We investigated the interaction of recombination and selection on the process of fixation of two linked loci with epistatic interactions in fitness. We consider both the probability of fixation of newly arising mutants (the static model) and the time to fixation under continued mutation (the dynamic model). Our results show that the fixation of a new advantageous combination is facilitated by higher fitness of the advantageous genotype and by weaker selection against the intermediate deleterious genotypes. Fixation occurs more rapidly when the recombination rates are small, except when selection against intermediate genotypes is weak and selection in favour of the double mutant is very strong. In these cases fixation is more rapid when the recombinant rate is large. Mutations of strong effects, deleterious when alone but beneficial when coupled, are fixed more easily than mutations of intermediate effects, at least for large recombination rates. Among the possible pathways the process of fixation might follow, independent substitutions lead to the fixation of the double mutant only when selection is weak. The relative importance of the other pathways depends on the interaction between recombination and selection. The coupled-gamete pathway (i.e. when the population waits until the double mutant appears and then drives it to fixation) is more important as selection intensity increases and the recombination rate is reduced. For all recombination rates, asymmetries in fitness of the intermediate genotypes increase the rate at which fixations occur. Finally, throughout the fixation process, the population will be monomorphic at least at one of the two loci for most of the time, which implies that there would be little opportunity to detect the presence of negative epistasis even if it were important for occasional evolutionary transitions.

Method-of-moments estimators (MMEs) for the two-gene coefficients of relationship and inbreeding, and for thxe four-gene Cotterman coefficients, are described. These estimators, which use co-dominant genetic markers, are most appropriate for estimating pairwise relatedness or individual inbreeding coefficients, as opposed to their mean values in a group. This is because, compared to the maximum likelihood estimate (MLE), they show reduced small-sample bias and lack distributional assumptions. The ‘efficient’ MME is an optimally weighted average of estimates given by each allele at each locus. Generally, weights must be computed numerically, but if true coefficients are assumed zero, simplifiedestimators are obtained whose relative efficiencies are quite high. Population gene frequency is assumed to be assayed ina larger, ‘reference population’ sample, and the biases introduced by small reference samples and/or genetic drift of the reference population are discussed. Individual-level estimates of relatedness or inbreeding, while displaying high variance, are useful in several applications as a covariate in population studies.

The total gametic disequilibrium between two loci linked to polymorphic inversions can be partitioned into two types of components: within and between chromosome arrangements. The within components depend on the gametic disequilibrium within each chromosome arrangement. The between components depend on the locus-inversion disequilibria. This partitioning has practical applications and is indispensable for studying the dynamics of these systems because inversions greatly reduce recombination in the heterokaryotypes while allowing free, and sometimes different, recombination in each of the homokaryotypes. We provide equations for the per generation change of the various disequilibria for systems with two and three chromosome arrangements, and the general recursive equations predicting the disequilibria after any number of generations for the case of two arrangements. Simulation studies were carried out using different values of the recombination parameters and all possible initial conditions. The results show a complex convergence to linkage equilibrium in inversion systems. The various disequilibria can have local maxima and minima while approaching equilibrium and, moreover, their dynamics cannot be described, in general, using a single parameter, i.e. an effective recombination rate. We conclude that the effects of inversions on gametic disequilibria must be carefully considered when dealing with disequilibriain inversion systems. The formulae provided in this paper can be used for such purpose.

