Robertson (1960) used probability transition matrices to estimate changes in gene frequency when sampling and selection are applied to a finite population. Curnow & Baker (1968) used Kojima's (1961) approximate formulae for the mean and variance of the change in gene frequency from a single cycle of selection applied to a finite population to develop an iterative procedure for studying the effects of repeated cycles of selection and regeneration. To do this they assumed a beta distribution for the unfixed gene frequencies at each generation.

These two methods are discussed and a result used in Kojima's paper is proved. A number of sets of calculations are carried out using both methods and the results are compared to assess the accuracy of Curnow & Baker's method in relation to Robertson's approach.

It is found that the one real fault in the Curnow-Baker method is its tendency to fix too high a proportion of the genes, particularly when the initial gene frequency is near to a fixation point. This fault is largely overcome when more individuals are selected. For selection of eight or more individuals the Curnow-Baker method is very accurate and appreciably faster than the transition matrix method.

Using models which describe the change, by natural selection, of the actual numbers of genes rather than their relative frequencies, it is demonstrated that the equation familiar to geneticists, i.e. dp/dt = sp(1 − p), is appropriate under a wide range of circumstances. It was pointed out that, for realistic treatment of the evolutionary process through which gene substitutions are repeated, the models must have the property such that the total population number remains constant or nearly constant throughout the process, and is not appreciably influenced by the genes being substituted.

The load or cost for a gene substitution was studied assuming a haploid population and the effects on the load of such factors as epistatic gene interaction in fitness, finite population number and slow change of environment were investigated. The load may become very large under a strong ‘reinforcing’ type epistasis between advantageous genes. In a finite population, the load for one gene substitution may be inflated by about unity if the product of the effective population number (Ne) and the selection coefficient (s) is large but Nesp0 is much smaller than unity, where p0 is the initial gene frequency. On the other hand, slow change of environment may decrease the load somewhat. It was concluded that despite these and other complicating factors, Haldane's original formula, –logep0, for a haploid population (−2 logep0 for the case of a diploid without dominance) is still useful for assessing the approximate amount of selective elimination that accompanies the process of gene substitution in evolution.

The effect of selection on individual performance for a quantitative trait is studied theoretically for populations of finite size. The trait is assumed to be affected by environmental error and by segregation at a single locus. Exact formulae are derived to predict the change in gene frequency at this locus, initially by finding the probability distribution of the numbers of each genotype selected from a finite population of specified genotypic composition. Assuming that there is random mating and no natural selection the results are extended to describe repeated cycles of artificial selection for a monecious population. The formulae are evaluated numerically for the case of normally distributed environmental errors.

Using numerical examples comparisons are made between the exact values for the predicted change in gene frequency with values obtained using approximate, but simpler, methods. Unless the gene has a large effect (α) on the quantitative trait, relative to the standard deviation of the environmental errors, the agreement between exact and approximate methods is satisfactory for most predictive purposes. The chance of fixation after repeated generations of selection is also evaluated using the exact method, and by means of a diffusion approximation and simple transition probability matrix methods. Except for very small values of population size (N) and large α the results from the diffusion equation agree closely with those from the exact method. Similar results are found from tests made of the prediction from the diffusion equation that the limit is only a function of Nα for a given intensity of selection and initial frequency, and that the rate of advance in gene frequency is proportional to 1/N for the same set of parameters.

Expected changes in the gene frequency and the population mean for a quantitative trait are described for selection in a population of size N at a single locus where the favoured allele has initial frequency q0 and selective value s. Models of additive and completely dominant gene action are compared. Results are generally expressed as the half-life of the total change relative to N.

If the favoured allele is additive or recessive the half-life of the gene frequency and mean of the trait are usually reduced when q0 or Ns is increased. However, if the dominant allele is favoured the half-life of gene frequency is still generally reduced as Ns is increased, but has a minimum at low or intermediate values of q0. Since inbreeding depression and selection oppose each other when the dominant allele is favoured the response in the mean of the quantitative trait may change in direction during selection.

Selection for large and small 13-day larval weight in Tribolium castaneum was studied for sixteen generations in a replicated experiment to evaluate the effectiveness of various selection methods and the importance of genotype by environment interactions under two levels of nutrition.

Direct selection responses generally were larger than correlated ones under both Good and Poor nutritional environments. However, contrary to theoretical expectations, those populations selected on average performance in both environments were not superior for this attribute.

Asymmetrical responses were observed to be dependent on the environment of selection. When selection was based on performance in the optimal environment, the asymmetry was observed toward small size. This situation in the sub – optimal environment was completely reversed. This phenomenon was discussed in terms of physiological limits rather than gene frequency and directional dominance.

It was proposed that selection of compound traits such as body weight at a fixed age may affect the component characters quite differently. As the latter are differentiated by direction and environment of selection, the compound trait may reflect parametric changes and enhanced genotype by environment interactions. Such changes hamper the precision of current selection theory for predicting response even in the short run.

1. The loss of mu 540, mu 138, and kappa 51 following the loss of the dominant genes required for their maintenance was studied. With mu 540 and mu 138 the loss usually occurred within 4–7 cell generations, but occasional cells with mu were found as late as generation 12 with mu 540 and generation 17 with mu 138. Kappa 51 was lost between 5 and 60 fissions in different clones. The variability in time of loss remains unexplained.

2. No trail of inheritance of resistance to specific kappa killing comparable to the trail of inheritance reported for mu 540 by Gibson & Beale (1962) was found.

3. No loss of kappa 51, mu 540, mu 138, or mu 130 was found following treatment of paramecia with RNase.

4. Didinium nasutum was shown to be able to acquire and maintain kappa 51 when it could not possibly have acquired any RNase-sensitive metagons from paramecia.

5. These results show that the metagon hypothesis cannot be accepted without a number of ad hoc and at present untestable assumptions.

Two mouse-adapted scrapie agents of different sheep origin were compared. The titre, reached in the brains of mice in the terminal stage of scrapie, is of the same order for both agents. There is a threefold difference between the incubation periods of the two agents in some mouse strains, of which C57 is one, and in this strain incubation of the 22A agent, given as a large dose by a peripheral route, occupies almost the whole life-span.

The most fundamental difference between the agents concerns the reversal of the ranking of incubation periods, typically in the VM and C57 mouse strams: incubation of ME7 in VM takes almost twice as long as in C57, whereas most sub-lines of 22A take half as long in VM as in C57. The implications of this type of host-genotype, agent-strain interaction are discussed in terms of the possible nature of agent differences, the possibility of latent infection and the consequences for scrapie eradication programmes.

The sites of mutations affecting host-controlled modification (HCM) have been mapped in E. coli K and E. coli B by conjugation and transduction experiments between mutants. These mutations all map close to the serB locus on the opposite side to the marker thr. Non-parental HCM has been observed among colonies obtained from Pl transduction experiments between HCM mutants. Control experiments have shown that these non-parental recombinants can not be accounted for by reversion of either parent and must result from recombination between mutants. Several genetic models are suggested which could account for these recombinants and an attempt is made to distinguish between various models by testing for complementation between mutants in a zygotic induction complementation test.