August 30, 1901.] 



SCIENCE. 



321 



Now so far as we know at the present 

 time there is no way of distinguishing skew 

 polj'gons due to atavism from such as are 

 due to selective annihilation. But in many 

 cases at least the skewness, especially when 

 slight, can be shown to be due to atavism ; 

 and this is apparently the commoner cause. 

 This conclusion is based first upon a study 

 of races produced experimentally and 

 whose ancestry is known, and secondly 

 upon certain cases of compound curves. 

 Take the case of the ray flowers of the com- 

 mon w^hite daisy. A collection of such 

 daisies gathered in the fields by DeVries 

 gave a mode of 13 ray flowers with a posi- 

 tive skewness of 1.2. The 12- or 13-rayed 

 wild plants were selected to breed from, and 

 their descendants, while maintaining a mode 

 at 13, had the increased positive skewness 

 of 1.9. The descendants of the 12-rayed 

 parents had a stronger leaning towards the 

 high ancestral number of ray flowers than 

 the original plants had. The 21-rayed 

 plants were also used to breed from. Their 

 descendants were above the ancestral con- 

 dition as the descendants of the 12-rayed 

 plants were below. The skewness — 0.13 is 

 comparatively slight. In this case we have 

 experimental evidence that polygons may be 

 skew totmrd the original ancestral condi- 

 tion. 



Of the compound polygons it is espec- 

 ially the bimodal polygon that frequently 

 gives hint of two races arising out of one 

 ancestral, intermediate condition. Con- 

 sequently we should expect the two con- 

 stituent polygons to be skew in opposite 

 directions ; and so we usuall}^ find them to 

 be. For example, Bateson has measured 

 the horns on the heads of 343 rhinoceros 

 beetles and has got a bimodal polygon. 

 The polygon with the lower mode has a 

 skewness of + 0.48 ; that with the higher 

 mode a skewness of — 0.03. One might 

 infer that the right-hand form, the long- 

 horned beetles, had diverged less than the 



short-horned from the ancestral condition. 

 Again, as is well known, the chinch bug 

 occurs in two forms — the long-winged and 

 the short-winged. Now, in a forthcoming 

 paper my pupil, Mr. Garber, will show that 

 the frequency polygon of the short-winged 

 form has a skewness of -f 0.44, while that 

 of the long-winged form has a skewness of 

 — 0.43. On our fundamental hypothesis 

 the ancestral condition must have been 

 midway between the modes. 



Still a third class of cases that gives 

 evidence as to the significance of skewness 

 is that where two place modes have moved 

 in the same direction but in difii'erent de- 

 grees. Thus the index (breadth -=- length) 

 of the shell of Littoi'ina Uttorea, the shore 

 snail, as measured by Bumpus, has at 

 Newport a mode of 90, at Casco Bay of 

 93. The skewness is positive in both 

 places and greater (-f .24) at the more 

 southern point than at Casco Bay (+ .13). 

 This indicates that the ancestral races had 

 a higher index even than those of Casco 

 Bay, probably not far from 96, and also 

 that the Littorina Uttorea of our coast 

 came from the northward, since the north- 

 ern shells are the rounder. We have his- 

 torical evidence that they did come from 

 the northward. Likewise the Littorinas 

 from South Kincardineshire, Scotland, have 

 a modal index of 88 and a skewness of 

 + 0.065, while those of the Humber, with 

 a mode of 91 have a skewness of + 0.048. 

 These figures suggest that if the mode were 

 97 the skewness would be 0, and this would 

 give practically the same value to the an- 

 cestral index as arrived at for the Lit- 

 torinas of our coast. It will be seen from 

 these illustrations that the form of the fre- 

 quency polygon may be of use in determin- 

 ing phylogeny. 



While skewness is thus often reminiscent, 

 we must not forget the possibility that it 

 may be, in certain cases, prophetic. This 

 has come out rather strongly in a piece of 



