Biogeographic Patterns of Estimation Bias of Biodiversity Indices

ABSTRACT Aim The application of biodiversity indices in environmental, conservation, and biogeographic assessments is routine. It is well known that because of mechanisms like limiting sampling efforts, direct application of biodiversity indices would risk estimation bias, misleading the final conclusions on biodiversity assessment. As an example, species‐level Shannon entropy may be the most widely used biodiversity index in the ecological literature, the counterpart of which in community ecology and biodiversity studies is phylogenetic entropy. However, it is well known that Shannon entropy directly estimated by the observed index is statistically biased, and a bias issue likewise exists when estimating phylogenetic entropy. Location Global and regional. Time Period Current time. Major Taxa Studied Animals and plants. Methods In this study, we first developed a Horvitz‐Thompson (HT) estimator of phylogenetic entropy that can significantly remove the estimating bias of the observed index when it is computed using observed species abundances along with an incomplete phylogenetic tree sampled for a local assemblage. We then applied the original and bias‐corrected entropy estimators to two broad‐spatial empirical datasets: amphibian occurrence records of Madagascar and Gentry forest plots of the world. We also applied and compared the estimation bias of species richness and Faith's phylogenetic diversity for drawing general conclusions. Results Numerically, the HT‐type phylogenetic entropy estimator performed well under local sample abundance‐varying simulations, while reasonably well under the simulation scenario when both local sample abundance and tree branch length were simultaneously altered. It performed consistently well when sample size was small (usually < 50). Empirically, the estimate bias of Shannon and phylogenetic entropy presented geographic distributional discordance patterns in both empirical datasets. In particular, at a global scale, high‐bias‐magnitude areas for Gentry forest‐plot tree species were usually located in highly diverse tropical forest ecosystems, such that it was recommended to employ statistical bias‐corrected biodiversity indices, like the HT estimators of Shannon and phylogenetic entropy, when conducting biodiversity comparisons in these areas. The situation for the spatial estimation bias pattern for species richness and Faith's phylogenetic diversity was similar in principle. Main Conclusions In summary, the proposed bias‐removed estimators for Shannon and phylogenetic entropy are simple to implement with potential biodiversity assessment values. For effectively removing the estimation bias of biodiversity metrics, the uncertainty of the phylogenetic tree should be taken into account.