Theory and application of an improved species richness estimator.

Species richness is an essential biodiversity variable indicative of ecosystem states and rates of invasion, speciation and extinction both contemporarily and in fossil records. However, limited sampling effort and spatial aggregation of organisms mean that biodiversity surveys rarely observe every species in the survey area. Here we present a non-parametric, asymptotic and bias-minimized richness estimator, Ω by modelling how spatial abundance characteristics affect observation of species richness. Improved asymptotic estimators are critical when both absolute richness and difference detection are important. We conduct simulation tests and applied Ω to a tree census and a seaweed survey. Ω consistently outperforms other estimators in balancing bias, precision and difference detection accuracy. However, small difference detection is poor with any asymptotic estimator. An R-package, Richness, performs the proposed richness estimations along with other asymptotic estimators and bootstrapped precisions. Our results explain how natural and observer-induced variations affect species observation, how these factors can be used to correct observed richness using the estimator Ω on a variety of data, and why further improvements are critical for biodiversity assessments. This article is part of the theme issue 'Detecting and attributing the causes of biodiversity change: needs, gaps and solutions'.

The sizes of life.

Recent research has revealed the diversity and biomass of life across ecosystems, but how that biomass is distributed across body sizes of all living things remains unclear. We compile the present-day global body size-biomass spectra for the terrestrial, marine, and subterranean realms. To achieve this compilation, we pair existing and updated biomass estimates with previously uncatalogued body size ranges across all free-living biological groups. These data show that many biological groups share similar ranges of body sizes, and no single group dominates size ranges where cumulative biomass is highest. We then propagate biomass and size uncertainties and provide statistical descriptions of body size-biomass spectra across and within major habitat realms. Power laws show exponentially decreasing abundance (exponent -0.9±0.02 S.D., R2 = 0.97) and nearly equal biomass (exponent 0.09±0.01, R2 = 0.56) across log size bins, which resemble previous aquatic size spectra results but with greater organismal inclusivity and global coverage. In contrast, a bimodal Gaussian mixture model describes the biomass pattern better (R2 = 0.86) and suggests small (~10-15 g) and large (~107 g) organisms outweigh other sizes by one order magnitude (15 and 65 Gt versus ~1 Gt per log size). The results suggest that the global body size-biomass relationships is bimodal, but substantial one-to-two orders-of-magnitude uncertainty mean that additional data will be needed to clarify whether global-scale universal constraints or local forces shape these patterns.