July 28, 1898] 



NATURE 



293 



by means of the former. To use a term I have introduced else- 

 where, the sport connotes a shifting of the focus of regression, 

 but any normal variation, however improbable, does not. In 

 the preface to the 1892 edition of his " Hereditary Genius," Mr. 

 Galton writes : "All true variations are (as I maintain) of this 

 kind \i.e. sports], and it is in consequence impossible that the 

 natural qualities of a race may be permanently changed through 

 the action of selection upon mere variations. The selection of 

 the most serviceable variations cannot even produce any great 

 degree of artificial and temporary improvement, because an 

 equilibrium between deviation and regression will soon be 

 reached, whereby the best of the offspring will cease to be better 

 than their own sires and dams." And again: "The case is 

 quite different in respect to what are technically known as 

 ' sports.' In these a new character suddenly makes its appear- 

 ance in a particular individual, causing him to differ distinctly 

 from his parents and from others of his race. Such new 

 characters are also fountl to be transmitted to descendants. 

 Here there has been a change of typical centre, a new point of 

 departure has somehow come into existence towards which re- 

 gression has henceforth to be measured, and consequently a real 

 step forward has been made in the course of evolution. When 

 natural selection favours a particular sport, it works effectively 

 toward the formation of a new species, but the favour that it 

 imultaneously shows to mere variations seems to be thrown 

 away so far as that end is concerned." 



I have cited these passages because Mr. Galton's letter seems 

 written with a view to their support, and because they contain 

 principles which I feel to be unproven and even opposed to 

 fiiirly well-established theory. I will take these principles in 

 order. 



{\) No real step fonvard can be made by the selection of mere 

 normal variations. 



This principle is stated as if it flowed from the theory of 

 regression ; but it is entirely opposed to that theory, and to Mr. 

 Galton's own law of ancestral heredity. According to that law, 

 if the average'midparents of the 1st, 2nd, 3rd . . . generations 

 possess on the average quantities h^, h^, /^j ... of a character 

 in excess of the general population, then the average offspring 

 w ill possess a quantity h of the character given by 



k = ^/;i Jr \ h„ + I k-i + . . . 



Now, if we select parents with deviations H from the general 

 population, these parents being "mere variations," whose 

 ancestry were entirely mediocre, or h, — h^ — o, we have 

 h =^ H, or the children have half their parents' character. 

 Their offspring, however, have not only exceptional parents 

 but exceptional grandparents ; thus, while they lose as to their 

 parents, they are a stage further removed from mediocrity in 

 their grandparents, and for them h■^ = ^ H, /i^ = H, and 

 /i,, = A^= . . . = o. Hence /^ = i (4 H) -f i H = i H. For 

 the grandchildren, /i =is(^H) + i {h H) -H i (J H) = i H. 

 Thus by a sin^^le selection from normal variations and in-and-in 

 breeding a stock has been established which differs by 4 H from 

 (he general population. Selection for only two generations leads 

 U) a stock with three-quarters of the required character, while 

 selection for three generations from mediocrity gives a stock 



table with 87-5 per cent, of the selected character. 

 I contend therefore, against Mr. Galton, that normal vari- 



lion really affords material for stable changes, and this without 

 that development "slowly through the accumulation of minute 

 and favourable variations during a long succession of gener- 

 ations " which he considers necessary. Artificial selection in 

 the matter of horse-breeding has, I believe, quite play enough 

 for great changes in the material provided by normal variation. 

 If we take a great thoroughbred sire and put first-class thorough- 

 bred mares to him, we should be utterly wrong in supposing a 

 regression in their offspring measured by ^ (the mean deviation 

 of sire and dam) towards the mediocre race-horse. The 

 sire and dam in this case have, even for thoroughbreds, ex- 

 ceptional pedigrees behind them. I think this goes a long way 

 I' explain the phenomenon noted by Mr. Galton, namely, cer- 



iin sires producing such a preponderance of standard per- 



rmers. There is another point which, I think, Mr. Galton has 

 under-estimated also, namely the efl^ect of fashion on the 

 breeder. Some years ago I saw a good deal of the inner 

 working of a large thoroughbred stud, of which two at least of 

 'the stallions were always very famous horses (costing 6000/. to 



NO. 1500, VOL. 58] 



9000/. ). I believe from forty to fifty public mares were put to 

 these stallions, besides from ten to twenty mares belonging to the 

 stud itself. Their lists were always full ; on the other hand, the 

 less fashionable stallions hardly had their complement of mares, 

 and the mares sent to them were often inferior or past their more 

 intense fecundity. This latter is a very important consideration. 

