i 4 W. A. SANDS 



(88-91) Enteric valve main armature, scale or spine development (reticulated 



scaly, minute, small, pronounced, very elongated) 

 (92-95) Enteric valve main armature, spine numbers (0-10, 10 + to 20, 20 -j- to 30, 



30 + to 40, no comparison if spines absent) 



(96) Enteric valve: presence or size of spicules on wall between or beyond 



cushions 



(97) Length of mixed segment of worker gut, relative to position of Malpighian 



knot 



(98) Worker: colour of head capsule 



(99) Worker: colour of head capsule pilosity 



The CLASP programme provides for the computation of a matrix of coefficients 

 of similarity between all the species, such that, as described by Sheals (1964) : 



Q Si+S 2 +S 3 S k (1) 



Sll= K 



where i and j refer to the OTU's being compared (in this case, species) and Si, 

 S2 . . . . Sk are the similarities between them for each of the characters used, to the 

 total K of characters for which comparisons are made. For qualitative characters 

 S is scored on a match/mismatch basis, for a match S = 1 and a mismatch, S = 0. 

 Similarity for quantitative characters is calculated by : 



c T l x i -XjI ( 2 ) 



bij = 1 — 



r 



where Xj, Xj are the ranked or continuous measurements, and 1 is the total range of 

 the character in all of the taxa. The similarity coefficient Sij between any two 

 species thus rates a value between o and 1, but is presented as a percentage which is 

 referred to as the phenon or phenetic level, or level of similarity. By the CLASP 

 programme the matrix of similarity coefficients was first examined using the method 

 of single-linkage cluster analysis. Every member of a group of species is similar 

 to some other member at a phenetic level greater than L but similar to all non- 

 members at phenetic levels less than or equal to L. L was first set to maximum 

 (100%) phenon level and progressively decreased until all groups coalesced when 

 sorting was terminated. A related form of clustering, median sorting, gave slightly 

 different results as might be expected. Here after the selection of the first pair, 

 the nearest neighbours of the mid point between them is taken rather than either 

 member of the pair as in single linkage clustering. This to some extent reduces 

 the likelihood of producing long chain clusters and seems intuitively more acceptable 

 in considering relationships with more than one member when adding a new OTU 

 to a cluster. 



An alternative method of seeking structure in the similarity matrix is that named 

 by Gower (1966), Principal Co-ordinates analysis. The matrix is first transformed 

 by subtraction of row and column mean values from each corresponding matrix 

 element added to the general mean of all elements, thus : 



aij = Sij — Si — Sj + S (3) 



