A strain of mice that had ceased to respond to selection for high litter size was inbred with continued selection. Depression of the mean proved the existence of residual genetic variance. Four lines survived the inbreeding, and one reached 20 generations with a mean equal to the original strain, thus disproving overdominance as a major cause of the residual variation. The four selected inbred lines were crossed and a new strain derived from the cross was maintained in parallel with the original strain. The new strain showed an improvement of 1·5 mice per litter over the original strain. Thus selection with inbreeding was able to achieve an advance beyond the limit attained by the original selection.

The hypothesis that the residual variation was due to genes with simple dominance was tested by seeing if it could account for the observations with reasonable values of the relevant parameters. The improvement made by the inbreeding and crossing required the elimination of about 30 recessive genes with effects (homozygote difference) of 0·5 phenotypic standard deviations and gene frequencies of 0·2. Consideration of the mean levels of the selected inbred lines in conjunction with the rate of depression found on inbreeding without selection showed that the selection with inbreeding had eliminated about 75% of the segregating reces-sives. The number of genes contributing to the residual variance was therefore about 40. The additive variance generated by these genes was just consistent with the estimate of zero from the realized heritability. Consideration of the original selection showed that about half the genes could have been still segregating when the response ceased. The hypothesis therefore requires the number of genes in the base population to have been about 80. The number of genes required, though large, does not seem impossible, and the hypothesis of genes with simple dominance can account for all the observations.