184 THE QUANTITATIVE METHOD IN BIOLOGY 



FORMATION OF A MONOMORPHIC CURVE INTO A 

 DIMORPHIC OR A POLYMORPHIC ONE BY EXTERNAL 

 CAUSES. — When variation steps exist in the series of possible 

 values of a certain property p, it may happen that a 

 monomorphic (one-humped) curve is obtained under certain 

 conditions of existence, whereas the curve is dimorphic or 

 polymorphic under other conditions without any change in 

 the hereditary properties. 



EXAMPLE : I have cultivated Chrysanthemum carinatum 

 in several groups, the conditions of existence being more and 

 more unfavourable from the first group to the last one ^ : the 

 first group under ordinary conditions in a garden, the intervals 

 between the specimens being rather large ; the second group 

 in the same soil, the intervals being too small to allow a full 

 development of each specimen, etc. 



The marginal florets of the terminal flower-head were counted 

 in all the specimens.^ In the first group the variation curve 

 was somewhat regular, with a distinct hump coinciding with 

 the value 21. In the second group the hump coincided with 13 ; 

 in the next groups the summit passed through the values 8, 5. 

 ... In certain groups two humps (belonging to the series 3, 5, 

 8, 13 ... ) were observed, with a depression between both. 

 In this experiment the variation of the measured property and 

 the succession of the steps (Fibonacci terms) was, of course, a 

 consequence of plasticity. There was no specific hereditary 

 difference between the groups. 



The specimens of the first group produced a number of 

 flowering branches ; flowers were abundant for a period of 

 about ten weeks. About a fortnight after the terminal flower- 

 heads had been investigated, a second group of flower-heads 

 produced by lateral branches were observed in their turn, and 

 so on, several successive groups of flower-heads being taken 

 with intervals of about a fortnight. The successive curves 

 were different from each other in the same way as the curves 

 of the terminal flower-heads of the groups cultivated under 

 different conditions. The successive summits coincided with 

 the Fibonacci terms, the order of decrease being 21 (terminal 

 heads), 13, 8, 5, 3 from the beginning to the end of the flower- 

 ing period. In certain curves two humps coinciding with two 

 successive terms were observed. The successive appearance 

 of the Fibonacci humps depends here on a social cause — i.e. 

 gradation. (See Part VIII.) 



1 This expenment was carried out in the Botanic Garden at Ghent with 

 the collaboration of J. V. BURVENICH. The seeds were obtained from 

 HAAGE and SCHMIDT, Erfurt. The subspecies cultivated was characterized 

 by simple flower-heads ; marginal florets white, central florets brownish. 



2 The property mentioned here is of the second degree. 



