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Chapter 25: Problem 23

Genotypes of leopard frogs from a population in central Kansas were determined for a locus \((M)\) that encodes the enzyme malate dehydrogenase. The following numbers of genotypes were observed: $$\begin{array}{cc} \text { Genotype } & \text { Number } \\ \text { \(M^{1} M^{l}\) } & 20 \\ \text { \(M^{1} M^{2}\) } & 45 \\ \text { \(M^{2} M^{2}\) } & 42 \\ \text { \(M^{1} M^{3}\) } & 4 \\ \text { \(M^{2} M^{3}\) } & 8 \\ \text { \(M^{3} M^{3}\) } & 6 \\ \text { Total } & 125\\\ \end{array}$$ a. Calculate the genotypic and allelic frequencies for this population. b. What would the expected numbers of genotypes be if the population were in Hardy-Weinberg equilibrium?

Short Answer

Expert verified
Genotypic frequencies are 0.16, 0.36, 0.336, 0.032, 0.064, and 0.048, and allelic frequencies are 0.356, 0.548, and 0.096. Expected genotype numbers are 15.875, 48.75, 37.5, 8.5, 13.125, and 1.125 under Hardy-Weinberg equilibrium.

Step by step solution

01

Determine Total Number of Individuals

The total number of individuals in the population is already given as 125, calculated as the sum of all genotype numbers: \(20 + 45 + 42 + 4 + 8 + 6 = 125\). This will be the denominator for calculating frequencies.
02

Calculate Genotypic Frequencies

Genotypic frequency is calculated as the number of individuals with a given genotype divided by the total number of individuals. For each genotype: - \(M^1M^1\) has frequency \(\frac{20}{125} = 0.16\)- \(M^1M^2\) has frequency \(\frac{45}{125} = 0.36\)- \(M^2M^2\) has frequency \(\frac{42}{125} = 0.336\)- \(M^1M^3\) has frequency \(\frac{4}{125} = 0.032\)- \(M^2M^3\) has frequency \(\frac{8}{125} = 0.064\)- \(M^3M^3\) has frequency \(\frac{6}{125} = 0.048\).
03

Calculate Allelic Frequencies

First, calculate the total number of alleles: \(2 \times 125 = 250\), as each individual has 2 alleles. Then, for each allele: - \(M^1\) appears in \(2 \times \) 20 from \(M^1M^1\), 45 from \(M^1M^2\), and 4 from \(M^1M^3\), totaling \((2 \times 20) + 45 + 4 = 89\). Frequency is \(\frac{89}{250} = 0.356\).- \(M^2\) appears in \(2 \times \) 42 from \(M^2M^2\), 45 from \(M^1M^2\), and 8 from \(M^2M^3\), totaling \((2 \times 42) + 45 + 8 = 137\). Frequency is \(\frac{137}{250} = 0.548\).- \(M^3\) appears in \(2 \times \) 6 from \(M^3M^3\), 4 from \(M^1M^3\), and 8 from \(M^2M^3\), totaling \((2 \times 6) + 4 + 8 = 24\). Frequency is \(\frac{24}{250} = 0.096\).
04

Calculate Expected Genotypic Frequencies under Hardy-Weinberg Equilibrium

Using Hardy-Weinberg equilibrium: - Expected frequency of \(M^1M^1\) is \( (0.356)^2 = 0.127\).- Expected frequency of \(M^1M^2\) is \(2 \times 0.356 \times 0.548 = 0.390\).- Expected frequency of \(M^2M^2\) is \( (0.548)^2 = 0.300\).- Expected frequency of \(M^1M^3\) is \(2 \times 0.356 \times 0.096 = 0.068\).- Expected frequency of \(M^2M^3\) is \(2 \times 0.548 \times 0.096 = 0.105\).- Expected frequency of \(M^3M^3\) is \( (0.096)^2 = 0.009\).
05

Calculate Expected Numbers of Each Genotype

Multiply each expected frequency by the total number of individuals (125):- Expected number of \(M^1M^1\) is \(0.127 \times 125 \approx 15.875\).- Expected number of \(M^1M^2\) is \(0.390 \times 125 = 48.75\).- Expected number of \(M^2M^2\) is \(0.300 \times 125 = 37.5\).- Expected number of \(M^1M^3\) is \(0.068 \times 125 \approx 8.5\).- Expected number of \(M^2M^3\) is \(0.105 \times 125 \approx 13.125\).- Expected number of \(M^3M^3\) is \(0.009 \times 125 = 1.125\).

