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Just a note

Partly for historical reasons, the lognormal distribution parameters are calculated in an unusual way.
  • Species are commonly, but not always, classed according to the log2 of their abundance. In other words, as being represented by 1 individual, 2 to 3, 4 to 7, 8 to 15, 16 to 31, and so on. Confusingly, these are known as octaves.
  • The class having the most species (so) is the mode.
  • Some authors standardise octaves by calculating the relative frequency of species in the ith class (fi), compared to their observed frequency in the mode (fo), as R = log2(fi/fo).
  • The distribution's standard deviation is estimated - usually by a complicated and obscure procedure.
  • A dispersion parameter, a, is calculated - where a is twice the variance.
  • The total number of species that could be observed in that community is estimated as so1.77254/a

In many cases a is approximately 0.2 - although this seems to be due to statistical peculiarities of the lognormal distribution, rather than any fundamental biological reasons.