Table 1.

Selected non-parametric measures of diversity properties (Stirling 2006f,o). N, number of categories of elements; ln, logarithm (usually natural); p_i, proportion of system comprises category i; n, number of attributes displayed by elements; σ, standard deviation of attributes within categories; μ, mean of attributes within categories; f (d_ij), function of distance in disparity space between categories i and j; D_W(S), aggregate disparity of system S; d_W(i, S\i), distance in disparity space between category i and the nearest remaining element in S if i is excluded.

property addressed	name	form
variety	category count (MacArthur 1965)	N
balance	Shannon evenness (Pielou 1969)	$\left(-{\sum }_i{p}_i\text{ln}{p}_i\right)/\text{ln}N$
disparity	Weitzman (1992a) (Solow & Polasky (1994a))	maxi∈S{DW(S\i)+dW(i,S\i)}f (dij)
variety/balance	Shannon & Weaver (1962)	$-{\sum }_i{p}_i\text{ln}{p}_i$
	Simpson (1949)	${\sum }_i{p}_i^2$
	Gini (1912)	$1-{\sum }_i{p}_i^2$
variety/balance/disparity	Junge (1994)	$\left(\sigma /\left(\mu ·\sqrt{n-1}\right)\right)·\left(1/\sqrt{N}\right)·\left(\sqrt{N-1}-\sqrt{N{\sum }_i{p}_i^2-1}\right)$