Ernest Warren 
145 
opinion, the standard deviations of families are not inconsiderable, and hence the 
correlation between brethren will be much less than unity. 
In Tables XVI. — XXI. (at the end of the present paper) are given the correla- 
tion tables for pairs of offspring. In Table XXII. the results both for aphis and 
daphnia are exhibited. 
TABLE XXII. 
Genus 
Dimension 
Pairs of Offspring 
368 individuals 
1114 pairs 
Pairs of Grandchildren 
291 individuals 
1894 pairs 
Hyalo- 
pterus 
Frontal Breadth 
Length of Antenna 
Ratio 
•6660 + [-0112]* 
•6785 + [-0109] 
•5890 ±[-01 32] 
•3890 + [^01 32] 
•4132 + [-0129] 
•3382 ± [•01 37] 
Daphnia 
Ratio 
•6934±[^0270]t 
Mean of Coefficients 
•656 
•380 
In the fourth column are given the coefficients for grandchildren. From the 
nature of the experiment the collections of grandchildren consisted of a mixture of 
sisters and cousins j in unknown proportions. The coefficients for the offspring are 
high, but for the following reasons further investigation is needed before it can be 
concluded that there is greater similarity among brethren in parthenogenesis than 
in sexually produced offspring. The value for the ratio is distinctly lower than 
for the absolute measures ; as in the case of comparing the S.D. of arrays with 
the mean of the standard deviations of the separate families, so in the case of 
the correlations the values for the ratio appeared the most normal. 
Each brood or collection of grandchildren lived on one leaf, and consequently 
every member of a family was subjected to a practically identical environment. 
Those that had an innutritions leaf would all tend to be small when adult and 
those with a particularly wholesome leaf would be large. 
We have seen, however, that there is considerable correlation between the 
ratio and the adult size of the animal, hence even in the parental correlation of 
1 - 
* These probable errors have been calculated from the usual formula ^67449 — — . I have made 
vn 
n=1114 but it is doubtful whether this gives an accurate probable error. 
+ 23 families, 168 pairs. 
J In a rough sort of way the correlation of true cousins might be found from this. If r = correlation 
of cousins and there be m pairs of sisters and m' of cousins, then(m + TO') •3801 = )n -6445 + ?«'?■. The 
proportions of sister and true cousin pairs from the total individuals and total pairs given in Table XXII, 
could not be widely different from the ratio 3 to 10. Hence the cousin correlation would be as high as 
•3, or nearly half the fraternal correlation. 
Biometrika i 11 
