Mendel’s?
No, all of them.
You will find that genetics has moved on somewhat since the nineteenth century.
You can’t substantiate a claim by saying you simply know something happened.
You asked what proved that such changes have the potential to occur. The fact that they
have occurred is surely very good evidence that they have the potential to do so.
By analogy, to show that acorns have the
potential to grow into oaks it is sufficient to show that acorns
have grown into oaks. It is then not necessary to go into the nitty-gritty of the biological details to prove this same proposition.
The sum of information I’m talking about is the total within each group, not the two end groups added together.
Then you have a strange idea of the meaning of the word "sum". What on earth could one mean by the "sum" of the information other than what you get if you add it up? That's what "sum" means.
If you wish to discuss whether
one of the two species so produced has less "information" than the original species, then feel free to provide some actual evidence. You could start by saying how you're quantifying information, but as you're a creationist I predict that you will never do so.
My original question phrased a bit differently: If this (ring species) is an example of how progressive changes occur in biological evolution, how do apparent small steps backward like this add up to big steps forward over time?
This is next to meaningless. If you are going to count speciation as a step "backwards", what are you going to count as a step
forwards --- extinction? If you exterminated one of the species in a ring, would you count this as an
increase in whatever you mean by "information"?