SECT. 4] COMMUNITIES OK ORGANISMS 423 



w from the terminal stands. Two stands which were near the center of the x axis 

 and close together on this axis but had the maximum "distance" between them 

 in terms of 80 minus w were then used as the basis of a y axis placed at right 

 angles to the x axis. This was repeated for a z axis at right angles to the other 

 two axes. The stands were thus ordered in three dimensions. Various physical 

 and chemical properties of the stands and their soils were then tested for 

 correlation with the ordering along each axis. The x axis seemed to represent 

 the change from drier, more open forest to mesic, closed-canopy forest ; the y 

 axis was related to drainage and soil aeration ; the z axis was related to the 

 influence of recent disturbances such as fires, grazing, etc. This same sort of 

 approach could be applied to planktonic or benthic communities if multiple 

 samples were taken at each station and might help, particularly in regions 

 where physical and chemical characteristics change over relatively short 

 distances, to identify the properties of the habitat which most affect each 

 species. A major objection to the method is that two samples with the same 

 fauna and the same numbers of individuals for all species but one may have a 

 very low score if that one species is rare in one sample and overwhelmingly 

 abundant in the other. It also tends to put great weight on the abundant 

 species and minimizes the effects of qualitative differences involving less 

 common species. 



Williams (1947) has suggested a method of comparing floras which avoids 

 some of these difficulties. It assumes that the numbers of individuals per 

 species follow a logarithmic series ; i.e. if n is the number of species with one 

 individual and a; is a constant less than unity, n, nxj'2, nx 2 /3, • • • • represent 

 the numbers of species with 1, 2, 3, • • • individuals. Fisher (Fisher, Corbet and 

 Williams, 1943) has shown that when this series holds, as it seems to in some 

 cases, the ratio n/x is a constant for all random samples from the same popula- 

 tion of species. This ratio, called an index of diversity, is denoted by a. It 

 follows from the properties of the logarithmic series that the number of species 

 expected in a sample is given approximately by a log e (A r /a), where N is the 

 number of individuals in the sample. On the assumption that two samples are 

 random samples from the same population, one can calculate the expected 

 number of species in common and compare this with the observed number 

 (Greig-Smith, 1957, pp. 122-126). The ratio observed/expected could be used 

 as an index of similarity upon which to base ordination. This may be a more 

 reliable method but, as Greig-Smith points out, some of the basic assumptions 

 are unproven ; e.g. one of the consequences of the logarithmic series is that rare 

 species should be the most numerous, whereas the experience of field botanists 

 is that moderately common species are more numerous than either rare or very 

 common species. 



The preceding review covers most of the methods which have been used to 

 identify assemblages of organisms. It has been noted that most of them have 

 more or less serious limitations. Some take account of abundances, others use 

 only presence and absence. The investigator must, therefore, choose the sort 

 which emphasizes the group properties in which he is most interested and then 



