Effect of population structure on the amount of polymorphism and the fixation probability under overdominant selection

Under overdominant selection, mutants substantially contribute to increase the amount of polymorphism. It is also known that under neutrality as the migration rates among demes decrease in a subdivided population, the amount of polymorphism increases along with the increase of the effective population size, N(e). In this study, under overdominant selection the effect of population subdivision on the amount of polymorphism was investigated using the diffusion approximation and the low migration approximation. It was shown that if selection is medium or strong (e.g., N(T)s > 1, where N(T) is the population size and s is the selective advantage of heterozygotes), the nucleotide diversity, pi, decreases along with the decrease of Nm against the increase of N(e), where N is the size of demes and m is the migration rate per deme. In addition, the ratio of the nucleotide diversity to the evolutionary rate also decreases along with the decrease of Nm. In some cases the ratio becomes smaller than that expected under neutrality as Nm decreases.     

The relation between the neutrality index for mitochondrial genes and the distribution of mutational effects on fitness

We explore factors affecting patterns of polymorphism and divergence (as captured by the neutrality index) at mammalian mitochondrial loci. To do this, we develop a population genetic model that incorporates a fraction of neutral amino acid sites, mutational bias, and a probability distribution of selection coefficients against new nonsynonymous mutations. We confirm, by reanalyzing publicly available datasets, that the mitochondrial cyt-b gene shows a broad range of neutrality indices across mammalian taxa, and explore the biological factors that can explain this observation. We find that observed patterns of differences in the neutrality index, polymorphism, and divergence are not caused by differences in mutational bias. They can, however, be explained by a combination of a small fraction of neutral amino acid sites, weak selection acting on most amino acid mutations, and differences in effective population size among taxa.     

The Maintenance of Single-Locus Polymorphism. IV. Models with Mutation from Existing Alleles

The ability of viability selection to maintain allelic polymorphism is investigated using a constructionist approach. In extensions to the models we have previously proposed, a population is bombarded with a series of mutations whose fitnesses in conjunction with other alleles are functions of the corresponding fitnesses with a particular allele, the parent allele, already in the population. Allele frequencies are iterated simultaneously, thus allowing alleles to be driven to extinction by selection. Such models allow very high levels of polymorphism to evolve: up to 38 alleles in one case. Alleles that are lethal as homozygotes can evolve to surprisingly high frequencies. The joint evolution of allele frequencies and viabilities highlights the necessity to consider more than the current morphology of a population. Comparisons are made with the neutral theory of evolution and it is suggested that failure to reject neutrality using the Ewens-Watterson test cannot be regarded as evidence for the neutral theory.     

Departure from neutrality at the mitochondrial NADH dehydrogenase subunit 2 gene in humans,but not in chimpanzees.

To test whether patterns of mitochondrial DNA (mtDNA) variation are consistent with a neutral model of molecular evolution, nucleotide sequences were determined for the 1041 bp of the NADH dehydrogenase subunit 2 (ND2) gene in 20 geographically diverse humans and 20 common chimpanzees. Contingency tests of neutrality were performed using four mutational categories for the ND2 molecule: synonymous and nonsynonymous mutations in the transmembrane regions, and synonymous and nonsynonymous mutations in the surface regions. The following three topological mutational categories were also used: intraspecific tips, intraspecific interiors, and interspecific fixed differences. The analyses reveal a significantly greater number of nonsynonymous polymorphisms within human transmembrane regions than expected based on interspecific comparisons, and they are inconsistent with a neutral equilibrium model. This pattern of excess nonsynonymous polymorphism is not seen within chimpanzees. Statistical tests of neutrality, such as TAJIMA''s D test, and the D and F tests proposed by FU and LI, indicate an excess of low frequency polymorphisms in the human data, but not in the chimpanzee data. This is consistent with recent directional selection, a population bottleneck or background selection of slightly deleterious mutations in human mtDNA samples. The analyses further support the idea that mitochondrial genome evolution is governed by selective forces that have the potential to affect its use as a "neutral" marker in evolutionary and population genetic studies.     

Very slightly deleterious mutations and the molecular clock

Summary The model of very slightly deleterious mutations was examined from the standpoint of population genetics in relation to the molecular evolutionary clock. The distribution of selection coefficients of mutants (in terms of amino acid changes) with small effect is thought to be continuous around zero, with an average negative value. The variance of selection coefficients depends upon environmental diversity and hence on total population size of a species. By considering various examples of amino acid substitutions, the average and standard error of selection coefficients and the reciprocal of population size are assumed to have similar values. The model predicts negative correlation between evolutionary rate and population size. This effect is expected to be partially cancelled with the generation time effect of intrinsic mutation rate. Implications of this prediction on the molecular evolutionary clock are discussed.     

