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The effect of directional and heterotic selection on the standardized variance of gene frequency (f=σ q (2) /¯q(1-¯q)) has been examined. It has been found that heterotic selection always results in f values lower than those expected due to drift alone. Additive directional selection can result in low f values, but values larger than those expected due to drift will be observed under additive selection with low initial gene frequency, or when the populations have been separated for a very long period of time in which case f expected due to drift is quite high (around 0.7 or greater). The effect of selection on f is unlikely to be detected if the observed value of f is less than 0.1.

The effect of t ' generations of reverse selection after t generations of forward selection can be described by expressing the change in the metric mean resulting from reverse selection (R) interms ofthe change in the metric mean due to the previous forward selection (Δx). An additive model of artificial selection in a population of effective size N with no natural selection has been considered.If reverse selection is continued for as many generations as the previous forward selection (t'=t), then the ratio R/Δx equals 1 - F where F is the inbreeding coefficient for a neutral locus at generation t and is estimated as [1-(1-1/2N)(t)]. The result of a single generation of reverse selection (t'=1) following t generations of forward selection can be described in terms of the ratio NR1/ηDx where R1 is the response to the first generation of reverse selection. The value of NR1/Δx is expected to be (1-F) /2F.For any period of reverse selection following any period of forward selection, the value of R/Δx never exceeds t '/t, and tends to decrease exponentially from this value as t increases.

A single locus model of the interaction between natural selection and artificial selection for a quantitative character in a finite population, assuming heterozygote superiority in natural fitness but additive action on the character, has been studied using transition probability matrices.If natural selection is strong enough to create a selection plateau in which genetic variance declines relatively slowly, then the total response to artificial selection prior to the plateau will be much less than that expected in the absence of natural selection, and the half-life of response will be shorter. Such a plateau is likely to have a large proportion, if not all, of the original genetic variance still present. In selection programmes using laboratory animals, it seems likely that the homozygote favoured by artificial selection must be very unfit before such a plateau will occur. A significant decrease in population fitness as a result of artificial selection does not necessarily imply that the metric character is an important adaptive character.These implications of this model of natural selection are very similar to those derived by James (1962) for the optimum model of natural selection. In fact, there seems to be no aspect of the observable response to artificial selection that would enable anyone to distinguish between these two models of natural selection.

Reverse and relaxed selection were carried out in sublines which were derived from six replicate lines of Drosophila during 86-89 generations of selection for increased abdominal bristle number, and the reverse selection sublines were reciprocally crossed with selection lines of their origin.The results of serial relaxed selection initiated at different generations of selection confirm that the accelerated responses observed in the selection lines were largely due to deleterious genes, particularly lethals, with large effects on the selected character. The decline in mean bristle number under relaxed selection was not much different between crowded and uncrowded relaxed sublines.Reverse selection initiated at generation 57 was very effective, though it failed to bring the mean back to the base population level, and the genetic differences between replicate sublines (two from each of the six lines) indicate that low bristle number genes were probably rare in the selection lines. The genes which were still segregating after 57 generations of selection, on the average, did not show any directional dominance. The contribution of the X-chromosome to selection response was proportional to its chromosome length.

Selection for post-weaning weight gain in mice from 21 to 42 days, on either a full or restricted feeding level during this period was carried out for seven generations. Control lines were maintained for each feeding level. The rate of selection response was higher on full feeding due to a higher heritability and a larger phenotypic variance. Realised heritabilities of 0.29±0.05 and 0.19±0.04 for selection on full and restricted feeding respectively, were in close agreement with base population estimates.Selection on full feeding led to positive correlated responses in 21 day weight, 42 day weight, food intake and efficiency between 21 and 42 days, and 42 day tail length, but with little change in reproductive performance.Correlated responses to selection on restricted feeding were reduced 21 day weight, but an increase in 42 day weight and increased efficiency from 21 to 42 days. However, overall reproductive performance fell.

A formula is presented for the large-sample variance of phenotypic, genetic and environmental correlation coefficients, estimated from two-fold nested genetic analyses of balanced or unbalanced offspring data. Where parents of these offspring are scored, offspring on parent regression estimates of genetic parameters may be obtained for each parental level of the nested model. The large-sample variance of the offspring-parent genetic correlation coefficients, computed from either level or by using mid-parent data, is given. The first formula is a correction and generalisation of an expression given by Grossman (1970), while the second formula is an extension of a relationship derived by Reeve (1955).