In 2005, Trevor Cotton and Richard Fortey coauthored an phylogenetic analysis of agnostid trilobites that included both eodisc

The Relationship of Agnostina to Eodiscina

This page last revised 30 June 2007 by S. Gon III

Summarized here are the main observations in Cotton & Fortey 2005 "Comparative morphology and relationships of the Agnostida," that together arugue for unity of the Agnostina and Eodiscina within Order Agnostida:

All Agnostina are eyeless and sutureless, as are some Eodiscina, allowing a hypothesis that Agnostina arose from a clade of blind, sutureless Eodiscina.
Primitive Eodiscina have a cephalon wider than long, but advanced eodiscines such as Weymouthiidae (and most Agnostina) bear longer cephala.
The obvious synapomorphy of very strong isopygy is seen in all Eodiscina and Agnostina, and unites all Agnostida.
Although in the past it was argued that Agnostina lack genal spines, a review of the taxa show this supposed synapomorphy of Agnostina is not true. There are species of Agnostina and Eodiscina that bear genal spines; e.g., in Eodiscus & Acidicus (in Eodiscina), and in the Condylopygoidea (Agnostina).
In Agnostina, there is a distinctive glabellar division into an anteroglabella and posteroglabella, and a pair of basal lobes corresponding to the occipital band. The furrow dividing antero- from posteroglabella corresponds to S3 in a typical trilobite, and the anteroglabella and posteroglabella consist of two segments each, as shown by muscle scars of underlying limbs in some specimens. There are transglabellar furrows of similar type in some Eodiscina, and in no Agnostida are there furrows anterior to the transglabellar furrow. So complete effacement of the S4 furrow also unites Agnostina and Eodiscina.
In Eodiscina, the structure of the cephalic axis is highly variable, and in primitive Eodiscina, differs from a typical polymeroid trilobite only in effacement of S4 and a transglabellar S3. The occipital lobe in some Eodiscina is similar to the paired basal lobes of Agnostina, bearing a narrow band connecting two lateral triangular basal lobes, the medial connecting band being hidden by the adjacent anterior glabellar lobe. The occipital lobe of Eodiscina is thus considered homologous to the agnostine basal lobes.
Many agnostines bear a median glabellar node on L2 (although effacement makes it difficult to ascertain the exact lobe in many cases). This is considered homologous to L2 spines or nodes on some Eodiscina, including several weymouthiids.
A preglabellar sagittal furrow is seen in both agnostine and eodiscines, but is effaced in many taxa. Nonetheless this is another unifying feature.
Although the hypostome of Agnostus pisiformis is striking distinctive from the typical polymeroid hypostome, that of another agnostine (Oidalagnostus trispinifer) is of typical polymeroid form, and that of Peronopsis interstricta is intermediate between A. pisiformis and O. trispinifer. The hypostome of an eodiscine, Pagetia ocellata, is of typical polymeroid type. Taken altogether, the known hypostoma of Agnostida are variable, and most are of polymeroid form.
Presence of only two or three thoracic segments in Agnostida was the basis of the old division of Trilobita into subclasses Miomera and Polymera. However, there are polymeroids with few thoracic segments, such as Thoracocare (Corynexochida) and Taklamakania (Asaphida), so the distinction on the basis of thoracic segment number alone is not valid. All agnostines bear only two segments, and eodiscines bear either three, or sometimes two segments. The structure of the thoracic segments of Agnostida is distinctive, and seems related to the function of enrollment.
The pygidial axis of Agnostina is distinctive, bearing furrows only anteriorly, with three pairs of axial ring furrows in condylopygoids, and two in all other Agnostina. Moreover, an axial node on the second pygidial segment (sometimes a spine) was considered an autapomorphy of agnostines. In contrast, the pygidial axis of eodiscines is variable, usually bearing several clear axial rings. When axial spines are present, they are often most prominent anteriorly, and often most prominent on the second segment. This is another uniting factor, though not consistently present among all eodiscines and agnostines.
The pleural fields of agnostine pygidia are effaced, while in most Eodiscina, there are pleural furrows. However, in most Weymouthiidae, pleural furrows are also effaced, making this a good synapomorphy of a weymouthiid-agnostine clade.

The result of the phylogenetic analysis conducted indicated that there are two large clades in the Agnostida corresponding roughly to Agnostina and Eodiscina, but that the agnostine clade includes eodiscines of the family Weymouthiidae. This strongly infers that the Agnostina and Weymouthiidae are closely related, uniting the Eodiscina and the Agnostina. Moreover, the Agnostina form a monophyletic clade nested within a clade that includes the weymouthiid genera Mallagnostus, Chelediscus, Tannudiscus and Jinghediscus, and this group falls within a larger weymouthiid clade.

To reiterate, the conclusion is that there is a strong link between the Agnostina and the Eodiscina via the family Weymouthiidae, and Agnostina are considered part of the order Agnostida, and thus are true trilobites.

Pertinent literature:

Cotton, T. J. & R.A. Fortey. 2005 Comparative morphology and relationships of the Agnostida. In: Koenemann, S. & Jenner, R. (eds.).
Crustacean Issues 16, Crustacea and Arthropod Relationships (CRC Press: Boca Raton).

Resser, C.E. 1938. Cambrian system (restricted) of the Southern Appalachians. Geol. Surv. Amer. Spec. Paper 15:1-140.

Shergold, J.H. 1991. Protaspis and early meraspis growth stages of the eodiscoid trilobite Pagetia ocellata Jell, and their implications for classification. Alcheringa 15: 65-86.

Walossek, D. & K.J. Müller. 1990. Upper Cambrian stem-lineage crustaceans and their bearing upon the monophyletic origin of Crustacea and the position of Agnostus. Lethaia 23:409-27.