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A certain gene in a tree species determines how long it takes for a seed to germinate. In one population, the alleles for this gene are [tex]T_1, T_2[/tex], and [tex]T_3[/tex].

The numbers of individuals with each of the possible genotypes are shown in the table.
\begin{tabular}{|l|l|}
\hline Genotype & Number of individuals \\
\hline [tex]T_1T_1[/tex] & 50 \\
\hline [tex]T_1T_2[/tex] & 60 \\
\hline [tex]T_1T_3[/tex] & 40 \\
\hline [tex]T_2T_2[/tex] & 50 \\
\hline [tex]T_2T_3[/tex] & 55 \\
\hline [tex]T_3T_3[/tex] & 45 \\
\hline
\end{tabular}

What is the frequency of the [tex]T_3[/tex] allele?



Answer :

GinnyAnswer
To determine the frequency of the \( T3 \) allele in this population, we need to follow a series of steps. Here's a detailed, step-by-step solution:

### Step 1: Calculate the Total Number of Individuals
First, we sum up the number of individuals with each genotype to get the total population size.
- Number of \( T1T1 \) individuals: 50
- Number of \( T1T2 \) individuals: 60
- Number of \( T1T3 \) individuals: 40
- Number of \( T2T2 \) individuals: 50
- Number of \( T2T3 \) individuals: 55
- Number of \( T3T3 \) individuals: 45

Adding these together:
[tex]\[ 50 + 60 + 40 + 50 + 55 + 45 = 300 \][/tex]

### Step 2: Calculate the Total Number of \( T3 \) Alleles
Each genotype contributes a certain number of \( T3 \) alleles:
- \( T3T3 \) individuals each have 2 \( T3 \) alleles.
- \( T1T3 \) and \( T2T3 \) individuals each have 1 \( T3 \) allele.

To find the total number of \( T3 \) alleles:
- Number of \( T3 \) alleles from \( T3T3 \) individuals: \( 2 \times 45 = 90 \)
- Number of \( T3 \) alleles from \( T1T3 \) individuals: \( 1 \times 40 = 40 \)
- Number of \( T3 \) alleles from \( T2T3 \) individuals: \( 1 \times 55 = 55 \)

Adding these together:
[tex]\[ 90 + 40 + 55 = 185 \][/tex]

### Step 3: Calculate the Frequency of the \( T3 \) Allele
The frequency of an allele is determined by dividing the total number of that allele by the total number of alleles in the population. Since each individual has 2 alleles, we multiply the number of individuals by 2:
[tex]\[ \text{Total number of alleles} = 300 \times 2 = 600 \][/tex]

Therefore, the frequency of the \( T3 \) allele is:
[tex]\[ \text{Frequency of } T3 = \frac{\text{Total number of } T3 \text{ alleles}}{\text{Total number of alleles}} = \frac{185}{600} \][/tex]

Simplifying this fraction:
[tex]\[ \frac{185}{600} \approx 0.3083 \][/tex]

Thus, the frequency of the [tex]\( T3 \)[/tex] allele in the population is approximately [tex]\( 0.3083 \)[/tex].

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