QUANTITATIVE INHERITANCE 213 



response to selection in one direction. And, for the same reasons, if selection is to be 

 used as a means of estimating the heritability, it is essential that selection should be 

 made in both directions and the heritability estimated from the divergence between 

 the two selected lines. 



There are two details of procedure connected with the estimation of heritability 

 from the response to selection that should be briefly mentioned. The first concerns 

 the selection differential. The selected parents may contribute unequally to the off- 

 spring from which the response is measured. It is therefore necessary to compute the 

 selection differential as the weighted mean of the superiority of each parent, the weight 

 being the number of offspring of that parent that were measured. It is of interest to 

 compare the weighted with the unweighted selection differential, because if the weighted 

 is less than the unweighted this gives evidence of natural selection opposing the arti- 

 ficial selection. It shows, in other words, that the best parents have produced fewer 

 offspring than the less good. The second point of procedure concerns the averaging 

 of the response from successive generations. The best way to do this is to plot the mean 

 of each successive generation against the cumulated selection differential. In other 

 words, plot each generation mean against the sum of the previous selection differentials 

 up to that point. This will give a graph such as that shown in figure 36. The slope 

 of the line up to any point is the ratio of the response to the selection differential, and 

 this ratio (RjS) provides the estimate of the realized heritability. The slope may 

 remain constant over many generations, in which case the average slope may be 

 estimated from a linear regression line fitted to the points, as illustrated in figure 36. 

 Or the slope may change, in which case the fitting of a linear regression over the whole 

 experiment would not be justified. There is always a disconcerting amount of erratic 

 variation of the mean values from one generation to the next. One cannot, in conse- 

 quence, hope to assess the rate of response with any degree of precision until at least 5, 

 or preferably even 10, generations have been obtained. Selection is therefore a 

 time-consuming method of study. 



Although selection takes a long time before reliable conclusions can be drawn, 

 it does not require a great deal of cage space at any one time. The amount of space 

 required is inversely related to the rate of inbreeding that can be tolerated. If the 

 aim is to produce a useful strain, then it is important to keep the rate of inbreeding low, 

 because there is no opportunity for selection between lines and whatever inbreeding 

 depression occurs must be tolerated. I suggest that for a program intended to 

 last for 10 or 20 generations, the selected individuals should be drawn from not fewer 

 than 10 families. This can be done with the greatest economy of space by mating 

 10 pairs in each generation and selecting the best two offspring from each family. 

 Selection within families in this way, however, reduces the selection differential because 

 the variation between families is not utilized. If, on the other hand, selection is made 

 purely on individual merit, which should usually give a better rate of progress, then it is 

 necessary to mate substantially more than 10 pairs in order that 10 families will be 

 represented among the selected individuals. 



