Relationship between the Tail statistic, τ, and Standard Deviation, σ.

<p>τ is the standard deviation of the rank abundance curve after reflection around the most dominant taxonomic unit, <i>i</i> = 1. The blue bars represent the rank abundance curve. Above each bar, the probability, Pr[<i>i</i>], of the <i>i</i>^th most dominant taxonomic unit has been labelled in italics. The natural numbers labelled in bold above the blue bars represent the rank, <i>i</i>, of each taxonomic unit. The name of each taxonomic unit is labelled along the x-axis. The grey bars represent the mirror image of the rank abundance curve. Treating <i>i</i> = 1of the symmetric distribution as μ = 1, the standard deviation, σ, is then 3.764, which also represents τ for this rank abundance curve and sample.