This gets kind of speculative here. It requires that every member of every subsequent generation of that subgroup cannot breed at different times than the general population (which would be a true loss of genetic information from that population). At least it seems speculative to me because I am unaware of this situation ocuring naturally. Is there one?
For Darwinism to be true, you must have new species arise through the injection of NEW information.
That's basically why (Darwinian) evolution never seems to pan out on close examination. This has never been demonstrated to happen, even under laboratory manipulation. And everything seems to go from higher organization to lower organization (Loss of information, as you mention in the frog example), not the reverse. It would seem to me that we are DEvolving, not Evolving, with fewer species and less genetic potentials.
We do from the Carassius Gibelio to the Carassius auratus, The Gibel Carp to the Goldfish
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There has been plenty of "New" information that has evolved in the Goldfish that are not found in the original Gibel Carp, So it's a gain not a loss. There are scores if not hundreds of new structures, organs, body shapes, tails shapes and numbers, types of scales, colors, tolerances, etc. Most of which are the result of multiple genes (i.e. the bubble eye in the bottom center picture takes 3 separate genes just for the sacs to form) that were gained separately/independently.
The information must improve the fitness of the organism for their environment,
It did, Try raising a carp in a fishbowl and see how long it last
and the new information must arise at a rate that explains the biological diversity of Earth and the fossil record.
Goldfish arose ~1100 years ago, So even if we take an extremely unlikely low estimate and say the Goldfish only differentiate from the carp by only 0.0005% (Their different chromosome number guarantees it's way higher) using simple math that would mean that if the genetics of a species can change 0.0005% in 1100 years then in 4.5 billion years the genetics of an organism can change by 2,250,000% which way more than the diversity of all life on Earth.
The first two conditions seem at least theoretically sound but have not been shown and the last has not come close to being met.
Yes it has in the Goldfish .