Species abundance and individual abundance. (A) The lognormal species abundance curve. The x axis shows log2(N), where N is bacterial abundance; the number of individuals within a species. The y axis shows the number of species, S, occurring at any abundance (N). Nmax (x axis) is the number of individuals in most abundant species, Nmin (x axis) is the number of individuals in the least abundant species, and N0 (x axis) is the modal species abundance. The total diversity, ST, is the area under the species abundance curve. The width of the species curve is inversely proportional to the spread parameter a. Here, one species with 224 ( = 1.6 × 107) individuals occurs at Nmax and one species with 20 (=1) individuals occurs at Nmin. (B) The individuals curve (solid) is found by multiplying abundance, N, by S, the number of species at that abundance (dots and dashes as in A not to scale). The total number of individuals in the sample is NT, which corresponds the area under the individuals curve. Nmax is the number of individuals in the most abundant species. Both Nmax and NT can be easily measured. This example obeys Preston's canonical hypothesis which states that the peak of the individuals curve coincides with Nmax. This fixes the value of a. A and B show that most species occur with very low abundance, so direct empirical measurement of diversity is impractical.