16 VARIATION AND DIFFERENTIATION IN CERATOPHYLLUM. 



VARIATION IN CERATOPHYLLUM-GENERAL RESULTS. 



Before analyzing our material in detail it is desirable for purposes of 

 orientation to examine in a general way the nature and amount of the 

 variation exhibited by the plant. To this end the present section is 

 devoted. 



In this section I shall only consider the variation in the number of 

 leaves to the whorl, when all the unmutilated whorls on the plant are 

 taken together without reference to their position, leaving until later 

 other characters studied. The frequency distributions for this char- 

 acter for each plant separately and for each series are given in table 1. 



We see at once from this table that the range of variation in leaf- 

 number is rather limited in Ceratophyllum. Whorls with 4 leaves and 

 whorls with 11 leaves include practically the whole of the variation in 

 this character, though whorls with 12 and 3 leaves do occur very rarely. 

 The great bulk of the whorls have either 8, 9, or 10 leaves. Consider- 

 ing the first four series, it is seen that whorls with 9 leaves occur more 

 frequently than do any other single class, thus making 9 the observation 

 mode. From mere inspection of the frequency distributions it is quite 

 clear that while Series I, II, III, and IV are all very closely alike in 

 respect to the character under consideration, on the other hand the two 

 series taken at the beginning of the growing season (V and VI) are in 

 some respects quite diiferent. The plants of these latter series are 

 generally small, and the distributions are irregular. The reason for this 

 irregularity will be discussed later, but for the present it needs merely 

 to be kept in mind that the distributions of Series V and VI represent 

 the action of special factors which do not influence the other series. 



In order to bring more vividly to the reader's mind the nature of the 

 variation in this character, the diagrams shown in fig. 3 have been pre- 

 pared. These give frequency polygons for the totals of each of the 

 series (distributions No. 44, 61, 62, 97, 139, and 176). These are so 

 plotted as to have equal areas; that is, the frequencies are reduced for 

 each series to percentages and then plotted to the same base unit. 



From these diagrams the essential similarity in the frequency distri- 

 butions for Series I, II, III, and IV comes out in a very striking way. 

 Series IV shows a higher frequency of whorls with 9 leaves and a lower 

 frequency of those with 6 leaves than do Series I, II, and III, but other- 

 wise differs very little from these. All the distributions show a marked 

 degree of asymmetry about the mode. The range below 9 whorls is 

 roughly twice as great as the range above that number. One point to 

 which I wish to call attention here, as it is shown very clearly by the 



