Estimating biodiversity using symbolic meta analysis

Global species richness is a key biodiversity metric. Concerns continue to
grow over its decline due to overexploitation and habitat destruction by
humans. Despite recent efforts to estimate global species richness, the
resulting estimates have been highly uncertain and often logically
inconsistent. Estimates lower down either the taxonomic or geographic
hierarchies are often larger than those above. Further, these estimates
have been typically represented in a wide variety of forms, including
intervals (a, b), point estimates with no uncertainty, and point estimates
with either symmetrical or asymmetrical bounds, making it difficult to
combine information across different studies. Here, we develop a Bayesian
hierarchical approach to estimate global species richness (we estimate
22.02m species; 95% HPD interval (10.43m, 35.28m)) that combines 50
estimates from published studies. The data mix of intervals and point
estimates are reconciled using techniques from symbolic data analysis.
This approach allows us to recover interval estimates at each species
level, even when data are partially or wholly unobserved, while respecting
logical constraints, and to determine the effects of estimation on the
whole hierarchy of obtaining future estimates for particular taxa at
various levels in the hierarchy.