Ritter & Salamini (1996) presented a systematic account of two-point linkage analysis in allogamous diploid plant species. Vowden et al. (1995) described an alternative approach that is implemented in a computer program LINKEM. This paper describes how the latter approach has been extended to three-point linkage analysis, and implemented in a new program LINK3EM that is available from the authors. The essence of the approach is for the computer program to derive the appropriate form of analysis for a specific cross from its ‘knowledge’ of the most general type of cross that can arise. This avoids the need for programming specific codes for the many different types of cross that can arise. The program allows different locus orderings and parental phases to be compared. The Haldane or Kosambi map functions can be specified, although it is also possible to estimate all three pairwise recombination fractions without any assumed map function.

Based on the outbred mouse strain Fzt: Du, which has been obtained by systematic crossing of four inbred and four outbred lines, a long-term selection experiment was carried out for total protein amount (PA) in the carcass, starting in 1975. An unselected control line (CO) was kept under the same management but without continuous protein analysis. The protein amount of male carcasses at 42 days of age (P42) increased from 2·9 g in generation 0 to 5·2 g at generation 70, representing 97% of a theoretical selection limit. The total selection response amounts to 2·3 g, which is about 80% above the initial value and corresponds to 9σp or 12σA . The estimated realized heritability of protein amount decreased from 0·56 to 0·03 at generation 70, which was due to an increase in phenotypic variance from 0·065 to 0·24 g2 and a reduction in genetic variance from 0·04 to 0·01 g2. Half the selection response was obtained after about 18 to 23 generations, a half-life of 0·25 to 0·3 Ne. The maximum selection response was 0·094 g/generation and the response was 0·01 g/generation at generation 70. The measurements of body weights at 0, 10, 21, 42 and 63 days throughout the experiment showed a strong correlated effect for all weights. The PA mice are one of the heaviest lines of mice ever reported, and do not differ significantly in their body composition from control mice at 42 days. The direct selection response was due primarily to increased general growth. Body weight and protein amount are phenotypically and genetically highly correlated (rp=0·82, rA≈1); however, selection for body weight led to fatter animals, whereas selection for protein opposed increased fatness (at least until selection age). This may be of general importance in animal breeding. The comparatively high selection response in this experiment seems due to the heterogeneity of the base population, the relatively high effective population size, and the duration of the experiment.

Temporally varying selection is considered to be one of the potential mechanisms of recombination evolution. We found earlier that simple cyclical selection for a trait controlled by multiple additive, dominant or semi-dominant loci can result in extremely complex limiting behaviour (CLB) of population trajectories, including ‘supercycles’ and more complex attractors. Recombination rate proved to be a key factor affecting the mode of CLB and the very existence of CLB. Therefore, we considered here a generalized model: the fixed recombination rate was replaced by a polymorphic recombination modifier. The modifier-dependent changes included: (a) supercyclical dynamics due to the recombination modifier in a system that does not manifest CLB when recombination rate is a fixed parameter; (b) appearance of a new level of superoscillations (super-supercycles) in a system that manifests supercycles with a fixed modifier; (c) chaotization of the regular supercyclical dynamics. The domain of attraction of these movements appeared to be quite large. It is noteworthy that the modifier locus is an active participant in the observed non-monotonic limiting movements. Interactions between short-period forced oscillations and the revealed long-period auto-oscillations appeared to result in new regimes of recombination evolution (for some range of linkage between the modifier locus and the selected system), as compared with those caused by the forced oscillations alone.

A novel selection algorithm for maximizing genetic response while constraining the rate of inbreeding is presented. It is shown that the proposed method controls the rate of inbreeding by maintaining the sum of squared genetic contributions at a constant value and represents an improvement on previous procedures. To maintain a constant rate of inbreeding the contributions from all generations are weighted equally and this is facilitated by modifying the numerator relationship matrix. By considering the optimization of the contributions of many generations the initial mating proportions (the genetic contributions to the next generation) are not equal to their long-term values, but are set equal to the expected long-term contributions given the current information. This is confirmed by the regression of the long-term contributions on the assigned mating proportions being close to one. The gain obtained from the selection algorithm is compared with the maximum theoretical genetic gain under constrained inbreeding. It is concluded that this theoretical upper bound is in general unattainable, but from this a concept of genetic efficiency in terms of resources and constraints is derived.