In highly integrated genetic systems, changes in any one component may have a deleterious effect on fitness, but coordinated, or compensatory, change in these components could lead to an overall increase in fitness compared with the current state. Wright designed his shifting-balance theory to account for evolutionary change in such systems, since natural selection alone can not lead to the new optimal state. A largely untreated aspect of the shifting-balance theory, that of the limiting impact of waiting for the production of new mutations, is analysed here. It is shown that the average time to double fixation of compensatory mutations is extremely long (of the order of tens or hundreds of thousands of generations), because selection is too effective in large populations, and mutations are too rare in small populations. Further, the probability that a new mutant will arise and undergo fixation quickly is extremely small. Tight linkage can reduce the time to fixation somewhat, but only in models in which the double heterozygote does not have reduced fitness. It is argued that the only reasonable way for compensatory mutations to become fixed in a population is if the new mutants are first allowed to achieve a moderate frequency through the relaxation of selection. Under these conditions, the time required to reach fixation is reasonably low, althoug the probability of being fixed is still small when the initial allele frequencies are low. It is likely that the waiting time for fixation of new mutants, which is here called phase zero, is the major limiting factor for the success of the shifting-balance process

Equal variances within quantitative trait locus (QTL) groups in the segregating population are a usual simplifying assumption in QTL mapping. The objective of this paper is to demonstrate the advantages of taking into account potential variance effect of QTLs within the framework of standard interval mapping approach. Using backcross case as an example, we show that the resolution power of the analysis may be increased in the presence of variance effect, if the latter is allowed for in the model. For a putative QTL (say, A/a) one can compare two situations, (i) and (ii) . It was found that, if the variance effect of A/a is large enough, then in spite of the necessity to evaluate an increased number of parameters, the more correctly specified model provides an increase in the resolution power, as compared to the situation (i). This is not unexpected, if either in (ii) is lower than from (i). But our conclusion holds even if . These advantages are illustrated on sweet corn data data (F3 families of F2 genotypes). In particular, the log-likelihood test statistics and the parameter estimates obtained for a QT locus in the distal region of chromosome 2 show that the allele enhancing the trait is recessive over the opposite allele simultaneously for the mean value and variance.

We study the dynamics under directional truncation selection of the genetic variability of a quantitative character controlled by a finite number of possibly linked loci with additive effects. After the first generation of selection, the build-up of linkage disequilibria (Bulmer effect) is analytically demonstrated from a genetical point of view in an infinite population. In the following generations, the dynamics of the system in a finite population are predicted using analytic recurrences under a multi-normal approximation, and computer simulations. The effects of recombination on the dynamics of linkage disequilibria induced by selection and drift, and the consequences for the additive genetic variance are then analysed and discussed from the simulation results. Compared to the rapid exploitation of genetic variability promoted by high recombination rates, low recombination rates promote an early storage of genetic variability in repulsion associations of alleles and a possible late release of genetic variance in the population, so that the variability of the character may be maintained over a longer period of time. In some cases, favourable recombination events in tightly linked systems induce an increase of the additive variance of the character, which may explain some results observed in long-term selection experiments. Our results emphasize that the joint effects of selection, linkage and drift must notbe neglected in theoretical quantitative genetics, and require further investigation.

Highly variable DNA polymorphisms called microsatellites are rapidly becoming the marker of choice in population genetic studies. Until now, microsatellites have not been utilized for Drosophila studies. We have identified eight polymorphic microsatellite loci in Drosophila melanogaster and used them to characterize the genetic variation in a wild population from the Tyrrell's winery in Australia. Microsatellites were isolated from a partial genomic DNA library. All microsatellites consist of (AC)n repeats ranging from n = 2 to n = 24. Six loci were assigned to chromosomal location by genetic mapping, with three loci on chromosome II, one locus on chromosome III and two loci on the X chromosome. Up to four microsatellite loci were multiplexed in the same reaction. Microsatellite variation is substantially greater than allozyme variation in the Tyrrell's Drosophila population. 80% of the microsatellite loci examined are polymorphic, compared with 28% of allozymes. The mean number of alleles per polymorphic locus is 5·2 in microsatellites compared with 30 in allozymes. The average observed heterozygosity of polymorphic microsatellites is 47% compared with 26% for allozymes. Microsatellite variation in Drosophila melanogaster is similar to that reported for other insects. Higher variability commends microsatellites over allozymes for genetic studies in Drosophila melanogaster.