at all (U.S. EPA 1973). 



An improved equi tabi 1 ity formula is presented below and must be used with 

 tables presented in Lloyd and Ghelardi (1964) and U.S. EPA (1973): 



where s 1 = tabulated value 



E m2 ^ 



Because a table is required to calculate E m ? it is not easily applied to computer 

 operations. 



Equi tabi 1 i ty has been found to be sensitive to even slight levels of 

 environmental degradation. Equi tabi 1 i ty levels below 0.5 have not been 

 encountered in southeastern U.S. streams known to be unaffected by oxygen- 

 demanding wastes, and in such streams Fm2 values are generally between 0.6 

 and 0.8. Even sliqht levels of degradation have been found to reduce E m 2 

 below 0.5 and generally to a range of 0.0 to 0.3. 



REDUNDANCY (R) 



Redundancy (R), as measured by Wilhm and Dorris (1968) and Cairns and 

 Dickson (1971), gives the relative position of the observed diversity index 

 (d) between theoretical maximum and minimum diversities (d and d . » 

 It is calculated as follows: max minj - 



R = ^max " ? 



d - d . 

 max mm 



Theoretical maximum and minimum diversities are calculated as follows: 



d = (1/N) [log 9 N!-s logo (N/s)f| 

 max L ^ ~ c J 



d min = (1/N) {log 2 N! - log 2 [N-(s-l)] !} 



Redundancy measures the repetition of information within a community, 

 thereby expressing the dominance of one or more species, and is inversely 

 proportional to the wealth of species. It is maximal when no choice of 

 species exists and minimal when there is a greater choice of species. 



EVENNESS (J 1 ) 



If the numbers of individuals, Nj, N?, . . . N s , in each of the s species 

 are portrayed in histogram form, s is the range of data or the width of the 

 histogram. The shape of the histogram is best described in what may be called 

 its "evenness." Thus, the distribution has maximum evenness if all the species 

 abundances are equal; the greater the disparities among the different species 

 abundances, the smaller the evenness. Evenness (J 1 ) is calculated as follows: 

 (Pielou 1969): 



log ? s 



