Some statistical methods are described for the detection and estimation of variability in the rate of evolution, from biometrical data on single characters in fossil lineages. The methods were applied to some published examples of protistan and mammalian lineages, extending between 0.8 and 6.4 Myr in duration. Of six cases examined, only one failed to show evidence for significant variation in the rate of evolution, and only four deviated significantly from a random walk pattern, despite significant net evolutionary change in all cases but one.

Formulae are developed for the fraction of the population that must be eliminated by selection in each generation in order to account for a given rate of evolution in a metrical trait. A combination of directional and stabilizing selection is assumed. The effects of competition based on phenotypic value are also considered. The formulae are applied to data on evolutionary rates and their variances. It is concluded that most selective elimination is due to stabilizing selection, and that even very rapid evolutionary change in a single character usually involves low levels of additional elimination. It is suggested that long-sustained evolutionary trends are unlikely to be caused either by gradual change of the optimum under stabilizing selection or by the effects of competitive selection in favor of extreme individuals. It is possible that genetic correlations between traits under selection may limit the response of a single trait to directional selection and hence produce very gradual change.

Ancestral polymorphisms are defined as variants that arose by mutation prior to the speciation event that generated the species in which they segregate. Their presence may complicate the interpretation of molecular data and lead to incorrect phylogenetic inferences. They may also be used to identify regions of the genome that are under balancing selection. It is thus important to take into account the contribution of ancestral polymorphisms to variability within species and divergence between species. Here, we extend and improve a method for estimation of the proportion of ancestral polymorphisms within a species, and apply it to a dataset of 33 X-linked and 34 autosomal protein-coding genes for which sequence polymorphism data are available in both Drosophila pseudoobscura and Drosophila miranda, using Drosophila affinis as an outgroup. We show that a substantial proportion of both X-linked and autosomal synonymous variants in these two species are ancestral, and that a small number of additional genes with unusually high sequence diversity seem to have an excess of ancestral polymorphisms, suggestive of balancing selection.

Population genomics is the study of the amount and causes of genome-wide variability in natural populations, a topic that has been under discussion since Darwin. This paper first briefly reviews the early development of molecular approaches to the subject: the pioneering unbiased surveys of genetic variability at multiple loci by means of gel electrophoresis and restriction enzyme mapping. The results of surveys of levels of genome-wide variability using DNA resequencing studies are then discussed. Studies of the extent to which variability for different classes of variants (non-synonymous, synonymous and non-coding) are affected by natural selection, or other directional forces such as biased gene conversion, are also described. Finally, the effects of deleterious mutations on population fitness and the possible role of Hill–Robertson interference in shaping patterns of sequence variability are discussed.

Models of the evolutionary advantages of sex and genetic recombination due to directional selection on a quantitative trait are analysed. The models assume that the trait is controlled by many additive genes. A nor-optimal selection function is used, in which the optimum either moves steadily in one direction, follows an autocorrelated linear Markov process or a random walk, or varies cyclically. The consequences for population mean fitness of a reduction in genetic variance, due to a shift from sexual to asexual reproduction are examined. It is shown that a large reduction in mean fitness can result from such a shift in the case of a steadily moving optimum, under light conditions. The conditions are much more stringent with a cyclical or randomly varying environment, especially if the autocorrelation for a random environment is small. The conditions for spread of a rare modifier affecting the rate of genetic recombination are also examined, and the strength of selection on such a modifier determined. Again, the case of a steadily moving optimum is most favourable for the evolution of increased recombination. The selection pressure on a recombination modifier when a trait is subject to strong truncation selection is calculated, and shown to be large enough to account for observed increases in recombination associated with artificial selection. Theoretical and empirical evidence relevant to evaluating the importance of this model for the evolution of sex and recombination is discussed.

Data were collected on the distribution of nine families of transposable elements among second and third chromosomes isolated from a natural population of Drosophila melanogaster, by means of in situ hybridization of element probes to polytene chromosomes. It was found that the copy numbers per chromosome in the distal sections of the chromosome arms followed a Poisson distribution. Elements appeared to be distributed randomly along the distal sections of the chromosome arms. There was no evidence for linkage disequilibrium in the distal sections of the chromosomes, but some significant disequilibrium was detected in proximal regions. There were many significant correlations between different element families with respect to the identity of the sites that were occupied in the sample. There were also significant correlations between families with respect to sites at which elements achieved relatively high frequencies. Element frequencies per chromosome band were generally low in the distal sections, but were higher proximally. These results are discussed in the light of models of the population dynamics of transposable elements. It is concluded that they provide strong evidence for the operation of a force or forces opposing transpositional increase in copy number. The data suggest that the rate of transposition perelement per generation is of the order of 10−4, for the elements included in this study.

