Mule? They are infertile? You can't use an infertile organism as argument. They can't breed and its a dead end.
Sorry for the misunderstanding, the mule is an example of the offspring of two distinct species that can still interbreed, not an example of a species that has arisen through speciation. If you read the other link (I know, its long) you'll find brief overviews of case studies of species near speciation. I'm not sure what kind of evidence I can present to you at this point, so I'm going to go with a logic argument that I believe leads to the conclusion that speciation is at least possible. I can't obviously demonstrate speciation other than with a computer simulation, and I doubt that would be satisfactory.
I see you already have some information concerning evolution and biology from your degree. I see you also acknowledge the possibility for genetic adaptation through random variation in a population. If you acknowledge that random mutation occurs, and you acknowledge that selection occurs such that mutations are beneficial to the organism generally become more dominant within a population over time (this is just adaptation I'm talking about), then I pose the following arguments: in addition to beneficial mutations, mutations occur that are detrimental to an organism's survival and mutations occur that generally have no effect on the ability of the organism to survive and procreate (neutral mutations). If you're willing to accept those arguments, I give you the following: neutral mutations may become dominant within a population if they occurred at the same time as a beneficial mutation.. that is, the same genetic code mutates beneficially and neutrally. In this case, the neutral mutation gets carried and passed along with the beneficial mutation.
If you accept all that, I present you with isolation: Specialization through adaptation leads populations of the same species to procreate within isolated groups. This may be due to any variety of factors including the presence of food sources and predators, geographic delimiters, and so on. At this point, you have the same species but two different gene pools that are subject to different selective pressures. This means different random mutations prove to be successful in each group, leading to each group developing different adaptations. This is very evident and plenty of evidence for it exists in biological literature.
I suppose the next part of the argument is most critical, and also the part we currently disagree on. With isolated populations, you already have groups that do not interbreed, even though they are physically capable of it. The next step for speciation to occur is for some mutation to happen that prevents the two seperate groups from interbreeding. According to some definitions, speciation has already occurred with the divergence of genetic code for adaptation. Lets take it a step further and say speciation requires not only distinct adaptations but the inability for the two groups to procreate.
Given the arguments I posed, there are two ways this could happen. First, the beneficial adaptations make the two groups inable to produce viable offspring. Second, a mutation that is neutral to the procreation of one specialized group prevents procreation with the other specialized group. Either way, we now have to genetically distinct groups that are unable to procreate with each other. They are both specialized in different ways, and they both have the same common ancestor species. At this point, speciation has occured.
Do you disagree with anything in this logic argument?
If you have a different definition of speciation I can try to adapt the argument to it. There are also of course asexual organisms for which the "interbreeding" argument is void. For these organisms, the same argument concerning isolation and selective pressures can be applied without the argument about interbreeding. Over time, with varying selective pressure between two isolated groups of the same species will lead each to develop successive adaptations (and the adoption of neutral genetic code) over time such that their limited genetic code diverges significantly enough for the two groups to be considered unique species.