Anti-evolutionists misinterpret and mislead when discussing the topic of "living fossils". An example can be found in the text of a bill proposed in the Arkansas legislature by Rep. Jim Holt:
(O)(i) Lobe-fined fish; (ii) Lobe-fined fish are "index fossils" for rock 325-410 million years old. These fish are still alive today. "Coelacanth" was found in 1938 and still inhabits the Indian Ocean. It is obvious that it cannot be an "index fossil" for any age rock.
A trivial critique is that some fishes are described as "lobe-finned", not "lobe-fined". However, the quality of care used in spelling in this instance is similar to the quality of care given to accuracy.
"Coelacanth" is a common name given to fish with a particular set of characteristics, not a particular species. Until the 20th century, coelacanths were known only from fossil remains, and were considered to be an extinct group. In the 1930's, a specimen of the modern species of coelacanth, Latimeria chalumnae, was caught off the island of Madagascar. Another species has been found off of Indonesia more recently.
The modern coelacanths, Latimeria spp., are members of the relict taxon of Sarcopterygian fishes, but are distinguishable from species known from the fossil record. This is important. A species that is distinguishable on its morphological characters can be told from related species. The last known fossil species in the clade that includes Latimeria spp. is placed in a different genus . Genus-level differences in morphology indicate that it would be difficult to mistake specimens of each species for the other.
There are several criteria that must obtain before a particular species can be utilized as an index fossil. It must be morphologically distinctive. This means that the species can be reliably identified and not mistaken for similar species. Defining characters which are not shared with other species enable this to happen. The species must have a limited stratigraphic extent, which means that it reliably appears only between a specified set of horizons, and thus a restricted period of time. A useful index fossil is also geographically widespread.
This leads us to the claim that appears in HB2548. It says that lobe-finned fish have been used as index fossils. That might be true, though as usual no references are given that might substantiate this claim. In the absence of such references, I will not stipulate that the anti-evolutionists have made a correct statement here. It isn't my job, though, to show that no lobe-finned fishes have been used as index fossils, which would be attempting to prove a negative. (Though I report the result of a literature search below that is a pass at such.) The burden of proof rests on the anti-evolutionists who claim that such is the case. If it is true, then they should be able to easily produce one or more references which specify the particular species of lobe-finned fish used as an index fossil. This has not happened. HB2548 says that lobe-finned fish are alive today, citing the "coelacanth". Yes, Latimeria spp. are lobe-finned fishes. It then goes on to conclude that since "coelacanths" are alive today, they cannot be an "index fossil" for any rock. This is a non sequitur. First, a search of the GeoRef database, which contains entries pertinent to earth science dating back to 1785, shows 40 hits for "Latimeria", 54,286 hits for "fossil", and 194 hits for "index fossil", but no hits at all for "Latimeria index fossil". If the modern species of coelacanth were used as index fossils, it would seem reasonable to expect that this would be reflected in the literature. It isn't. It is incumbent upon the anti-evolutionists to show that their claim that Latimeria spp. have been used as index fossils is anything but a falsehood. Second, in general it would disestablish a particular index fossil if it were found to have a much larger stratigraphic extent than its previous application had covered. However, the case of the "coelacanth" does not show an example of this. Third, while Latimeria spp. are referred to as "living fossils", the fact of the matter is that Latimeria spp. are known only from extant specimens and have never been found as fossils themselves. The "example" given by HB2548 is misleading and quite possibly false in a variety of its claims and implications, and no substantiation is given that it could even possibly be true in its claims regarding "index fossils".
Wesley R. Elsberry
 Schwimmer David R.; Stewart J D.; Williams G. Dent. 1994. Giant fossil coelacanths of the Late Cretaceous in the Eastern United States. Geology (Boulder).22; 6, Pages 503-506.
Coelacanths from Sulawesi