42fi FAGEK [CHAP. 19 



based on more biological assumptions than the preceding two. The lengths 

 marked out on the stick are supposed to represent the "sizes" of non-over- 

 lapping, contiguous niches in the community and, therefore the numbers of 

 individuals of the different species occupying them. Niche is, of course, used in 

 its original sense, i.e. what an animal does in the community. MacArthur 

 reported satisfactory agreement between theory and observation in the case 

 of bird species from relatively small, and therefore presumably homogeneous, 

 areas. When bird censuses from large areas were considered, the common 

 species were more common and the rare species were rarer than predicted. 

 Kohn (1959) has reported extraordinary fit of observation with expectation in 

 the case of species oiConus in Hawaii. MacArthur has suggested that fit or non- 

 fit with prediction might be used as a measure of the relative homogeneity of 

 the area sampled. Hairston (1959), working with soil fauna from samples 

 carefully selected for homogeneity, found, however, that the common species 

 were more common and the rare species were rarer than predicted. He suggests 

 that this is an expression of the organization of the community as opposed to 

 the random structure assumed in MacArthur's formulation. If this suggestion 

 is correct, one should find increasing divergence between observation and 

 prediction as one adds together more and more samples from a homogeneous 

 community and thus more completely shows up the organization, and decreasing 

 divergence if one combines samples from quite different communities thus 

 reducing the order. This is the case in the examples he presents. Again, one is 

 faced with the question of whether a community is an organized system or 

 simply a random collection of species which are able to adjust to the prevailing 

 conditions. Hairston's evidence agrees best with the assumption of at least 

 some organization. 



The concept of diversity of a community is directly related to the structure 

 in terms of relative abundances. A number of indices of diversity have been 

 proposed but most of them, like the constant a in the Fisher and Williams 

 distribution, are of doubtful reliability because of the unproven assumptions 

 underlying the parent distributions. Two measures have been proposed which 

 are independent of the form of the parent distribution. Margalef (1958) has 

 suggested the use of the natural logarithm of the number of permutations of N 

 objects of which N a are alike, Nt, are alike, etc., multiplied by a constant 

 which converts the value into the number of "bits" of information contained 

 in the community. Information in the community in this form may be con- 

 sidered as the number of questions with yes/no answers which would have to 

 be asked to define the community completely. As the formula for permutations 

 contains factorials, the computation of the index becomes formidable when N 

 is even a moderate size. Margalef, therefore, suggests the use of a simpler 

 index due to Gleason (1922) which is based on the assumption that the number 

 of species in a sample is a linear function of the logarithm of the number of 

 individuals. Hairston (1959) has shown that Margalef 's justification for this 

 substitution, the stability of the index with increasing sample size when tested 

 on the frequencies of letters in a Spanish text, is invalid because the letters tend 



