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Just a note

Although we have only shown the distribution for i = 1 to 10, the log series distribution is infinite. Where i can have be any positive number a log series distribution is a continuous curve - and is often drawn that way.

However, where i is the number of individuals in a species, i must be discrete. Fairly obviously, if we add up the height of each bar in the first graph, their sum is one. So if your survey found s species, and you want to approximate the number of species in each bar, α should be s/−loge(1−x).

The second graph shows several forms of this distribution using frequency polygons.