Of course, the word 'prove' is inappropriate.

In another thread, Ragnar proposes that a population of spiders becoming two reproductively isolated populations of spiders is evidence of evolution.  But this 'evolution' means nothing in itself.  Mere change- the most barbaric definition of evolution- is not what anyone disputes.

It is the inference and extrapolation that such changes are sufficient to justify the allegation that all biological diversity on this planet is the result of such changes that is disputed.  With that in mind, let's turn our attention to these hypothetical spiders (Ragnar can provide documentation of them if he'd like so we can get into more detail).

First of all, just because two populations do NOT reproduce together does not mean that they cannot.   And by 'cannot' we can consider whether or not this merely represents mating preferences or if there really is some sort of biological difference that prevents them from mating.

I often have Darwin's finches invoked against me.  What people don't realize is that most of those finch populations CAN interbreed, they just don't typically.  I read another article recently that said that two morphological exact snail populations would not reproduce together.  But CAN they reproduce?  This question is important because evolution in its grander statements, trying to justify such mechanisms to apply to all observed life forms, does not require explaining one massive snail, spider, or finch population that does not but can reproduce with each other.

We have very large morphological differences throughout the biological order, and these difference ultimately arise (for 99% of the biological order we are discussing) because of different genetic information.

So, consider this population of snails... followed by a mock up of genetic information contained in the organisms...

Sn1- ABCDEFG
Sn2- ABCDEFG
Sn3- ABCDEFG
Sn4- ABCDEFG
Sn5- ABCDEFG
Sn6- ABCDEFG
Sn7- ABCDEFG
Sn8- ABCDEFG
Sn9- ABCDEFG

Not all of this information will be expressed in any given organism and within a single population there can be plenty of variation.  However, in order for morphological changes to occur, there has to be a change in the expression of the existing information or the introduction of new information.  This goes for both major and minor morphological changes.

If its only an expression of existing information, then if this group splits, you will only see the same informaton in the resulting population, and thus nothing that can justify the inference that such a process is the cause of all the huge morphological differences that permeate our biological system.

But how can new information be introduced?  Old information does not support evolution.  You need to see new information eventually, or its just a big circle.

WHAT WE ACTUALLY OBSERVE is that as groups diverge, their gene pool gets smaller, not bigger.  That's a tautology, isn't it.  The most radical morphological changes we OBSERVE are in populations that are effectively inbreeding (by definition!) but there is not enough variation to counteract the negative consequences of whatever brand of mutation starts to crop up, or was always present, but masked by the larger gene pool.

Thus, if you take a population of dogs and continue to breed for a specific trait, eventually you will have an unhealthy pool of dogs.  Their best hope for health is to have the biggest gene pool possible.  This is a fact.

So, its interesting that when we see spiders becoming reproductively distinct that is evidence for evolution, but when animal husbandry professionals do the same with dogs, cows, cats, and horses, they have to be constantly aware of the problems of inbreeding and the FACT that they could ruin the population altogether.  

Indeed, we did not have to wait until the 20th century to see Ragnar's 'evolution in action.'  Whoever discovered that the chihuahua and the St Bernard would not reproduce together, I don't know, hundreds of years ago probably, would have had the same type of evidence in hand.  Why did not one infer that such a process could account for all biological organisms and their diversity on this planet?  Probably because it was prima facie evidence against such a notion- any divergences of gene pools made genetic abnormalities more likely to be expressed, and therefore more likely that the population would eventually fail.  

No new information=no meaningful evidence for evolution.

And not all new information is good for the organism that receives it.

Now, I said that all of this can just as easily fit into a Creationist POV in the 'falsification' thread, and here is how.

A population can successfully diverge and maintain its health (its reproductive health probably being the most important aspect, from this POV) proportional to the quality of the genetic code in the first place.

Imagine a computer program designed to reproduce itself.  In order to get the program onto another computer, we are not allowed to just make a copy of the original file, but must have the program generate its own copy, which then is passed onto another computer.  Provided the initial copy is perfect, this process can progress for quite a long time.  Even if it is perfect, external factors, such as physical hard drive corruption, will affect the coding of the program (which is now reproducing exponentially).

If the changes are bad enough, the program simply won't be able to reproduce.  The length of time that the program can 'run its biological course' will be proportional to the quality of the original program and then adjusted statistically according to frequency of 'external factors' coming in.

You could have one copy of the program break up into two families that are no longer compatible, such that a computer in one family will not be able to communicate with the computer having the program in another family.   We might call this a 'species.'

However, what are we actually observing?  We are observing the continual DETERIORIATION of the program.   Its not getting better as it goes, its getting worse.

From a Creationist POV, and possibly from an ID POV (I can't say for sure) the number of copies and 'families' that are possible may be numerous providing the original file started out perfect.

From evolution's standpoint, though, there is no such thing as a perfect file.  EVERY FILE is composed of flaws that managed to survive and reproduce.  Because of the extraordinary quality of still existing copies, doctors (and the rest of us) can recognize that Down's Syndrome is a bad thing.  Nobody in the real world thinks that Down's Syndrome is just another potential evolutionary direction.  From evolution's standpoint, there are not diseases to be cured (or at least, there shouldn't be), rather, we are just controlling and maintaining our own arbitrarily discerned conception of what constitutes a normal, healthy, human being.

So, divergence within limits is allowed within Creationism and other views, as such, it cannot 'prove evolution.'  I would argue it is far more consistent with Creationism then Evolutionism, but that is neither here nor there.  If its evidence consistent with two different views, it cannot be raised as evidence for only one of them.