150 OUTLINES OF EVOLUTIONARY BIOLOGY 



of petals in flowers and the number of flowers in inflorescences. 

 An example of this will be given later on in the case of the 

 grape hyacinth. 



Substantive Variations. Examples of this type of variation are 

 seen in the shape, size and colour of the human body and of its 

 various parts. The total height of the individual, the shape of 

 such features as the nose, ears and fingers, the colour of eyes 

 and hair, are all subject to very great variation. The same is 

 true of the shape and size of leaves and the colour of many 

 flowers. Numerous physiological variations, which doubtless 

 depend upon unrecognized and perhaps unrecognizable differences 

 in structure, may also be classed under this head, as for example 

 the variations in the egg-laying powers of fowls and the milk- 

 giving powers of cows, and in the percentage of sugar present 

 in the roots of the sugar beet. 



Fluctuating Variations. The variations which come under this 

 heading are also spoken of as normal, individual or continuous. 

 They may be either meristic or substantive. They are 

 characterized by the fact that they pass into one another by very 

 minute or even insensible gradations, which fluctuate on either 

 side of a mean or average condition, so that the extent to which 

 a given organism (or part of an organism) varies can be 

 graphically represented in the form of a curve. Fluctuating 

 meristic variations lend themselves most readily to this graphic 

 method of treatment, for all we have to do is to count the 

 numerically varying parts in a sufficiently large number of cases 

 and plot our curve accordingly. 



The manner in which this is done is represented in the 

 accompanying diagram (Fig. 72), which expresses graphically the 

 results obtained by counting the number of flowers in 202 in- 

 florescences of the common grape hyacinth (Muscari sp.). The 

 number of flowers in an inflorescence ranged from 20 to 42, and 

 the number of inflorescences showing each of the different numbers 

 of flowers ranged from 1 to 29. 



The base line of the diagram is divided into a number of equal 

 parts (abscissae) corresponding to the number of flowers (from 20 

 to 42). At one side an ordinate is erected on the base line and 

 divided into a number of equal parts corresponding to the 

 number of the individual inflorescences (from 1 to 29) bearing the 

 different numbers of flowers. Lines are then ruled parallel to 

 the base line and to the ordinate respectively, so as to divide the 



