November 29, 1912] 



SCIENCE 



755 



In the use of the method in actual cases, the 

 scale is of definite quantities. For theoretical 

 purposes, we may plot survival on a vertical 

 scale from to 2. In this case means no 

 survival, i. e., all individuals in the specified 

 class died prematurely. At 1, we have one in- 

 dividual attaining the age of reproduction for 

 each corresponding parent. At 2 we have two 

 progeny attaining maturity for each corre- 

 sponding parent. Now if the survival line is 

 level (Fig. 13a) natural selection is not active; 



some low value in the other direction, and at 

 some point between rise to a point or become 

 level as in Figs. 146 and 14c. In the case of 

 Fig. 14Cj the species will evolve until selection 

 becomes periodic, but in Fig. 135 we have a 

 diiferent condition. Here it is carried to a 

 point where natural selection becomes impo- 

 tent. It is in such a case that determinate 

 evolution has free play and may, in some cases, 

 carry the species further. In still other cases 

 there is an absolute limit of variation in the 



Fig. 14. Theoretical survival curves. Dotted line, survival rate; solid line, 

 theoretical polygon; dash line, polygon of freqiiency of young individuals. 



but if it be in any degree inclined (Fig. 13(f) 

 natural selection is in operation. Figs. 13b, 13c 

 and 13/, I have drawn the survival curve as 

 one would expect it from some descriptions of 

 the action of natural selection, but such ab- 

 rupt changes in the survival rate must be de- 

 cidedly exceptional. The actual line is ordi- 

 narily a gentle curve, the survival rate always 

 being low and gradually becoming lower or 

 higher from class to class, as in Figs. 13d, e 

 and g-l. The periodic selection where the 

 species is kept stationary is illustrated in Figs. 

 13i to 13L There is every gradation of course 

 between this and secular selection. The point 

 to which selection would carry the species 

 might be close to the present mode. 



The survival curve, if we had the data to 

 construct it for a sufficient length, would prob- 

 ably, in many cases, especially those involving 

 measurements, touch in one direction and 



characteristic; for instance, blackish color 

 would have a limit at absolute black (Fig. 

 156). In such a case the survival curve would 

 come to a sudden stop on the particular rate 

 for that point. If the inclination is upward 



Fig. 15. (o) Theoretical survival curves with 

 the mutation alone affected by a differential sur- 

 vival rate. (6) The polygon of frequency and of 

 survival rate are limited in one direction. 



