EFFECTS OF INBREEDING AND CROSSBREEDING. 45 



in time between the two periods. The average date of birth for the 

 first period comes out 1909.04 or 1909.07, depending on whether the 



■ years are weighted by the number of Ktters born or the number of 



' ; individuals. The average for the second period is 1912.93 in both 



I cases. The periods may thus be considered as 3.88 years apart on 

 the average. The yearly rate of decline in each character on this 

 basis is given in the next to the last column of Table 2. The last 



'} column gives the rate of decline found, as described in Part I, by 

 fitting the best straight line to the yearly averages for all inbred 

 young born between 1907 and 1915. It appears that the decline 



I within an average family has been about twice as rapid as that in the 

 inbred stock as a whole. The reason is easy to understand. The 

 vigorous families expanded at the expense of the families in which 



iji hereditary weaknesses had become fixed, and this expansion to some 



I extent obscured the decline within the famihes. 



DETAILED STUDY OF FAMILY CHARACTERS. 



I ; The existence of a significant degree of differentiation among the 

 ' families would lead us to expect a correlation between the average 

 I of a character in the first period and its average in the second. 

 Inspection of Tables 7 to 15 in fact soon shows that families which 

 were high in rank in one period tended to be above the average in 

 the other, and conversely. Among the extreme families listed in 

 Table 1, Family 1 produced the smallest litters from 1906 to 1910 

 as well as from 1911 to 1915. Family 3 had the smallest percentage 

 born alive in both periods excepting. Family 15, which became 

 extinct in 1911, while Family 13 led in birth weight in both periods, 

 and Family 2 made the poorest gains. 



More conclusive evidence can be obtained by calculating the 

 coefficients of correlation between the averages in the two periods. 

 This has been done for each character, using the product-moment 

 method (Table 3). It will be seen that all of the correlations are 

 positive and the lowest is +0.25. Unfortunately, the probable 

 errors are also rather high, owing to the small number of families 

 (22) on which the correlations are based. Nevertheless, a pronounced 

 and lasting differentiation among the families is demonstrated in 

 most of the cases. In regard to rate of growth, we find correlations 

 of +0.65, +0.64, and +0.68 for birth weight, gain, and weight at 

 33 days, respectively, with a probable error of only ±0.08 in each 

 case. The permanent differentiation in size of litter is of similar 

 degree, with a correlation of +0.65 ±0.08 between the periods. In 

 regard to the other element in fertility, the frequency of litters, the 

 correlation of +0.25 ±0.13 can merely be said to be consistent with 

 a genetic differentiation. Total fertility, as measured by the number 



