## Evenness or Equitability

Three measures of diversity that have been widely used in ecology are Simpson's index, Shannon's entropy, and the total number of species or species richness. Some species diversity indices are based on the concept of evenness or equitability. Simply put, the concept of evenness refers to the extent to which each species is represented among the sample. The extremes would range from one species being dominant and all other species being present in very low numbers (one individual for each species) to all species being represented by equal numbers. For example, in a sample of 10 species, one extreme would be a sample with one species represented by 99 individuals and the other nine being represented by one individual each. The other extreme would be where each of the 10 species was each represented by 100 individuals. The diversity index is based on a calculation of the extent of evenness of the distribution of individuals across the species.

where D is the index ofspecies diversity, p is the relative abundance of the ith species (N is the number of the ith species). The use of natural logarithms is usual because this gives the information in binary digits (logi0 100 is 2, ln 100 is 4.6, log10 1000 is 3, ln 1000 is 6.9).

There is some confusion in the literature in that the Shannon-Wiener index is sometimes mistakenly called the Shannon-Weaver index. This confusion has come about partly because Shannon collaborated with Weaver on several occasions to publish papers and books, in particular the book The Mathematical Theory of Communication. However, in an earlier publication, Shannon pays tribute to Norbert Wiener for his contribution to the theories in cybernetics. The often-mistaken assumption that Shannon and Weaver developed the function H stems partly from the confusion arising from the joint author names of Shannon and Weaver.

With reference to the data in Table 1, the ShannonWiener index for the samples of moths collected each

 Species Month May Jun. Jul. Aug. A 0 7 149 87 B 0 0 2 85 C 47 96 2 0 D 4 44 31 0 E 22 36 92 5 F 0 2 195 60 G 0 0 84 51 H 1 144 255 38 0 13 32 87 J 25 41 24 3 Number of individuals 99 383 866 416 Number of species 5 8 10 8

p, is the proportion of the ith species in the sample. For example, 47 individuals of species C were caught in May. P, in this case is 47/99 = 0.4747, P,2 = 0.225.

month would be calculated as follows. This example is for the moths collected in May:

= (0-47x - 0.74) + (0-04x - 3.2) = - X-0.35)+ (-0.13)

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