This paper analyses the effects of selection against deleterious alleles maintained by mutation (‘ background selection’) on rates of evolution and levels of genetic diversity at weakly selected, completely linked, loci. General formulae are derived for the expected rates of gene substitution and genetic diversity, relative to the neutral case, as a function of selection and dominance coefficients at the loci in question, and of the frequency of gametes that are free of deleterious mutations with respect to the loci responsible for background selection. As in the neutral case, most effects of background selection can be predicted by considering the effective size of the population to be multiplied by the frequency of mutation-free gametes. Levels of genetic diversity can be sharply reduced by background selection, with the result that values for sites under selection approach those for neutral variants subject to the same regime of background selection. Rates of fixation of slightly deleterious mutations are increased by background selection, and rates of fixation of advantageous mutations are reduced. The properties of sex-linked and autosomal asexual and self-fertilizing populations are considered. The implications of these results for the interpretation of studies of molecular evolution and variation are discussed.

An approximate expression, is derived for the rate of change in frequency of an inversion introduced at a low initial frequency into a multi-locus system at equilibrium under recombination and selection. It is shown that this expression gives accurate predictions of the rate of progress of the inversion, even if the initial population is perturbed somewhat from equilibrium. Extensions to the cases where there are sex differences in recombination and selection are considered. An implication of the results is that selection pressure for newly arisen inversions depends on the existence of a stable equilibrium with linkage disequilibrium. The expected chance of survival of a new inversion in a large population is shown to be approximately one half the square root of the loss in fitness due to recombination.

Data were collected on the distribution of ten families of transposable elements among fourteen X chromosomes isolated from a natural population of Drosophila melanogaster, by means of in situ hybridization to polytene chromosomes. It was found that, with the exception of roo, the copy number per chromosome followed a Poisson distribution. There was no evidence for linkage disequilibrium, either within or between families. Some pairs of families of elements were correlated with respect to the identity of the sites that were occupied in the sample, although there was no evidence for a correlation with respect to the sites at which elements attained relatively high frequencies. Elements appeared to be distributed randomly along the distal part of the X chromosome. There was, however, a strong tendency for elements to accumulate at the base of the chromosome. Element frequencies per chromosome band were generally low, except at the base of the chromosome where bands in subdivisions 19E and 20A sometimes had high frequencies of occupation. These results are discussed in the light of models of the population dynamics of transposable elements. It is concluded that they provide strong evidence for the operation of a force or forces opposing transpositional increase in copy number. The accumulation of elements at the base of the chromosome is consistent with the idea that unequal exchange between elements at non-homologous sites is such a force, although other possibilities cannot be excluded at present. The data suggest that the rate of transposition per element per generation is of the order of 10−4, for the elements included in this study.

An approximate equation is derived, which predicts the effect on variability at a neutral locus of background selection due to a set of partly linked deleterious mutations. Random mating, multiplicative fitnesses, and sufficiently large population size that the selected loci are in mutation/selection equilibrium are assumed. Given these assumptions, the equation is valid for an arbitrary genetic map, and for an arbitrary distribution of selection coefficients across loci. Monte Carlo computer simulations show that the formula performs well for small population sizes under a wide range of conditions, and even seems to apply when there are epistatic fitness interactions among the selected loci. Failure occurred only with very weak selection and tight linkage. The formula is shown to imply that weakly selected mutations are more likely than strongly selected mutations to produce regional patterning of variability along a chromosome in response to local variation in recombination rates. Loci at the extreme tip of a chromosome experience a smaller effect of background selection than loci closer to the centre. It is shown that background selection can produce a considerable overall reduction in variation in organisms with small numbers of chromosomes and short maps, such as Drosophila. Large overall effects are less likely in species with higher levels of genetic recombination, such as mammals, although local reductions in regions of reduced recombination might be detectable.

Theoretical models of the effects of selection against deleterious mutations on variation at linked neutral sites (background selection) are used to predict the relations between chromosomal location and genetic variability at the DNA level, in Drosophila melanogaster. The sensitivity of the predictions to variation in the mutation, selection and recombination parameters on which they are based is examined. It is shown that many features of the observed relations between chromosomal location and level of genetic diversity in D. melanogaster can be explained by background selection, especially if the weak selective forces acting on transposable elements are taken into account. In particular, the gradient in diversity in the distal portion of the X chromosome, and the lack of diversity on chromosome 4 and at the bases of the major chromosomes, can be fully accounted for. There are, however, discrepancies between predicted and observed values for some loci in D. melanogaster, which may reflect the effects of forces other than background selection.

