When its a snakestone.
Just a quick post on tarphycerids today - haven't much time. The Tarphycerida were the earliest group of cephalopods to develop a coiled shell, back in the lower Ordovician. Sweet et al. (1964) regarded tarphycerids as sharing a common ancestor in the lower Ordovician Bassleroceratidae with the Oncocerida, the lineage ancestral to modern nautilids. Though tarphycerids are therefore more closely related to nautilids than to coleoids (and therefore, unlike the other Palaeozoic cephalopods I've covered so far, have a case to actually be regarded as nautiloids), the fact that the earliest oncocerids were not coiled (Sweet, 1964a) indicates that the coiled form was independently derived in tarphycerids from nautilids. A few tarphycerid lineages later became more loosely coiled, or uncoiled.
Most tarphycerids were more or less evolute. Closely coiled cephalopod shells can be described as evolute, involute or convolute, though these aren't distinct forms so much as lines on a spectrum. In involute forms, the successive whorls of the shell overlap and cover the earlier whorls to some degree. This is taken to the extreme in convolute forms such as modern Nautilus in which the later whorls entirely conceal the older whorls. In evolute forms, however, the successive whorls lie alongside each other and remain clearly visible. There seems to have been a repeated tendency for evolute forms to be replaced by involute forms - I'm guessing because the involute arrangement was more sturdy and robust. Evolute shells are described as 'serpenticone', which refers to an old English belief that such shells were the petrified remains of coiled snakes. Indeed, it was not uncommon for coiled cephalopod fossils to be sold as 'snakestones' (supposedly protecting against snakebite) with carved snake heads attached to them.
One tarphycerid genus, Lituites, was one of the earliest fossil cephalopods recognised, and though officially published by Bertrand in 1763, Bertrand was merely validating a name that pre-dated Linnaeus (Furnish & Glenister, 1964). Lituitidae started life as coiled shells, but soon changed their growth pattern and grew in a straight line, with the straight segment of shell far larger than the coiled section - lituitids might be up to a foot in length, with the coiled section less than an inch across. While most tarphycerid families were widespread (albeit uncommon), lituitids are only known from northern Europe (and mostly from erratic boulders, which are an absolute bugger to place stratigraphically).
Many tarphycerids showed changes in growth habit through their life. The siphuncle often changed in position - all tarphycerids had ventral siphuncles when young, but for many species they became dorsal with age. Juvenile tarphycerids had standard round apertures, but in many species the aperture changed significantly in form at maturity, becoming contracted by ingrowing lobes of the shell with deep hyponomic and ocular sinuses. Whether and how this change in aperture form was reflected by any change in soft-body morphology can, of course, only be speculated upon. It is worth noting, as well, that the mature body chamber was often spectacularly long - in the family Ophidioceratidae, it may occupy more than an entire whorl of the shell. Again, in the absence of soft-body fossils there is no way of knowing whether the adult body was similarly long, or whether the animal was shorter and able to retreat deep into its shell.
Tarphycerids survived into the mid-Devonian - Sweet (1964b) separated the lineage including all later forms as the order Barrandeocerida, but all more recent authors seem to include the barrandeocerids in the Tarphycerida* (e.g. Turek, 2008). A number of barranderocerids became non-planar coilers (torticones), adopting a more gastropod-like form. Because non-planar coils would not have had such a centred buoyancy distribution compared to planar forms, these species would have probably been benthic in their lifestyle. The tarphycerids disappeared at about the same time as the ecologically similar nautilids and ammonoids were diversifying.
*The concept of paraphyletic taxa in a phylogeny-based classification is a bit like the concept of God in a secular society. People may not actually have anything against the idea, they may argue vociferously for the retention of the idea, but as time goes by they just refer to the idea less and less, and eventually the realisation dawns that there's just no real practical point in hanging on to it.
Furnish, W. M., & B. F. Glenister. 1964. Nautiloidea - Tarphycerida. In Treatise on Invertebrate Paleontology pt K. Mollusca 3 (R. C. Moore, ed.) pp. K343-K368. The Geological Society of America and The University of Kansas Press.
Sweet, W. C. 1964a. Nautiloidea - Oncocerida. In Treatise on Invertebrate Paleontology pt K. Mollusca 3 (R. C. Moore, ed.) pp. K277-K319. The Geological Society of America and The University of Kansas Press.
Sweet, W. C. 1964b. Nautiloidea - Barrandeocerida. In Treatise on Invertebrate Paleontology pt K. Mollusca 3 (R. C. Moore, ed.) pp. K368-K382. The Geological Society of America and The University of Kansas Press.
Sweet, W. C., C. Teichert & B. Kummel. 1964. Phylogeny and evolution. In Treatise on Invertebrate Paleontology pt K. Mollusca 3 (R. C. Moore, ed.) pp. K106-K114. The Geological Society of America and The University of Kansas Press.
Turek, V. 2008. Boionautilus gen. nov. from the Silurian of Europe and North Africa (Nautiloidea, Tarphycerida). Bulletin of Geosciences 83 (2): 141-152.