100 EVOLUTION IN COLOR-PATTERN OF THE LADY-BEETLES. 



tion by even flow in the lateral process of the black area in the pronotum. 

 But, in addition to these, I believe we have a third intermediate method, 

 evolution by waves; for most of the characters, while showing some degree 

 of discontinuity in variation and segregation in heredity, are not so dis- 

 crete as to be properly called unit-characters. They are better described 

 by Galton's expression " positions of organic stability," interpreting 

 position in a broad sense. I prefer the expression "centers of variation." 

 Thus, in the size of spot 1, instead of two unit-characters at 5 and 15 

 units diameter, it seems to me we have more probably two centers of vari- 

 ation at these two points. This distinction would be of little importance 

 were it not for some important evolutionary consequences. 



The centers of variation (and here I am not speaking of the clear-cut 

 cases of unit-characters) may be the result of either of two possible 

 causes. In one kind, the germinal centers of variation, the positions of 

 organic stability are those of the germ-plasm, depending upon the nature 

 of its structure and processes. In the other kind, that of somatic centers 

 of variation, we have positions of organic stability of the soma, the germ- 

 plasm in this case not showing any corresponding favor for one degree 

 rather than another. We may illustrate this latter type by considering the 

 evolution of a pattern from one in which two spots are separate to one in 

 which they are confluent. It seems to me not only possible but probable 

 that it is easier for the spots to develop separately or in full confluence 

 than with a narrrow connecting band. Now, as the determiners move on 

 in the direction of confluence (whatever may cause the movement) , indi- 

 viduals which have intermediate determiners will be more likely to have 

 the confluence either less or more than that determined by the germ-plasm. 

 The result will be a bimodal polygon of frequency, until the germ-plasm 

 has progressed far enough to carry all the individuals past the position of 

 disfavor. 



In fig. 92 I have aimed to illustrate this in a hypothetical case. For the 

 polygon of frequency I have taken the one used in Davenport (1904) to 

 illustrate the normal curve. Now, I have assumed arbitrarily that the 

 magnitude 20 of the character is a position of organic stability, being 

 favored at the expense of other magnitudes to the extent that it receives 

 eight times as many individuals as it would otherwise receive; that the 

 neighboring classes are favored fourfold; those next adjoining twofold; 

 those next are unaffected. The next three classes are reduced to the 

 extent of getting only one-half, one-quarter, and one-eighth, respectively, 

 of their quota. The numbers thus obtained have been reduced to percent- 

 ages. The polygon of frequency centered over 20 with the changes thus 

 produced is shown as the first position in table 22 and fig. 92. Now, let 

 the character evolve by the increase of the magnitude by any factor of 

 evolution. The polygon will move to the right and assume the succes- 

 sive positions shown in table 22. In fig. 92 these curves are graphically 

 represented, with a few omitted to avoid overcrowding. 



