animals. But such year-class failure is less likely in stable climates, and 

 a series of failures is unlikely. Extinction is thus more probable as 

 environmental stress increases. 



The actual number of species present in any place is a product both of 

 the loss of species by extinction and of their replacement with new species. 

 In a few specialized organisms, such as birds, a limit to the number of species 

 that can accumulate is set by a restricted number of possible niches. For 

 most other kinds of animals and plants, the number of possible niches is 

 much larqer than the number of existing species. The patterns of diversity 

 presently evident arc the products of different environments of the earth 

 (Colinvaux 1973). 



The use of species diversity indices to analyze biological communities 

 originates from efforts to apply information theory to complex biological 

 problems. Workers who have explored the theoretical use of diversity indices 

 in biology, suggested refinements, or attempted studies include Brillouin 

 (1960), Lloyd and Ghelardi (1964), Wilhm and Dorris (1966, 1968) Lloyd et al . 

 (1968), Margalef (1968), Pielou (1969), Wilhm (1967, 1970abc, 1972), and 

 Cairns and Dickson (1971). Several indices have been generally acceDted: 

 mean diversity (d), equitability (E m ), redundancy (R), evenness (J'), and 

 richness (SR). 



FORTRAN computer programs for calculating species diversity indices are 

 available from the following sources: Wilhm (1970b), Cairns and Dickson (1971), 

 and Orr et al . (1973). 



MEAN DIVERSITY (d) 



In general, the fundamental objective of information theory is applied to 

 biology is to provide insight into community structure. The biological 

 information theorist asks how much new knowledge or "information" about 

 the species composition of a community can be obtained by drawing individuals 

 at random. If the community is composed of only one species, then no new 

 composition information is obtained after the first drawing. But if the 

 community is composed of numerous species, possibly with each individual being 

 a different species, then much new information is gained with each drawinq. 

 Information theory attempts to quantify the information contained in the 

 community in terms of "bits" of information per individual. 



Mathematically stated, "information" equals the uncertainty of correctly 

 predicting the identity of an individual randomly chosen from a community. 

 Where uncertainty is high, information per individual is high. The mean amount 

 of uncertainty of prediction of any individual's identity equals the mean number 

 of bits of information per individual, and this number is referred to as the 

 species diversity index. Mean information per individual is commonly measured 

 usinq the function developed by and named after Shannon and Weaver (1964). 

 The formula for the Shannon-Weaver function is: 



s. 

 d - -£ (N./N) loq 2 (N./N) 

 i=i 



where d = mean number of bits of information per individual, or the species 



20 