The total genomic copy numbers of ten families of transposable elements of Drosophila melanogaster in a set of ten isogenic lines derived from a natural population were estimated by slot-blotting. The numbers of euchromatic copies of members of each family were determined for each line by in situ hybridization of element probes to polytene chromosomes. Heterochromatic numbers were estimated by subtraction of the euchromatic counts from the total numbers. There was considerable variation between element families and lines in heterochromatic abundances, and the variance between lines for many elements was much greater for the heterochromatin than for the euchromatin. The data are consistent with the view that much of the β-heterochromatin consists of sequences derived from transposable elements. They are also consistent with the hypothesis that similar evolutionary forces control element abundances in both the euchromatin and heterochromatin, although amplification of inert sequences derived from transposable elements may be in part responsible for their accumulation in heterochromatin.

A population genetics model of the role of asymmetric pairing and unequal exchange in the stabilization of transposable element copy number in natural populations is proposed and analysed. Monte Carlo simulations indicate that the approximations incorporated into the analysis are robust in the relevant parameter ranges. Given several simple assumptions concerning transposition and excision, equal and unequal exchange, and chromosome structure, predictions of the relative numbers of transposable elements in various regions of the Drosophila melanogaster genome are compared to the observed distribution of roo/B104 elements across chromosomal regions with differing rates of exchange, and between X chromosomes and autosomes. There is no indication of an accumulation of elements in the distal regions of chromosomes, which is expected if unequal exchange is reduced concomitantly with normal crossing over in the distal regions. There is, however, an indication of an excess of elements relative to physical length in the proximal regions of the chromosomes, which also have restricted crossing over. This observation is qualitatively consistent with the model's predictions. The observed distribution of elements between the mid-sections of the X chromosomes and autosomes is consistent with the predictions of one of two models of unequal exchange.

This paper describes analytical and simulation models of the population dynamics of transposable elements in randomly mating populations. The models assume a finite number of chromosomal sites that are occupable by members of a given family of elements. Element frequencies can change as a result of replicative transposition, loss of elements from occupied sites, selection on copy number per individual, and genetic drift. It is shown that, in an infinite population, an equilibrium can be set up such that not all sites in all individuals are occupied, allowing variation between individuals in both copy number and identity of occupied sites, as has been observed for several element families in Drosophila melanogaster. Such an equilibrium requires either regulation of transposition rate in response to copy number per genome, a sufficiently strongly downwardly curved dependence of individual fitness on copy number, or both. The probability distributions of element frequencies, generated by the effects of finite population size, are derived on the assumption of independence between different loci, and compared with simulation results. Despite some discrepancies due to violation of the independence assumption, the general pattern seen in the simulations agrees quite well with theory.

Data from Drosophila population studies are compared with the theoretical models, and methods of estimating the relevant parameters are discussed.

An expression is derived for determining the probability of survival of a new favourable mutation in a large random-mating population with overlapping generations. For a gene of small effect, in a near-stationary population, an approximate formula similar to the usual one for discrete generations is obtained. The implications of these results for the evolution of life histories are discussed, using the partial derivatives of the chance of survival of a gene, with respect to changes in age-specific fecundities and survival probabilities. The properties of these derivatives are very similar to those of the derivatives of the intrinsic rate of increase, analysed by Hamilton (1966), thus providing a genetical basis for his conclusions concerning the evolution of life histories.

Mutation-selection balance in a multi-locus system is investigated theoretically, using a modification of Bulmer's infinitesimal model of selection on a normally-distributed quantitative character, taking the number of mutations per individual (n) to represent the character value. The logarithm of the fitness of an individual with n mutations is assumed to be a quadratic, decreasing function of n. The equilibrium properties of infinitely large asexual populations, random-mating populations lacking genetic recombination, and random-mating populations with arbitrary recombination frequencies are investigated. With ‘synergistic’ epistasis on the scale of log fitness, such that log fitness declines more steeply as n increases, it is shown that equilibrium mean fitness is least for asexual populations. In sexual populations, mean fitness increases with the number of chromosomes and with the map length per chromosome. With ‘diminishing returns’ epistasis, such that log fitness declines less steeply as n increases, mean fitness behaves in the opposite way. Selection on asexual variants and genes affecting the rate of genetic recombination in random-mating populations was also studied. With synergistic epistasis, zero recombination always appears to be disfavoured, but free recombination is disfavoured when the mutation rate per genome is sufficiently small, leading to evolutionary stability of maps of intermediate length. With synergistic epistasis, an asexual mutant is unlikely to invade a sexual population if the mutation rate per diploid genome greatly exceeds unity. Recombination is selectively disadvantageous when there is diminishing returns epistasis. These results are compared with the results of previous theoretical studies of this problem, and with experimental data.