4 Descendenz und Hybriden. 



The author brings forward a number of interesting observations 

 on Ferns, both wild and cultivated, tending to show that Varia- 

 tion is in every way as marked — and probably much more 

 so — in the wild state than under cultivation. He also points 

 out that the „type" and the „sport" may grow side by side 

 under identical conditions and hence denies the truth of Hens- 

 low's second proposition mentioned above. Henslow has 

 also held that destruction of individuals, operating in infancy, 

 takes place before the varietal or specific characters appear. 

 Druery states, however, that it is perfectly easy to distinguish 

 the form from the earliest appearance of the leaf. 



E. Drabble (London). 



PEARSON , Karl , Mathematical Contributions to the 

 Theory of Evolution. XII. On a generalized 

 Theory of Alternative Inheritance with special 

 reference to Mendel's Laws. (Proc. Royal Soc. London. 

 Vol. LXXII. No. 487. Jan. 14, 1904.) 



The fundamental conception of the Mendelian Theory is 



the permanence of identity of parental gametes on crossing. 



This may be represented symbolically thus: 



(AA 1 ) X (««*) = (A + A 1 ) (« -f a 1 ) = (A«) + (Aß 1 ) 

 -\- (A 1 «) -\- (A l «') where in the first expression we have the 

 parental zygotes, in the second the breaking up into gametes, 

 and in the third the zygotes of the resulting offspring. 



This expression can be generalized at once by replacing 

 the simple couplet (AA 1 ) by n such couplets and supposing the 

 original parental zygotes to be of the form (Ai Ai) + (A2 A2) 

 + (A3 A3) + . . . + (An An), and («1 «1) -j- («s cw) + («3 as) 

 -j- .... -j- («n an), in which each corresponding pair of couplets 

 on crossing obeys the above symbolic formula. 



It is required to find how the population will change, if at 

 all, if these hybrids breed at random and are equally fertile 

 amongst themselves. The above conception dispenses with 

 Mendel's ideas of recessive and dominant characters, and 

 the terms protogenic (a a) and al löge nie (A Aj couplets 

 are used. 



Developing the theory it is found that 1) segregation oecurs 

 when the hybrids cross. When they cross at random, presup- 

 posing no artificial, natural, or reproduetive selection to take 

 place, a stable population is established. Any selection however 

 would at once produce a progressive change in the race. 

 2) Regression of the offspring of any ancestor is linear. 3. The 

 ancestral correlation forms a geometric series. 



The parental correlation is 1 /s ; the ratio of diminution of 

 ancestral correlation at each stage is */-> anc ' the correlation 

 between brothers is 0,4 — exactly the values given by Galton's 

 Statistical enquiry. It is thus apparent that inheritance is no 

 funetion of the number of couplets determining the Constitution. 



