I know how estimates of species richness in a small area are made. But how do you estimate the total number of species on a global scale?
One example of such a method can be found in Mora et al. 2011.
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You might be interested in the below works as well as the references that they cite.
May, R. M. (1988). How many species are there on Earth? Science, 241(4872), 1441–1449.
Millennium Ecosystem Assessment. (2005). Ecosystems and Human Well-Being: Synthesis (p. 137). Washington, D.C.: Island Press.
It's worth noting that many estimates of species richness at large scales are based on the use of the species-area relationship to upscale richness measurements from small scales to large scales.