VENRICK: PERCENT SIMILARITY: THE PREDICTION OF BIAS 



TABLE 3. —Comparison of two phytoplankton associations using the 

 standardized /: /' = ///. Original values of/ are given in Table 2. 



DISCUSSION AND CONCLUSIONS 



In spite of the numerous approximations and as- 

 sumptions which underlie the formulae for the per- 

 cent similarity index and its variance, the formulae 

 appear to be good predictors. This is true even when 

 the equations are applied to actual species abun- 

 dances which are unlikely to fulfill all the conditions 

 met by computer simulation (i.e., normality and in- 

 dependence of species distributions and accurate 

 knowledge of heterogeneity). 



An important result of this study is the elucidation 

 of the relationship between the bias of / and such 

 community parameters as the number of species, 

 their abundances, heterogeneity, and diversity. Deci- 

 sion about the importance of these dependencies is 

 hampered by the vagueness of the concept "similar", 

 i.e., that which is being measured by /. In my own 

 mind, the concept is strongly linked to differences of 

 relative abundances, and ultimately to q. In some 

 situations the dependency of/ on factors other than 

 heterogeneity may be desirable, or at least irrelevant, 

 as, for instance, when / values within one set of items 

 are compared with/ values between that set and a dif- 

 ferent set. Silver (1975) calculated values of/ be- 

 tween the diatom associations in the stomachs of 

 several salps and compared these with the indices 

 between salps and nearby water samples. Finding no 

 difference, she concluded that salps are nonselective 

 feeders. In this comparison, any differences in any of 

 the community parameters between the first set of 

 indices (salp-salp) and the second (salp-water) are 

 directly related to the concept of selective feeding 

 and are validly confounded into a similarity index. A 

 similar situation is presented by time series of / 

 values (e.g., Miller 1970; McGowan and Walker 

 1979) where all comparisons are within the same 

 general system and temporal changes in species 

 number or diversity are important aspects of the 

 evolution of the system, as measured by changes in 

 /. 



On the other hand, / values from within quite dif- 

 ferent systems are occasionally compared, leading to 

 decisions about the relative similarity of items within 

 the systems. In a study of plants ad homoptera in 

 fields (Murdoch et al. 1972), several fields were sur- 

 veyed for plant and insect abundances. Values of/ 

 between fields were lower for plants than for insects, 

 leading to the conclusion that "the insect assem- 

 blages on different fields are more alike than are the 

 plants." To the extent that the observed difference 

 could reflect only different biases of the index in the 

 two systems (caused, for instance, by different num- 

 bers of species of plants and insects), this conclusion 

 seems unjustified. Such a comparison between 

 plants and insects would be validated by the use of 

 standardized/' values to remove the contribution of 

 species number, abundances, and diversity so that 

 the index accurately reflects the heterogeneity of the 

 two systems. 4 



Numerous similarity indices have been proposed 

 with different theoretical frameworks and different 

 attributes. Intercomparisons have given different 

 results depending upon the conditions of the com- 

 parison and the evaluation criteria (Morisita 1959; 

 Grassle and Smith 1976; Pielou 1979; Bloom 1981; 

 Wolda 1981). There is little evidence to suggest that 

 other similarity indices are independent of the un- 

 derlying community structure, nor is there reason to 

 expect the relationships to be similar to those ob- 

 served for the percent similarity index. The ultimate 

 selection of a similarity index is less important than a 

 thorough understanding of the behavior of that index 

 under various conditions. Without such background 

 information, interpretation of any similarity index is 

 subject to serious error. 



ACKNOWLEDGMENTS 



I am grateful to John McGowan and Patricia Walker 

 for making available their raw zooplankton data, to 

 discussions with Tom Hayward and Patricio Bernal 

 which demonstrated the vague nature of my own con- 

 cept of similarity and gave direction to my concluding 

 section, and to many fellow computer users who 

 waited patiently through my endless simulation 

 studies. 



The work was supported in part by the Marine Life 

 Research Group of Scripps Institution of Oceano- 

 graphy and in part by a grant from the Office of 

 Naval Research. 



"Elsewhere in the paper these authors use a value of/ which has 

 been corrected for internal heterogeneity of the associations. 



383 



