WenJun Zhang School of Life Sciences, Sun Yat-sen University, Guangzhou 510275, China; International Academy of Ecology and Environmental Sciences, Hong Kong Computational Ecology and Software ISSN 2220-721X http://www.iaees.org/publications/journals/ces/online-version.asp 2026 16 3 220 239 International Academy of Ecology and Environmental Sciences Hong Kong 3 April 2026 9 May 2026 1 September 2026 species richness estimation hierarchical weighted cross-calibration biodiversity dark extinction environmental DNA eukaryotic diversity Monte Carlo simulation microbial species concept taxonomic impediment Chao estimators The total number of species on Earth is a fundamental metric in ecology and conservation biology, yet after three centuries of taxonomic effort estimates span two orders of magnitude (2 million to over 1 billion), with little sign of convergence. This persistent uncertainty stems from three intertwined challenges: the preponderance of rare and undersampled species, the methodological incommensurability of extrapolation, decompositional, and molecular approaches, and the lack of a universal species concept for microorganisms. This study proposes the Hierarchical Weighted Cross-Calibration (HWCC) framework, a four-layer probabilistic integration method that synthesizes domain-specific expert estimates, higher-taxon regression constraints, statistical lower bounds (Chao-class estimators), and molecular correction factors derived from eDNA metabarcoding. The seven essential dimensions of the estimation problem are systematically reviewed and quantified: (1) calibration of the known-species baseline, (2) efficacy testing of classical macroecological extrapolations, (3) statistical inference of unseen species, (4) domain-decomposed estimation for major trophic and habitat guilds, (5) quantification of taxonomic dark matter revealed by high-throughput sequencing, (6) dynamic correction for net species loss under contemporary extinction rates, and (7) philosophical and operational reconstruction of the microbial species concept. Monte Carlo propagation of all quantified uncertainties (10^6 iterations) yields a median global eukaryotic species richness of 71 million, with a 90 % credible interval of 65-78 million. When prokaryotic molecular operational units based on a 95 % average nucleotide identity threshold are included, the interval broadens to 72-86 million. The estimate represents a 7- to 8-fold upward revision from the widely cited 8.7 million and implies that the denominator for current extinction-rate calculations, and thus the magnitude of unrecognized "dark extinctions", has been underestimated by an order of magnitude. The HWCC framework is openly structured for iterative refinement with new data and provides a probability density distribution rather than a single-point estimate, enabling risk-explicit incorporation into global conservation targets and biodiversity scenarios. http://www.iaees.org/publications/journals/ces/articles/2026-16(3)/estimating-global-species-richness.pdf