Answered

In the previous question, you used the Hardy-Weinberg equation to determine the frequencies of the genotypes for $HH$, $Hh$, and $hh$, given gene frequencies of $H = 0.2$ and $h = 0.8$. These frequencies were:

$HH = 0.04 \quad Hh = 0.32 \quad hh = 0.64$



Now, determine the expected numbers of each organism in the population (total size $= 150$):

Number of HH = □

Number of Hh = □

Number of hh = □

Verified Answer :

  • Multiply the total population size \(N = 150\) by each genotype frequency.
  • The number of \(HH\) individuals is \(150 \times 0.04 = 6\).
  • The number of \(Hh\) individuals is \(150 \times 0.32 = 48\).
  • The number of \(hh\) individuals is \(150 \times 0.64 = 96\).
  • The final counts are: Number of \(HH = \boxed{6}\), Number of \(Hh = \boxed{48}\), Number of \(hh = \boxed{96}\).

Explanation

  1. Analysis of the Data and Population Parameters

We are given a population of size \(N = 150\) and the genotype frequencies for a specific gene with alleles \(H\) and \(h\). The provided frequencies are:

  • Frequency of \(HH = 0.04\)
  • Frequency of \(Hh = 0.32\)
  • Frequency of \(hh = 0.64\)

The goal is to determine the expected number of individuals for each of these three genotypes in the total population. This is done by multiplying the total population size by the frequency of each genotype.

  1. Calculating the Number of HH Individuals

To find the expected number of individuals for the homozygous dominant genotype \(HH\), we multiply the total population by the genotype frequency:
\[\text{Number of } HH = N \times \text{Frequency}(HH) = 150 \times 0.04\]
Calculating this, we get:
\[150 \times 0.04 = 6\]
Thus, the expected number of individuals with the \(HH\) genotype is 6.

  1. Calculating the Number of Hh Individuals

To find the expected number of individuals for the heterozygous genotype \(Hh\), we perform a similar calculation using its frequency:
\[\text{Number of } Hh = N \times \text{Frequency}(Hh) = 150 \times 0.32\]
Calculating this, we get:
\[150 \times 0.32 = 48\]
Thus, the expected number of individuals with the \(Hh\) genotype is 48.

  1. Calculating the Number of hh Individuals

To find the expected number of individuals for the homozygous recessive genotype \(hh\), we use its frequency:
\[\text{Number of } hh = N \times \text{Frequency}(hh) = 150 \times 0.64\]
Calculating this, we get:
\[150 \times 0.64 = 96\]
Thus, the expected number of individuals with the \(hh\) genotype is 96.

  1. Verification and Final Answer

To ensure our results are correct, we sum the expected counts for each genotype and verify that they equal the total population size:
\[6 + 48 + 96 = 150\]
The sum confirms that our calculations are consistent with the total population size of 150.

  • Number of \(HH = \boxed{6}\)
  • Number of \(Hh = \boxed{48}\)
  • Number of \(hh = \boxed{96}\)

Examples

The Hardy-Weinberg principle is essential in population genetics for understanding how gene frequencies remain constant from generation to generation in the absence of evolutionary forces. By applying these calculations, biologists can determine if a population is evolving or is in genetic equilibrium. For instance, in conservation biology, scientists use this method to estimate the number of individuals carrying a specific trait or disease in endangered populations, helping them manage genetic diversity and plan protection strategies.

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