Counting taxonomic richness from discrete biochronozones of unknown duration: a simulation

Counts of taxonomic richness and derivates such as origination and extinction rates should ideally be scaled against absolute time. However, calibration of the fossil record with absolute time is often wanting or lacking at the zone level, which is the most resolved level that can be reached for long-distance correlations based on faunal content. For discrete biochronozones based on the maximal association principle (Oppel zones, concurrent-range zones, unitary-association zones), the relation between taxonomic richness and absolute duration of maximal associations is explored by means of an inverse Monte-Carlo approach. Simulations indicate that only a minor and negligible fraction (6% on average) of changes in taxonomic richness can be explained by changes in absolute duration of maximal associations. This very weak relation is shown to hold whatever the mean values of Poisson-type distributions of longevity of taxa, the various degrees of completeness of the record, and the intensity of a superimposed extinction phase. Hence, biochronozones based on the principle of maximal association provide a very robust and reliable basis for counts of taxonomic richness. However, as the mean of the distribution of longevities strongly controls the taxonomic richness and the number of constructed maximal associations, great caution is required when comparing fluctuations of taxonomic richness of different clades in time and space. On the other hand, and all other things being equal, the comparison of taxonomic richness of clades across stratigraphic successions is shown to be reliable irrespective of the biostratigraphic completeness of the sequences. Finally, during extinction phases, the number of zones is shown to increase, whereas the mean duration of zones is found to decrease strongly, leading to a significantly negative correlation between the percentage of disappearing taxa and the total amount of time represented by zones. This last result clearly emphasizes the methodological inappropriateness of the widely used equal zone-duration approach.