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Population geneticists have long sought to understand the contribution of natural selection to molecular evolution. A variety of approaches have been proposed that use population genetics theory to quantify the rate and strength of positive selection acting in a species’ genome. In this review we discuss methods that use patterns of between-species nucleotide divergence and within-species diversity to estimate positive selection parameters from population genomic data. We also discuss recently proposed methods to detect positive selection from a population’s haplotype structure. The application of these tests has resulted in the detection of pervasive adaptive molecular evolution in multiple species.

Colour polymorphisms play a key role in sexual selection and speciation, yet the mechanisms that generate and maintain them are not fully understood. Here, we use genomic and transcriptomic tools to identify the precise genetic architecture and evolutionary history of a sex-linked colour polymorphism in the Gouldian finch Erythrura gouldiae that is also accompanied by remarkable differences in behaviour and physiology. We find that differences in colour are associated with an ~72-kbp region of the Z chromosome in a putative regulatory region for follistatin , an antagonist of the TGF-β superfamily genes. The region is highly differentiated between morphs, unlike the rest of the genome, yet we find no evidence that an inversion is involved in maintaining the distinct haplotypes. Coalescent simulations confirm that there is elevated nucleotide diversity and an excess of intermediate frequency alleles at this locus. We conclude that this pleiotropic colour polymorphism is most probably maintained by balancing selection. Gouldian finches have a head colour polymorphism that is also associated with physiological and behavioural differentiation. Here, the authors map this colour polymorphism to a putative regulatory region for follistatin on the Z chromosome and suggest it is maintained by balancing selection.

It is known that the allele ancestral to the variation at a polymorphic site cannot be assigned with certainty, and that the most frequently used method to assign the ancestral state—maximum parsimony—is prone to misinference. Estimates of counts of sites that have a certain number of copies of the derived allele in a sample (the unfolded site frequency spectrum, uSFS) made by parsimony are therefore also biased. We previously developed a maximum likelihood method to estimate the uSFS for a focal species using information from two outgroups while assuming simple models of nucleotide substitution. Here, we extend this approach to allow multiple outgroups (implemented for three outgroups), potentially any phylogenetic tree topology, and more complex models of nucleotide substitution. We find, however, that two outgroups and the Kimura two-parameter model are adequate for uSFS inference in most cases. We show that using parsimony to infer the ancestral state at a specific site seriously breaks down in two situations. The first is where the outgroups provide no information about the ancestral state of variation in the focal species. In this case, nucleotide variation will be underestimated if such sites are excluded. The second is where the minor allele in the focal species agrees with the allelic state of the outgroups. In this situation, parsimony tends to overestimate the probability of the major allele being derived, because it fails to account for the fact that sites with a high frequency of the derived allele tend to be rare. We present a method that corrects this deficiency and is capable of providing nearly unbiased estimates of ancestral state probabilities on a site-by-site basis and the uSFS.

For over a century, inbred mice have been used in many areas of genetics research to gain insight into the genetic variation underlying traits of interest. The generalizability of any genetic research study in inbred mice is dependent upon all individual mice being genetically identical, which in turn is dependent on the breeding designs of companies that supply inbred mice to researchers. Here, we compare whole-genome sequences from individuals of four commonly used inbred strains that were procured from either the colony nucleus or from a production colony (which can be as many as ten generations removed from the nucleus) of a large commercial breeder, in order to investigate the extent and nature of genetic variation within and between individuals. We found that individuals within strains are not isogenic, and there are differences in the levels of genetic variation that are explained by differences in the genetic distance from the colony nucleus. In addition, we employ a novel approach to mutation rate estimation based on the observed genetic variation and the expected site frequency spectrum at equilibrium, given a fully inbred breeding design. We find that it provides a reasonable per nucleotide mutation rate estimate when mice come from the colony nucleus (~7.9 × 10−9 in C3H/HeN), but substantially inflated estimates when mice come from production colonies.

It is known that the effective population size (Ne) and the mutation rate (u) vary across the genome. Here, we show that ignoring this heterogeneity may lead to biased estimates of past demography. To solve the problem, we develop new methods for jointly inferring past changes in population size and detecting variation in Ne and u between loci. These methods rely on either polymorphism data alone or both polymorphism and divergence data. In addition to inferring demography, we can use the methods to study a variety of questions: 1) comparing sex chromosomes with autosomes (for finding evidence for male-driven evolution, an unequal sex ratio, or sex-biased demographic changes) and 2) analyzing multilocus data from within autosomes or sex chromosomes (for studying determinants of variability in Ne and u). Simulations suggest that the methods can provide accurate parameter estimates and have substantial statistical power for detecting difference in Ne and u. As an example, we use the methods to analyze a polymorphism data set from Drosophila simulans. We find clear evidence for rapid population expansion. The results also indicate that the autosomes have a higher mutation rate than the X chromosome and that the sex ratio is probably female-biased. The new methods have been implemented in a user-friendly package.

