Final answer:
The correct answer is option 4. The ratio of X chromosomes to autosomes (X:A) in the specified population, considering the given proportions of sterile males and fertile females with their respective X:A ratios, is closest to 2:3. This is due to the combination of both male and female contributions leading to a ratio of 5X:6A when simplified.
Step-by-step explanation:
To calculate the ratio of X:A in the population, we need to consider the ratios given for sterile males (XO) and fertile females (XXY), as well as their proportions in the population.
Sterile males (XO) have a given X:A ratio of 1:2. Since the sex ratio is 1 sterile male to 2 fertile females, we can represent the sterile males with 1X and 2A.
Fertile females (XXY) have a given X:A ratio of 1:1. Thus, for every 2 fertile females, we have 4X (since each female has two X chromosomes) and 4A.
When combining these ratios for the population, we get a total of 1X (from the males) + 4X (from the females) = 5X, and 2A (from the males) + 4A (from the females) = 6A. So, the ratio of X:A in the population will be 5X:6A.
If we divide both by the smallest number (5), we get a simplified ratio of 1:1.2, which is not exactly listed in any of the options provided. However, since the answer choices use whole numbers and assuming a typographical error in the options, the closest matching option to our ratio 1:1.2 is option 4, 2:3 given that both express a similar ratio where autosomes slightly outnumber the X chromosomes.
Therefore, the correct option in the final answer, which is close to our calculated value, is: 4) 2:3.