422 FAGEK [CHAP. 10 



index such as the modified geometric mean suggested above. Given such a 

 "score" for all pairs of species in the samples, one can write down a set of 

 rules which will lead to the largest possible groups within which all species are 

 "associated" and will decide between possible groups of the same size which 

 have members in common. The rules and mechanics of isolating the groups are 

 given in Fager (1957) and will not be repeated here. It may be pointed out that 

 although the description appears complicated when read, the mechanics are 

 quite straightforward and easily worked out on a set of samples. The pro- 

 cedure has the advantages of being definable and, therefore, repeatable by any 

 worker using the same samples, of requiring a minimum of subjective judgment 

 and of separating out the largest group or groups first and thus considerably 

 reducing the work as compared with procedures which build up groups from 

 pairs of species. 



A quite different approach is advocated by those ecologists who feel that 

 every assemblage of organisms is an individual point on a continuum and that 

 attempts to group assemblages into community types lead to artificial classifica- 

 tions (Gleason, 1939). Instead of trying to identify recurrent groups with more 

 or less constant species composition they work toward an ordination of sets of 

 samples, each set taken from what is thought to be a homogeneous area (stand). 

 Curtis and his co-workers (Curtis and Mcintosh, 1951 ; Brown and Curtis, 1952 ; 

 Bray and Curtis, 1957) have been particularly active in the application of this 

 viewpoint to forest ecology in the northern United States. In some of their 

 earlier work they were able to order the different stands by using importance 

 values for the four dominant tree species based on the sum of % relative 

 density, % relative dominance and % relative frequency in the samples taken 

 within each stand. There was a good deal of overlap in the plots of importance 

 values of the four species versus the stands ordered according to moisture 

 conditions, but the higher importance values for two species tended to be 

 associated with dry conditions, for another species they were associated with 

 less dry conditions and for the fourth with the most moist locations sampled. 

 In the 1957 paper they calculated scores for stands based on frequency of 

 occurrence of shrubs and herbs in a number of quadrats within the stand, 

 density of the major tree species within the stand and a measure of size of 

 the same tree species within the stand. These were all converted to percentages 

 relative to the highest value for a species in the set of 59 stands and then the 

 scores of all the species present in each stand were converted to percentages of 

 the total score for that stand. An index of similarity was then calculated for 

 each pair of stands : index of similarity = 200wJ(a + b), where w is the sum of the 

 lesser of the two score values for each species common to the two stands, a is 

 the total score of one stand, b that of the other stand ; as a and b are both 100 

 in their case, the index reduces to w. The theoretical range of the index is to 

 100 but the maximum value found between replicate sets of samples from 

 the same stand was 80. The two stands with least similarity were then placed 

 at the ends of a line (x axis) and each of the other stands was ordered upon this 

 line in terms of its "distance", measured as 80 minus the appropriate value of 



