SECT. 4] COMMUNITIES OF ORGANISMS 427 



to be randomly or evenly dispersed whereas organisms are most often aggre- 

 gated. The index would be expected to be stable when applied to samples of 

 increasing size from even or random distributions but quite unstable when 

 applied to such samples from aggregated distributions. The other index of 

 diversity which is distribution-free is that suggested by Simpson (1949). It is 

 the probability that two individuals selected independently and at random 

 from a sample will be of the same species : ][ %(wj- 1)/N(N — 1), where n x is 

 the number of individuals of species x, N is the total number of individuals in 

 the sample, and the sum is over all species present. If all individuals are of one 

 species, the index takes its maximum value, 1 ; if there are S species all with 

 the same number of individuals and the total number of individuals, N, is 

 much greater than S, the index takes a minimum value, approximately l/S. A 

 limitation of this index, and even more of the information-based one suggested 

 by Margalef, is that their values are determined primarily by numbers of in- 

 dividuals of the abundant species and little affected by considerable differences 

 in abundances of the rarer species. In view of the preceding discussion, it is 

 probably fair to say that indices of diversity are likely to be misleading though 

 they may in particular situations give interesting results (Margalef, 1958). 



Three other statistics which the plant ecologists (Braun-Blanquet, 1932) 

 have found useful in their descriptions of the position of a species in a com- 

 munity are fidelity, vitality and periodicity. Fidelity is a measure of the 

 restriction of a species to the community. This may range from species which 

 are found only in the community to those which are found elsewhere but are 

 most abundant in the community and, finally, to those which are about equally 

 abundant in a number of communities. As mentioned previously, species with 

 high frequency and high fidelity are excellent indicators of the community. In 

 addition, those with high fidelity are most likely to have specific physiological 

 and behavioral characteristics related to the conditions in the area occupied 

 by the community. They are, therefore, probably the best choices for study of 

 the biological adjustments necessary for successful coping with the specific 

 conditions. Vitality is a measure of the completeness of the life cycle in a com- 

 munity. Thus, there ma} r be some species which are often present but in poor 

 physiological condition, others which are present as healthy adults but do not 

 breed and others which carry out their complete life cycles within the com- 

 munity. Periodicity measures changes of abundance with time, usually in 

 terms of seasons. This has a clear-cut meaning for intertidal and benthic 

 communities where one may have seasonal changes in both the animals and 

 plants associated with a definite location and these changes occur in more or 

 less the same manner every year. In the case of plankton communities, one 

 will seldom, if ever, be dealing with the same piece of water at any one geo- 

 graphic location and yet the annual recurrence of phytoplankton blooms in 

 the spring and in the late summer or fall in north temperate regions, involving 

 essentially the same species in the same sequence, suggests that the concept 

 of periodicity within a community is relevant here too (Allen, 1945; Lillick, 

 1940). 



