No. 540] 



MENDELIAN PROPORTIONS 



349 



equal facility, there would still be much in favor of the 

 recessive. In the supposed ratio 9:6:1 it is possible for 

 any one of the dominants or heterozygotes to lose a de- 

 terminer. In other words, on the average fifteen out of 

 sixteen individuals have an opportunity to vary toward 

 lefthandedness ; that is, 93.9 per cent. On the other 

 hand, only the heterozygotes and the recessive can vary 

 toward righthandedness ; seven out of sixteen, therefore, 

 have this possibility, or 43.7 per cent, of the population. 

 If, therefore, the addition of the factor were as easily 

 accomplished as the loss of the factor — which is probably 

 never true — loss of a factor would be more than twice as 

 likely to occur as gain. With the ratio 1:2:1 opportuni- 

 ties are of course equal for upward and downward muta- 

 tion. In a population with more than 25 per cent, of 

 recessives, the number of heterozygotes plus recessives 

 is greater than the number of heterozygotes plus domi- 

 nants, as, for example, with the ratio 1:4:4, in which the 

 recessives make up 44.4 per cent, of the population. 



It would seem from the above that there is a constant 

 tendency for the proportion of individuals showing non- 

 important recessive characters to increase, unless indeed 

 mutative changes occur so slowly that the population is 

 constantly held back to a stable ratio. We are led natur- 

 ally to the thought that for species in general the indi- 

 viduals showing recessive mutations may be expected to 

 increase at the expense of the original type, unless the 

 characters lost are of some real importance to existence 

 or to mating. Just this sort of tiling lias probably taken 

 place with the shepherd's purse, Bursa bursa-pastoris. 

 It can hardly be doubted that the numerous species de- 

 scribed by Almquist 8 are derived from a single original 

 species. If the total number of Bursas in the world re- 

 mains the same from century to century and these ele- 

 mentary species appear in some number from time to 



"Noted by Dr. George Harrison Shnll, "Advance Print from the Pro- 

 ceedings of the Seventh International Zoological Congress, Boston Meeting, 

 1907." 



