A. The answer to your dilemma is that "mayfly" as you are using it really covers a very large number of species (one authority lists over 500 species in No. America), and the environmental requirements for them range from still to flowing water, warm to cold water, and with varying food requirements. Mayflies, in general, are usually found in cold, well-oxygenated, unpolluted waters so that they do have a history of being associated with trout populations. The mayflies that I suspect you are seeing hatching from the Missouri are members of the family Ephemeridae. These are large, burrowing mayflies which construct tubes in the mud bottom and use their gills to create a water current through the tubes to bring in microscopic food particles. These are much different from the smaller, cold-water forms which are active foragers on and between the stones in mountain trout streams. So, the answer to your question is "yes" and "no" - it depends on what mayflies you are talking about in terms of their environmental requirements being similar to trout.

I know of no certain "bug" that indicates the presence of trout. Water quality biologists have come up with a series of rankings that they have assigned to various aquatic insects that indicate their tolerance to pollution. They calculate indices by combining the numbers of different bugs, multiplying by their tolerance index, summing these and dividing by the number of bugs. This gives a "biotic index" which can roughly give an indication of water quality, which in turn, can give you an idea of whether or not you might find trout there.