In the 1960s the new technique of gel electrophoresis revealed what was then considered to be an astonishing amount of molecular variation in natural populations, with about 30% of genetic loci being polymorphic. It was thought at the time that natural selection the dominant principle in evolutionary biology could not account for such high levels of variability the costs of selection would be too high. This prompted the proposal of the neutral theory of molecular evolution (Kimura 1968; King & Jukes 1969; Kimura 1983), which postulated that most molecular evolution did not involve natural selection at all: in this model, selectively neutral mutations arose and their frequencies simply fluctuated at random, as is inevitable in a finite population. Tropical forests pose a similar puzzle for ecologists. The enormous numbers of species seem to challenge our classical notions that coexistence requires that each species has its own unique niche: how can so many species construct unique niches from such a small number of requirements sun, water, a patch of ground? The same puzzle in a different context became known as the 'paradox of the plankton' (Hutchinson 1961). As in molecular evolution, so too in ecology a neutral theory has been proposed which may resolve our puzzle (Bell 2001; Hubbell 2001) and is attracting much attention. The theory's advocates have more in mind than tropical trees, but I will restrict myself to trees to make the discussion specific. This was the context in which the theory was first proposed (Hubbell 1979) and one of the main biological areas where we have a puzzle apparently requiring a radical solution. Hereafter I will refer to the neutral theory of biodiversity as NTB. The underlying stochastic theory is the same in the two areas, although it has been studied for much longer in population genetics, as neutral advocates point out (Hubbell 2001; Volkov et al. 2003). This means we can import many results from the population genetics literature, simply interpreting the biology in a different way. In this paper I will import an important result concerning the time-scale of the neutral process, which raises serious difficulties for the NTB as an explanation of tropical forest diversity. This difficulty has been noted before (Leigh 1999; Lande et al. 2003), but does not appear to be as widely known as it should. Nonetheless, as I will discuss, neutral theory can still provide useful null models for the interpretation of data. In the fir t section, I gather together some basic theoretical results that are common to both population genetics and NTB. This is for two reasons. First of all, it serves to emphasize that we really are talking about the same theory, giving us the confidence to bring into the body of NTB an important result from population genetics concerning the time-scale of the neutral process. This will be done in the third section. Secondly, people may find it useful to have these basic results gathered toget er in one place they are currently somewhat scattered about. Having emphasized the underlying identity of the theory, I then briefly explore the implications of the biological differences between the worlds of molecular evolution and biodiversity for the likely future development of the theory in the biodiversity context.