An Observation on Parthenogenesis. 



157 



1. The standard deviation (S. D.) of the mothers 



weighted according to the number of offspring 



produced . = 2*2208 



2. The standard deviation of the offspring = 2*9503 



3. The standard deviation of array of offspring = 2-6104 



4. The coefficient of correlation - 0*466 ±0*0539 



5. The coefficient of regression of offspring on 



mothers.... - 0*619 ±0*0809 



According to Mr. Galton's theory of ancestral heredity, a child, on 

 the average, inherits l/4th of any inherited character from either of its 

 parents, 1/1 6th from any one of its grandparents, l/64th from any one 

 of its eight great. grandparents, and so on. 



From a mathematical standpoint Professor Pearson* has examined 

 Mr. Galton's theory, and he finds that if it be expressed in the form 



/ 1 y S.D. of offs pring 



S.D. of individual parent of the nth generation 



the coefficients of correlation and regression between offspring and any 

 generation of ancestors flow directly from it. Professor Pearson shows 

 that the total regression of the progeny on the mid-parent of any genera- 

 tion is constant and is equal to 0*6, while the correlation and regression of 

 an individual parent of the nth generation (supposing equal variability 

 for all generations) = 0*6(J) n and the correlation of the mid-parent 



of the nth generation = 0*6/ -i- 



\ si* I 



Hence the coefficients of correlation and regression of an individual 

 parent of the 1st generation {i.e., father or mother) = O^J) 1 = 0*3, and 



the coefficient of regression, as we have just seen above, = 0*6. 



Now, on comparing observation with theory, we see that the par- 

 thenogenetic mother appears to act like a mid-parent ; the coefficients 

 of correlation and regression being respectively 0*466 and 0*619. 



Further, we know — P' °^ P are — = -i- = 0*71, and in the present 

 S.D. of progeny ^2 r 



S.D. of parthenogenetic mothers 2*22 A * K 



case — - — ~ = ttxt — yj'iD. 



b.D. oi progeny 2*95 



Among my notes there are recorded the measurements of twenty- 

 six grandchildren, the offspring of seven grandparents. With these 

 the coefficients of correlation and regression were calculated. On 

 account of the altogether insufficient number of individuals, the results 

 were bound to be very uncertain, but they appear to favour the view 

 that inheritance in parthenogenetic generations resembles that from 



* ' Eoy. Soc. Proc.,' vol. 62, pp. 386—412. 



the coefficient of correlation of the mid-parent = 0*6( — — j = 0*424, and 



