What exactly is natural selection and precisely where does it occur?

I agree with you that mutation is non-selective, but this is a rubbish description of mutation. For a start there is not need for a change in amino acid sequence to produce a potentially adaptive mutation and for another 'rearrangement' simply suggests the sort of recombinatorial shuffling you get with sexual reproduciton and totally fails to encompass the wide spectrum of potential genetic mutations.Your cases 2 and 4 I would argue are, or at least can be, selective. Assortative mating and other forms of sexual selection certainly are. It should be obvious from your own definition of Natural selection that this is the case since sexual selection will clearly lead to differential reproductive success of the sexually favoured traits. The gene flow one is more arguable since there is a clear overlap with the issue of mate selection as to the degree of gene flow between populations.So really drift and mutation are the only solid candidates I see here for clearly non-selective mechanisms of allele frequency change.With only the non-selective factors you may get evolution in the trivial sense of changes in allele frequency but never the sort of adaptive evolution that is what makes evolutionary biology so interesting.TTFN,WK

Like who? It clearly isn't non-selective and it fits E.O Wilsons definition perfectly. A genetic trait which is favoured by sexual-selection will lead to its possessors contributing more offspring to the next generation by virtue of a better chance of mating.What you really seem to be trying to say is that 'mate choice' is not necessarily natural selection, but 'mate choice' is also not necessarily the same as sexual selection.TTFN,WK

Sexual selection is a sub-class of natural selection. As your quote from E.O. Wilson showed it fits the criteria but is restricted to reproductive success differences based upon the interactions of members of the population with potential mates and competitors for mates rather than with their environment in total.The other members of the population are as much a part of the environment as anything else so why do you think sexual selection is not merely a specific type of natural selection, in much the way that Modulous posited that Artificial selection could be a sub class of natural selection where the key environmental factor was the whim of human beings.What is the distinction that makes it not a from of NS?TTFN,WK

Its 'assortative mating', in this case leading to members of a class choosing members of their own class to mate with.TTFN,WK