Quantitative biochronology of Devonian ammonoids from Morocco and proposals for a refined unitary association method

Based on a rich dataset, the biostratigraphy of the late Emsian and the Eifelian (Early-Middle Devonian) ammonoids from the Moroccan Tafilalt is re-evaluated. We processed this dataset (comprising 53 species from 15 sections) with the unitary association method (UAM), by means of the UA-graph freeware. This led to the construction of a sequence of 17 UAs (maximal sets of actually or virtually coexisting taxa), which are grouped into 10 laterally reproducible association zones. This biostratigraphical subdivision of this interval is in some parts finer than the classically used empirical stratigraphical scheme and than a previous graphic correlation analysis. It enabled us to measure regional ammonoid diversity of this interval in detail. The UAM is a powerful biochronological method, which benefits from complementary tools to analyse conflicting intertaxon stratigraphical relationships inherent to complex biostratigraphical datasets. In cases of under-constrained superpositional relationships between the taxa, the UAM can yield results, which are not parsimonious in terms of reconstructed virtual coexistences. We suggest several additions to complement the algorithmic steps of the method. The most important is the exhaustive or heuristic reconstruction of possible solutions resolving the observed biostratigraphical contradictions (conflicting inter-taxon superpositional relationships and cycles between maximal cliques) and the selection among the solutions of the most-parsimonious one(s) in terms of reconstructed virtual coexistences. Multiple equivalent results may then be processed with standard consensus techniques. Finally, the robustness of the results can be tested by bootstrapping methods to provide confidence estimates on the ranges and associations of studied taxa.