Yes, Varroa - speciffically v. destructor. My project involved returning the bees to their original size. To briefly summarize, honeybees are not native to the US. When they were introduced here, an attempt was made to increase the size of the bee and therefore yields. The natural cell size was <4.9mm. By size, I mean cell diameters. Now they average 5.3mm. The brood cycle was around 19 days. Now it is around 21. For whatever reason, larger bees are capped a little longer. The reproduction cycle of v destructor requires uncapped drone cells and a period of capped time to actually reproduce. If you shorted the brood cycle of the bees, the Varroa population decreases. My results supported this and others, such as Dee Lusby and Michael Bush have found similar results. I'd suggest reading Huber's book if you're interested in what European honeybees were like before being manipulated by US producers.
So, the question is: why isn't everyone using Small Cell? The main reason is skepticism and that it's time consuming and expensive. You have to do a series of regressions to reduce the size of the bee and therefore shorten the broodcycle. The workers build comb to pretty tight tolerances and do not like building on 4.9 foundation. So you gradually reduce cell size. You have to cull a lot of comb while reducing sizes. Also, a bigger queen doesn't like laying in a larger cell and will lay in the supers if you let her. Honeycomb is larger than brood comb and, of course, drone comb is larger still. You basically have to force them to use small cell. Incidentally, I also fogged my bees with FHMO and scheduled oxalic acid treatments. These along with a screened bottom board kept my bees alive and healthy and chemical free.
Regarding queenless hives and laying workers, you can salvage a queenless hive pretty easily. While queen mandibular pheromone does direct hive activities, it takes a while for a worker to start laying; like weeks. In my experience, it's pretty rare. If that's actually the case though, you just shake all the bees off the frames on the ground and the laying worker (being too heavy to fly) can't get back in the hive and with fresh eggs, they make a new queen. What usually happens is you get a queen that becomes unproductive and for whatever reason, the workers don't supercede her and then they don't have fresh eggs. You can remove the queen and wait a day and give them fresh eggs from another hive and they'll make a new queen. While it is easier to just buy a new queen, at $30 per queen it's expensive and you're basically completely changing the genetics and potentially the temperament of your bees. Once you get healthy, easy-going bees, you don't want to introduce an unknown queen and therefore genes unless that's your goal.
