The rhizomorphic lycopsids are a putatively monophyletic group delimit
ed by the rhizomorphic syndrome: centralized determinate growth and se
condary thickening in their rooting systems. A cladistic analysis of t
he most completely understood species provides the basis for two alter
native, new classifications of the group, one following strict phyloge
netic classification criteria, the other more traditionally Linnean. B
oth are based on the same preferred most-parsimonious cladogram and pl
ace the rhizomorphic lycopsids in one order, the Isoetales. Also, both
classifications delimit the same suprageneric groups: Hizemodendron Lepidodendron + Lepidophloios, Diaphorodendron + Synchysidendron, Sig
illaria, and Chaloneria + Isoetes are well supported as monophyletic c
lades, but the basal plexus of bisporangiate-coned ulodendrids (Paraly
copodites + Oxroadia + Paurodendron) is paraphyletic. Both classificat
ions differ from all previous studies in 1) assigning all rhizomorphic
lycopsids to a single order, and 2) recognizing the trees Diaphoroden
dron plus Synchysidendron as a distinct family the Diaphorodendraceae.
A generally applicable paleobotanical taxonomic philosophy is outline
d that broadly reflects a phylogenetic framework based on living speci
es (if available) and reconstructed whole-plant fossil species. These
core species provide a framework into which are interpolated satellite
taxa: fossil isolated organs and partial plants.