When a favourable mutation sweeps to fixation, those genes initially linked to it increase in frequency; on average, this reduces diversity in the surrounding region of the genome. In the first analysis of this ‘hitch-hiking’ effect, Maynard-Smith and Haigh (1974) followed the increase of the neutral allele that chanced to be associated with the new mutation in the first generation, and assumed that the subsequent increase was deterministic. Later analyses, based on either coalescence arguments, or on diffusion equations for the mean and variance of allele frequency, have also made one or both of these assumptions. In the early generations, stochastic fluctuations in the frequency of the selected allele, and coalescence of neutral lineages, can be accounted for correctly by following relationships between genes conditional on the number of copies of the favourable allele. This analysis shows that the hitch-hiking effect is increased because an allele that is destined to fix tends to increase more rapidly than exponentially. However, the identity generated by the selective sweep has the same form as in previous work, h[r/s] (2 Ns)−2r/s, where h[r/s] tends to 1 with tight linkage. This analysis is extended to samples of many genes; then, genes may trace back to several families of lineages, each related through a common ancestor early in the selective sweep. Simulations show that the number and sizes of these families can (in principle) be used to make separate estimates of r/s and Ns.

Methods of identification of quantitative trait loci (QTL) using a half-sib design are generally based on least-squares or maximum likelihood approaches. These methods differ in the genetical model considered and in the information used. Despite these differences, the power of the two methods in a daughter design is very similar. Using an analogy with a one-way analysis of variance, we propose an equation connecting the two test-statistics (F ratio for regression and likelihood ratio test in the case of the maximum likelihood). The robustness of this relationship is tested by simulation for different single QTL models. In general, the correspondence between the two statistics is good under both the null hypothesis and the alternative hypothesis of a single QTL segregating. Practical implications are discussed with particular emphasis on the theoretical distribution of the likelihood ratio test.

Quantitative trait loci (QTLs) responsible for variation in sternopleural bristle number in crosses between the laboratory lines of Drosophila melanogaster OregonR and CantonS were mapped using information from allele frequency changes of two families of retrotransposon markers in divergently selected populations. QTL effects and positions were inferred by likelihood, using transition matrix iteration and Monte Carlo interval mapping. Individuals from the selected populations were genotyped for markers spaced at an average distance 4.4 cM. Four QTLs of moderate effect ranging from 0·6 to 1·32 bristles accounted for most of the selection response. A permutation test of the correspondence between the mapped QTLs and the positions of bristle number candidate genes suggested that alleles at these candidate genes were no more strongly associated with selected changes in marker allele frequency than were randomly chosen positions in the genome.

We investigated three aspects of adaptation to variable environments in Daphnia pulex (Cladocera: Crustacea): (1) effects of temporal variation on the evolution of phenotypic plasticity ; (2) plasticity in sexual versus asexual lineages; (3) maintenance of genetic variation in variable environments. We performed a 72-day quasi-natural selection experiment comparing three patterns of variation: constant temperatures, varying but predictable temperature change, and unpredictable temperature change. All populations were begun with an identical array of 34 clones. During selection clonal variation declined in all populations and different patterns of environmental variation had little effect on amounts of genetic variation. Sexual and asexual lineages differed in size and growth rate, but did not differ in amounts of plasticity or in adaptation to variable environments. The primary target of selection was the Malthusian parameter (r) and life history traits of development time, offspring size and offspring number. The heritability of plasticity was generally lower than trait heritability. Because of this difference, the selection response on the mean of the traits overwhelmed the selection response on plasticity. Lower heritabilities of plasticity are very typical, suggesting that our results will be typical of responses to selection in nature. Our results suggest that selection will act mostly on trait means within environments and that plasticity will evolve often as a correlated trait. Because selection on plasticity is based on its across-deme, global fitness, this process will usually be slow. Comparative studies need to shift from closely related, local population differences to those of more distantly related populations or even different species.

To test whether stressful conditions altered levels of heritable variation in fecundity in Drosophila melanogaster, parent–offspring comparisons were undertaken across three generations for flies reared in a combined stress (ethanol, cold shock, low nutrition) environment or a control environment. The stressful conditions did not directly influence fecundity but did lead to a reduced fecundity in the offspring generations, perhaps reflecting cross-generation maternal effects. Both the heritability and evolvability estimates were higher in the combined stress treatment, reflecting an apparent increase in the additive genetic variance under stress. In contrast, there were no consistent changes in the environmental variance across environments.