320 



SCIENCE. 



[N. S. Vol. XIV. No. 348. 



ventral diameter : at Tampa, by about 1.5 

 mm.; at Morehead, 2.5 mm.; and at Cold 

 Spring Harbor, 6 mm. The fossil Pedens 

 have an excess of about 4 mm. 



Comparing the fossils with the Pedens of 

 Morehead we find, as shown above, that 

 the fossils are more elongated. Comparing 

 the depth of the right valves having a 

 height of 59 mm. , we get : 



From the lowest level, Jack's Bank 8.8 mm. 

 " " highest " " " 9.1mm. 



" Morehead 19.7 mm. 



Hence the. recent shells are much more 

 nearly spherical than the fossils; there is 

 a phylogenetic tendency toward increased 

 globosity. 



The average number of rays in the dif- 

 ferent localities is as follows : 



Here it appears that there is a phylogenetic 

 tendency toward a decrease in the number 

 of rays of Peden irradians. To summarize : 

 The scallop is becoming, on the average, 

 more globose, and the number of its rays is 

 decreasing and its valves are probably be- 

 coming more exactly circular in outline. 

 The foregoing examples illustrate the way in 

 which quantitative studies of the individ- 

 uals of a species can show the change in its 

 average condition both at successive times 

 and in different places. 



But the quantitative method yields more 

 than this. It is well known that if the 

 condition of an organ is expressed quanti- 

 tatively in a large number of individuals of 

 a species the measurements or counts made 

 will vary, i. e., they will fall into a number 

 of classes. The proportion of individuals fall- 

 ing into a class gives what is known as the 

 ' frequency ' of the class. Now it appears 

 that in many cases the middle class has the 



greatest frequency (and is consequently 

 called the mode) and as we depart from it the 

 frequency gradually diminishes, and dimin- 

 ishes equally at equal distances above and 

 below the mode. One can plot the distribu- 

 tion of frequencies by laying off the succes- 

 sive classes at equal intervals along a base 

 line and drawing perpendiculars at these 

 points proportional in length to the fre- 

 quency. If the tops of these perpendiculars 

 be connected by a line there is produced a 

 ' frequency polygon.' The shape of the fre- 

 quency polygon gives much biological 

 information. When the polygon is sym- 

 metrical about the model ordinate we may 

 conclude that no evolution is going on ; 

 that the species is at rest. But very often 

 the polygon is more or less unsymmetrical 

 or ' skew.' A skew polygon is character- 

 ized by this : that the polygon runs from the 

 mode further on one side than on the 

 other. This result may clearly be brought 

 about by the addition of individuals to one 

 side or their subtraction from' the other 

 side of the normal frequency polygon. The 

 direction of skewness is toward the excess 

 side. The skew frequency polygon indi- 

 cates that the species is undergoing an evo- 

 lutionary change. Moreover, the direction 

 and degree of skewness may tell us some- 

 thing of the direction and rate of that 

 change. There is one difficulty in interpre- 

 tation, however, for a polygon that is skew 

 may be so either from innate or from ex- 

 ternal causes. In the case of skewness by 

 addition we may think that there is an in- 

 nate tendency to produce variants of a 

 particular sort, representing, let us say, the 

 atavistic individuals. In this case skewness 

 points to the past. The species is evolving 

 from the direction of skewness. In the 

 case of skewness by subtraction there are 

 external causes annihilating some of the in- 

 dividuals lying at one side of the mode. 

 Evolution is clearly occurring away from 

 that side and in the direction of skewness. 



