In a population where 8% of the men are red-green colour blind, what are the expected proportions of genotypes for the males and females? (Assume the trait does not affect survival or fertility.)
To determine the expected proportions of genotypes for males and females in a population where 8% of men are red-green color blind, we need to know the mode of inheritance of the trait. Based on the provided information, we can assume that red-green color blindness is an X-linked trait, meaning it is located on the X chromosome.
In humans, males have one X and one Y chromosome (XY), while females have two X chromosomes (XX). Since red-green color blindness is a recessive trait, it is more prevalent in males because they only have one X chromosome.
Let's calculate the expected proportions of genotypes for males and females:
For males:
- The frequency of red-green color blindness in males is 8% or 0.08.
- Since red-green color blindness is recessive and located on the X chromosome, males with only one X chromosome will express the trait if they possess the recessive allele.
- The proportion of males who are color blind is equal to the proportion of males who have one copy of the recessive allele, which can be calculated as the square root of the frequency of the trait. Therefore, √0.08 ≈ 0.283.
- The remaining males (1 - 0.283 = 0.717) are not color blind.
Therefore, the expected proportions of genotypes for males would be:
- Males who are color blind (XcY): 28.3% (approximately)
- Males who are not color blind (XY): 71.7% (approximately)
For females:
- Since females have two X chromosomes, they can have three possible genotypes: XX, XcXc, and XcX.
- The frequency of the recessive allele can be determined by the square root of the frequency of colorblindness in males. Therefore, √0.08 ≈ 0.283.
- The proportion of females who are color blind (XcXc) is equal to the square of the frequency of the recessive allele, which can be calculated as 0.283 * 0.283 = 0.08.
- The proportion of females who are carriers (XcX) is equal to twice the product of the frequency of the recessive allele and the frequency of females who are not color blind. Therefore, 2 * 0.283 * (1 - 0.283) ≈ 0.404.
- The remaining females (1 - 0.08 - 0.404 = 0.516) are not color blind or carriers.
Therefore, the expected proportions of genotypes for females would be:
- Females who are color blind (XcXc): 8%
- Females who are carriers (XcX): 40.4% (approximately)
- Females who are not color blind or carriers (XX): 51.6% (approximately)
These are the expected proportions of genotypes for males and females in the given population, assuming that 8% of men are red-green color blind.