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Key Concepts

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

Genotypic Frequencies
Genotypic frequencies tell us the proportion of each genotype in a population. They're essential in understanding how traits are distributed among individuals. Let鈥檚 say you have a population of leopard frogs with various genotypes. Genotypes like \(M^1M^1\), \(M^1M^2\), and \(M^2M^2\) represent different pairs of alleles for an enzyme. To find the genotypic frequency, you divide the number of frogs with a particular genotype by the total number of frogs. For example, if 20 frogs have the \(M^1M^1\) genotype out of a total of 125 frogs, their genotypic frequency is \(\frac{20}{125} = 0.16\).
Knowing genotypic frequencies helps us to check if a population is in Hardy-Weinberg equilibrium, a state where allele and genotype frequencies remain constant over generations in the absence of evolutionary influences.
Allelic Frequencies
Allelic frequencies give us insight into how common each allele is in a population. Unlike genotypic frequencies, they consider not only the genotypes but also the number of each allele per individual. In our frog population, each frog has two alleles, making a total of 250 alleles (2 alleles times 125 frogs).
Let's calculate the frequency of the \(M^1\) allele. It's present in genotypes \(M^1M^1\), \(M^1M^2\), and \(M^1M^3\). We count each appearance: twice for \(M^1M^1\) (since both alleles are \(M^1\)), once for each \(M^1M^2\) and \(M^1M^3\). Add those up for a total, then divide by the total number of alleles. Repeat this process for \(M^2\) and \(M^3\), and you get the allelic frequencies.
These frequencies help us predict genetic diversity and understand changes in allele prevalence over time.
Population Genetics
Population genetics explores how genetic composition in a population changes over time. This can be due to factors like natural selection, genetic drift, and mutation. A fundamental concept here is the Hardy-Weinberg equilibrium. It serves as a baseline model where, if certain conditions are met, genotype and allele frequencies remain constant.
The conditions include no mutations altering alleles, no individuals entering or leaving the population, random mating, a very large population size to minimize random changes, and no selection. If a population meets these conditions, it's in genetic equilibrium, theoretically staying genetically stable.
However, real populations often deviate due to evolutionary forces. This deviation provides insight into the dynamics of evolution, helping scientists track and predict genetic changes. Population genetics, using principles like those underpinning Hardy-Weinberg, is crucial for understanding biodiversity and the adaptability of organisms to environmental changes.

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Most popular questions from this chapter

A population of water snakes is found on an island in Lake Erie. Some of the snakes are banded and some are unbanded; banding is caused by an autosomal allele that is recessive to an allele for no bands. The frequency of banded snakes on the island is 0.4, whereas the frequency of banded snakes on the mainland is 0.81. One summer, a large number of snakes migrate from the mainland to the island. After this migration, \(20 \%\) of the island population consists of snakes that came from the mainland. a. If both the mainland population and the island population are assumed to be in Hardy-Weinberg equilibrium for the alleles that affect banding, what is the frequency of the allele for bands on the island and on the mainland before migration? b. After migration has taken place, what is the frequency of the allele for the banded phenotype on the island?

Briefly describe the differences between directional selection, overdominance, and underdominance. Describe the effect of each type of selection on the allelic frequencies of a population.

Define natural selection and fitness.

Two chromosome inversions are commonly found in populations of Drosophila pseudoobscura: Standard (ST) and Arrowhead (AR). When the flies are treated with the insecticide DDT, the genotypes for these inversions exhibit overdominance, with the following fitnesses: $$\begin{array}{cc} \text { Genotype } & \text { Fitness } \\ \text { ST/ST } & 0.47 \\ \text { ST/AR } & 1 \\ \text { AR/AR } & 0.62 \\ \end{array}$$ What will the frequencies of \(S T\) and \(A R\) be after equilibrium has been reached?

Define inbreeding and briefly describe its effects on a population.
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