My Treatment free regime has been well documented on here many times - the short answer to your question is nothing. I do regular sugar rolls and most of the time there are only low levels of mites in my hives - I see 'spikes' occasionally and I keep a close eye on that colony when I see it ... inevitably the infestation levels return to more 'normal' levels. I watch closely for signs of varroa related disease and thankfully have never seen any.
I don't preach that treatment free is the way forward for everyone and if a new beekeeper was intending being treatment free I would actively discourage them. I don't lose colonies - I lost one this year to a swarm that caught me out and a subsequent queen failure but I can't say that varroa has ever contributed significantly to any colony I've lost over the years .. yes, I've had the odd colony dwindle and I've starved at least one that I can remember. But .. my colonies survive, thrive and provide a honey crop that pays for their upkeep.
If I found a colony that were unable to reduce the mite load on their own I would treat - OA by sublimation - I've not had to do it yet but it's pointless being a beekeeper, monitoring varroa and not being prepared to do something about it if TF is not working. The last thing I want is weak or dead colonies.
I don't know why my bees manage to live alongside varroa and maintain mite levels at a level they cope with. Often I find no mites in my sugar rolls at all ... more often than not it's one or two, rarely more than 5. I've seen 15 on one occasion and had a few sleepless night over that one - next sugar roll down to 5 and then 2 !
I think it's a combination of bees, location, high levels of hive insulation, foundation free, local concentrations/combinations of forage (not many high value intensive crops eg: OSR/Heather where I live), low interference inspections and LUCK ... who knows ? It works for me and I keep doing it but don't follow me - I'm well off the beaten track and there are always risks.