Estimating the global number of tropical tree species, and Fisher’s paradox

How many tropical tree species are there in the world? Slik et al. (1) address this question in an elegant way, but this question is far harder than one might initially suppose. Significant uncertainties still remain, which I attribute in large part to an unsolved conundrum that I call “Fisher’s paradox.” Except for a few charismatic groups of organisms such as birds and butterflies, ecologists still do not know the numbers of species in most taxonomically or functionally defined groups, including tropical trees. Surveying herbaria and published species descriptions cannot tell us how many tropical tree species remain undiscovered and undescribed. Experienced tropical botanists and plant biogeographers may provide expert opinions on how many tropical tree species there are, but Slik et al. note that it is difficult to assess the accuracy of such opinions. Is there some way to come up with a more reliable estimate? Slik et al. think so and use a method first applied to estimating tree species richness in Amazonia (2, 3). The method involves extrapolating estimates of species richness to an entire biogeographic region from tree species inventories in many sample plots scattered across the region. The accuracy of this extrapolation relies on a curious stability property of Fisher’s logseries (4), a statistical distribution widely used to describe patterns of relative species abundance in ecological communities, including tropical tree communities. The stability property has to do with the relative stability of Fisher’s αα, the diversity parameter of the logseries, in the face of changes in sample size. The fit of the logseries to relative tree species abundance data over large numbers of plots is often remarkably precise. Consider Fig. 1, which is a fit of the logseries to rank species abundance data for 4,962 tree species in 1,170 plots scattered across …