The effect of demographic population factors and individual biological parameters on the rate of the neutral molecular evolution

The dependence of the rate of neutral molecular evolution on both biological parameters and demographic population factors has been investigated. Real genetic data and an individual-based model of the population dynamics were used for the study. The first part of the study deals with tracing the neutral molecular evolution occurring in the model concurrently with adaptive speciation. The second part concerns the effect of individual biological parameters and demographic population factors of members of the Order Testudines (Turtles) on the relative rate of evolution of the mitochondrial CytB gene. It has been shown that demographic population factors and individual biological parameters affect the rate of the neutral molecular evolution.     

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.     

Evolutionary Consequences of DNA Mismatch Inhibited Repair Opportunity

Double strand breaks (DSBs) are often repaired via homologous recombination. Recombinational repair processes are expected to be influenced by nucleotide heterozygosity through mismatch detection systems. Unrepaired DSBs have severe biological consequences and are often lethal. We show that natural selection due to inhibition of recombinational repair associated with polymorphisms could influence their molecular evolution. The main conclusions from this analysis are that, for increasing population size, mismatch detection leads to a limit on average heterozygosity of otherwise selectively neutral polymorphism, an excess of rare variants, and a slowing down of the rate of neutral molecular evolution. The first two results suggest that mismatch detection may account for the surprisingly narrow range of observed average heterozygosities, given the great variation in population size between species.     

Molecular Clock of Neutral Mutations in a Fitness-Increasing Evolutionary Process

The molecular clock of neutral mutations, which represents linear mutation fixation over generations, is theoretically explained by genetic drift in fitness-steady evolution or hitchhiking in adaptive evolution. The present study is the first experimental demonstration for the molecular clock of neutral mutations in a fitness-increasing evolutionary process. The dynamics of genome mutation fixation in the thermal adaptive evolution of Escherichia coli were evaluated in a prolonged evolution experiment in duplicated lineages. The cells from the continuously fitness-increasing evolutionary process were subjected to genome sequencing and analyzed at both the population and single-colony levels. Although the dynamics of genome mutation fixation were complicated by the combination of the stochastic appearance of adaptive mutations and clonal interference, the mutation fixation in the population was simply linear over generations. Each genome in the population accumulated 1.6 synonymous and 3.1 non-synonymous neutral mutations, on average, by the spontaneous mutation accumulation rate, while only a single genome in the population occasionally acquired an adaptive mutation. The neutral mutations that preexisted on the single genome hitchhiked on the domination of the adaptive mutation. The successive fixation processes of the 128 mutations demonstrated that hitchhiking and not genetic drift were responsible for the coincidence of the spontaneous mutation accumulation rate in the genome with the fixation rate of neutral mutations in the population. The molecular clock of neutral mutations to the fitness-increasing evolution suggests that the numerous neutral mutations observed in molecular phylogenetic trees may not always have been fixed in fitness-steady evolution but in adaptive evolution.     

Second-order moments of segregating sites under variable population size

The identification of genomic regions that have been exposed to positive selection is a major challenge in population genetics. Since selective sweeps are expected to occur during environmental changes or when populations are colonizing a new habitat, statistical tests constructed on the assumption of constant population size are biased by the co-occurrence of population size changes and selection. To delimit this problem and gain better insights into demographic factors, theoretical results regarding the second-order moments of segregating sites, such as the variance of segregating sites, have been derived. Driven by emerging genomewide surveys, which allow the estimation of demographic parameters, a generalized version of Tajima's D has been derived that takes into account a previously estimated demographic scenario to test single loci for traces of selection against the null hypothesis of neutral evolution under variable population size.     

Transition between stochastic evolution and deterministic evolution in the presence of selection: general theory and application to virology.

