The total number of species on earth and the rate at which new species are created are fundamental questions for ecology, evolution and conservation. These questions have typically been approached separately, despite their obvious interconnection. In this study
we approach both questions in conjunction, for all terrestrial animals. To do this, we combine two previously unconnected bodies of theory: general ecosystem models and individual based ecological neutral theory. General ecosystem models provide us with estimated numbers of individual organisms, separated by functional group and body size. Neutral theory, applied within a guild of functionally similar individuals, connects species
richness, speciation rate and number of individual organisms. In combination, for terrestrial endotherms where species numbers are known, they provide us with estimates for speciation rates as a function of body size and diet class. Extrapolating the same rates to guilds of ectotherms enables us to estimate the species richness of those groups, including species yet to be described. We find that speciation rates per species per million
years decrease with increasing body size. Rates are also higher for carnivores compared to omnivores or herbivores of the same body size. Our estimate for the total number of terrestrial species of animals is in the range 1.03 − 2.92 million species, a value consistent
with estimates from previous studies, despite having used a fundamentally new approach. Perhaps what is most remarkable about these results is that they have been obtained using only limited data from larger endotherms and their speciation rates, with the predictive process being based on mechanistic theory. This work illustrates the potential of a new approach to classic eco-evolutionary questions, while also adding weight to existing predictions. As we now face an era of dramatic biological change, new methods will be needed to mechanistically model global biodiversity at the species and individual organism level. This will be a huge challenge but the combination of general ecosystem models and neutral theory that we introduce here is a way to tractably achieve it.