diversity index. 



s = number of taxa in the sample 



N. = number of individuals in the taxon 

 l 



N = total number of individuals 



A few of the authors cited earlier in this section and Hurlbert (1971) 

 have criticized the Shannon-Weaver function as improperly used in many studies. 

 However, the U.S. Environmental Protection Aqency (1973) has provisionally 

 accepted and recommended the function for aquatic macrobenthos studies. 



The index, d, possesses features that make it a useful method for 

 summarizinq communitv diversity. The index is dimensi onless and expresses 

 the relative importance of each species in the community. As sample size 

 is increased, the d of the progressively pooled samples increases rapidly at 

 first and then levels off. Since diversity of progressively pooled samples 

 asymptotically approaches the diversity of the population, and since diversity 

 of individual samples are hiqhly variable, it is preferable to report the 

 diversity of the pooled samples. Diversity had leveled off by the fifth pooled 

 sample in most of the areas sampled by Wilhm (1970abc). The range of d varies 

 from zero to any positive number. A value of zero is obtained_when all 

 individuals belong to the same species. The maximum value of d depends on the 

 number of individuals counted and is obtained when all individuals belong to 

 different species. The d usually varies between three and four in clean-water 

 stream areas and is usually less than one in polluted stream areas (Wilhm 

 1970abc). 



A low diversity index indicates a larqely monotypic community dominated 

 by a few abundant organisms. Often the total number of species is low. In 

 addition, a low diversity index often suggests that deqraded environmental 

 conditions exist which favor the proliferation of a few tolerant species and 

 the removal of less tolerant forms. A high diversity index indicates a 

 heterogeneous community in which abundance is distributed more evenly among 

 a number of species. The total number of species is generally high. 



EQUITABILITY (E m ) 



As measured by Marqalef ( 1 9B7 ) and Krebs (1972), equitability (E ) is 

 a retio of the observed d to a maximum theoretical diversity (d max ) computed 

 as though all individuals were equally distributed amonq the species. Maxi- 

 mum diversity here is measured simply as loq 9 s; therefore 



E = d/loq s 

 m c 



As equitability increases, the species become more evenly distributed 

 and their distributions conform more closely to perfect theoretical distri- 

 butions. Equitability may range from to 1, except that in samples containino 

 only a few specimens with several taxa_represented , values of E greater than 

 1 may occur. The estimates of E™ and d improve with increased sample size, and 

 samples containing fewer than TOO specimens should be evaluated with caution if 



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