Low-latitudinal standard Permian radiolarian biostratigraphy for multiple purposes with Unitary Association, Graphic Correlation, and Bayesian inference methods

The ideal goal of biostratigraphic studies is to make stratigraphic ranges of all species clear and to fix globally synchronous biohorizons as age controls. However, it is difficult to achieve this goal in simple, traditional ways, and so a new solution is proposed for Permian radiolarian biostratigraphy. To achieve this goal (including to establish a globally applicable biostratigraphy, to estimate the numerical age of biohorizons, and to determine stratigraphic ranges at species level), all 400 known Permian radiolarian species, approximately 70 stratigraphic sections, and 1560 samples from 350 previously published papers about the low-latitude Tethys and Panthalassa oceans were analyzed. Issues of Permian studies are summarized and a solution is proposed from the Cenozoic point of view. Considering traditional methods, as well as successful methods in Cenozoic radiolarian studies, here we implement newly proposed methods that have never been used for Permian radiolarian studies: Unitary Association Method (UAM), “Minimum Disordered Biohorizon Algorithm” (MDBA), Graphic Correlation (GC), and ‘Reiteration Estimation Rounds’ (RER). Of these, our proposed RER is a new method to predict the probability of the estimated age for a sample by Bayesian inference and joint probability (both statistical methods). As these four methods are applicable to any biostratigraphic study, the principals and practical applications of these methods are carefully explained so non-specialists can understand the logical procedure. As a result, 15 Unitary Association Zones (UAZs) are established for the entire Permian biostratigraphic scheme by UAM, the numerical ages of 42 first occurrences (FOs) are estimated from non-parametric data from the middle Guadalupian (middle Permian) to the uppermost Lopingian (uppermost Permian) by MDBA and GC, and the statistical likelihood UAZ ranges of 165 species in the entire Permian were obtained using the RER procedure. A usability test of our UAZs shows that 97.96% of the 933 tested samples from previously published papers are well correlated and without contradiction. Within the statistical error of Cenozoic synchronous biohorizons at 1.4 Myr, 23 of 42 FOs are potentially regarded as synchronous events. As the statistical likelihoods of UAZ ranges are estimated by Bayesian inference, these ranges can be updated by anyone.