SECT. 4 | COMMUNITIES OF ORGANISMS 425 



negative binomial distribution (Bliss and Fisher, 1953). This has a low value 

 when there is much aggregation and a high value when there is little ; it is in- 

 finity for random distributions. If the species are aggregated, as many are, the 

 median plus quartile values may be a more realistic abundance measure than 

 the usual mean plus standard deviation. Either aggregation or evenness im- 

 mediately raise problems of cause which may involve the behavior of the 

 organisms, their life history (particularly their method of reproduction) and 

 discontinuities in the physical properties of the habitat. As Hutchinson (1953) 

 has pointed out, one or all of these may be the basis for an observed aggregated 

 distribution. 



The abundance of a species relative to the abundance of all other species 

 which are found with it provides more information about the structure of a 

 community than does absolute abundance. It is general experience that within 

 the different size ranges a few species provide the bulk of the individuals in 

 each community, and usually in each sample, while the other species are 

 represented by relatively few individuals (e.g., Sanders, 1960). This may be 

 expressed for each species in terms of an average percentage of the total 

 individuals in the samples but a more informative measure is the following : in 

 each sample the species are ordered in terms of the number of individuals; 

 individuals are then summed in order starting with the species with the greatest 

 number of individuals, and those species which have been included in the 

 summation when it reaches the value of half the total individuals present are 

 considered numerical dominants in the sample. The frequency of this dominance 

 is an important measure of the species' position in the community. It is prob- 

 ably most meaningful if the summation is done using animals which fall within 

 a moderate range of sizes. A supplementary way of looking at dominance is 

 suggested in Eager (1957). The species are ranked in terms of abundance 

 within each sample. The ranks for each species are summed over all samples 

 and the set of sums is tested for concordance (Kendall, 1955, pp. 94-102). If 

 there is significant concordance, it may be concluded that the dominance 

 relations between species tend to be constant over the set of samples and the 

 overall dominance position of a species is given by the rank of its sum of ranks. 



A number of different parent distributions have been suggested to account 

 for the observed distributions of individuals per species in communities. Of 

 these, the most extensively examined are the logarithmic series (Fisher, 

 Corbet and Williams, 1943), the truncated log-normal distribution (Preston, 

 1948) and the distribution of relative lengths marked out by the random place- 

 ment of n— 1 points on a stick of unit length (MacArthur, 1957). As noted 

 earlier, the logarithmic series predicts that rare species will be the most 

 numerous while experience suggests that moderately common species are in 

 fact the most numerous. The latter is predicted by the log-normal distribution, 

 and Williams (1933) has accepted the closer relation to observation of Preston's 

 formulation. As Goodall (1952) points out, however, the difference between 

 expectations for the two distributions is seldom sufficiently great to make an 

 objective decision between them. MacArthur's distribution is, at least formally, 



