The evolution of molecular quantitative traits, such as codon usage bias or base frequencies, can be explained as the result of mutational biases alone, or as the result of mutation and selection. Whereas mutation models can be investigated easily, realistic modelling of selection-directed genome evolution is analytically intractable, and numerical calculations require substantial computer resources. We investigated the evolution of optimal codon frequency under additive and multiplicative effects of selected linked codons. We show that additive selective effects of many linked sites cannot be effective in genomes when the number of selected sites is greater than the effective population size, a realistic assumption according to current molecular data. We then discuss the implications of these results for isochore evolution in vertebrates.

The rate of accumulation of deleterious mutations by Muller's ratchet is investigated in large asexual haploid populations, for a range of parameters with potential biological relevance. The rate of this process is studied by considering a very simple model in which mutations can have two types of effect: either strongly deleterious or mildly deleterious. It is shown that the rate of accumulation of mildly deleterious mutations can be greatly increased by the presence of strongly deleterious mutations, and that this can be predicted from the associated reduction in effective population size (the background selection effect). We also examine the rate of the ratchet when there are two classes of mutation of similar but unequal effects on fitness. The accuracy of analytical approximations for the rate of this process is analysed. Its possible role in causing the degeneration of Y and neo-Y chromosomes is discussed in the light of our present knowledge of deleterious mutation rates and selection coefficients.

Parentage studies often estimate the number of parents contributing to half-sib progeny arrays by counting the number of alleles attributed to unshared parents. This approach is compromised when an offspring has the same heterozygous genotype as the shared parent, for then the contribution of the unshared parent cannot be unambiguously deduced. To determine how often such cases occur, formulae for co-dominant markers with n alleles are derived here for Ph, the probability that a given heterozygous parent has an offspring with the same heterozygous genotype, and Pa, the probability that a randomly chosen offspring has the same heterozygous genotype as the shared parent. These formulae have been derived assuming Mendelian segregation with either (1) an arbitrary mating system, (2) random mating or (3) mixed mating. The maximum value of Pa under random mating is 0·25 and occurs with any two alleles each at a frequency of 0·5. The behaviour with partial selfing (where reproduction is by selfing with probability s, and random mating otherwise) is more complex. For n [les ] 3 alleles, the maximum value of Pa occurs with any two alleles each at a frequency of 0·5 if s < 0·25, and with three equally frequent alleles otherwise. Numerically, the maximum value of Pa for n [ges ] 4 alleles occurs with n* [les ] n alleles at equal frequencies, where the maximizing number of alleles n* is an increasing function of the selfing rate. Analytically, the maximum occurs with all n alleles present and equally frequent if s [ges ] 2/3. In addition, the potential applicability of these formulae for evolutionary studies is briefly discussed.

Members of the Polycomb group (Pc-G) and trithorax group (trx-G) of genes, as well as the enhancers of trx-G and Pc-G (ETP), function together to maintain segment identity during Drosophila development. In order to obtain new marked P mutations in these genes, we screened for dominant modifiers of the extra-sex-combs phenotype displayed by males mutant for the polyhomeotic (ph) gene, a member of the Pc-G group. Five P{lacW} insertions in four different genes were found to stably suppress ph: two are allelic to trithorax, one is the first allele specific to the Minute(2)21C gene, and the remaining two define new trx-G genes, toutatis (tou) in 48A and taranis (tara) in 89B10-13. tou is predicted to encode a 3109 amino acid sequence protein (TOU), which contains a TAM DNA-binding domain, a WAKZ motif, two PHD zinc fingers and a C-terminal bromodomain, and as such is likely to be involved in regulation of chromatin structure as a subunit of a novel chromatin remodelling complex. In a previous study, we found that insertion of a P{ph} transposable element containing ph regulatory sequences creates a high frequency of mutations modifying ph homeotic phenotypes. One such insertion enhanced the ph phenotype and we show that it is a new allele of UbcD1/eff, a gene encoding a ubiquitin-conjugating enzyme that is involved in telomere association and potentially in chromatin remodelling.

