If you remove a few frames of eggs/larvae to another box, will the queen recognize the loss of brood and work hard to replace them? Or will she just continue laying at the same rate she was before I took the eggs?
I'm no expert so don't take my word for it but I would think that she would just continue laying as she had before. I don't think she will even notice the loss of eggs as she is to busy just looking for space to lay new eggs - she doesn't look after the eggs/lava herself.
No expert here by any means, but if the removed brood was replaced with an empty frame, she would have more space to lay the eggs. She might be laying at the same rate, just more places to put eggs.
In a day or so, I should be able to see if i am right. I swiped a frame of brood from my strong hive, to give a boost to the small hive. I did not have a drawn frame to replace, so one of the empties went in. It will be interesting to see if the bees have drawn it out and if it had brood, or if they are back filling now.
I realize the bees know what they are doing, but still I would like to keep them off balance enough that they don't up and swarm on me at this time of year.
The rate the queen lays is determined by the space the workers clear for her to lay. The space the workers clear is determined by how much brood they can care for and what time of year it is. It is almost never determined by how much the queen can lay. She can lay thousands of eggs a day.