504 



NA TURE 



[September 22, 1898 



You see that if this diagram (which is based on very few 

 specimens) really represents the law of variability in these 

 buttercups, no amount of natural or other selection can produce 

 a race with less than five petals out of them. While it is con- 

 ceivable that selection might quickly raise the normal number of 

 petals, it could not diminish it, unless the variability of the race 

 should first change.^ 



These examples, which are typical of others, must suffice to 

 show the way in which the theory of Chance, as developed by 

 Prof. Pearson, can express the facts of organic variation. 



I think you will agree that they also show the importance 

 ■of investigating these facts. For of the four characters we have 

 -examined, we have seen that two, namely human stature and 

 the antero-lateral carapace length of Carcimis tiicettas, vary so 

 as to afford nearly equal material for selective modification in 

 either direction ; one character, the number of Midler's glands in 

 rswine, offers distinctly greater facility for selective modification 

 in one direction than in the opposite direction ; and in the last 

 •character, the number of petals in a race of buttercups appears 

 to offer scope for modification in one direction only, at least by 

 :selection in one generation. 



Knowledge of this kind is of fundamental importance to the 

 theory of Natural Selection. You have seen that the new 

 >method given to us by Prof. Pearson affords a means of express- 

 ing such knowledge in a simple and intelligible form ; and I, at 

 least, feel very strongly that it is the duty of students of animal 

 -evolution to use the new and powerful engine which Prof. 

 Pearson has provided, and to accumulate this kind of knowledge 

 in a large number of cases. 



I know that there are people who regard the mode of treat- 

 ment which I have tried to describe as merely a way of saying, 

 with a pompous parade of arithmetic, something one knew 

 before. This criticism of Prof. Pearson's work was actually 

 made to me the other day by an eminent biologist, whose name 

 I will not repeat. If there be any here who hold such an opinion, 

 .1 would ask them to read Mr. Francis Galton's Essays on 

 ^Heredity ; where a simple and quite unexpected relation 

 between parents and offspring is shown to be a direct con- 

 sequence of the fact that they vary by chance. This is the first 

 and the most striking deduction from the mathematical theory 

 of organic variation, but it is not the only one. It is enough, 

 however, to show that the new method is not only a simple 

 means of describing the facts of variation, which facts very few 

 .people knew before, but it is a powerful instrument of research, 

 which ought to be quickly and generally adopted by those who 

 -care for the problems of animal evolution. 



I think I have said enough to convince you how entirely 

 Prof. Pearson's method promises to confirm the assertion that 

 organic variation obeys the law of chance. 



The other objections to Darwin's theory are not so easily 

 answered. It is said that small variations cannot be supposed 

 to affect an animal's chance of life or death ; but few persons 

 Slave taken any pains to find out in any given case whether the 

 •death-rate is in fact affected by small variations or not. It is 

 said that the process of Natural Selection is so slow that the age 

 -of the earth does not give time for it to operate, but I know of 

 few cases in which any attempt has been made to find out by 

 actual observation how fast a species is really changing. 



I can only attempt to discuss the importance of small vari- 

 ations, and the rate of organic change, in the one case which I 

 happen to know. The particular case I have myself studied is 

 the variation in the frontal breadth of Carcimis riia-nas.- 



During the last six years my friend, Mr. Herbert Thompson, 

 and I have studied in some detail the state of this character in 

 the small shore-crabs which swarm on the beach below the 

 laboratory of the Marine Biological Association at Plymouth. 



I will show you that in those crabs small changes in the size 

 ■of the frontal breadth do, under certain circumstances, affect the 

 death-rate, and that the mean frontal breadth among this race 

 of crabs i«, in fact, changing at a rate sufficiently rapid for all 

 the requirements of a theory of evolution. , 



In Table IV. you see three determinations of the mean frontal 

 ibreadth of these crabs, expressed in terms of the carapace-length 

 taken as looo. You see that the mean breadth varies very 



1 Of course we know that selection does change the variability of a race. 



- In 1894 I gave an account of the variation of this dimension in female 

 specimens of various sizes (,Roy. Soc. Ptoc, vol. Ivii.), and I put forward an 

 hypothesis of the amount of selective destruction ilue to variation in this 

 •char.icter. That hypothesis neglected several important facts wh ch I now 

 know, and was open to other objections. I desire to replace it by the results 

 of the observations here recorded. 



rapidly with the length of the crab, so that it was necessary to 

 determine it separately in small groups of crabs, such that the 

 length of no two crabs in a group differed by more than a fifth 

 of a millimetre. The first column of the table shows you the 

 mean frontal breadth of twenty-five such groups, between lo and 

 15 millimetres long, collected in 1893. These crabs, were 

 measured by Mr. Thompson. The second column shows you 

 the mean frontal breadth in twenty-five similar groups of crabs, 

 collected in 1895, and also measured by Mr. Thompson. You 

 see that in every case the mean breadth in a group of crabs 

 collected in 1895 is less than it was in crabs of the same size 

 collected in 1893. The third column contains the result, so far 

 as it is yet obtained, of my own measurement of crabs collected 

 this year. It is very incomplete, because the 1895 crabs were 

 collected in August and September, and I was anxious to com- 

 pare them with crabs collected this year at the same season, so 

 that there has not yet been time to measure the whole series. 

 The measurements are sufficient, however, to show that the 

 same kind of change has taken place during the last three years 

 as that observed by Mr. Thompson in the interval between 1893 

 and 1895. Making every allowance for the smallness of the 

 numbers so far measured this year, there is no doubt whatever 

 that the mean frontal breadth of crabs from this piece of shore 

 is considerably less now than it was in 1895 among crabs, of the 

 same size. ^ 



Table IV. — The Mean Frontal Breadth ratio of Male C^rcinus 

 moenas from a particular patch of beach in Plymouth, in 

 the years 1893, 1895, and 1898. 



NO. 1508, VOL. 58] 



These results all relate tp male crabs. The change in female 

 crabs during this time has been less than the change in male 

 crabs, but it is, so far as my measurements at present permit 

 me to speak, going on in the same direction as the change in 

 male crabs. 



I think there can be no doubt, therefore, that the frontal 

 breadth of these crabs is diminishing year by year at a rate 

 which is very rapid, compared with the rate at which animal 

 evolution is commonly supposed to progress. 



I will ask your patience for a little while longer, that I may 

 tell you why I feel confident that this change is due to a selective 



1 I shall, of course, consider it my duty to justify this statement by more 

 extensive measurement as soon as possible. In the meantime I may say 

 that I have measured other small groups of crabs, male and female, from the 

 same place, at different seasons of the years 1896-9S, and the results agree 

 with those recorded in the table. 



