the migrant and the local population. Since the migration rate is the same in both generation, but the difference in allele frequencies between the migrant population and local population in generation 1 is greater than generation 2. According to given values, the difference in allele frequencies between the migrant and the local population in generation 1 is 0.2 whereas in generation 2 it is 0.18.

This results in the greater value of the change in allele frequency in generation 1 than generation 2.

c.

Summary Introduction

To determine: The allele frequency in the population after many generations.

Introduction: The movement of genetic variation from one population to another population is known as gene flow. Gene flow plays two important roles in evolution that are; it equalizes allele frequencies to remove genetic differences between populations. It makes two populations more similar. The second effect of gene flow is to establish new alleles into a population from a different population. Dispersal is the movement of individual or gametes and results in gene flow.

Explanation of Solution

After many generations, the evolutionary effect of gene flow becomes constant after some point. According to the study, some individuals do not reproduce after the dispersal and do not contribute to genetic mixing. Gene flow plays two crucial roles in evolution that are it equalizes allele frequencies to remove genetic differences between populations and makes two populations more similar.

Therefore, allele frequency becomes constant and similar after many generations.