SECT. 4] COMMUNITIES OF ORGANISMS 419 



sources of energy. In many cases, a community wiJl be associated with a 

 particular physical habitat, but if emphasis is to be on the action-reaction aspect 

 of relations between organisms it seems sounder practice to base the definition 

 on the species group rather than the habitat type. 



3. Identification of Communities 



Given a series of samples in which co-occurrence is expected to have biological 

 meaning, how can the species groups be identified? The usual method is to 

 calculate a matrix of indices of relationship between all possible pairs of 

 species and then rearrange this matrix so that species showing high positive 

 values of the index are grouped together (Kontkanen, 1957). Product-moment 

 correlation coefficients may be used as indices but, because organisms are nearly 

 always clumped, some transformation of the raw abundance values will be 

 needed in order to make their distribution sufficiently close to normal. With 

 the usual sets of samples there is the additional problem raised by the fact that, 

 in order to avoid the use of too many zero values, the correlation coefficients 

 of different pairs of species will often be based on different numbers of observa- 

 tions. As is well known, the significance of a given value of coefficient changes 

 with a change in the number of observations upon which it is based. Probably 

 the best way of making such values comparable is to change them to unit 

 normal variates by way of Fisher's z transformation (Fisher, 1950, pp. 197- 

 204). The organisms can then be grouped either by putting together all species 

 which have positive values over a certain limit (see later discussion of pro- 

 cedure for use with dichotomies) or by cutting the matrix in columns and 

 moving these around until adjacent columns "match" more or less well in 

 terms of the sign and magnitude of values in each row. There will, however, 

 seldom be perfect "matches" and, as no rules are available for deciding when 

 they are good enough, there will often be many species whose association with 

 one group or another will have to be based on purely subjective judgment. In 

 the hands of a worker with much experience with the organisms involved, this 

 method is rapid and fairly reliable. Its major drawbacks are the necessity for 

 experience and the practical impossibility of defining exactly the basis of deci- 

 sions involved in the assignment of species to groups. 



If one is in the fortunate position of having a matrix in which all correlation 

 coefficients are based on the same number of samples, there are a number of 

 grouping procedures which start with the pair of species having the highest 

 correlation and build up groups from this by adding the species with highest 

 average correlation with the initial pair, then adding a fourth to the trio, etc. 

 (Olson and Miller, 1958; Holzinger and Harman, 1941). Rules are given for 

 deciding on the limits of groups, based on the relative magnitudes of the 

 average intra- and extra-group correlations of the last-added species. These 

 procedures have the disadvantage that the buildup of groups is slow. 



It has also been suggested that tetrachoric correlation coefficients may be 

 used because, although less efficient, they are easier to calculate and do not 



