I find it ironic that this claim is championed by young-earth advocates, since it is a known paradigm of Darwinian evolution called allopatric speciation. What these critics of evolution claim is that this speciation only applies to the family or order level and, since it only allows for the loss of information not gain, it demonstrates that an intelligent agent directly created the original kinds with all of the genetic differences of the particular genera and species already in place but not expressed.
Now I've read very little about information theory, but what I have read contradicts this (although, I think these critics of evolution are partially excused because some defenders of evolution describe it in these same categories). According to Information and the Origin of Life by Bernd-Olaf Küppers it's a misunderstanding of information theory to claim that these scenarios involve a loss of information. Information is, by definition, expressed. If it is not expressed, it is not information; it is potential information (or technically, "syntactic" or "Shannon" information). For example, a string of 100 characters of gibberish may have more potential information than a string of 30 characters that makes up a coherent sentence since the first string contains more characters to which one could ascribe meaning. But in point of fact, the string of 100 characters of gibberish does not convey any information insofar as it is gibberish, whereas the string of 30 characters that make up a coherent sentence does convey actual information. Thus, if the meaningless string of 100 characters turned into the meaningful string of 30 characters by losing 70 characters, this would involve an increase in information.
Let me illustrate this. If you have a string of characters
nbtldwepob( kvpkhla&u jsgv *xfndistvl,emc nbijnsmv $hsfgevlvs.ecjn
and it experiences a mutation so that only every third character is expressed, it leaves us with the following string:
two plus five is seven
Now according to the critics of evolution -- at least those who argue as I've indicated -- the first string contains more information than the second. But this is false. The first string has more characters, certainly, but it doesn't have any meaning, and hence conveys no information. The second string, on the other hand, does have meaning and does convey information. If the first string evolved into the second as I've illustrated, this would be an increase in information, since it goes from a series of characters that's meaningless to one that's meaningful.
Potential information is essentially just the building blocks before they are actually arranged into any kind of meaningful order. Any combination is equally likely or unlikely as any other, regardless of whether they have any meaning. This isn't "nothing", since it is an actual series of the building blocks in question, but the sequence is irrelevant. Potential information can "carry" information, but is not true information itself.
Beyond this is semantic information, in which there is a code where meaning is attached to certain sequences. To use one of our previous examples, 30 characters making up a coherent sentence has more semantic information than 100 characters of gibberish, since the former means something and the latter does not. The next level is pragmatic information, where the information evokes action. Obviously, these three dimensions of information are all inter-related: the pragmatic level presupposes the semantic level, which in turn presupposes the potential. Moreover, semantic information cannot exist by itself without evoking a response, and thus always leads to the pragmatic level. The point in all of this is that these critics equivocate between potential information on the one hand and semantic or pragmatic information on the other.
What this illustrates is that actual (i.e. semantic or pragmatic) information always requires a context. If our meaningless sequence of 100 characters lost 70 characters, and became a meaningful, coherent sentence, it would constitute an increase in information. If a genetic mutation prevented some kind of protein synthesis, but the overall effect was a positive one, it would constitute an increase in information. If a mutation prevented some minor aspect of an animal's normal morphological development, but the change made the animal more able to survive in its particular environment, it would constitute an increase in information. The context determines whether the change constitutes an increase or a decrease in information, and in the above contexts, the acquired meaning, or the improved adaptability of the cell or the individual animal means that the changes in question were increases in information.
(cross-posted at Quodlibeta)