We present here a self-contained analytic review of the role of stochastic factors acting on a virus population. We develop a simple one-locus, two-allele model of a haploid population of constant size including the factors of random drift, purifying selection, and random mutation. We consider different virological experiments: accumulation and reversion of deleterious mutations, competition between mutant and wild-type viruses, gene fixation, mutation frequencies at the steady state, divergence of two populations split from one population, and genetic turnover within a single population. In the first part of the review, we present all principal results in qualitative terms and illustrate them with examples obtained by computer simulation. In the second part, we derive the results formally from a diffusion equation of the Wright-Fisher type and boundary conditions, all derived from the first principles for the virus population model. We show that the leading factors and observable behavior of evolution differ significantly in three broad intervals of population size, N. The "neutral limit" is reached when N is smaller than the inverse selection coefficient. When N is larger than the inverse mutation rate per base, selection dominates and evolution is "almost" deterministic. If the selection coefficient is much larger than the mutation rate, there exists a broad interval of population sizes, in which weakly diverse populations are almost neutral while highly diverse populations are controlled by selection pressure. We discuss in detail the application of our results to human immunodeficiency virus population in vivo, sampling effects, and limitations of the model.     

Transition between Stochastic Evolution and Deterministic Evolution in the Presence of Selection: General Theory and Application to Virology

We present here a self-contained analytic review of the role of stochastic factors acting on a virus population. We develop a simple one-locus, two-allele model of a haploid population of constant size including the factors of random drift, purifying selection, and random mutation. We consider different virological experiments: accumulation and reversion of deleterious mutations, competition between mutant and wild-type viruses, gene fixation, mutation frequencies at the steady state, divergence of two populations split from one population, and genetic turnover within a single population. In the first part of the review, we present all principal results in qualitative terms and illustrate them with examples obtained by computer simulation. In the second part, we derive the results formally from a diffusion equation of the Wright-Fisher type and boundary conditions, all derived from the first principles for the virus population model. We show that the leading factors and observable behavior of evolution differ significantly in three broad intervals of population size, N. The “neutral limit” is reached when N is smaller than the inverse selection coefficient. When N is larger than the inverse mutation rate per base, selection dominates and evolution is “almost” deterministic. If the selection coefficient is much larger than the mutation rate, there exists a broad interval of population sizes, in which weakly diverse populations are almost neutral while highly diverse populations are controlled by selection pressure. We discuss in detail the application of our results to human immunodeficiency virus population in vivo, sampling effects, and limitations of the model.     

Introduction: Choice of spouse and mobility

Marriage comprises both individual lives and population evolution. Anthropology shows that marriage, within cultural rules, is based on parameters of different natures such as psychology or economy with implications that concern also the genetic level. The creation of a general model of marriage is quite complex as it must include factors that change in time and space between and inside societies. The marriage as a factor of social mobility is of great interest, but it can not be limited to this factor alone, because the union between two individuals and two families is also the necessary preamble to biological reproduction and population genetic pool evolution.     

A population biological approach to the collective dynamics of countries undergoing demographic transition

Birth rates have been declining in higher-income countries since the middle of the 19th century. A growing number of other countries have entered this demographic transition to lower fertility, as socioeconomic development continues. Analyses of this demographic transition vary widely, but most analyze individual populations in isolation from others, and most come from fields outside the biological sciences. Here, we develop a population biological model of population dynamics in higher-income countries. Individual countries evolve through density-regulated growth, where gradual evolution toward higher population densities boosts productivity (and hence socioeconomic growth) through economics of agglomeration and scale, in turn reducing birth rates. The exchange of technology and capital between countries can further boost productivity gains in any given country, thus contributing to its demographic transition. As a result, countries can down-regulate one another's population growth through mutual improvements in productivity. The model is fitted to time series data on population size, GDP per capita, and birth rates for the United States, the United Kingdom, and France. The metapopulation dynamics are also characterized across a range of parameter values close to the fitted values. This work may help advance population biological approaches to understanding the implications of the fertility demographic transition for modern human populations. This is relevant to developing long-term predictions of the earth's total population size, which must be based upon a model that incorporates underlying mechanisms.     

