750 



SCIENCE 



[N. S. Vol. XXXVI. No. 935 



THE ANALYSIS OF NATURAL SELECTION^ 

 The actual operation of natural selection 

 is rarely investigated. The various methods 

 that have been employed -will be here consid- 

 ered seriatim, in order that their advantages 

 and limitations may be noted. 



1. The comparison of the mean magnitude 

 of the characteristic in question in those in- 

 dividuals that died either with that of the 

 survivors or with that of the whole number. 

 This method is simple and where the differ- 

 ence is considerable does provide proof that 

 secular^ natural selection was operative. Its 

 shortcomings are that it furnishes no analysis 

 of the operation of selection and that periodic' 

 natural selection is not detected by it. 



2. The index of correlation between the 

 length of time of successful resistance to the 

 adverse condition and the magnitude of the 

 characteristic in question. This method has 

 been used by Dr. F. E. Lutz on Ampelophila. 

 In addition to demonstrating the action of 

 natural selection, it may in some cases, as in 

 Ampelophila, throw valuable light on the ac- 

 tion of the cause of death. Its limitation is 

 its failure both to discriminate between peri- 

 odic and secular selection and to analyze the 

 distribution of the incidence of natural selec- 

 tion. 



3. In addition to comparing the means of 

 the individuals that perished and survived, 

 Bumpus, in his well-known sparrow observa- 

 tion, compared the extremes with the whole 

 number, in this way being able to detect any 

 periodic selection that may have taken place, 

 as well as the secular selection. This method, 

 too, falls short, because a still closer analysis 

 is desirable, and because the result hinges on 

 the particular choice of the percentage of the 

 whole chosen to represent the extreme. 



4. We have a further step in analysis in 



^ This article was written while the author was 

 on the staff of the Station for Experimental 

 Evolution at Cold Spring Harbor, N. T., of the 

 Carnegie Institution of Washington. 



' Pearson 's term for the form of natural selec- 

 tion which favors one extreme over the other. 



^Pearson's term for the form of natural selec- 

 tion which favors the mode at the expense of the 

 extremes. 



Weldon's method of showing the results of 

 his classic experiment in subjecting Oarcinus 

 to clay suspended in water. Here the poly- 

 gon of the perished is superimposed upon the 

 polygon of frequency for the whole number. 

 The eye can then wander along the polygons 

 and observe the relation of the two throughout 

 their courses, which makes a fuller analysis 

 possible. But in making the analysis the mind 

 must compute the ratio for each class as best 

 it can. 



The method which I wish to propose deter- 

 mines these ratios precisely and plots them 

 graphically. The survival rate is determined 

 for each class, and plotted, preferably superim- 

 posed upon the polygon of frequency of the 

 whole number, so that the numbers used are 

 shown. Since the probable error of the sur- 

 vival rates increases towards the extremes 

 where based upon fewer individuals, some 

 method of combining classes is frequently de- 

 sirable. Only such combining should be done 

 as is considered absolutely necessary, because 

 the analysis is less discriminative by just so 

 much. The combining may be done by arbi- 

 trarily adding the classes in groups of 2, 3, 4, 

 etc., or by combining the most extreme eighth 

 in one direction, the next eighth, and so forth. 

 This may be done absolutely, or in some 

 cases, to the nearest class. The particular 

 method depends largely upon the number em- 

 ployed. Eougher grouping and a larger num- 

 ber of classes are permissible where there are 

 large numbers. In Fig. 1 I have applied the 

 method to Weldon's experiment with crabs 

 (male Garcinus rrimnas) in muddy water. The 

 survival rate is determined for each class and 

 a survival curve thus established. It will be 

 seen that, even with this large number of 

 classes, the curve is clearly inclined. In Figs. 

 2 and 3 I have replotted the curve in four and 

 eight classes, respectively, of about equal num- 

 bers to smooth out the irregularities arising 

 from the small numbers in the extreme classes. 

 With so active a natural selection, one can well 

 believe that, in spite of the criticism of Cun- 

 ningham, there actually took place in nature 

 the evolution shown by the statistics gathered 

 in the successive years of the crabs at Ply- 

 mouth. 



