144 
Variation and Inheritance in Aphis 
In the 6th column is given the average S.D. of an array calculated from the 
formula o-Vl — and in 4th and 5th columns the S.D. of parents and offspring. 
The general standard deviations for arrays are of considerable magnitude, being 
in fact greater than the S.D.'s of the parents. The mean S.D.'s of the families 
are much less than those of arrays. We should expect the former to be smaller; 
for although all the parents which produce an array are alike in the particular 
dimension, yet they are unlike in their ancestry. 
In this table is also given the ratio (expressed as a percentage) of the mean 
S.D. of the families to the standard deviation of parents, offspring, and arrays. 
To these results are also added those obtained from daphnia ; and in the bottom 
line of the table the means of the percentages are given. 
It must be realised that tlie families are too small to give a very reliable 
determination of the standard deviation, but nevertheless the mean results probably 
give a I'ough indication of actual fact. According to these results the variability 
of the family is seen to be 60 °/„ of that of all the parents, or in other words if we 
bred from a single individual yet more than half of the racial variability would 
remain. 
It is unfortunate that at present there are no data available from which family 
variability may be deduced for sexual forms and we must await further investigations 
before a comparison can be made with these results from parthenogenetic families. 
In the meantime it may be seen that the present results are antagonistic to 
the views on variation and inheritance expounded by A. Sedgwick*; for with a 
family variability of GO of the racial it is difficult to see " that genetic variations 
cannot occur in asexual reproduction, and that if any indefinite variability 
recalling genetic variability makes its appearance it must be part of the genetic 
variability and directly traceable to the zygote from which the asexual generations 
started." 
(11) The Correlation between Members of the same Brood. 
Let any member of a family be chosen, then we wish to find a number which 
will express its probable degree of similarity to any other member taken at 
random from the same family. Just as the mean standard deviation of all the 
families would be a measure of the dissimilarity of nifmbers of a family, so the 
correlation coefficient for all possible pairs of brethren would be a measure of their 
resemblance. If the S.D. of every family be very small or 0, that is if there 
be very little or no variation among brethren, the correlation would be perfect and 
equal to 1. If, on the other hand, the S.D. is large there is much dissimilarity 
among brethren, and consequently the correlation would be expiessed by a 
number much less than 1. We have already seen that, contrary to a prevailing 
* Presidential Address to Section D of the British Association, 181)9. Reprinted in Nature, Vol. 60, 
p. 507. 