Xie & Xu (2000) present a model for mapping quantitative trait loci in an autotetraploid population. However, one aspect of their model, namely gamete formation, does not properly represent the biological process in autotetraploid species. This paper gives a more realistic formulation for this part of the model, and discusses the consequences for multipoint mapping.

Genomic copy numbers and the rates of movement of nine families of transposable elements (TEs) of Drosophila melanogaster were estimated in two sets of mutation accumulation lines: Beltsville and Madrid. Southern blotting was used to screen a large number of samples from both genetic backgrounds for TEs. The Madrid lines were also screened by in situ hybridization of TEs to polytene chromosomes, in order to obtain more detailed information about the behaviour of TEs in the euchromatin. Southern blotting data provided evidence of insertions and excision events in both genetic backgrounds, occurring at rates of approximately 10−5 and 10−6 per element copy per generation, respectively. In contrast, in situ data from the Madrid background presented a completely different picture, with no evidence for excisions, and a significantly higher rate of transposition (1·01×10−4). Direct comparison of the two data sets suggests that the Southern blotting technique had serious deficiencies: (i) it underestimated element abundance; (ii) it revealed less than 30% of the new insertions detected by in situ hybridization; and (iii) changes in the size of restriction fragments from any source were spuriously identified as simultaneous insertion–excision events. Our in situ data are consistent with previous studies, and suggest that selection is the main force controlling element spread by transposition.

Haseman and Elston (1972) developed a robust regression method for the detection of linkage between a marker and a quantitative trait locus (QTL) using sib pair data. The principle underlying this method is that the difference in phenotypes between pairs of sibs becomes larger as they share a decreasing number of alleles at a particular QTL identical by descent (IBD) from their parents. In this case, phenotypically very different sibs will also on average share a proportion of alleles IBD at any marker linked to the QTL that is lower than the expected value of 0·5. Thus, the deviation of the proportion of marker alleles IBD from the expected value in pairs of sibs selected to be phenotypically different (i.e. discordant) can provide a test for the presence of a QTL. A simple regression method for QTL detection in sib pairs selected for high phenotypic differences is presented here. The power of the analytical method was found to be greater than the power obtained using the standard analysis when samples of sib pairs with high phenotypic differences were used. However, the use of discordant sib pairs was found to be less powerful for QTL detection than alternative selective genotyping schemes based on the phenotypic values of the sibs except with intense selection, when its advantage was only marginal. The most effective selection scheme overall was the use of sib pairs from entire families selected on the basis of high within-family variance for the trait in question. There is little effect of selection on QTL position estimates, which are in good agreement with the simulated values. However, QTL variance estimates are biased to a greater or lesser degree, depending on the selection method.

We present likelihood-based methods for assigning the individuals in a sample to source populations, on the basis of their genotypes at co-dominant marker loci. The source populations are assumed to be at Hardy–Weinberg and linkage equilibrium, but the allelic composition of these source populations and even the number of source populations represented in the sample are treated as uncertain. The parameter of interest is the partition of the set of sampled individuals, induced by the assignment of individuals to source populations. We present a maximum likelihood method, and then a more powerful Bayesian approach for estimating this sample partition. In general, it will not be feasible to evaluate the evidence supporting each possible partition of the sample. Furthermore, when the number of individuals in the sample is large, it may not even be feasible to evaluate the evidence supporting, individually, each of the most plausible partitions because there may be many individuals which are difficult to assign. To overcome these problems, we use low-dimensional marginals (the ‘co-assignment probabilities’) of the posterior distribution of the sample partition as measures of ‘similarity’, and then apply a hierarchical clustering algorithm to identify clusters of individuals whose assignment together is well supported by the posterior distribution. A binary tree provides a visual representation of how well the posterior distribution supports each cluster in the hierarchy. These methods are applicable to other problems where the parameter of interest is a partition of a set. Because the co-assignment probabilities are independent of the arbitrary labelling of source populations, we avoid the label-switching problem of previous Bayesian methods.

