This paper begins with a survey of the patterns in discovering and recording species of animals and plants, from Linnaeus' time to the present. It then outlines various approaches to estimating what the total number of species on Earth might be: these approaches include extrapolation of past trends; direct assessments based on the overall fraction previously recorded among newly studied groups of tropical insects; indirect assessment derived from recent studies of arthropods in the canopies of tropical trees (giving special attention to the question of what fraction of the species found on a given host-tree are likely to be ‘effectively specialized' on it); and estimates inferred from theoretical and empirical patterns in species-size relations or in food web structure. I conclude with some remarks on the broader implications of our ignorance about how many species there are.
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