Processes such as speciation and adaptation, natural selection, micro-evolution - by whatever names you choose to call them - are scientifically demonstrable facts.  Macro-evolution, the process of indefinite speciation or adaptation needed to support the evolutionary hypothesis, has not been demonstrated, however.  On the contrary, there is plenty of evidence that there are natural boundaries which militate against indefinite speciation - through infertility and even death.
In short, the transforming power of the process known as natural selection appears to be strictly limited.

Let's look at real life example of natural selection in action to see how strong a foundation it provides for macro-evolution to take place:

According to many leading and influential evolutionists, one of the most unambiguous examples of evolution at work occurred at the very time that Darwin was so deeply engaged in the study of his "beloved barnacles".

"We should expect to find the most rapid evolutionary changes in populations suddenly exposed to new conditions.  It is therefore natural that one of the most striking changes which has been observed in a wild population ... is the phenomenon of 'industrial melanism', the appearance and spread of dark forms of a number of species of moths.
"Melanic forms were first reported in 1850 from Manchester in the Peppered Moth, Biston Betularia."²

"[the case of the peppered moths] is the most striking evolutionary change ever to be witnessed by man."³

Sir Gavin De Beer, writing in the somewhat more prestigeous Encyclopaedia Britannica, stated (1974):

"One of the most striking examples of observable evolution is the phenomenon known as industrial melanism."⁴

Richard Leakey, the renowned fossil collector agreed (1979):

"The peppered moth is a striking example of evolution in action. ... but, sadly for Darwin, no one knew it at the time.  This is just the evidence he needed to show the effectiveness of natural selection."⁵

And so did Professor Stephen Jay Gould (1984):

"... we have abundant, direct, observational evidence of evolution in action [including] the famous populations of British moths that became black when industrial soot darkened the trees upon which the moths rest."⁶

To cut a long story short, many evolutionists believed that the change in the percentages of light and dark coloured moths was primarily due to the fact that, during the Industrial Revolution, some areas of Britain became heavily polluted by soot pouring out of factory chimneys, from industrial processes such as the Bessemer furnaces (invented in 1856) which produced huge quantities of steel, and so on.  As the pollution increased, earning the Midlands the title of 'The Black Country', (so the story went) a change began to take place in the colour distribution within the peppered moth population:

"A black mutant of the peppered moth Biston betularia was found at Manchester in 1848.  Until that time the prevalent form of this species was light grey with dark speckles."⁷

This final, rather longer, description is from the website of the Biology department of the University of Cincinnati's Clermont College.  Although it is somewhat verbose I have left it unedited because I believe it constitutes a perfect example of a certain kind of intransigent Darwinist thinking:

"One of the best documented examples of natural selection in modern times is the English Peppered Moth.  Typically, this moth is whitish with black speckles and spots all over its wings.  During the daytime,  Peppered moths are well-camouflaged as they rest on the speckled lichens on tree trunks.  Occasionally a very few moths have a genetic mutation which causes them to be all black, so they are said to be melanistic.  Black moths resting on light-colored, speckled lichens are not very well camouflaged, and so are easy prey for any moth-eating birds that happen by.  Thus, these melanistic moths never get to reproduce and pass on their genes for black color.

However, an interesting thing happened to these moths in the 1800s.  With the Industrial Revolution, many factories and homes in British cities started burning coal, both for heat and to power all those newly-invented machines.  Coal does not burn cleanly, and creates a lot of black soot and pollution.  Since lichens are extremely sensitive to air pollution, this caused all the lichens on city trees to die.  Also, as the soot settled out everywhere, this turned the tree trunks (and everything else) black.  This enabled the occasional black moths to be well-camouflaged so they could live long enough to reproduce, while the "normal" speckled moths were gobbled up.

Studies done in the earlier 1900s showed that while in the country, the speckled moths were still the predominant form,  in the cities, they were almost non-existant.  Nearly all the moths in the cities were the black form.  It was evident to the researchers studying these moths that the black city moths were breeding primarily with other black city moths while speckled country moths were breeding primarily with other speckled country moths.  Because of this, any new genetic mutations in one or the other of those populations would only be passed on within that population and not throughout the whole moth population.  Additionally, because the city and country environments were different, there were different selective pressures on city vs. country moths that could potentially drive the evolution of these two populations of moths in different directions. The researchers pointed out that if this were to continue for a long enough time, the city and country moths could become so genetically different that they could no longer interbreed with each other, and thus would be considered distinct species.  In this case, what actually happened is that the people of England decided they didn't like breathing and living in all that coal pollution, thus found ways to clean things up.  As the air became cleaner,  Lichens started growing on city trees again, thus the direction of the selective pressure (birds) was once again in favor of the speckled moths. By now, English cities, as well as countrysides, all have speckled moths, and all are interbreeding at random, thus were not separated for long enough to develop into separate species.⁸"

