BIOGEOGRAPHICAL BOUNDARIES 225 



referred to the so-called diversity indices dependent, in various de- 

 grees of complexity, on the ratio between the number of species 

 and the number of individuals, in a sample oi an area. From such 

 an index he was able to provide geographical plots of heterogeneity 

 of communities of phytoplankton. 



The application of these techniques to ecology is only just be- 

 ginning, and many difficulties remain to be solved. Most tests of 

 affinity or association between organisms have been dependent 

 on the presence or absence of species in a sample or a quadrat. 

 There are weaknesses in this approach which is unduly sensitive 

 to sampling errors and to variations in sample or quadrat size. 

 The groups of concurrent species determined from small samples 

 will frequently be different from those found in large samples. 



But there is no reason \vhy these methods should be applied 

 only to the presence or absence of species. We have already started 

 to use them in Edinburgh in the analysis of similarity or dis- 

 similarity of patterns of long-term fluctuations in abundance, and 

 they could be used also in the grouping or separation of genetic 

 or morphological features. 



Biologists of all kinds are attempting to carry their work from 

 the study of individual organisms into the study of natural popu- 

 lations and. communities. In making this step, mathematical tech- 

 niques of the kind I have mentioned will be most useful. But 

 success will be limited unless the results can be based on repeated 

 sampling. More careful attention must be paid, in the future, to 

 two technical problems; the design of field equipment and the 

 design of field surveys. 



Biologists have sometimes been accused of collecting too much 

 material. It may be that, for oceanic biology at least, they have 

 not collected enough. 



REFERENCES 



Abramova, V. D. 1956. Plankton as an indicator of waters of different 



origins in the North Atlantic seas. Trans. Knipovich Polar Set. 



Inst. (PINRO), 9, 69-91. (In Russian.) 

 Allee, W. C, Alfred E. Emerson, Orlando Park, Thomas Park, and Karl 



P. Schmidt. 1949. Principles of Animal Ecology. W. B. Saunders 



Company, Philadelphia, Pa. 



