BUT ....Breeding for mite tolerance may not be necessary ... I started out with a swarm and decided (for a variety of reasons) that I was not going to treat for varroa .. I have five good colonies that have all descended from that original swarm and one that came, last year, from a compost bin cut out from miles away from home. They are all surviving and look healthy ... it's too early to inspect properly but through the clear crownboards and on the landing boards they seem fine.
So ... I'm NOT trying to breed selectively, I haven't lost a colony yet for any reason and it's working for me ...
The worst case scenario is that you do lose your bees ....but before that happens, as a vigilant beekeeper, you will see the signs of a weakening colony .. heavy mite fall, DWV, lethargy, reducing numbers, dysentry etc. ... all associated with a varroa infestation that has become out of control (and YES - I've seen that in other colonies - I look after one that seems to attract every bloody varroa mite in the county no matter how much it gets treated) and it's not too late to give them a hand with an OA Sublimation.
Some colonies seem to be targets for varroa mites and yet colonies next to them have very few ... I don't begin to understand why ... it's such a complicated set of factors that there is, at present, an element of luck involved in becoming treatment free - certainly as a hobbyist with just a few hives there is going to be a risk ... but until you take that risk with a colony or two - you won't know.
The thinking that 'Your bees will die if they are not treated' does not always hold true ... it might have done once upon a time ... but it's not always the case now.