Gary LaGrange >  what can be done to stem the tide.

I'm not sure what you mean by 'lots of them'.  They have been in pretty much all of my hives for over ten years. A dozen or so in  a hive doesn't concern me any longer, as long as they are in the outer reaches of the hive, away from the brood. 
It is hard to say what might work for you but some things I've done.

Hives in full sun. (sorry Charles Linder)

Queenright hives.  By mid May any hives I find that are queenless get combined....right then. No dallying.  Usually, it seems that the beetles are a jump ahead of me. On the occasions that I am ahead, I make the most of it. 

Don't leave too much extra space. In spring I used to stack supers on every hive. Now...one at a time. 

I use inner covers. When I remove the top, there are usually a handful of beetles on top of the ic. This is actually good...in my opinion. It is an indication that your bees are driving the beetles away from the nest...as far as possible. Before going any further, I crush any I see.  I do not run migratory covers any more as the beetles sequestered beneath will scatter when it is removed. 

By late May here, the beetle population has grown. I limit my inspections. I do not remove frames 1 or 10 in my hives or frames 1 or 5 in my nucs. The bees will have driven the beetles to the outer edges and removing these frames has everybody scrambling. I try not to do anything that might undo the bees' work to corral them.

I don't use screened bottom boards. One reason is shb access. The bees will try to drive them away from the brood nest, often to the edges of a bottom board. If you are using a screened bottom, the beetles can slip through and the bees aren't able to follow. Then the beetles return through the mesh when and where works best for them. 

I no longer do late season splits.

I only pull honey supers that I can finish extracting within 24 hours...48 hours in a pinch.

I don't worry about soil treatments. As I said in another post, by the time they hit the dirt, that colony is already in trouble. 


I'm sure....tomorrow I'll remember a dozen other things. 
Good luck.

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