236 Influence of Environment on Plants 



Gallon, and others the statistical examination of individual differ- 

 ences in animals and plants has become a special science, which is 

 primarily based on the consideration that the application of the 

 theory of probability renders possible mathematical statement and 

 control of the results. The facts show that any character, size of 

 leaf, length of stem, the number of members in a flower, etc. do not 

 vary haphazard but in a very regular manner. In most cases it is 

 found that there is a value which occurs most commonly, the average 

 or medium value, from which the larger and smaller deviations, the 

 so-called plus and minus variations fall away in a continuous series 

 and end in a limiting value. In the simpler cases a falling off occurs 

 equally on both sides of the curve ; the curve constructed from such 

 data agrees very closely with the Gaussian curve of error. In more 

 complicated cases irregular curves of different kinds are obtained 

 which may be calculated on certain suppositions. 



The regular fluctuations about a mean according to the rule of 

 probability is often attributed to some law underlying variability 1 . 

 But there is no such law which compels a plant to vary in a par- 

 ticular manner. Every experimental investigation shows, as we have 

 already remarked, that the fluctuation of characters depends on 

 fluctuation in the external factors. The applicability of the method 

 of probability follows from the fact that the numerous individuals of a 

 species are influenced by a limited number of variable conditions 2 . 

 As each of these conditions includes within certain limits all possible 

 values and exhibits all possible combinations, it follows that, accord- 

 ing to the rules of probability, there must be a mean value, about 

 which the larger and smaller deviations are distributed. Any cha- 

 racter will be found to have the mean value which corresponds with 

 that combination of determining factors which occurs most frequently. 

 Deviations towards plus and minus values will be correspondingly 

 produced by rarer conditions. 



A conclusion of fundamental importance may be drawn from 

 this conception, which is, to a certain extent, supported by experi- 

 mental investigation 3 . There is no normal curve for a particular 

 character, there is only a curve for the varying combinations of 

 conditions occurring in nature or under cultivation. Under other 

 conditions entirely different curves may be obtained with other 

 variants as a mean value. If, for example, under ordinary conditions 

 the number 10 is the most frequent variant for the stamens of Serf urn 

 spectabile, in special circumstances (red light) this is replaced by the 

 number 5. The more accurately we know the conditions for a par- 



1 de Vries, Mutatiomtheorie, Vol. i. p. 35, Leipzig, 1901. 



'- Klebs, WillkUrl. Ent. Jena, 1903, p. 141. 



3 Klebs, " Studien iiber Variation," Arch, fiir Entw. 1907. 