The nearly neutral and selection theories of molecular evolution under the fisher geometrical framework: substitution rate, population size, and complexity

The general theories of molecular evolution depend on relatively arbitrary assumptions about the relative distribution and rate of advantageous, deleterious, neutral, and nearly neutral mutations. The Fisher geometrical model (FGM) has been used to make distributions of mutations biologically interpretable. We explored an FGM-based molecular model to represent molecular evolutionary processes typically studied by nearly neutral and selection models, but in which distributions and relative rates of mutations with different selection coefficients are a consequence of biologically interpretable parameters, such as the average size of the phenotypic effect of mutations and the number of traits (complexity) of organisms. A variant of the FGM-based model that we called the static regime (SR) represents evolution as a nearly neutral process in which substitution rates are determined by a dynamic substitution process in which the population's phenotype remains around a suboptimum equilibrium fitness produced by a balance between slightly deleterious and slightly advantageous compensatory substitutions. As in previous nearly neutral models, the SR predicts a negative relationship between molecular evolutionary rate and population size; however, SR does not have the unrealistic properties of previous nearly neutral models such as the narrow window of selection strengths in which they work. In addition, the SR suggests that compensatory mutations cannot explain the high rate of fixations driven by positive selection currently found in DNA sequences, contrary to what has been previously suggested. We also developed a generalization of SR in which the optimum phenotype can change stochastically due to environmental or physiological shifts, which we called the variable regime (VR). VR models evolution as an interplay between adaptive processes and nearly neutral steady-state processes. When strong environmental fluctuations are incorporated, the process becomes a selection model in which evolutionary rate does not depend on population size, but is critically dependent on the complexity of organisms and mutation size. For SR as well as VR we found that key parameters of molecular evolution are linked by biological factors, and we showed that they cannot be fixed independently by arbitrary criteria, as has usually been assumed in previous molecular evolutionary models.     

Divergence and Polymorphism Under the Nearly Neutral Theory of Molecular Evolution

The nearly neutral theory attributes most nucleotide substitution and polymorphism to genetic drift acting on weakly selected mutants, and assumes that the selection coefficients for these mutants are drawn from a continuous distribution. This means that parameter estimation can require numerical integration, and this can be computationally costly and inaccurate. Furthermore, the leading parameter dependencies of important quantities can be unclear, making results difficult to understand. For some commonly used distributions of mutant effects, we show how these problems can be avoided by writing equations in terms of special functions. Series expansion then allows for their rapid calculation and, also, illuminates leading parameter dependencies. For example, we show that if mutants are gamma distributed, the neutrality index is largely independent of the effective population size. However, we also show that such results are not robust to misspecification of the functional form of distribution. Some implications of these findings are then discussed.     

Effects of the shape of distribution of mutant effect in nearly neutral mutation models

Models of the theory of nearly neutral mutation incorporate a continuous distribution of mutation effects in contrast to the theory of purely neutral mutation which allows no mutations with intermediate effects. Previous studies of one such model, namely the house-of-cards mutation model, assumed normal distribution of mutation effect. Here I study the house-of-cards mutation model in random-mating finite populations using the weak-mutation approximation, paying attention to the effects of the distribution of mutant effects. The average selection coefficient, substitution rate and average heterozygosity in the equilibrium and transient states were studied mainly by computer simulation. The main findings are: (i) Very rapid decrease of the substitution rate and very slow approach to equilibrium as selection becomes stronger are characteristics of assuming normal distribution of mutant effect. If the right tail of the mutation distribution decays more rapidly than that of the normal distribution, the decrease of substitution rate becomes slower and equilibrium is achieved more quickly. (ii) The dispersion index becomes smaller or larger than 1 depending on the time and the intensity of selection, (iii) LetN be the population size. When selection is strong the ratio of 4N times the substitution rate to the average heterozygosity, which is expected to be 1 under neutrality, is larger than 1 in earlier generations but becomes less than 1 in later generations. These findings show the importance of the distribution of mutant effect and time in determination of the behaviour of various statistics frequently used in the study of molecular evolution.     

