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Questions The co‐existence of high numbers of species has always fascinated ecologists, but what and where are the communities with the world records for plant species richness? The species–area relationship is among the best‐known patterns in community ecology, but does it give a consistent global pattern for the most saturated communities, the global maxima? Location The world. Methods We assembled the maximum values recorded for vascular plant species richness for contiguous areas from 1 mm2 up to 1 ha. We applied the power function to relate maximal richness to area and to make extrapolations to the whole Earth. Results Only two community types contain global plant species maxima. The maxima at smaller spatial grain were from oligo‐ to meso‐trophic, managed, semi‐natural, temperate grasslands (e.g. 89 species on 1 m2), those at larger grains were from tropical rain forests (e.g. 942 species on 1 ha). The maximum richness values closely followed a power function with z = 0.250: close to Preston's ‘canonical’ value of 0.262. There was no discernable difference between maxima using rooted presence (i.e. including only plants rooted in the plot) vs shoot presence (i.e. including any plant with physical cover over the plot). However, shoot presence values must logically be greater, with the curves flattening out at very small grain, and there is evidence of this from point quadrats. Extrapolating the curve to the terrestrial surface of the Earth gave a prediction of 219 204 vascular plant species, surprisingly close to a recent estimate of 275 000 actual species. Conclusions Very high richness at any spatial grain is found only in two particular habitat/community types. Nevertheless, these high richness values form a very strong, consistent pattern, not greatly affected by the method of sampling, and this pattern extrapolates amazingly well. The records challenge ecologists to consider mechanisms of species co‐existence, answers to the ‘Paradox of the Plankton’.

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One Sentence Summary: Empirical evidence from grasslands around the world demonstrates a humped-back relationship between plant species richness and biomass at the 1 m 2 plot scale.Abstract: One of the central problems of ecology is the prediction of species diversity. The humped-back model (HBM) suggests that plant diversity is highest at intermediate levels of productivity; at low productivity few species can tolerate the environmental stresses and at high productivity a small number of highly competitive species dominate. A recent study claims to have comprehensively refuted the HBM. Here we show, using the largest, most geographically diverse dataset ever compiled and specifically built for testing this model that if the conditions are met, namely a wide range in biomass at the 1 m 2 plot level and the inclusion of plant litter, the relationship between plant biomass and species richness is hump shaped, supporting the HBM. Our findings shed new light on the prediction of plant diversity in grasslands, which is crucial for supporting management practices for effective conservation of biodiversity. 4Main Text: The relationship between plant diversity and productivity is a topic of intense debate (1-6). The HBM states that plant species richness peaks at intermediate productivity, taking above-ground biomass as a proxy for annual net primary productivity (ANPP) (7-9). This diversity peak is driven by two opposing processes; in unproductive and disturbed ecosystems where there is low plant biomass, species richness is limited by either stress, such as insufficient water and mineral nutrients, or high levels of disturbance-induced removal of biomass, which few species are able to tolerate. In contrast, in the low disturbance and productive conditions that generate high plant biomass it is competitive exclusion by a small number of highly competitive species that is hypothesized to constrain species richness (7-9). Other mechanisms proposed to explain the unimodal relationship between species richness and productivity include disturbance (10), evolutionary history and dispersal limitation (11,12), and density limitation affected by plant size (13).Different case studies have supported or rejected the HBM, and three separate meta-analyses reached different conclusions (14). This inconsistency may indicate a lack of generality of the HBM, or it may reflect a sensitivity to study characteristics including the type(s) of plant communities considered, the taxonomic scope, the length of the gradient sampled, the spatial grain and extent of analyses (14,15), and the particular measure of net primary productivity (16). Although others would argue (6), we maintain that the question remains whether the HBM serves as a useful and general model for grassland ecosystem theory and management. 5 We quantified the form and strength of the richness-productivity relationship using novel data from a globally-coordinated (17), distributed, scale-standardized and consistently designed survey, in which plant richness and biomass were m...