A community measure that takes both species abundance and species richness into account is the Shannon diversity index?H. To calculate?H, the proportion?pi?of species?i?in the community is used. Assume that the community consists of?S?species. Then

(a) Assume that?S?= 5 and that all species are equally abundant; that is,?p₁?=?p₂?= ? ? ? =?p₅. Compute?H.

(b) Assume that?S?= 10 and that all species are equally abundant; that is,?p₁?=?p₂?= ? ? ? =?p₁₀. Compute?H.

(c) A measure of equitability (or evenness) of the species distribution can be measured by dividing the diversity index?H?by ln?S. Compute?H/?ln?S?for?S?= 5 and?S?= 10.

(d) Show that, in general, if there are?N?species and all species are equally abundant, then

H = (P ln P + P2 ln P2 + + Ps ln ps) H In S 1