Testing the generalized neutrality hypothesis

Various tests of the hypothesis of selective neutrality based on gene frequency are now available. These tests take as null hypothesis the concept of “strict neutrality”: all new mutants are required to be selectively identical to each other. For evolutionary questions, however, (as opposed to those of genetic polymorphism), a wider null hypothesis might be of interest. Since deleterious alleles have essentially no evolutionary importance, one might wish to test the null hypothesis that only neutral or deleterious mutations occur. The principal alternative to this hypothesis is that there exists heterotic selection of some form for some alleles tending to maintain a level of genetic polymorphism higher than that under neutrality. In this paper an assessment is made of the usefulness of a test of strict neutrality first proposed by this author (Ewens, 1972) as a test of null hypothesis of “generalized neutrality,” i.e. that only neutral or deleterious alleles occur. At the same time some remarks will be made about estimation of the fundamental parameter θ defining these processes.     

A Study on a Nearly Neutral Mutation Model in Finite Populations

As a nearly neutral mutation model, the house-of-cards model is studied in finite populations using computer simulations. The distribution of the mutant effect is assumed to be normal. The behavior is mainly determined by the product of the population size, N, and the standard deviation, sigma, of the distribution of the mutant effect. If 4N sigma is large compared to one, a few advantageous mutants are quickly fixed in early generations. Then most mutation becomes deleterious and very slow increase of the average selection coefficient follows. It takes very long for the population to reach the equilibrium state. Substitutions of alleles occur very infrequently in the later stage. If 4N sigma is the order of one or less, the behavior is qualitatively similar to that of the strict neutral case. Gradual increase of the average selection coefficient occurs and in generations of several times the inverse of the mutation rate the population almost reaches the equilibrium state. Both advantageous and neutral (including slightly deleterious) mutations are fixed. Except in the early stage, an increase of the standard deviation of the distribution of the mutant effect decreases the average heterozygosity. The substitution rate is reduced as 4N sigma is increased. Three tests of neutrality, one using the relationship between the average and the variance of heterozygosity, another using the relationship between the average heterozygosity and the average number of substitutions and Watterson's homozygosity test are applied to the consequences of the present model. It is found that deviation from the neutral expectation becomes apparent only when 4N sigma is more than two. Also a simple approximation for the model is developed which works well when the mutation rate is very small.     

Large number of replacement polymorphisms in rapidly evolving genes of Drosophila. Implications for genome-wide surveys of DNA polymorphism

We present a survey of nucleotide polymorphism of three novel, rapidly evolving genes in populations of Drosophila melanogaster and D. simulans. Levels of silent polymorphism are comparable to other loci, but the number of replacement polymorphisms is higher than that in most other genes surveyed in D. melanogaster and D. simulans. Tests of neutrality fail to reject neutral evolution with one exception. This concerns a gene located in a region of high recombination rate in D. simulans and in a region of low recombination rate in D. melanogaster, due to an inversion. In the latter case it shows a very low number of polymorphisms, presumably due to selective sweeps in the region. Patterns of nucleotide polymorphism suggest that most substitutions are neutral or nearly neutral and that weak (positive and purifying) selection plays a significant role in the evolution of these genes. At all three loci, purifying selection of slightly deleterious replacement mutations appears to be more efficient in D. simulans than in D. melanogaster, presumably due to different effective population sizes. Our analysis suggests that current knowledge about genome-wide patterns of nucleotide polymorphism is far from complete with respect to the types and range of nucleotide substitutions and that further analysis of differences between local populations will be required to understand the forces more completely. We note that rapidly diverging and nearly neutrally evolving genes cannot be expected only in the genome of Drosophila, but are likely to occur in large numbers also in other organisms and that their function and evolution are little understood so far.     

Theoretical Study of near Neutrality. II. Effect of Subdivided Population Structure with Local Extinction and Recolonization

There are several unsolved problems concerning the model of nearly neutral mutations. One is the interaction of subdivided population structure and weak selection that spatially fluctuates. The model of nearly neutral mutations whose selection coefficient spatially fluctuates has been studied by adopting the island model with periodic extinction-recolonization. Both the number of colonies and the migration rate play significant roles in determining mutants' behavior, and selection is ineffective when the extinction-recolonization is frequent with low migration rate. In summary, the number of mutant substitutions decreases and the polymorphism increases by increasing the total population size, and/or decreasing the extinction-recolonization rate. However, by increasing the total size of the population, the mutant substitution rate does not become as low when compared with that in panmictic populations, because of the extinction-recolonization, especially when the migration rate is limited. It is also found that the model satisfactorily explains the contrasting patterns of molecular polymorphisms observed in sibling species of Drosophila, including heterozygosity, proportion of polymorphism and fixation index.     