This information is presented by an Assistant Professor of Biology at Clermont College, who might be expected to know that the so-called mutants were actually shades of dark brown, rather than black, but no matter.  What does matter is this rider, presumably added at the time of the update in November, 1999:

"However, an article in the 24 May 1999 issue of The Scientist 13(11) presents and discusses data which may refute this long-held idea."⁹

I was particularly struck by the tentative nature of the phrase "may refute" (my italics) in this sentence.
The article. in question, by Jonathan Wells, a postdoctoral biologist at the University of California, Berkeley, and a fellow of the Discovery Institute, Seattle, is rather modestly entitled "Second Thoughts about Peppered Moths", and it carefully details studies as far back as 1973, through to as recently as 1998, which for many people effectively demolish the myth of the peppered moth as a living demonstration of natural selection in action.  For example:

• East Anglia, to this day a mainly rural area with very little industrial pollution/darkening of tree bark,  nevertheless saw the incidence of Biston betularia carbonaria - the darker, melanic version - rise to some 80 (eighty) per cent of the Biston betularia population in that area
• The frequency of melanics was measured in southeastern Michigan from 1960 to 1995, and was found to have dropped from more than 90 per cent to under 20 per cent over that period.  Unfortunately for the natural selection theory, there were no "perceptable changes in local lichen floras" - supposedly a key factor in the environmental changes which favoured one variety of Biston betularia over the other
• The all-important experiments by Bernard Kettlewell, of Oxford University, in the 1950s nearly all involved placing moths in positions where, following studies in the 1980s, we know they do not normally rest.  Textbooks which cover this topic typically depict moths resting on the trunk of a tree to show the camoflage effect of light or dark colouring against light/lichen-covered or darkened bark.  Yet in all the formal studies only two moths have ever been recorded resting on the main trunk of a tree (mostly they rest on the sides or underside of branches near to the top of a tree).
• We now know that the allegedly 'mutant' melanic form of the peppered moth is not "mutant" at all:

  "Genetically, the difference between the light and the melanic forms [of the peppered moth] has been shown to be due to a single gene, the allele for melanism being dominant to that for lighter coloration."¹⁰

• We actually have no idea when the melanic form of the peppered moth first began to become the dominant form in 19th century England, only when it was first noted by naturalists.  Dobzhansky's comment, quoted earlier, that the light grey speckled variety was the most numerous prior to the 1848 sighting is purely speculative, whilst his careful use of the phrase "the prevalent form" leaves room to suppose that the darker moths may have been around for any previous length of time you care to think of, possibly simply unrecognised as an alternative form of Biston betularia.

When interviewed for an article in the British broadsheet newspaper the Sunday Telegraph on this subject, self-styled Neo-Darwinist Richard Dawkins airily dismissed the whole matter in these words:

"The details of any experiments done 40 years ago are bound to be vulnerable to detailed criticism.  But, in any case, nothing momentous hangs on these experiments." ¹¹

Well, "momentous" might indeed be a bit strong, but it ain't mere trivia, either.
If "industrial melanism" was truly regarded by scientists as "one of the most striking examples of observable evolution" and "just the evidence [Darwin] needed to show the effectiveness of natural selection" - and given that there are few, if any, other such apparently clearcut examples of "observable evolution" - then Darwin's "natural selection" would appear to have suffered a substantial body blow, to say the least.  Jonathan Wells, showing an admirable honesty and objectivity, ends his article thus:

"The fact that peppered moths do not normally rest on tree trunks invalidates Kettlewell's experiments and poses a serious problem for the classical explanation of industrial melanism in peppered moths.  Although cryptic colouration and selective predation have not been ruled out, one recent review concludes that 'there is little persuasive evidence in the form of rigorous and replicated observations and experiments, to support this explanation at the present time.'¹²
 
"Yet textbooks continue to present the classical story of industrial melanism in peppered moths as an example of evolution in action.  Clearly this is misleading.  In particular, it is misleading to illustrate the story with photographs showing moths on tree trunks where they do not rest in the wild.  Our students deserve better." ¹³
(Italics added for emphasis)

It is only fair to point out that Dr Wells' comments have also been subjected to criticism, and Professor Arthur S. Lodge carries details of this debate in the Industrial Melanism section of his website¹⁴.

In fact, earlier observations by T.G. Sargent, of the North American Cryptic Moth (phygalia titea (Cramer)¹⁵) do indeed cast further doubt on the effect of colouration and selective predation on the survival of different varieties with a species of moth, because they showed that darker individuals can rest on light-coloured backgrounds without suffering greater predation than the moths who settle on locations where their coloration acts as camouflage.

By the way, we did ask the author of the material on the Clermont College website why she used the phrase "may refute" (italics added).  And guess what, it's because the textbooks don't yet mention any of the research cited in Mr Wells' article.
A number of learned journals, yes, but in the textbooks, no!  Looks like Darwinism may be about the conservation of the status quo?