Forgive me for diving off the deep end here but this brings up an interesting bit of semantics for me. My guess - only a guess - is that what we mean by "minimum" is more along the lines of achieving the most results relative to the time we spend. So maybe, e.g., 20 minutes does more than twice as much for you at 10 minutes. Or maybe it means that even though 20 minutes doesn't do twice as much, the amount more it does is still work the extra time spent, and the increase in results per time spent starts to go down after 20 minutes.
This will vary by the practitioner and the exercise, of course, but I think even a very small amount can be effective. Effective means it has an effect, and I feel better after I've done a minute's worth of swings in a variety of formats, e.g., a single Q&D series, or even something as simply as picking up a bell and swinging it for a minute non-stop.
I raise the language issue only because I'm in a very busy period in my life right now and don't train nearly as much as I like to, but I still feel benefit from very short bouts of exercise in a variety of format. Besides a minute of swings, a 15-second bar hang has an effect for me. Yesterday I did 5 deadlifts (a single and two doubles, 130 kg @ 69 kg) in the space of 5 minutes and I feel it had an effect.
Maybe minimum effective dose means the minimum to have a training effect, i.e., the minimum to enable us to continue to progress. Is that how we're using it around here in a training context? And maybe my ramble above is all for naught if that's true, but effect and training effect are related but different things, IMHO. At the least, minimum effective dose for maintenance and for progress are different things.