We tested, using the sawfly Priophorus pallipes feeding on leaves of mountain birch, whether the expression of genetic (co)variation of larval development time and body size can be altered by exposing larvae to diets with differential seasonal changes in quality. In nature, larvae feed mainly on mature leaves, but occasionally they are forced to consume senescing leaves. Sixty families were assayed on three experimentally simulated diets: mature leaves of high quality, senescing leaves of rapidly declining quality, and senesced leaves of low quality. The intuitively obvious positive phenotypic and genetic correlations between development time and final mass were observed when the larvae consumed leaves of stable high quality, but low and declining food quality prevented long-growing individuals and families from achieving high final mass, switching the correlations to close to zero or negative in these treatments. The amount of genetic variation for body size showed a non-linear change across the diet quality gradient, whereas genetic variation for development time increased with decreasing diet quality. The among-trait difference in the degree reaction norms crossed along the diet gradient caused the changes in the expression of genetic (co)variation within the environments. Our results show that seasonally varying diet quality induces dramatic changes in the genetic (co)variation of development time and body size, and that simultaneous analysis of reaction norms and environment-specific expression of genetic (co)variation is necessary for the understanding of the genetic characteristics underlying the construction of phenotypes in heterogeneous environments.

In the medaka, Oryzias latipes, sex is determined chromosomally. The sex chromosomes differ from those of mammals in that the X and Y chromosomes are highly homologous. Using backcross panels for linkage analysis, we mapped 21 sequence tagged site (STS) markers on the sex chromosomes (linkage group 1). The genetic map of the sex chromosome was established using male and female meioses. The genetic length of the sex chromosome was shorter in male than in female meioses. The region where male recombination is suppressed is the region close to the sex-determining gene y, while female recombination was suppressed in both the telomeric regions. The restriction in recombination does not occur uniformly on the sex chromosome, as the genetic map distances of the markers are not proportional in male and female recombination. Thus, this observation seems to support the hypothesis that the heterogeneous sex chromosomes were derived from suppression of recombination between autosomal chromosomes. In two of the markers, Yc-2 and Casp6, which were expressed sequence-tagged (EST) sites, polymorphisms of both X and Y chromosomes were detected. The alleles of the X and Y chromosomes were also detected in O. curvinotus, a species related to the medaka. These markers could be used for genotyping the sex chromosomes in the medaka and other species, and could be used in other studies on sex chromosomes.

An allele of the behavioural mutant pawn-B96 has been reported as a typical recessive gene but was found to show a peculiar inheritance. When the F2 progeny from crosses between the wild-type and pwB96 were obtained by autogamy, the 1[ratio ]1 phenotypic segregation ratio was observed as expected. However, two-thirds of the wild-type progeny in the F2 were thought to be heterozygotes because they became mixed progeny of wild-type and pawn clones in successive autogamies. Four marker genes showed the expected segregation ratio and stable phenotypes in these crossings. This result and the results of crossings using segregants from the above crosses indicated that parental pwB96 is a tetrasomy of the chromosome carrying the pwB gene. To determine the cause of chromosomal duplication in the mutant, the stability of the chromosome carrying the pwB locus was examined by genetic analyses. The disomy of both pwB and wild-type and the tetrasomy of pwB showed genotypes that were relatively stable during several autogamous generations. However, in clones initially pure for the tetrasomy of wild-type, disomic cells appeared within a few autogamous generations. The difference between the stabilities of the tetrasomy of pwB96 and that of the wild-type might be due partly to differences between the growth rate of tetrasomy and disomy in pwB96 and the wild-type, but mostly the result of an unknown contribution of the chromosome carrying the pwB96 allele to the tetrasomic composition.

