50 



NA TURE 



[September 22, 1898 



chance whether you draw a red card or a black one. Suppose 

 you draw a red card, and keep it. The chance that your second 

 •card will be red is not so great as the chance that it will be 

 black ; because there are only twenty-five red cards and twenty- 

 ■six black cards left in the pack. 



Now Prof. Pearson has shown how to deal with cases of this 

 kind also ; and how to determine, from the results of statistical 

 observation, whether one is dealing with such cases or not. 



I am no mathematician, and I do not dare even to praise the 

 mathematical process by which this result was achieved. I will 

 •only say that it is experimentally justified by the fact that most 

 •statistics relating to organic variation are most accurately repre- 

 ■sented by the curve of frequency which Prof. Pearson deduces 

 for the case where the contributory causes are mutually inter- 

 dependent.^ 



The first case of an asymmetrical distribution in animals which 

 I ask you to look at is the frequency of variations in the size of 

 part of the carapace of shore crabs. The crabs measured were 

 ^99 females from the Bay of Naples. In this case the distribu- 



series of deviations from the mean length of the antero-lateral 

 margin is as definite a character of the crabs as the mean itself ; 

 and in every generation a series of deviations from the mean is 

 regularly produced, according to a law which we can learn if we 

 choose to learn it. 



Now suppose it became advantageous to the crabs, from some 

 change in themselves or in their surroundings, that this part of 

 their carapace should be as long as possible. Suppose the 

 crabs in which it was shorter had a smaller chance of living, and 

 of reproducing, than the crabs in which it was longer. 



Suppose that crabs in which this dimension is longest were as 

 much more productive than those in which it was shortest, as 

 the most prolific marriages are more fertile than the least 

 prolific marriages among ourselves. Prof Pearson has pointed 

 out that half the children born in England are the offspring of 

 a quarter of the marriages. If we suppose the productiveness 

 among crabs to vary as much as it does among ourselves, only 

 that in crabs the productiveness is greater, the greater the 

 length of this bit of the carapace, then half of the next 



52 53 54 55 56 57 

 Fig. 



8 59 ■ 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 

 -Diagram showing the height (in inches) of each of 25,878 American recruits. 



76 77 



tion of variations (see Fig. 3) is very nearly symmetrical, and in 

 an account of these crabs which I wrote before Prof. Pearson's 

 memoir was published, I treated them as symmetrical. The 

 ■curve actually drawn on the diagram is one constructed by Prof. 

 Pearson himself from the data given by my measurements of the 

 crabs, and it fits the observations very sensibly better than the 

 symmetrical curve. So that this dimension of a crab's carapace 

 ■does vary by chance, but the chance of a given deviation from 

 the mean length is not quite the same in both directions. 



Now, admitting for the moment that these differences in the 

 length of a part of the crab's carapace can affect the crab's 

 ■chances of survival, you see that natural selection has abundant 

 material on which to work. The production of this regular 



1 Even the distribution of human stature, which has been so successfully 

 treated by the older, so-called "normal" curve, is more accurately repre- 

 •sented by a curve of Prof. Pearson's type ; but in this case the difference 

 between the two is so slight as to be inappreciable for all practical purposes ; 

 •so that Mr. Gallon's practice and Prof. Pearson's theory are alike justified. 



NO. 1508, VOL. 58] 



generation of crabs will be produced by that quarter of thf" 

 present generation in which the antero-lateral margin is longest. 

 And as the offspring will inherit a large percentage of the 

 parental character, the meian of the race may be sensibly raised 

 in a single generation. 



This view of the possible effect of selection seems to have 

 escaped the notice of those who consider that favourable vari- 

 ations are of necessity rare, and likely to be swamped by inter- 

 crossing when they do occur. You see that in this case there 

 are a few individuals considerably different from the mean in 

 either direction, and a very large number which differ from the 

 mean a little in either direction. If such deviation be associated 

 with some advantage to the crabs, so that crabs which possess 

 such abnormality are more fertile than those which do not, it is 

 a certainty that the mean character of the next generation will 

 change, if only a little, in the direction advantageous to the 

 race ; and the opportunity for selective modification of this kind 

 to occur in either direction is very nearly the same. 