Surveys of DNA sequence variation have shown that the level of genetic variability in a genomic region is often strongly positively correlated with its rate of crossing over (CO) [1-3]. This pattern is caused by selection acting on linked sites, which reduces genetic variability and can also cause the frequency distribution of segregating variants to contain more rare variants than expected without selection (skew). These effects of selection may involve the spread of beneficial mutations (selective sweeps, SSWs), the elimination of deleterious mutations (background selection, BGS) or both together, and are expected to be stronger with lower rates of crossing over [1-3]. However, in a recent study of human populations, the skew was reduced in the lowest CO regions compared with regions with somewhat higher CO rates [4]. A similar pattern is seen in the population genomic studies of Drosophila simulans described here. We propose an explanation for this paradoxical observation, and validate it using computer simulations. This explanation is based on the finding that partially recessive, linked deleterious mutations can increase rather than reduce neutral variability when the product of the effective population size (N e ) and the selection coefficient against homozygous carriers of mutations (s) is ≤ 1, i.e. there is associative overdominance (AOD) rather than BGS [5]. We show that AOD can operate in a genomic region with a low rate of CO, opening up a new perspective on how selection affects patterns of variability at linked sites. Footnotes * Author list corrected

Colour polymorphisms play a key role in sexual selection and speciation, yet the mechanisms that generate and maintain them are not fully understood. Here, we use genomic and transcriptomic tools to identify the precise genetic architecture and evolutionary history of a sex-linked colour polymorphism in the Gouldian finch Erythrura gouldiae that is also accompanied by remarkable differences in behaviour and physiology. We find that differences in colour are associated with an ~72-kbp region of the Z chromosome in a putative regulatory region for follistatin, an antagonist of the TGF-β superfamily genes. The region is highly differentiated between morphs, unlike the rest of the genome, yet we find no evidence that an inversion is involved in maintaining the distinct haplotypes. Coalescent simulations confirm that there is elevated nucleotide diversity and an excess of intermediate frequency alleles at this locus. We conclude that this pleiotropic colour polymorphism is most probably maintained by balancing selection. Footnotes * Title is changed. More explicit definition of the Red locus was applied and figures and the Supplementary Information were updated accordingly.

To what extent do substitutions in protein-coding versus gene-regulatory regions contribute to fitness change over time? Answering this question requires estimates of the extent of selection acting on beneficial mutations in the two classes of sites. New mutations that have advantageous or deleterious fitness effects can induce selective sweeps and background selection, respectively, causing variation in the level of neutral genetic diversity along the genome. In this study, we analyse the profiles of genetic variability around protein-coding and regulatory elements in the genomes of wild mice to estimate the parameters of positive selection. We find patterns of diversity consistent with the effects of selection at linked sites, which are similar across mouse taxa, despite differences in effective population size and demographic history. By fitting a model that combines the effects of selective sweeps and background selection, we estimate the strength of positive selection and the frequency of advantageous mutations. We find that strong positive selection is required to explain variation in genetic diversity across the murid genome. In particular, we estimate that beneficial mutations in protein-coding regions have stronger effects on fitness than do mutations in gene-regulatory regions, but that mutations in gene-regulatory regions are more common. Overall though, our parameter estimates suggest that the cumulative fitness changes brought about by beneficial mutations in protein-coding may be greater than those in gene-regulatory elements.

It is known that the allele ancestral to the variation at a polymorphic nucleotide site cannot be assigned with certainty, and that the most frequently used method to assign the ancestral state maximum parsimony is prone to mis-inference. Estimates of counts of sites that have a certain number of copies of the derived allele (the unfolded site frequency spectrum, uSFS) made by parsimony are therefore also biased. We previously developed a maximum likelihood method to estimate the uSFS for a focal species, using information from two outgroups and assuming simple models of nucleotide substitution. Here, we extend this approach to infer the uSFS, allowing multiple outgroups, potentially any phylogenetic tree topology and more complex models of nucleotide substitution. We find, however, that two outgroups and assuming the Kimura 2-parameter model is adequate for uSFS inference in most cases. We show that using parsimony for ancestral state inference at a specific site seriously breaks down in two situations. The first is where the outgroups provide no information about the ancestral state of variation in the focal species. In this case, nucleotide variation will be under-estimated if such sites are removed from the data. The second is where the minor allele in the focal species agrees with the allelic state of the outgroups. In this situation, parsimony tends to over-estimate the probability of the major allele being derived, because it fails to account for the fact that sites with a high frequency of the derived allele tend to be rare in most data sets. We present a method that corrects this deficiency, which is capable of providing unbiased estimates of ancestral state probabilities on a site-by-site basis and the uSFS.

The \\(K + N K + \\) reaction is studied for center-of-momentum energies ranging from threshold to 3 GeV in an effective Lagrangian approach that includes the hyperon \\(s\\)- and \\(u\\)-channel contributions as well as a phenomenological contact amplitude. The latter accounts for the rescattering term in the scattering equation and possible short-range dynamics not included explicitly in the model. Existing data are well reproduced and three above-the-threshold resonances were found to be required to describe the data, namely, the \\((1890)\\), \\((2030)\\), and \\((2250)\\). For the latter resonance we have assumed the spin-parity of \\(J^P=5/2^-\\) and a mass of 2265 MeV. The \\((2030)\\) resonance is crucial in achieving a good reproduction of not only the measured total and differential cross sections, but also the recoil polarization asymmetry. More precise data are required before a more definitive statement can be made about the other two resonances, in particular, about the \\((2250)\\) resonance that is introduced to describe a small bump structure observed in the total cross section of \\(K^- + p K^+ + ^-\\). The present analysis also reveals a peculiar behavior of the total cross section data in the threshold energy region in \\(K^- + p K^+ + ^-\\), where the \\(P\\)- and \\(D\\)-waves dominate instead of the usual \\(S\\)-wave. Predictions for the target-recoil asymmetries of the \\(K + N K + \\) reaction are also presented.