Weak selection and protein evolution

The "nearly neutral" theory of molecular evolution proposes that many features of genomes arise from the interaction of three weak evolutionary forces: mutation, genetic drift, and natural selection acting at its limit of efficacy. Such forces generally have little impact on allele frequencies within populations from generation to generation but can have substantial effects on long-term evolution. The evolutionary dynamics of weakly selected mutations are highly sensitive to population size, and near neutrality was initially proposed as an adjustment to the neutral theory to account for general patterns in available protein and DNA variation data. Here, we review the motivation for the nearly neutral theory, discuss the structure of the model and its predictions, and evaluate current empirical support for interactions among weak evolutionary forces in protein evolution. Near neutrality may be a prevalent mode of evolution across a range of functional categories of mutations and taxa. However, multiple evolutionary mechanisms (including adaptive evolution, linked selection, changes in fitness-effect distributions, and weak selection) can often explain the same patterns of genome variation. Strong parameter sensitivity remains a limitation of the nearly neutral model, and we discuss concave fitness functions as a plausible underlying basis for weak selection.     

The effects of Hill-Robertson interference between weakly selected mutations on patterns of molecular evolution and variation

Associations between selected alleles and the genetic backgrounds on which they are found can reduce the efficacy of selection. We consider the extent to which such interference, known as the Hill-Robertson effect, acting between weakly selected alleles, can restrict molecular adaptation and affect patterns of polymorphism and divergence. In particular, we focus on synonymous-site mutations, considering the fate of novel variants in a two-locus model and the equilibrium effects of interference with multiple loci and reversible mutation. We find that weak selection Hill-Robertson (wsHR) interference can considerably reduce adaptation, e.g., codon bias, and, to a lesser extent, levels of polymorphism, particularly in regions of low recombination. Interference causes the frequency distribution of segregating sites to resemble that expected from more weakly selected mutations and also generates specific patterns of linkage disequilibrium. While the selection coefficients involved are small, the fitness consequences of wsHR interference across the genome can be considerable. We suggest that wsHR interference is an important force in the evolution of nonrecombining genomes and may explain the unexpected constancy of codon bias across species of very different census population sizes, as well as several unusual features of codon usage in Drosophila.     

Correlated evolutionary divergence of egg size and a mitochondrial protein across the Isthmus of Panama

An explicit assumption of studies that employ a mitochondrial DNA (mtDNA) molecular clock is that mtDNA evolves independently of morphology. Here we report a very strong correlation between egg size divergence and cytochrome c oxidase-1 (CO1) amino acid sequence divergence among sister species of bivalve molluscs separated by the Central American Isthmus (i.e., "geminate" species). Analyses of the molecular data reveal that CO1 sequences likely did not diverge as a function of time or evolve in response to positive natural selection. Given that an excess of CO1 amino acid polymorphism exists within species (as expected if most mutations are only slightly deleterious), a third hypothesis is that reductions in effective population size could simultaneously increase the fixation rate of nearly neutral mtDNA polymorphisms and in some way also facilitate egg size evolution. The remarkable strength of the relationship between egg size and CO1 amino acid sequence demonstrates that, even in the absence of an obvious functional relationship or clock-like evolution, the amounts of molecular and morphological change can be tightly correlated, and therefore may reflect common processes. Accordingly, the assumption that the evolutionary divergence of molecules and morphology are independent must always be carefully examined.     

Patterns of inbreeding depression and architecture of the load in subdivided populations

Inbreeding depression is a general phenomenon that is due mainly to recessive deleterious mutations, the so-called mutation load. It has been much studied theoretically. However, until very recently, population structure has not been taken into account, even though it can be an important factor in the evolution of populations. Population subdivision modifies the dynamics of deleterious mutations because the outcome of selection depends on processes both within populations (selection and drift) and between populations (migration). Here, we present a general model that permits us to gain insight into patterns of inbreeding depression, heterosis, and the load in subdivided populations. We show that they can be interpreted with reference to single-population theory, using an appropriate local effective population size that integrates the effects of drift, selection, and migration. We term this the "effective population size of selection" (NS(e)). For the infinite island model, for example, it is equal to NS(e) = N1 + m/hs, where N is the local population size, m the migration rate, and h and s the dominance and selection coefficients of deleterious mutation. Our results have implications for the estimation and interpretation of inbreeding depression in subdivided populations, especially regarding conservation issues. We also discuss the possible effects of migration and subdivision on the evolution of mating systems.     

