An oversimplification, but likely correct for most situations:

Regarding mite immigration (or horizontal transfer) and mite  
virulence:  It may be that even in isolated situations very low  
horizontal transfer is high enough to prevent avirulent mites from  
becoming the predominant genotype.  For both Gotland bees early on,  
and more recently for Arnot forest bees there is very little evidence  
that they are doing well because of mite avirulence.

Regarding mite immigration and swamping of any genetic resistance:   
There may be different outcomes in terms of mite population growth  
depending on bee genotype.  In highly susceptible colonies, the added  
immigrant mites, put through unchecked reproduction may greatly  
increase mite densities, shorten survival, etc.  In highly resistant  
colonies, constant high immigration can potentially be dealt with.  As  
risky as modelling is, it may not be that difficult to show an  
inconsequential effect of even hundreds or thousands of mites coming  
into a colony that targets mites before or in their first cycle of  
reproduction.  What some report as "mite bombs" at critical times of  
year with robbing and collapsing colonies may be a different story.

Anecdotal observations from research apiaries, not from formal  
experiments:  Highly susceptible unselected bees can get to damaging  
levels, collapsing colonies, dead colonies fairly consistently from a  
queen introduction in the spring to the the middle or late summer in  
southern Louisiana (say March or April to July or August).  Highly  
resistant colonies kept in the same apiaries or in nearby apiaries  
(say one to two miles), same time course from queen introduction to  
mite counts, are more often than not observed to simultaneously  
maintain very low mite levels.  Mongrel (supersedures through several  
generations), local "survivors" may have moderate or cycling levels,  
may weaken, sometimes die, but they do not go through the inevitable  
demise of highly susceptible sources.

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