QUANTITATIVE INHERITANCE 195 



environment of an individual are the only determinants of its phenotypic value.) 

 The question has precise meaning only when framed in terms of the variation between 

 inidividuals: how much of the variation is caused by genetic differences between 

 individuals and how much by nongenetic differences? To answer the question it is 

 necessary to eliminate one cause of variation and to measure the variation remaining, 

 which will be due to the other cause only. If the amount of variation is measured as the 

 variance, then the total variance when both causes are operating is the sum of the 

 variances when each cause is operating separately. It is not possible in practice to 

 eliminate nongenetic causes of variation, because, however careful the experimenter 

 may be in insuring uniformity of external conditions, there always remains a substantial 

 amount of nongenetic variation from intangible causes. The genetic variation, however, 

 can be eliminated by inbreeding, although this is practicable only with fast-breeding 

 laboratory animals. A strain that has been inbred by brother-sister mating for upwards 

 of 20 generations is, for practical purposes, free of genetic variability. The variation 

 within the strain, therefore, is purely environmental in origin. There is, however, 

 a difficulty here, because inbred animals have often been found to be more susceptible 

 than noninbred animals to the normal range of environmental differences. An inbred 

 line therefore does not always provide a reliable measure of the environmental variation 

 for comparison with a noninbred strain. The difficulty can be overcome by taking a 

 cross between two inbred lines. If both lines are highly inbred, then the first genera- 

 tion of the cross (that is, the F x ) is equally free of genetic variation and provides a 

 more reliable estimate of the environmental variation. Better still, however, is to make 

 several different crosses between highly inbred lines and base the estimate of environ- 

 mental variance on the mean variance within the crosses. This overcomes the possible 

 objection that one cross provides only one particular genotype whose sensitivity to 

 environmental differences may not be typical. The observed variance of the individuals 

 of a genetically variable strain is the sum of the genetic variance in that strain and 

 the environmental variance. Subtraction of the environmental variance, estimated 

 from the cross-bred individuals, therefore gives an estimate of the genetic variance. 

 In this way the total, or phenotypic, variance in the variable strain may be partitioned 

 into two components, genetic and environmental. This partitioning expresses the 

 degree of genetic determination, as the percentage of the total variation that is attribu- 

 table to genetic differences among individuals of the strain. 



An example of the estimation of the degree of genetic determination is provided 

 by the following data on the age of vaginal opening in female mice, from Yoon. 1465 

 Two inbred strains, BALB/c and C57BL/10, were crossed (Yoon's cross 2), and the age 

 of vaginal opening was recorded from 192 F 1 animals and 163 F 2 animals. The 

 variance among the F x animals was 19.1 and the variance among the F 2 animals was 

 34.9. The difference, which estimates the genetic variance among the F 2 individuals, 

 was 15.8. The degree of genetic determination in the F 2 of this particular cross was 

 therefore 15.8/34.9 = 45 + 8 per cent. (The standard error is calculated from 

 equation 4, as explained below.) 



