August 21, 1908] 



SCIENCE 



253 



From whicli it is seen that aftex generation 

 F^ tliere is no tendency for the ratios of the 

 three possible types to change, any such 

 change being purely a matter of chance. It 

 is assumed that there is no selective mating 

 and that each type of mating is equally fruit- 

 ful. This point has already been brought out 

 by Hardy in Science, July 10, 1908, p. 49. 



Hyhnds of Higher Order 

 By a process similar to the above it may 

 be shown that when the two types differ in 

 respect of two Mendelian characters, or a 

 single character consisting of two factors, the 

 population tends to assume the following 

 ratios for the various types: 



no tendency for the relative numbers of the 

 various zygotic types to change, oSers a ra- 

 tional explanation of the rapid development 

 of races having strikingly different character- 

 istics, when a species is first brought under 

 domestication. Let us consider for a mo- 

 ment the condition of the wild species. 

 Amongst our wild gray squirrels are occasion- 

 ally seen black specimens ; also albinos. These 

 varietal characters have originated presumably 

 by the loss, either gradually or in any other 

 manner, of a character formerly possessed. 

 This change may have occurred at any time 

 in the history of the species, or even before 

 the species existed in its present form. There 

 is no tendency, with random mating, for the 



TABLE n. 

 Typeformuhe, AABB, AABb, AAbh, AaBB, AaBb, Aabb, aaBB, aaBb, aabb, 



" ratios: 



Generation Fo, n i 



" F„ (i2 2nt i» 



F,, (a^-l-l-ai)^ a'i(a + i,i) ^aH' aH{a + U) aH + ai\i + {a) ^aV ai^{i + ia) {i'+iaiy 



3a!'r- + 

 ai' 

 " Fs, (<r.2 + ^ai)^ Wi+ tV'" I«''+ Wi+ fa«''+ iW'^ 20''+ {i^ + iai)' 



lap 

 " F„, a* 2a^i a'p 2aH 4aH- '2ai' aH' 2(iP i* 



That is, the proportions of the various types 

 tend to assume the relative numbers shown in 

 the last line of the above table, and thereafter 

 there is no tendency for these ratios to change. 

 It is interesting to note that the terms of the 

 last line of table II. may be obtained from 

 those of the last line of table I. by multiply- 

 ing by a" + 2ai -f- i" (= the square of a + i) ; 

 thus, multiplying a" the fii'st term in the last 

 line of table I., by a' -\-2ai-\- i", gives the 

 first three terms of the last line of table II. 



If the original population consists of two 

 types which differ in respect of three Men- 

 delian characters, the ratios of the twenty- 

 seven resulting types in the final population 

 may be obtained from the last line of table 

 II., as that was from the last line of table I. 



The fact that in such a mixed population, 

 with no selectional mating, and with equal 

 fruitfulness of the various matings, there is 



new characters to spread through the species. 

 In fact, there is probably a tendency toward 

 their elimination by natural selection. Such 

 a tendency, however, would operate very 

 slowly in the case of a recessive character, 

 which is transmitted unseen in far more in- 

 dividuals than those showing it (under the 

 conditions assumed). It is entirely possible 

 that all the varietal variations which are pos- 

 sible to this species actually exist in the wild 

 species, each in exceedingly small proportions, 

 because it has originated in a very small frac- 

 tion of the species, and does not tend to 

 spread over the species unless favored by nat- 

 ural selection. Should the species be domes- 

 ticated, the art of the breeder, who would 

 naturally be attracted by new types that crop 

 out (which occurs when heterozygotes are 

 mated) would seize these forms and establish 

 races from them. 



