EGG PRODUCTION. 65 



ally high producing mother is, on the average, as likely to pro- 

 duce exceptionally poor as exceptionally high producing daugh- 

 ters and vice versa. On the other hand a correlation coefficient 

 of I means a perfect association or correlation. In the present 

 case a correlation coefficient of -|-i would indicate that an 

 exceptionally good mother always and invariably produced an 

 exceptionally good daughter which was, as compared with 

 daughters in general, exactly as exceptional relatively as the 

 mother was as compared with other mothers. As the correla- 

 tion coefficient takes different values between zero and one it 

 indicates varying degrees of association or correlation between 

 the characters under consideration. 



There are several different ways in which the problem of the 

 correlation between mother and daughter in respect to egg 

 production may be approached. In the first place it is possible 

 to make a table in which each daughter and her mother shall be 

 individually entered. From such a table the correlation between 

 mother and daughter in respect to egg production can be meas- 

 ured. It is obvious, however, that this procedure weights each 

 mother with her own fecundity. This arises from the fact that 

 while each individual daughter has an individual mother there 

 are not as many individual mothers as there are daughters. If 

 a mother produces six daughters she will appear six times in 

 the table with whatever egg record she may have made. The 

 mother with only three daughters will have her egg record 

 appear only three times in the table and so on. In general, 

 the mother's egg record by this procedure will be weighted 

 according to the number of daughters which she had in the 

 experiment. It is apparent that this method is not a perfect 

 one, but it is the only practicable way of dealing with ordinary 

 statistics of fecundity yet devised which enters every individual 

 offspring separately in the correlation table. It is a method 

 which has been used by Pearson * (though not exclusively) in 

 the study of the inheritance of fecundity in race horses and of 

 fertility in man. To be entirely fair it would be necessary in 



* Cf. Pearson, K., Lee A., and Bramley-Moore, L. IMathematical 

 Contributions to the Theory of Evolution. VI— Genetic (Reproductive) 

 Selection : Inheritance of Fertility in Man and of Fecundity in Thor- 

 oughbred Racehorses. Phil. Trans. Roy. Soc. Vol. 192A, pp. 257-330. 

 1899. 