Statistical properties of neutral evolution

Neutral evolution is the simplest model of molecular evolution and thus it is most amenable to a comprehensive theoretical investigation. In this paper, we characterize the statistical properties of neutral evolution of proteins under the requirement that the native state remains thermodynamically stable, and compare them to the ones of Kimura's model of neutral evolution. Our study is based on the Structurally Constrained Neutral (SCN) model which we recently proposed. We show that, in the SCN model, the substitution rate decreases as longer time intervals are considered. Fluctuations from one branch of the evolutionary tree to another are strong, leading to a non-Poissonian statistics for the substitution process. Such strong fluctuations are in part due to the fact that neutral substitution rates for individual residues are strongly correlated for most residue pairs. Interestingly, structurally conserved residues, characterized by a much below average substitution rate, are also much less correlated to other residues and evolve in a much more regular way. Our results can improve methods aimed at distinguishing between neutral and adaptive substitutions as well as methods for computing the expected number of substitutions occurred since the divergence of two protein sequences. In particular, we compute the minimal sequence similarity below which no information about the evolutionary divergence of the compared sequences can be obtained.     

Analysis of population structure in autotetraploid species.

Population structure parameters commonly used for diploid species are reexamined for the particular case of tetrasomic inheritance (autotetraploid species). Recurrence equations that describe the evolution of identity probabilities for neutral genes in an "island model" of population structure are derived assuming tetrasomic inheritance. The expected equilibrium value of FST is computed. In contrast to diploids, the correlation of genes between individuals within populations with respect to genes between populations (FST) may vary among loci due to the particular segregation patterns expected under tetrasomic inheritance and is consequently inappropriate for estimating demographic parameters in such populations. We thus define a new parameter (rho) and derive its relationship with Nm. This relationship is shown to be independent from both the selfing rate and the proportion of double reduction. Finally, the statistical procedure required to evaluate these parameters using data on gene frequencies distribution among autotetraploid populations is developed.     

An exact steady state solution of Fisher's geometric model and other models

Because nearly neutral substitutions are thought to contribute substantially to molecular evolution, and much of our insight about the workings of nearly neutral evolution relies on theory, solvable models of this process are of particular interest. Here, I present an analytical method for solving models of nearly neutral evolution at steady state. The steady state solution applies to any constant fitness landscape under a dynamic of successive fixations, each of which occurs on the background of the population's most recent common ancestor. Because this dynamic neglects the effects of polymorphism in the population beyond the mutant allele under consideration, the steady state solution provides a decent approximation of evolutionary dynamics when the population mutation rate is low (Nu<1). To demonstrate the method, I apply it to two examples: Fisher's geometric model (FGM), and a simple model of molecular evolution. Since recent papers have studied the steady state behavior of FGM under this dynamic, I analyze its behavior in detail and compare the results with previous work.     

The mode of evolution of molecular markers in populations of house mice under artificial selection for locomotor behavior

A complete understanding of the mode of evolution of molecular markers is important for making inferences about different population genetic parameters, especially because a number of studies have reported patterns of allelic variation at molecular markers that are not in agreement with neutral evolutionary expectations. In the present study, house mice (Mus domesticus) from the fourteenth generation of a selection experiment for increased voluntary wheel-running activity were used to test how selection on a complex behavior affects the distribution of allelic variation by examining patterns of variation at six microsatellite and four allozyme loci. This population had a hierarchical structure that allowed for simultaneous testing of the effects of selection and genetic drift on the distribution of allelic variation by comparing observed patterns of allele frequencies and estimates of genetic divergence at multiple hierarchical levels to expectations under models of neutral evolution. The levels of genetic divergence among replicate lines and between selection groups, estimated from microsatellite data or pooled microsatellite and allozyme data, were not significantly different from expectations under neutral evolution. Furthermore, the pattern of change of allele frequencies between the base population and generation 14 was largely in agreement with expectations under neutral evolution (although the PGM locus exhibited a pattern of change within populations that was difficult to explain under neutral evolution). Overall the results generally provide support for the neutral evolution of molecular markers.     

