QUANTITATIVE INHERITANCE 21 1 



and so the heritability may, in principle, be estimated from the ratio of the response 

 obtained to the selection differential applied : 



h 2 = R/S. 



The selection differential, S, is the difference between the mean value of the selected 

 animals and the mean of all the measured animals, including themselves, out of which 

 they were selected. If the individual values of the character are normally distributed 

 and the selected individuals are all those with measurements exceeding a certain value, 

 then the selection differential depends only on the proportion selected and the standard 

 deviation. For example, if the best 25 per cent of individuals are selected their mean 

 superiority, which is the selection differential, will be about 1.3 standard deviations; 

 and if the best 50 per cent are selected the selection differential will be about 0.8 standard 

 deviations. The proportion selected depends, in turn, on the number of offspring 

 produced by the parents. On the average two offspring per pair of parents must be 

 selected if the strain is to maintain itself. So, if each pair produce 8 young, 2 must 

 on the average be selected, and the maximum possible selection differential will be 1.3(7 

 corresponding to 25 per cent selection. The selection differential can be increased by 

 waiting for the parents to produce more young. With laboratory mammals the 

 production of more young means waiting for second or third litters, and this takes time 

 and adds to the interval between generations. The highest rate of progress in time 

 is therefore not necessarily achieved by the highest possible selection differential. 

 The best procedure depends on the number of young per litter and the interval between 

 litters. An examination of the procedure for selection applied to mice, 335 shows that 

 it is best to raise only one litter unless the number per litter is as low as 4, when it 

 becomes worth while to wait for second litters ; third litters are worth waiting for only 

 if the number per litter is as low as 2. (The number per litter means, of course, the 

 number of offspring measured and available for selection.) 



At the risk of being rash, I shall make the following generalization about how 

 rapidly an investigator may reasonably hope to improve a strain of laboratory mammals, 

 such as mice, rats, and perhaps rabbits, by selection. The selection differential achieved 

 will be about one standard deviation, and the heritabilities of most characters will 

 lie between about 20 and 50 per cent. The rate of improvement will therefore be 

 between about one-fifth and one-half of a standard deviation per generation. If 5 

 generations can be covered in a year, which is just possible with mice, the investigator 

 can reasonably hope for between 1 and 2.5 standard deviations of improvement in a 

 year. 



The prediction of a response to selection is theoretically valid only for one genera- 

 tion, because the selection must be expected to change the genetic properties on which 

 the response depends. But experiments have shown that, in practice, the initial rate 

 of response can be expected to continue for 5 or perhaps even 10 generations. Eventu- 

 ally, selection applied to a closed population leads to a limit beyond which there is no 

 further response. The time required to reach the limit, and the final level reached, 



