K. Pkahson and A. Lee 383 



if the stock inates with its like, will bo vcry small or zero*. We cannot uiifortu- 

 nately oii tho present niatcrial detenninc absolutely its value ; for, in tht; first 

 place we liave no correlations wiUi i(r;iii(li>arciil,s or higher ascendant.s, aiid in Uic 

 second place the assortative iiiatiiig ciiefHciüiits are so large, that we cannot aft'urd to 

 negloct them to a tirst approxiniation, as we havo done for the case of eye-colour 

 in man and c'dat-cnlour in lioi\s(_'s-)-. 



Wliat, howcvoi-, the jjivscnt invest^igation inipresses npon one is tJiis: Parcntal 

 con-elation being fi-oni -40 to •') in valne is nineh higher than we eould antieiimte 

 f'rom Mr (ialton's Nutural Inheritance data. Ifence selectiou is far niore rapid in 

 its effects than we supposed a fow years ago, two to four generations sufticc to 

 effect what we originally considered would need (i to 8. Further, fJic regression 

 after such selection may well be zero. I have not worked out yet the multiple 

 regi-ession foi'nuilae allowing for assortative mating; they present considerable 

 difRculty owing to the coniplexity introduced by the correlations between relations- 

 in-law due to such mating. But neglecting for a nionient the efleet of assortative 

 mating, the series of ancestral correlations, 



■4() ■:32 -28 -Iß 



proceeding by a factor '7 would give a zero-regression :uul not differ widely froni 

 the ancestral cori'elations we know for eye-colour in nian:|:. I lay no stress on 

 tliese particular number.s, but I wish to emphasise the point that a few generations 

 of selectiou in the case of man suffice to establish a breed, and that regression for 

 this breed may well be insensible. 



(viii) Cruss Purentul Inheritance. 



I have defined cross heredity to be the correlation of two difterent organs in 

 twü blüod relations§. We are now for the first tinie in a position to estimate its 

 maguitude. 



We See at once that tliese coefficients of cross heredity are for sonie cases 

 almost as large as the coefficients of direet heredity, and on the whole sensibly 

 larger than the values whieli l)ut a few years ago were supposed to be those of the 



* The physical asptct of this is iierfcctlj- casj- to iinderstainl. When we select one iiarent the off- 

 spring advance 3.5 to 40 p.c. on the geneial populatiou, when we seleet two parents 70 to SO p.c. If we 

 select two parents and four grandparents, tliere is another percentage increase which brings us up into 

 the 90 per Cents., and if we select for three generations we have nearly the 100 per cent. of the required 

 eharacter. Now suppose the selected stock to inbreed or otherwise mate with its likes for this special 

 charaoter. Why will the regression now that selection ceases be zero or insensible? For this simple 

 reason, that while we cease to select wilhin the stock, yet each new generation has an additional selected 

 generation of ancestry behind it, and tho inliuence of this aucestry balances the regressional 

 tendency. This is the simple verbal explanation of the cessatiou of regression with selectiou. The 

 algebraical expressiou of its possibility was first given in my memoir of 1898 : see R. S. Pioc. Vol. 62, 

 p. 401. 



t Ibid. p. •2-24, See also R. S. Pruc. Vol. (52, p. 388. 



X Biometrika, Vol. ii. p. 222. e and p of p. 224 would be •.'>(j and -44 respectively. 



§ Phil. Tram. Vol. 187, A, p. 259. See also R. S. Pruc. Vol. C2, p. 410. 



49—2 



