Ancistroceras is one of the two ancestral lituitids

Lituitidae

The Lituitidae is a family of evolved tarphycerids characterized by a long orthoconic section that follows a coiled juvenile portion at the apex, along with a generally tubular siphuncle, which like that of the barrandeocerids is composed of thin connecting rings.-Taxonomic Position:Flower and...

 from the late Early Ordovician (Arenigian). The other being Holmiceras

Holmiceras

Holmiceras is one of two ancestral lituitids from the late Early Ordovician . The other being Ancistroceras.Holmiceras begins with about 1.5 to 2 loosely coiled whorls followed by a rapidly expanding orthocone, much like Ancistroceras except for the apical whorls and that Holmiceras is known only...

.

The shell is weakly annulate, starts off with 1.5 to 2 contiguous or slightly separated whorls followed by a rapidly expanding orthocone with an apical angle of about 30 deg. Growth lines are sinuous, show a pronounced hyponomic sinus in the coiled juvenile portion at the apex but almost none at the mature aperture of the orthcone. Holmiceras is similar except that its whorls are more losely coiled and it is known only from the Arenigian where as Ancistroceras ranges through most of the Middle Ordovician.

Ancistroceras may have given rise to Rhynchorthoceras

Rhynchorthoceras

Rhynchorthoceras is a Middle Ordovician genus characterized by a rapidly expanded, weakly annulate orthocone, like the orthoconic section of Ancistroceras, but with only a curved, cyrtoconic apex instead of juvenile whorls....

by a loss of the juvenile coiled portion, replacing it with a short semi-tubular cyrtoconic section. Ancistroceras may also have given rise to Lituites

Lituites

Lituites is an extinct nautiloid genus from the Middle Ordovician and type for the Lituitidae, a tarphycerid family that in some more recent taxonomies has been classified with the orthocerids and listed under the order Lituitida...

by evolving a narrower, less rapidly expanding, orthocone along with greater ornament and a complex aperture.

References

• Flower, R. H. 1950. A Classification of the Nautiloidia. Jour Paleontology, V.24, N.5, pp 604–616, Sept
• Furnish & Glenister, 1964. Nautiloidea -Tarphycerida. Treatise on Invertebrate Paleontology Part K, Mollusca 3 ...Nautiloidea