Scan of human genome reveals no new Loci under ancient balancing selection

There has been much speculation as to what role balancing selection has played in evolution. In an attempt to identify regions, such as HLA, at which polymorphism has been maintained in the human population for millions of years, we scanned the human genome for regions of high SNP density. We found 16 regions that, outside of HLA and ABO, are the most highly polymorphic regions yet described; however, evidence for balancing selection at these sites is notably lacking--indeed, whole-genome simulations indicate that our findings are expected under neutrality. We propose that (i) because it is rarely stable, long-term balancing selection is an evolutionary oddity, and (ii) when a balanced polymorphism is ancient in origin, the requirements for detection by means of SNP data alone will rarely be met.     

Impact of mating systems on patterns of sequence polymorphism in flowering plants

A fundamental challenge in population genetics and molecular evolution is to understand the forces shaping the patterns of genetic diversity within and among species. Among them, mating systems are thought to have important influences on molecular diversity and genome evolution. Selfing is expected to reduce effective population size, Ne, and effective recombination rates, directly leading to reduced polymorphism and increased linkage disequilibrium compared with outcrossing. Increased isolation between populations also results directly from selfing or indirectly from evolutionary changes, such as small flowers and low pollen output, leading to greater differentiation of molecular markers than under outcrossing. The lower effective recombination rate increases the likelihood of hitch-hiking, further reducing within-deme diversity of selfers and thus increasing their genetic differentiation. There are also indirect effects on molecular evolutionary processes. Low Ne reduces the efficacy of selection; in selfers, selection should thus be less efficient in removing deleterious mutations. The rarity of heterozygous sites in selfers leads to infrequent action of biased conversion towards GC, which tends to increase sequences' GC content in the most highly recombining genome regions of outcrossers. To test these predictions in plants, we used a newly developed sequence polymorphism database to investigate the effects of mating system differences on sequence polymorphism and genome evolution in a wide set of plant species. We also took into account other life-history traits, including life form (whether annual or perennial herbs, and woody perennial) and the modes of pollination and seed dispersal, which are known to affect enzyme and DNA marker polymorphism. We show that among various life-history traits, mating systems have the greatest influence on patterns of polymorphism.     

Contrasting patterns of nonneutral evolution in proteins encoded in nuclear and mitochondrial genomes

We report that patterns of nonneutral DNA sequence evolution among published nuclear and mitochondrially encoded protein-coding loci differ significantly in animals. Whereas an apparent excess of amino acid polymorphism is seen in most (25/31) mitochondrial genes, this pattern is seen in fewer than half (15/36) of the nuclear data sets. This differentiation is even greater among data sets with significant departures from neutrality (14/15 vs. 1/6). Using forward simulations, we examined patterns of nonneutral evolution using parameters chosen to mimic the differences between mitochondrial and nuclear genetics (we varied recombination rate, population size, mutation rate, selective dominance, and intensity of germ line bottleneck). Patterns of evolution were correlated only with effective population size and strength of selection, and no single genetic factor explains the empirical contrast in patterns. We further report that in Arabidopsis thaliana, a highly self-fertilizing plant with effectively low recombination, five of six published nuclear data sets also exhibit an excess of amino acid polymorphism. We suggest that the contrast between nuclear and mitochondrial nonneutrality in animals stems from differences in rates of recombination in conjunction with a distribution of selective effects. If the majority of mutations segregating in populations are deleterious, high linkage may hinder the spread of the occasional beneficial mutation.     

Revisiting the false positive rate in detecting recent positive selection

There is increasing interest in studying the molecular mechanisms of recent adaptations caused by positive selection in the genomics era. Such endeavors to detect recent positive selection, however, have been severely handicapped by false positives due to the confounding impact of demography and the population structure. To reduce false positives, it is critical to conduct a functional analysis to identify the true candidate genes/mutations from those that are filtered through neutrality tests. However, the extremely high cost of such functional analysis may restrict studies within a small number of model species. In particular, when the false positive rate of neutrality tests is high, the efficiency of the functional analysis will also be very low. Therefore, although the recent improvements have been made in the (joint) inference of demography and selection, our ultimate goal, which is to understand the mechanism of adaptation generally in a wide variety of natural populations, may not be achieved using the currently available approaches. More attention should thus be spent on the development of more reliable tests that could not only free themselves from the confounding impact of demography and the population structure but also have reasonable power to detect selection.