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Given that the frequency of color blind females is 1 in 25000, calculate the expected frequency of female carriers using the Hardy-Weinberg principle.

Biology

ScanSolve AI Answer

Answer

0.01257

Step-by-step solution

4 steps
  1. Understand the genetic basis of color blindness.

    Color blindness is an X-linked recessive trait. For females, the genotypes are XCXCX^C X^C (normal vision), XCXcX^C X^c (carrier), and XcXcX^c X^c (color blind). According to the Hardy-Weinberg principle, if pp is the frequency of the dominant allele (XCX^C) and qq is the frequency of the recessive allele (XcX^c), then the frequency of color blind females (XcXcX^c X^c) is q2q^2.

  2. Calculate the frequency of the recessive allele (qq).

    The frequency of color blind females is given as 1 in 25000.

    q2=125000q^2 = \frac{1}{25000}

    To find qq, take the square root of q2q^2:

    q=125000q = \sqrt{\frac{1}{25000}} q=125000q = \frac{1}{\sqrt{25000}} q=15010q = \frac{1}{50\sqrt{10}} q≈150×3.16227766q \approx \frac{1}{50 \times 3.16227766} q≈1158.113883q \approx \frac{1}{158.113883} q≈0.006324555q \approx 0.006324555
  3. Calculate the frequency of the dominant allele (pp).

    Using the Hardy-Weinberg equation p+q=1p + q = 1:

    p=1−qp = 1 - q p=1−0.006324555p = 1 - 0.006324555 p=0.993675445p = 0.993675445
  4. Calculate the frequency of female carriers.

    Female carriers have the genotype XCXcX^C X^c. Their frequency in the population is given by 2pq2pq.

    2pq=2×0.993675445×0.0063245552pq = 2 \times 0.993675445 \times 0.006324555 2pq≈2×0.006284552pq \approx 2 \times 0.00628455 2pq≈0.01256912pq \approx 0.0125691

    Rounding to five decimal places, the expected frequency of carriers is 0.01257.

    The expected frequency of the carriers of this allele in the population is approximately 0.01257\boxed{0.01257}.

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