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252 MISSOURI BOTANICAL GARDEN. 



structure of flowers, the Diptera, Lepidoptera and Hymen- 

 optera. These groups are of general distribution, and 

 species with flowers adapted to representatives of each of 

 them may be found in almost every flora. The problem 

 here is much more involved. Conclusions must, in this 

 case, rest upon the demonstration of the interdependence 

 of fauna and flora and statistical comparisons of the floras 

 and faunas of different regions. 



It is well known that the three orders of insects men- 

 tioned are represented in very different proportions in 

 different regions, and the investigations of several workers 

 have shown that there are corresponding differences in the 



constitution of the flora. 



It is Hermann Miiller to whom our knowledge of the 

 influence of tho insect fauna upon the constitution of the 

 flora is largely due, for it was his contribution of the statis- 

 tical methods' of work which has made possible much which 

 has been done since his time. So long as observations 

 were confined to individual species showing adaptations to 

 a single insect visitor or groups of visitors, conclusions 

 were "necessarily much limited and unsatisfactory. The 

 development of methods which would permit of a statis- 

 tical comparison of the adaptations of different flowers as 

 a whole to insect visitors is clearly a step of fundamental 

 importance, and, if the methods be trustworthy, permits 

 of advances and conclusions of an accuracy otherwise quite 

 unattainable, though the number of factors is so great and 

 conditions are so complex that comparisons must remain 



only approximate. 



In several papers, Miiller developed various phases of the 

 statistical methods, but it was in his book on Alpine flowers 

 that he especially applied and illustrated these methods, and 

 a review of the theoretical portion of this classic work will 

 explain and illustrate the statistical method as developed 

 by the German naturalist. Thomson, Loew, Warniir- 



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