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3. Imagine that varroa mites (a pest for honey bees) develop a resistance to acaricides (a pesticide that kills arachnids). Further imagine that this resistance is due to a mutation in an autosomal gene and is recessive. Suppose you have a lazy beekeeper who does not check her hives regularly, but because she knows mites are present, still treats them each winter with an acaricide when bees are sedentary and no mites can be introduced from outside the colony. After three years, she finds that the number of varroa mites in each hive is far greater than what it was previously. She suspects resistance among the mites and, sure enough, testing by an independent laboratory in August (prior to this year's treatment with acaricide) finds that 97 out of every 1000 mites are resistant to her acaricide. Based on this information and taking all calculations and answers to 6 decimal points. 1 What percent of the mite population prior to the next scheduled treatment are expected to be heterozygotes? (2 pts) If, this year, the hives are treated three times in succession, and by the end of the third treatment the acaricide has killed 100% of susceptible mites, by what percent would the mite population be reduced? (2 pts) R What is the frequency of each allele (dominant and recessive) in the population of mites before the treatment this three-round treatment? (1 pt each blank) R What is the frequency of each allele after the three treatments? (note, this requires some thought! (1 pt each blank) Based on the information here, would the frequency of the recessive allele been higher, lower, or the same as compared to three years ago? (2 pts)

Answer :

Final answer:

The percent of the mite population expected to be heterozygotes before the next treatment is 17.6%. After three successive treatments with acaricide, the mite population will be reduced by approximately 90.703441%. The frequency of the recessive allele would have been higher compared to three years ago.

Explanation:

To calculate the percent of the mite population expected to be heterozygotes before the next treatment, we need to use the Hardy-Weinberg equation. In this case, the recessive allele is responsible for the resistance to acaricides. The equation is: p^2 + 2pq + q^2 = 1, where p is the frequency of the dominant allele (susceptible) and q is the frequency of the recessive allele (resistant). We know that 97 out of 1000 mites are resistant, so the frequency of the recessive allele (q) is 97/1000 = 0.097. To find the frequency of the dominant allele (p), we subtract q from 1: p = 1 - 0.097 = 0.903. Now we can plug in the values: 2pq = 2 * 0.903 * 0.097 = 0.1757, which is approximately 0.176. So, the percent of the mite population expected to be heterozygotes is 17.6%.



If the hives are treated three times in succession and the acaricide kills 100% of susceptible mites, this means that only mites with the resistant allele will survive. After each treatment, the number of resistant mites will increase, while the number of susceptible mites will decrease. Since we know that 97 out of 1000 mites are resistant, the mite population will be reduced by 97% after each treatment. So, after the third treatment, the mite population will be reduced by a total of 97% * 97% * 97% = 90.703441%. Rounded to 6 decimal points, the population will be reduced by 90.703441%.



Before the treatment, the frequency of the dominant allele (p) was 0.903 and the frequency of the recessive allele (q) was 0.097.



After the three treatments, all susceptible mites have been eliminated, so the frequency of the dominant allele (p) becomes zero. The resistant mites have the recessive allele (q), and their frequency remains the same at 0.097.



Based on the information provided, the frequency of the recessive allele (q) would have been higher compared to three years ago. This is because the resistant mites with the recessive allele survived the treatments and passed on their genes, leading to an increase in the frequency of the recessive allele.

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