568 



NATURE 



[October 3, 1901 



variation. In the new century careful and quantitative studies 

 will be made on these factors. We shall get at quantitative ex- 

 pressions of the more complicated forms of heritage in the same 

 way as Gallon has given us an expression of a simple form of 

 inheritance. We shall hope to understand why some qualities 

 blend and others refuse to do so. We shall learn the laws of 

 mingling of qualities in hybrids and get an explanation of the 

 monstrosities and the sterility which accompany hybridisation. 

 What we call reversion and prepotency will acquire a cytological 

 explanation, and it may be that the theory of fertilisation will 

 be seriously modified thereby. When we can predict the out- 

 come of any new combination of germplasms, then, indeed, we 

 shall have got at the laws of inheritance. 



As for the other factor, that of variation, I anticipate interest- 

 ing developments in our knowledge of its laws and of its causes. 

 The methods by which this knowledge is to be acquired are 

 doubtless comparative observation, experimentation and a 

 quantitative study of results. Within the last decade a profouud 

 student of variation (Bateson) has declined to discuss its causes, 

 holding that we had no certain knowledge of them. Even the 

 categories of variation are still unenumerated. The science of 

 variation is therefore one of those that we may hope to see 

 established in this century. I feel convinced that statistical 

 studies are first of all necessary to lay the foundations of the 

 science. 



As an illustration o. an application of statistics to evolution 

 studies I will give some account of my work during the past two 

 years on the scallop of our east coast, Pecteti irradians. 



Pecten iiradians is a bivalve mollusc of flattened lenticular 

 form that inhabits our coast from Cape Cod southward. The 

 Cape Cod limit is a rather sharp one, but southward our scallop 

 passes gradually into the closely related forms of the South 

 American coast. This fact would seem to indicate its southerly 

 origin. To get light on the evolution of the group, I have 

 studied and measured more than 3000 shells, chiefly from four 

 localities : — (i) Cold Spring Harbour, Long Island ; (2) More- 

 head, North Carolina; (3) Tampa, Florida ; and (4) the late 

 Miocene or early Pliocene fossils of the Nansemond River. 

 The fossil shells, to which I shall frequently refer, were found 

 embedded in the sand of Jack's Bank, one mile below Suffolk, 

 Virginia. The bank rises to a height of twenty-five to thirty 

 feet. Shells were obtained from three layers, respectively one 

 foot, six feet and fifteen feet above the base of the bluff'. Of 

 course, the upper shells lived later than the lower ones and 

 may fairly enough be assumed to be their direct descendants. 

 The time interval between the upper and lower levels cannot 

 be stated. As I have measured suHicient shells from the 

 bottom and top layers only I shall consider them chiefly. I 

 wished to get recent Pectens from this locality, but the nearest 

 place where they occur in quantity is Morehead, North 

 Carolina. These Pectens may therefore stand as the nearest 

 recent descendants of the Pectens of the Nansemond River. 



The Pecten shells have a characteristic appearance in each 

 of the localities studied. After you have handled them for 

 some time you can state in 95 per cent, of the cases the locality 

 from which any random shell has come. First of all the shells 

 difl^er in colour, especially of the lower valve. In the speci- 

 mens from Cold Spring Harbour this is a dirty yellow, from 

 Morehead, yellow to salmon, from Tampa, white through clear 

 yellow to bright salmon. Second, the anterio-posterior 

 diameter of the shell becomes relatively greater than the 

 vertical diameter as you go north. Thus the anterio-posterior 

 diameter exceeds, on the average, the dorso-ventral diameter : 

 at Tampa, by about I '5 nr.m. ; at Morehead, 2'5 mm. ; and at 

 Cold Spring Harbour, 6 mm. The fossil Pectens have an excess 

 of about 4 mm. 



Comparing the fossils with the Pectens 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 

 „ ,, highest ,, ,, ,, 



,, Morehead 



S-S mm. 

 9' I mm. 

 197 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 different localities is as 

 follows : — 



Lower level. Jack's Bank 



Middle ,, „ 



Upper ,, ,, ,, ., 

 Morehead and Cold Spring Harbour 



Tampa 



22 -6 



22T 

 217 

 17-3 



20'5 



NO. 1666, VOL. 64] 



Here it appears that there is a phylogenetic tendency toward 

 a decrease in the number of rays of Pecten irradians. To 

 summarise : the scallop is becoming, on the average, more 

 globose, and the number of its rays is decreasing, and its valves 

 are probably becoming more exactly circular in outline. The 

 foregoing examples illustrate the way in which quantitative 

 studies of the individuals 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 quantita- 

 tively in a large number of individuals of a species the measure- 

 ments or counts made will vary, i.e. they will fall into a number 

 of classes. The proportion of individuals falling 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 fre- 

 quency (and is consequently called the mode), and as we depart 

 from it the frequency gradually diminishes, and diminishes 

 equally at equal distances above and below the mode. One can 

 plot the distribution of frequencies by laying off the successive 

 classes at equal intervals along a base line and drawing perpen- 

 diculars at these points proportional in length to the frequency. 

 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 symmetrical about the modal ordinate we may con- 

 clude 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 characterised by this, that the 

 curve runs from the mode further on one side than on the other. 

 This result may clearly be brought about by the addition of indi- 

 viduals to one side or their subtraction from the other side oi 

 the normal frequency curve. The direction of skewness is to- 

 ward the excess side. The skew frequency polygon indicates 

 that the species is undergoing an evolutionary change. More- 

 over, the direction and degree of skewness may tell us some- 

 thing of the direction and rate of that change. There is one 

 difficulty in interpretation, however, for a polygon that is skew 

 may be so either from innate or from external causes. In the 

 case of skewness by addition we may think that there is an 

 innate tendency to produce variants of a particular sort, repre- 

 senting, let us say, the atavistic individuals. In this case skew- 

 ness points to the past. The species is evolving frotit the 

 direction of skewness. In the case of skewness by subtraction, 

 there are external causes annihilating some of the individuals 

 lying at one side of the mode. Evolution is clearly occurring 

 away from that side and in the direction of skewness. 



Now so far as we know at the present time there is no way 01 

 distinguishing skew polygons 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 experi- 

 mentally and whose ancestry is known, and secondly upon 

 certain cases of compound curves. Take the case of the ray 

 flowers of the common white daisy. A collection of such daisies 

 gathered in the field and studied by De Vries gave a mode of 

 13 ray flowers with a positive skewness of i '2. The 12- or 

 i3-rayed wild plants were selected to breed from, and their 

 descendants, while maintaining a mode at 13, had the increased 

 positive skewness of I '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 condition as the descendants of the 12-rayed 

 plants were below. The skewness -0T3 is comparatively 

 slight. In this case we have experimental evidence that curves 

 may be skew toward the original ancestral condition. 



(Jf the compound polygons it is especially the bimodal polygon 

 that frequently gives hint of two races arising out of one 

 ancestral, intermediate condition. Consequently we should | 1 

 expect the two constituent polygons to be skew in opposite j 

 directions ; and so we usually find them to be. For example, 1 1 



