"Your argument leaves out one important fact in the discussion about evolution that is separate from the mathematical probabilities but equally as relevant.
I'm glad you are removing the discussion from those horribly mutated and grotesque probability calculations. They truly are meaningless.
"1) The moth that you describe is still a moth after it mutated.
As it should. Given the length of time (short, short, short) we have been observing moths it would surprise me if we witnessed a subgroup become something other than moths.
"2)The Canine that you described is still a Canine.
Again, this is not unexpected.
"I contend that Micro evolution is clearly a fact and no scientist has ever and will never prove Macro Evolution, (A dog becoming a Lion) has ever occurred.
That is very good (that a dog has not become a Lion that is).
Part of the problem is in your understanding of what constitutes a species. You seem to believe that speciation requires large 'macro' morphological change. This isn't true. Speciation simply requires a full or partial (but mostly full) cessation of gene flow between two groups, as in sympatric speciation where two groups share a geographical locale but do not exchange genes or allopatric speciation where a species is divided into smaller groups that are separated geographically. As long as the two groups, the parent and daughter, are restricted in intergroup gene flow, any difference in selection type and degree, or drift, will inevitably result in morphological differences. Accumulated small differences do result in large differences.
To see this in action, look up 'ring species' such as the Asian Greenish Warbler (Phylloscopus trochiloides), where two subspecies (Phylloscopus trochiloides viridanus and Phylloscopus trochiloides plumbeitarsus), although they share a geographic range do not interbreed. They are still (arguably) considered the same species (albiet different subspecies) because there exists a potential gene flow through the other three geographically connected subspecies. Remove that potential gene flow and they become different species.
Note: The definition of species is fluid not because taxonomists can't make up their mind (which is sometimes the case) but because in many cases the differences between real live animals are difficult to categorize (think platypus)
The dog population (Canis lupus familiaris) will not become a new species by jumping (a saltation event) to a totally new morphology such as a Lion's (Panthera leo); it (the population) will become a slightly different dog which in turn will become a slightly different dog than its predecessor which in turn will increasingly differentiate from there through a number of generations. Eventually the morphological differences between the original Canis lupus familiaris and the new Canis lupus ?????? will be enough to be recognizably different animals, as different as a dog is to a lion.
What is interesting is the incredible variation between the extremes in extant dogs. If we hadn't witnessed their development and facilitate their interbreeding, they would probably be classified as a number of different species rather than as a number of different subspecies.
These minor changes, which are easily observed, will inevitably result in fairly large morphological differences, enough for even an anti-evolutionist to admit as different 'kinds' (putatively a higher taxon than species). This 'additive or cumulative change' is ubiquitous in things we observe and/or create.
Ex: If we take a white pigment and add just a little green pigment we end up with a pigment that is white with a tinge of green. As we add more and more green pigment eventually what was white will be considered green (maybe with a tinge of white). This is cumulative change. In evolution this would be an accumulation of 'micro' evolutionary changes that amount to a 'macro' evolutionary change.
OK, I can hear it now, the normal anti-evolutionist outcry when confronted with gradual incremental change - 'But it's still a pigment'. Although this analogy (a pigment/dog is still a pigment/dog) is enticing in its conclusion, it really is a false analogy. Consider that a wolf and a lion are still Carnivora, a wolf and a whale are still Mammalia, a wolf and an Angel fish are still Animalia, and a wolf and a maple tree are still Eukaryota.
Which of these is the best analog to the pigments of the above example? If your first impulse is to restrict pigments to species, perhaps the electromagnetic spectrum is a better analog for the higher taxa.
In any case, small additive changes will accumulate into larger differences unless there is a mechanism that bounds the changes. In the case of the electromagnetic spectrum (light) colours are bounded (restricted) by our ability to 'see' them. We can not see all frequencies of light so colours can be said to have an upper and a lower bound, no increase in frequency will result in a different colour beyond our upper limit of vision (~780 nm). Strictly speaking the light simply becomes invisible but it still makes my point - incremental change will accumulate unless some mechanism presents a barrier to that accumulation.
Why should evolutionary change be any different? Because we have not been observing and recording the changes in species long enough to 'see' macro changes? No, the simple observation, or more precisely, the lack of observation is not enough to conclude it will not happen. For us to conclude that accumulation is restricted we need to hypothesize and test for a bounding mechanism. Without that mechanism, we logically have to conclude that accumulated changes will build up to large changes.
"I challenge you to recite one instance where it can be proven scientifically, (Observed) that any species has ever become another species trough evolution.
I challenge you to prove it could not and has not happened.
It is up to you to provide the mechanism that prevents accumulated 'micro' changes from becoming large 'macro' changes. The transitional sequences in the fossil record spanning the large jumps in time we are too transitory to witness, tell us that the small changes we see in extant species (and we do have examples of new species) do indeed accumulate and result in huge change. What we find in DNA verifies this accumulation of change and the relationship of apparently morphologically disparate extant species. (eg. artiodactyls and cetaceans).
"I won't hold my breath!
Good, you'll need to breathe to find that mechanism.
Well said:)