91Ó°ÊÓ

Mu Jean Manning, Charles Kerfoot, and Edward Berger studied genotypic frequencies at the phosphoglucose isomerase (GPI) locus in the cladoceran Bosmina longirostris (a small crustacean known as a water flea). They collected 176 of the animals from a single location in Union Bay in Seattle, Washington, and determined their GPI genotypes by using electrophoresis (J. Manning, W. C. Kerfoot, and E. M. Berger. 1978. Evolution 32:365-374). $$\begin{array}{cc} \text { Genotype } & \text { Number } \\ \text { \(S^{I} S^{I}\) } & 4 \\ \text { \(S^{1} S^{2}\) } & 38 \\ \text { \(S^{2} S^{2}\) } & 134\\\ \end{array}$$ Determine the genotypic and allelic frequencies for this population.

Step by step solution

01

Calculate Total Number of Individuals

Start by identifying the total number of individuals counted in the population. This is the sum of all individuals across the different genotypes: \(4 + 38 + 134 = 176\).

02

Determine Genotypic Frequencies

The genotypic frequency is determined by dividing the number of individuals with each genotype by the total number of individuals in the population. For \(S^1 S^1\), it is \(\frac{4}{176}\). For \(S^1 S^2\), it is \(\frac{38}{176}\). For \(S^2 S^2\), it is \(\frac{134}{176}\).

03

Calculate Allelic Frequencies

First, note that each individual contributes two alleles to the gene pool. Calculate the frequency of each allele. Start with allele \(S^1\): \(2 \times 4 + 38\) alleles are \(S^1\). For allele \(S^2\), \(2 \times 134 + 38\) alleles are \(S^2\). Divide each by total alleles \(2 \times 176\).

04

Compute Frequencies Numerically

Perform the calculations: \([S^1]\) frequency is \(\frac{8 + 38}{352}\) and \([S^2]\) frequency is \(\frac{268 + 38}{352}\). This results in allelic frequencies of \([S^1]\) = \(\frac{46}{352}\) and \([S^2]\) = \(\frac{306}{352}\).

05

Simplify and Express Frequencies as Decimals

Convert the fractions into decimals: \([S^1] \approx 0.1307\) and \([S^2] \approx 0.8693\). Hence, the genotypic frequencies are approximately \(0.0227\) for \(S^1 S^1\), \(0.2159\) for \(S^1 S^2\), and \(0.7614\) for \(S^2 S^2\).

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Key Concepts

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

Genotypic Frequency

Genotypic frequency tells us how often a particular genotype appears in a population. In the exercise, this involved calculating the frequency of each genotype (\( S^1 S^1 \), \( S^1 S^2 \), \( S^2 S^2 \)) within the Bosmina longirostris population. To find these frequencies, we divide the number of individuals of each genotype by the total number of individuals collected.

• For example, for genotype \( S^1 S^1 \), there were 4 individuals out of a total of 176. So, the frequency is \( \frac{4}{176} \), which simplifies to approximately 0.0227.
• Similarly, genotype \( S^1 S^2 \) is present in 38 individuals, leading to a frequency of \( \frac{38}{176} \), simplifying to about 0.2159.
• For \( S^2 S^2 \), with 134 individuals, the frequency is \( \frac{134}{176} \) approximating to 0.7614.

These frequency calculations tell us the proportion of each genotype within the population, providing insight into genetic diversity.

Allelic Frequency

Allelic frequency refers to how often an allele appears in a population's gene pool. Each individual contributes two alleles, and these need to be counted and divided by the total number of alleles to find the frequency of each.

• For allele \( S^1 \), each \( S^1 S^1 \) genotype contributes 2 \( S^1 \) alleles, and each \( S^1 S^2 \) genotype contributes 1 \( S^1 \) allele. Thus, total \( S^1 \) alleles are \( 2 \times 4 + 38 = 46 \).
• Similarly, total \( S^2 \) alleles are obtained from \( S^1 S^2 \) and \( S^2 S^2 \) contributions, \( 2 \times 134 + 38 = 306 \).
• The total number of alleles is twice the number of individuals (because each has two alleles), so \( 2 \times 176 = 352 \).

Therefore, the frequency of \( S^1 \) becomes \( \frac{46}{352} \approx 0.1307 \), and \( S^2 \) is \( \frac{306}{352} \approx 0.8693 \). Knowing these frequencies helps us understand allele prevalence and potential evolutionary changes.

Hardy-Weinberg Equilibrium

The Hardy-Weinberg Equilibrium provides a framework for understanding how genetic variation is maintained under specific conditions. It states that allele and genotype frequencies will remain constant from generation to generation in the absence of evolutionary influences.
This principle relies on five conditions:

• No mutations changing allele frequencies.
• No migration introducing or removing alleles.
• No selection favoring specific alleles over others.
• A large population ensuring random mating and genetic drift prevention.
• Random mating, ensuring allele combinations occur by chance.

If these conditions are met, we can predict genotype frequencies using allelic frequencies:

• For genotype \( S^1 S^1 \), the expected frequency is \( p^2 \), where \( p \) is the frequency of \( S^1 \).
• For \( S^2 S^2 \), it’s \( q^2 \), with \( q \) as the frequency of \( S^2 \).
• The heterozygous \( S^1 S^2 \) frequency is \( 2pq \).

In the given exercise, these values help check whether the observed genotype frequencies align with those predicted by Hardy-Weinberg, indicating whether the population is in equilibrium.