How Mites Kill a hive: Homegrown Destruction

If you buy a package of bees that has only 100 mites, and feed it and take care of it through the summer and fall.... it will reward you by dropping dead in midwinter!
Randy Oliver, who can be found at scientificbeekeeping.com, developed a mite and bee population calculator that takes our best understanding from researcher's measurements about how bee and mite populations change over time.
The mite model is a calculator that calculates what mite population you'd have, and how many mites you'd find in an alcohol wash, if you checked your model hive (video here, and writeup of technique here).

Try these exercises with the mite model:
• Using your region, and 100 mites, see how late you can start treating and still save the hive. Pretend you're using formic, it's effective, and killing 80% of the mites each time.
• How few hives need to be in the hive at the beginning of the year to not have the hive die?
• How many treatments do you have to do to get the ending number of mites to the same level you started with?
• The final lesson, but the most important: Set up the model with your ideal treatment regimen. Now add mites that are migrating in on the backs of your bees...

Math Kills! Every schoolchild knows this.

This is a model, an elaborate calculator. The math that kills is exponential: for every mite that enters a cell, on average 2 will come out - a mother and her daughter. Well, there is a lot more to the story than that, but it will work for our explanantion.
April.......100 mites.
May..........200 mites. That's not so bad... there's 60,000 bees in the hive, for crying out loud!
June.........400 mites.
July.........800 mites. Even if each mite kills one bee, it's barely making a dent...
August.......1600 mites.
September....3200 mites. Still a lot of bees though...
October......6400 mites. But only 25,000 bees by the end of October, due to the summer bees dying off, leaving only the winter bees alive. Uh oh, lots of dead bees showing up on the ground at the front of the hive...
November.....still 6400 mites, since the queen isn't laying eggs anymore, so mite reproduction has ended. But, doesn't matter...because by December....
December.....curtains. The hive will be killed by this mite load.

Your results and mileage will vary. Many people fall into the trap where they get a hive and it makes it through one winter, but by the second winter, it dies out. Others don't have their first year hive make it even that far. With a hive autopsy, it is possible to confirm or deny the role of mites in a deadout. But almost always, if a hive went into winter strong, and is a mess of dead bees on the bottom of the hive with maybe 2 cups of sad (dead) bees clinging to the combs in January, it's almost always mites.
One thing is true for all: it is possible to have as few as 100 mites in January, or in April with a new hive, and have a lethal level of mites by October.
To find out the two main ways this happens and (even better!) how to counter this, see the next page...