202 PHYSIOLOGIC GENETICS 



necessary to measure 200 offspring if both parents are measured and 400 offspring if 

 only one parent is measured. 



The situation discussed above is likely to apply when the labor of measurement is 

 the limiting factor, rather than the amount of breeding or rearing space available. 

 When labor of measurement is not the limiting factor, then it is often possible to rear 

 and measure more than one offspring from each parent or pair of parents without any 

 reduction of the number of parents that can be used. The limiting factor is then the 

 number of parents. If this is fixed, it follows that any increase in the number of off- 

 spring measured will improve the precision of the estimate. The question then is how 

 many offspring are worth measuring. The reduction in the expected standard error 

 effected by increasing the number of offspring from 1 to 8 is shown by the inset graphs 

 in figure 34. The figures on the vertical scale give the factors by which the standard 

 error obtained from equations (8) and (9), or from the main graphs in figure 34, are 

 to be multiplied. The improvement in precision depends on the phenotypic corre- 

 lation between offspring of the same parents, and graphs for four correlations, ranging 

 from 0.05 to 0.5, are given. The cause of the correlation is immaterial in this connection ; 

 it may be genetic or nongenetic, or both. When the correlation is high there is little 

 to be gained by increasing the number of offspring measured, but when the correlation 

 is low a substantial improvement of precision results from even a small increase in the 

 number of offspring. If the value of the correlation is not known beforehand, it would 

 seem worth while, as a general rule, to aim at measuring about four offspring from 

 each parent or pair of parents. 



Planning on paper is easy, but executing the plan by obtaining and measuring 

 the animals exactly as required is often impossible. Even if it is planned to measure 

 only a few offspring from each parent, some parents will inevitably fail to produce the 

 required number of offspring, and there may be other losses later, so that the plan cannot 

 be strictly followed. This raises two problems. The first is at the stage of the collec- 

 tion of data : should the experimenter discard all families that have failed to provide 

 the right number; and if he does not discard them, should he supplement the total 

 number of offspring by measuring more than was planned from some other families ? 

 My answer is that he should include every animal measured and measure any additional 

 animals that he can, because every additional offspring measured adds something to the 

 precision of the estimate. The second problem then arises with the computation of 

 the offspring-parent regression from the data, because the number of offspring will 

 not be the same for all parents. How is the computation to be made? (In what 

 follows I shall use the word family to mean the offspring of one parent or pair of parents, 

 and the word parent to mean equally the single, measured parent or the mean of both 

 parents, according to which regression is to be computed.) 



There are two simple courses of action, neither of which makes the best use of the 

 data. One is to take each offspring separately and count each parent as many times 

 as it has offspring. This gives too much weight to the larger families but is reasonably 

 satisfactory when the heritability is low and there is very little resemblance between 



