Fitting the generalized inverse Gaussian-Poisson distribution (GIGP) to observed frequency distributions of taxa from the Late Triassic Molteno Formation of South Africa has yielded estimates of the corresponding preserved biodiversities. Three extrapolations have been made on the basis of the uniquely rich megaflora/insect coassemblages from 100 taphocoenoses: insect species—335 observed, 7740 preserved; vegetative species—206 observed, 667 preserved; gymnosperm ovulate orders—16 observed, 84 preserved. The reliability of the results varies according to the abundance and observed diversity of the taxa. These results, with further estimations in a companion paper of existed diversity (regional, continental and global), hint at Late Triassic floral and faunal richness akin to today. This conflicts with the traditionally held model of an increasing cone of biodiversity through time and suggests a phase of explosive evolution in the Triassic hitherto unsuspected. Application of the GIGP to other well-documented collections from other periods might reveal a pattern of diversity trends offering fundamentally new insights into the evolving terrestrial biosphere.