Julian S. Huxley 



275 



cannot exceed V2 (since q cannot be less than 1), and is always less than 

 the previous preponderance of females. In each generation there will 

 always be a proportion of non- viable YY zygotes (the highest possible 

 figure being a little over | of the total zygotes). 



A few numerical results may be of interest. 



Thus the final as well as the initial sex-ratio will always show a 

 preponderance of females. 



The proportion of YY zygotes in the second generation will be -^ of 

 the total when p = ^, between | and ^ when ^ = y^. In the generation 

 with the limiting sex-ratio it will be over -^^ when p = ^, almost | when 



(B) Wfwn c/ is ZZ, $ is ZW. 



Suppose that ^ of the ZZ zygotes in each generation are trans- 

 formed into females. If the constitution of the nth abnormal generation 

 be UnZZ : IZW, then pUnZZ will be transformed into females, and the 

 sex- ratio will be 



(1 -p)Un {ZZ) .^:1 {ZW)+pUn (ZZ).^ ={l-p)Ur,^:l +pUn ?• 



Of the gametes, the spermatozoa will be all Z. 

 The ova will.be (1 -f- 2pUn) Z.lW. 



The constitution of the next generation will therefore be 

 1 -f- 2pUr,ZZ : IZW. . 



Thus Un+i = 1 + 2pUn. 



Hence Un increases without limit, since Wg > ^i . and the increase is 

 larger in each generation. Hence eventually all the zygotes will be of 

 constitution ZZ, and the sex-ratio will therefore become 1 — p f/'-.p^. 



Once the final sex-ratio is attained (which will take longer the 

 smaller p is), a subsequent swing-back will give nothing but males. 

 When p is large (> |), a swing-back after very few generations will give 



