APPLICABILITY OF A COEFFICIENT OF CORRELATION 349 



Illustration 10. Viability of dominants and rcccssivcs in F 2 generation 



of Mendelian hybrids 



Fj D(R) X D(R), according to Mendelian theory, gives in F 2 a 

 population with somas 3 D : R. Let there be N individual families in this 

 population and the number of individuals per family be variable. This 

 variation may be due solely to fluctuations in the number of zygotes 

 produced, or it may be in part attributable to the failure of some of the 

 zygotes to reach maturity. This failure may be random or differential 

 with respect to the alternative characters involved. If differential, 

 one might expect a correlation between the actual number of individuals 

 per family and the deviation from the probable number of either of the 

 alternative types of individuals which it contains. 



In current Mendelian literature discrepancies between observed and 

 theoretical ratios are often explained as due to selective fertilization or 

 to a lower viability of particular zygotes. 



If the latter explanation be correct r lz , the correlation between the 

 number in the litter and the deviation from their probable frequency of 

 the number which shows a particular character, should have a statistic 

 ally significant value. As an illustration of the kind of data to which 

 this test may be applied, I take YULE S (1914) table of DARBISHIRE S 

 (1904) results for albinos in mice families. If the fertilized ovum which 

 is to produce an albino be less capable of development than that which is 

 to develop into a normal individual r tg should take a substantial positive 

 value, i.e., the relative numbers of albino young should be larger in the 

 large litters, since the small litters are assumed to be small in part be 

 cause albino-producing fertilized ova are supposed to be less viable. 



The actual results are : 



/= 4.5868 a= 1.1322 

 &amp;lt;T,= 1.7518 &amp;lt;r a = 1.0752 

 ^ = 38.193 V a = 94-963 



r** = -3756 .0527 

 r^ = .0287 .0612 



where / = number in litter, a = number of albinos in litter, and z = 

 deviation of number of albinos from their probable value. 



The constant of critical significance, r tg , is sensibly zero, with due 

 regard to its probable error. Hence there is no evidence of a greater 

 intra-nterine mortality of albino zygotes. 



GENETICS 3: Jl 1918 