An importance-sampling method is presented that allows the simulation of the history of a selected allele in a population of variable size. A sample path describing the number of copies of an allele that arose as a single mutant is generated by simulating backwards from the current frequency until the allele is lost. The mathematical expectation of a quantity or statistic is then estimated by taking averages over replicate simulations, weighting each replicate by the ratio of its probabilities under the Markov chains for the forward and backwards processes. This method was used to find the average age of a selected allele in an exponentially growing population. In terms of the effect on average allele age, selection in favour of an allele is not equivalent to exponential growth. To generate gene genealogies of a sample of copies of a selected allele, the neutral coalescent model is simulated for the subpopulation containing only the selected allele. From the resulting intra-allelic genealogy, it is possible to calculate the likelihood of the selection intensity as a function of the observed level of variability at marker loci closely linked to the selected allele. This method was used to estimate the intensity of selection affecting the Δ32 allele at the CCR5 locus in Europeans and a mutant at the MLH1 locus associated with colorectal cancer in the Finnish population.

In this paper the fitness of the ΔF508 heterozygote is assessed and the age of the ΔF508 mutation in the cystic fibrosis locus is estimated. Data from three microsatellite loci are applied. The analysis is performed conditional on the present-day frequency of the ΔF508 mutation and based on assumptions about the demographic history of the European population and the mutation rate in the three microsatellite loci. It is shown that the data gives evidence of positive selection (up to 2–3% per ΔF508 heterozygote), but also that data could be explained by negative selection of roughly the same order of magnitude. The age of the ΔF508 mutation is subsequently estimated; it is found that the mutation is at least 580 generations old, but could be much older depending on the microsatellite mutation rate and the exact number of substitutions experienced in the history of the three microsatellite loci.

GAGA factor is an important chromosomal protein involved in establishing specific nucleosome arrays and in regulating gene transcription in Drosophila melanogaster. We developed a transgenic system for controlled heat-shock-dependent overexpression of the GAGA factor 519 amino acid isoform (GAGA-519) in vivo. Efficient production of stable protein from these transgenes provided genetic rescue of a hypomorphic Trithorax-like (Trl) lethal allele to adulthood. Nevertheless, supplemental GAGA-519 did not suppress position effect variegation (PEV), a phenomenon commonly used to measure dosage effects of chromosomal proteins, nor did it rescue other lethal alleles of Trl. The results suggest requirements for the additional isoforms of GAGA factor, or for more precise regulation of synthesis, to carry out the diverse functions of this protein.

The advancements made in molecular technology coupled with statistical methodology have led to the successful detection and location of genomic regions (quantitative trait loci; QTL) associated with quantitative traits. Binary traits (e.g. susceptibility/resistance), while not quantitative in nature, are equally important for the purpose of detecting and locating significant associations with genomic regions. Existing interval regression methods used in binary trait analysis are adapted from quantitative trait analysis and the tests for regression coefficients are tests of effect, not detection. Additionally, estimates of recombination that fail to take into account varying penetrance perform poorly when penetrance is incomplete. In this work a complete probability model for binary trait data is developed allowing for unbiased estimation of both penetrance and recombination between a genetic marker locus and a binary trait locus for backcross and F2 experimental designs. The regression model is reparameterized allowing for tests of detection. Extensive simulations were conducted to assess the performance of estimation and testing in the proposed parameterization. The proposed parameterization was compared with interval regression via simulation. The results indicate that our parameterization shows equivalent estimation capabilities, requires less computational effort and works well with only a single marker.

We reconsider deterministic models of mutation and selection acting on populations of sequences, or, equivalently, multilocus systems with complete linkage. Exact analytical results concerning such systems are few, and we present recent and new ones obtained with the help of methods from quantum statistical mechanics. We consider a continuous-time model for an infinite population of haploids (or diploids without dominance), with N sites each, two states per site, symmetric mutation and arbitrary fitness function. We show that this model is exactly equivalent to a so-called Ising quantum chain. In this picture, fitness corresponds to the interaction energy of spins, and mutation to a temperature-like parameter. The highly elaborate methods of statistical mechanics allow one to find exact solutions for non-trivial examples. These include quadratic fitness functions, as well as ‘Onsager's landscape’. The latter is a fitness function which captures some essential features of molecular evolution, such as neutrality, compensatory mutations and flat ridges. We investigate the mean number of mutations, the mutation load, and the variance in fitness under mutation–selection balance. This also yields some insight into the ‘error threshold’ phenomenon, which occurs in some, but not all, examples.