 I have recently been investigating the fertility of 4000 brood- 

 rnares. In this case, in one-hundred coverings we find about 

 sixty-three cases in which foals are born and survive to be 

 yearlings, but the standard deviation in this average fecundity is 

 as high as nineteen foals ; in other words, there is an immense 

 difference in the capacity of different mares to produce viable 

 offspring. Now a breeder sends not only his best-bred, but 

 his most fecund best-bred mares to the most famous and, there- 

 fore, most costly stallions. The result is that comparatively few 

 horses are the sires of the bulk of the best yearlings. It must 

 be remembered that in England we have only some 4000 

 thoroughbred foals annually, and only a certain fraction of these 

 ever become racers. It would by no means surprise me to find 

 that a quarter of this contribution was due to some six or ten 

 fashionable sires. The American conditions are probably some- 

 what similar. In other words the second-rate stallions, besides 

 their inferiority in breed, are given far less chance of producing 

 performers. 



To complete Mr, Galton's argument it would be necessary to 

 show (i) that the sires who produced only one performer had as 

 much chance of producing performers as those who produced 

 71 to 154, and (2) that their pedigree was as good as the 

 latters'. Thus it seems to me that Mr. Galton's first principle 

 is opposed to his own law of ancestral heredity, which I look 

 upon as demonstrated to a first approximation by observed 

 facts, and secondly does not, I venture to think, receive support 

 from his data for American horses. 



(2) Sports are more highly inherited than normal variations. 

 This seems to me a principle which can only be proven by 

 extensive experiment. In the first place, a " sport " must be 

 carefully distinguished from a normal variation of an improbable 

 degree ; and this is not always easy, especially in a case like that 

 of Mr. Galton's American trotters, where high prepotency is 

 asserted to be a spcrt. In this case it is inheritance in a high 

 degree which leads to the discovery of the sport. But what is 

 the degree of inheritance to be expected when fashion has deter- 

 mined the frequency, it would be hard to say. Further, as I have 

 pointed out under (i), the degree of inheritance depends on the 

 stability of the stock, and the performances of the pedigree of 

 the five leading stallion trotters as compared with the perform- 

 ances of the pedigree of the average stallion trotter are not 

 given by Mr. Galton. The degree of inheritance of the char- 

 acter of the sire by the offspring depends on what I have else- 

 where termed the coefficient of stability ; and not only is this 

 pedigree often missing in the selection of what is termed a 

 normal variation, but also in the case of what is termed a 

 "sport." It becomes, therefore, difficult to compare the rates 

 of inheritance in the two cases. 



There is a well-known case of sheep often cited to show that 

 sports are strongly inherited, but the details of this case are not 

 wholly clear. Polydactyly, which iome might term a sport, 

 does not seem to me to indicate any intensity of heredity 

 beyond what may be inferred from an application of the law 

 of ancestral heredity to the pedigree. No direct experiments 

 on sports are known to me. Accordingly I think we must 

 wait until experiment has shown that sports are more highly 

 heritable than normal variations, before we assert that a 

 case of high degree of inheritance is evidence in itself of 

 a sport. Personally I may be bold to set up an opinion against 

 such an authority as Mr. Galton, but the more I learn of race in 

 man, horses and dogs, the less inclined I am to trust sports as a 

 fundamental factor more important than normal variation' in the 

 establishment of stable stocks. 



But this second principle differs from the first, which I believe 

 to be erroneous, because it ought to be capable of being settled 

 by direct experiment, and is at present only a matter of opinion. 

 Is it absolutely hopeless to wish for the farm which Mr. Gallon 

 once dreamed about, where direct experiment might test the 

 laws of heredity on plants and animals ? 



Karl Pearson. 



1 I would prefer the term continuous variation. I should not necessarily 

 have treated variation according to the normal law of error, as the opposite 

 to a sport. 



