no. 3645 PORTUNIDAE — STEPHENSON, WILLIAMS, LANCE 5 



individuals concerned. Alternatively, the square root of this quantity 

 (i.e., the Euclidean distance itself) may be used as a measure of 

 "taxonomic distance" (TD). Preliminary investigations using other 

 measures — the correlation coefficient, the nonmetric coefficient, and 

 Euclidean distance standardized to zero mean and unit variance — 

 suggested that these offered no advantages over the NFD and TD 

 values. The latter, therefore, have been used throughout this study. 

 Strategy. — In the present problem we were concerned not only 

 with the overall configuration of inter-relationships but also with the 

 possible light that this might throw on certain specified problems. 

 We used three approaches: 



(1) Direct comparison of intergroup NFD and TD values: Since 

 the original values relate only to distances between individuals, a 

 further definition of individual/group or group/group distance is 

 required. The distance between group centroids commonly is used 

 for this purpose, but this is troublesome to calculate from the inter- 

 individual NFD or TD values and requires manipulation of the 

 original data. We, therefore, have preferred to use the "group-average" 

 measure of Sokal and Michener (1958), whereby the distance between 

 two groups is defined as the average of all interindividual between- 

 group NFD or TD values. 



(2) Classification: General accounts of classificatory methods are 

 given in Sokal and Sneath (1963), MacNaughton-Smith (1965), and 

 Williams and Dale (1965). Four methods were used: (a) nearest and 

 farthest neighbor sorting of the NFD values; (b) centroid sorting 

 using the original data; (c) the nonmetric coefficient; and (d) informa- 

 tion analysis (Williams, Lambert, and Lance, 1966). The results were 

 disappointing: groups were not clear-cut, and the configurations 

 obtained by various methods differed considerably. Although it 

 would now be possible to increase the clarity of the picture by the 

 greater power of "flexible" sorting (Lance and Williams, 1967), the 

 process is not to be recommended in the current situation. The 

 variability of the results suggests that at least part of the system is 

 more or less continuous, with the result that ordination, rather than 

 classification, is likely to represent the most fruitful approach. The 

 classificatory approach, therefore, was abandoned, and the results are 

 not presented in this paper. 



(3) The efficient representation of a multidimensional system in 

 fewer dimensions normally would be undertaken by principal com- 

 ponent analysis. In our case, however, several attributes are missing 

 from one of the individuals, a fact that would complicate the calcula- 

 tion. It is desirable, therefore, to ordinate the interindividual matrix 

 of mean NFD values. This problem is discussed in Sokal and Sneath 

 (1963), but the methods given therein are empirical, since at that 



