>Once alleles for resistance are present in the population, then it is simple math to determine the number of generations for that allele to increase in frequency. 

This sort of statement usually comes from someone who is not familiar with the topics of genetics, pesticide resistance etc. On the other hand, the following comes from some who is. As you can see, the math is not "simple" nor is resistance solely reducible to math.

> Results of a survey of mites from the Carl Hayden AZ lab and from cooperators in five locations (Arizona, California, Florida, Maine, North Dakota) showed that some mites were susceptible to all three acaricides (Amitraz, Coumaphos, Fluvalinate) in the spring of 2003, but by fall most mites were resistant. Mites were resistant to all chemicals, even from beekeepers that do not treat colonies with acaricides.

> Resistance is rarely totally dominant (Carriere, 2003) but could be expressed at some level in heterozygotes especially if the resistance confers a gain of function, e.g. detoxification of chemicals by enzymes, reduced penetration and enhanced elimination of toxins. Females that have two copies of a resistant allele (RR) would produce offspring that also are homozygotes. Heterozygote foundress mites would produce 0.5 heterozygote and 0.5 homozygote susceptible offspring if the male parent had the susceptible allele, and 0.5 homozygous resistant and 0.5 heterozygous offspring if their male parent carried the resistant allele. Therefore, each heterozygote has a 0.5 probability of producing all resistant individuals and a 0.5 probability that half of their offspring will be resistant depending on the genotype of the male parent. 

> The homozygous resistant state would not change due to brother-sister mating and its frequency would increase with each generation. Under these conditions, it is not surprising to find increased frequency of resistant individuals over time, especially if pressure from acaricides is removing homozygous susceptible individuals from the population. Varroa resistance could also be sex-linked, but since varroa males do not come in direct contact with the acaricides (other than through the accumulation in the wax) and their resistance has never been tested, this is only a speculation. Of course, unless we are able to rear varroa off host and in an artificial environment, we can only hypothesize such events.  

> Once the operating systems of varroa resistance are determined, it may be possible to develop a successful management program to counteract resistant varroa. According to Milani and Vedova (2002), resistant mites left untreated for 4-6 years will lose their resistance to fluvalinate. Why this is so and what mechanisms are being used for such a switch, need to be determined. Identifying resistance mechanisms in varroa will be challenging though, because it will require rearing esterase-free and susceptible mites in an isolated area and subjecting them to known chemical regimes.

Sammataro, D., Untalan, P., Guerrero, F., & Finley, J. (2005). The resistance of varroa mites (Acari: Varroidae) to acaricides and the presence of esterase. International Journal of Acarology, 31(1), 67-74.

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