Answer: In a population with a single dominant allele responsible for PCB resistance, if 45% of seeds from a randomly mating population of resistant weeds germinate in contaminated soil, the frequency of the resistance allele (R) is approximately 0.6 or 60%.
Explanation: To calculate the frequency of the resistance allele, we can use the square root rule. Since resistance is due to a dominant allele, the proportion of the resistant homozygotes (RR) and heterozygotes (Rr) in the population equals the frequency of the resistance allele (R).
Let p represent the frequency of the resistance allele (R). The proportion of homozygous resistant individuals (RR) would be, p * p = p^2.
The proportion of heterozygous individuals (Rr) would be 2 * p * (1 - p).
Given that 45% of seeds germinate in contaminated soil (Rr + RR = 0.45), We can solve for,p:
- p^2 + 2 * p * (1 - p)
= 0.45.
Solving the quadratic equation,
we get p ≈ 0.6.
Therefore, the frequency of the resistance allele (R) is about 60%.
To find the proportions of heterozygous and homozygous dominant individuals, we can substitute the value of p back into the formulas.
The proportion of heterozygotes (Rr) is ,
2 * 0.6 * (1 - 0.6) = 0.48, and
the proportion of homozygous dominants (RR) is ,
0.6^2 = 0.36.
In conclusion, when 45% of seeds from a population of resistant weeds germinate in contaminated soil, the frequency of the PCB-resistance allele (R) is about 60%. Among all germinating plants, approximately 48% will be heterozygous (Rr), and about 36% will be homozygous dominant (RR).
To know more about Resistance Allele;
The frequency of the PCB-resistance allele is approximately 0.67. Approximately 44% of the plants that germinate will be heterozygous, and approximately 45% of the plants that germinate will be homozygous dominant.
To calculate the frequency of the PCB-resistance allele, we can use the Hardy-Weinberg equation. Let's assume that the frequency of the PCB-resistance allele is represented by 'p'.
According to the question, 45% of the seeds from a randomly mating population of resistant weeds will germinate in contaminated soil. This means that the germination rate of the resistant seeds is 0.45.
Since the resistance to PCBs is controlled by a single dominant allele, the frequency of the resistant genotype (RR) can be calculated using the equation p^2, where p is the frequency of the PCB-resistance allele.
Therefore, p^2 = 0.45.
Taking the square root of both sides, we get p = √0.45 ≈ 0.67.
So, the frequency of the PCB-resistance allele is approximately 0.67.
To calculate the proportion of heterozygous individuals, we can use the equation 2pq, where p is the frequency of the PCB-resistance allele and q is the frequency of the recessive allele.
Since there is only one dominant allele (PCB-resistance allele), the recessive allele frequency (q) can be calculated as 1 - p.
Therefore, q = 1 - 0.67 = 0.33.
Using the equation 2pq, we can calculate the proportion of heterozygous individuals as 2 * 0.67 * 0.33 = 0.44.
So, approximately 44% of the plants that germinate will be heterozygous.
To calculate the proportion of homozygous dominant individuals, we can use the equation p^2, where p is the frequency of the PCB-resistance allele.
Using the frequency of the PCB-resistance allele (p = 0.67), we can calculate the proportion of homozygous dominant individuals as 0.67^2 = 0.45.
So, approximately 45% of the plants that germinate will be homozygous dominant.
Explore PCB-resistance allele frequency and dominant plant proportions in resistant weed populations. Learn more here.
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