TTI. Mathematical Contributions to the Theory of Evolution. XII. On a 

 Generalised Theory of Alternative Inheritance, ivith special Reference to 

 MENDEL'S Laws. 



By KAIIL PEARSON, F.R.S. 



Received September 11, Read November 26, 1903. 



(1.) Introductory. On a Generalised Theory of Alternative Inheritance, with special 



Reference, to MENDEL'S Laws* 



IT seems likely to be of interest at the present time to consider rather at length a 

 fairly full mathematical theory of the pure gamete. We do not venture to call this 

 theory a generalised Mendelian theory of inheritance, partly because it is not even the 

 most general theory of the pure gamete conceivable, partly because MENDEL'S original 

 theory of heredity was perfectly clear and perfectly simple, and is not the theory here 

 developed. The pure and simple Mendelian theory seems to have been discarded in 

 the light of recent experimental results by more than one Mendelian, both in this 

 country and abroad. The original Mendelian theory has been replaced by what are 

 termed " Mendelian Principles." In this aspect of investigation the fundamental 

 principles propounded by MENDEL are given up, and for each individual case a pure 

 gamete formula of one kind or another is suggested as describing the facts, t This 

 formula is then emphasised, modified or discarded, according as it fits well, badly, or 

 not at all with the growing mass of experimental data. 



It is quite clear that it is impossible while this process is going on to term 

 anything whatever Mendelian as far as theory is concerned. The present investigation 

 is therefore not a generalised Mendelian theory of heredity : we speak of it merely 

 as a generalised theory of alternative inheritance, and it is based on the conception 

 that the gamete remains pure, and that the gametes of two groups, while they may 

 link up to form a complete zygote, do not thereby absolutely fuse and lose their 



* I owe the incentive to this memoir to Professor W. F. R. WELDON, who had already worked at some 

 of the simpler special cases and who placed his results entirely at my disposal. 



t See especially TSCHERMAK, ' Zeitschrift f. d. landwirthsch. Versuchswesen,' Jahrg. IV. (" Ueber 

 Ziichtung neuer Getreiderassen ") ; DE VEIES, ' Ber. d. deutsch. botan. Gesellsch.,' vol. xviii. (1900), 

 pp. 435-443 ; BATESON, ' Proc. Camb. Phil. Soc.,' vol. 12, p. 53 ; ' Nature,' April and May, 1903. 



(361.) 4.3.04 



