Coverage‐based rarefaction fails to quantify relative species richness

Coverage‐based rarefaction (CBR) is a high‐profile tool for assessing biodiversity that provides relative species richness estimates by leveraging the Good‐Turing index u to interpolate. In contrast to alternatives such as the Shannon and Simpson indices, CBR's main appeal is providing values in units of species. CBR is tested against a series of other biodiversity measures. Data are both simulated and empirical, in the latter case drawn from an eclectic global database of terrestrial organisms. Various challenges are presented. First, species counts are simulated under the geometric Weibull (GW), Poisson log normal, and discretised Weibull abundance distributions. CBR and six other diversity estimators are then computed. Second, diversity estimates are computed for species inventories and then recomputed after excluding the single most common species in each one, which stands in for random inclusion of high counts in replicate samples. Third, randomly selected pairs of inventories are either 1) analysed separately with richness estimates summed, or 2) combined and only then analysed. Fourth, estimates are compared for randomly paired inventories: each pair must include an identical or highly similar number of singletons (= species sampled once). On average, fitting GW in simulation consistently returns an accurate and precise estimate of richness. GW returns much the same values regardless of how the empirical data are treated. CBR often overestimates by a large margin when dominants are excluded, underestimates by a large margin when data are combined, and nearly randomises values for singleton‐matched inventory pairs. In other words, CBR does not respond predictably to variation in species richness and cannot reconstruct it when the data have strong internal structure. Because better options are available, it is neither wise nor necessary to standardise by coverage in order to estimate richness.