Why do species vary in their rate of molecular evolution?

Despite hopes that the processes of molecular evolution would be simple, clock-like and essentially universal, variation in the rate of molecular evolution is manifest at all levels of biological organization. Furthermore, it has become clear that rate variation has a systematic component: rate of molecular evolution can vary consistently with species body size, population dynamics, lifestyle and location. This suggests that the rate of molecular evolution should be considered part of life-history variation between species, which must be taken into account when interpreting DNA sequence differences between lineages. Uncovering the causes and correlates of rate variation may allow the development of new biologically motivated models of molecular evolution that may improve bioinformatic and phylogenetic analyses.     

FIXATION OF SLIGHTLY BENEFICIAL MUTATIONS: EFFECTS OF LIFE HISTORY

Recent studies of rates of evolution have revealed large systematic differences among organisms with different life histories, both within and among taxa. Here, we consider how life history may affect the rate of evolution via its influence on the fixation probability of slightly beneficial mutations. Our approach is based on diffusion modeling for a finite, stage‐structured population with stochastic population dynamics. The results, which are verified by computer simulations, demonstrate that even with complex population structure just two demographic parameters are sufficient to give an accurate approximation of the fixation probability of a slightly beneficial mutation. These are the reproductive value of the stage in which the mutation first occurs and the demographic variance of the population. The demographic variance also determines what influence population size has on the fixation probability. This model represents a substantial generalization of earlier models, covering a large range of life histories.     

Formulating a Historical and Demographic Model of Recent Human Evolution Based on Resequencing Data from Noncoding Regions

Background

Estimating the historical and demographic parameters that characterize modern human populations is a fundamental part of reconstructing the recent history of our species. In addition, the development of a model of human evolution that can best explain neutral genetic diversity is required to identify confidently regions of the human genome that have been targeted by natural selection.

Methodology/Principal Findings

We have resequenced 20 independent noncoding autosomal regions dispersed throughout the genome in 213 individuals from different continental populations, corresponding to a total of ∼6 Mb of diploid resequencing data. We used these data to explore and co-estimate an extensive range of historical and demographic parameters with a statistical framework that combines the evaluation of multiple models of human evolution via a best-fit approach, followed by an Approximate Bayesian Computation (ABC) analysis. From a methodological standpoint, evaluating the accuracy of the parameter co-estimation allowed us to identify the most accurate set of statistics to be used for the estimation of each of the different historical and demographic parameters characterizing recent human evolution.

Conclusions/Significance

Our results support a model in which modern humans left Africa through a single major dispersal event occurring ∼60,000 years ago, corresponding to a drastic reduction of ∼5 times the effective population size of the ancestral African population of ∼13,800 individuals. Subsequently, the ancestors of modern Europeans and East Asians diverged much later, ∼22,500 years ago, from the population of ancestral migrants. This late diversification of Eurasians after the African exodus points to the occurrence of a long maturation phase in which the ancestral Eurasian population was not yet diversified.     

Mathematical modeling of evolution of horizontally transferred genes

We describe a stochastic birth-and-death model of evolution of horizontally transferred genes in microbial populations. The model is a generalization of the stochastic model described by Berg and Kurland and includes five parameters: the rate of mutational inactivation, selection coefficient, invasion rate (i.e., rate of arrival of a novel sequence from outside of the recipient population), within-population horizontal transmission ("infection") rate, and population size. The model of Berg and Kurland included four parameters, namely, mutational inactivation, selection coefficient, population size, and "infection." However, the effect of "infection" was disregarded in the interpretation of the results, and the overall conclusion was that horizontally acquired sequences can be fixed in a population only when they confer a substantial selective advantage onto the recipient and therefore are subject to strong positive selection. Analysis of the present model in different domains of parameter values shows that, as long as the rate of within-population horizontal transmission is comparable to the mutational inactivation rate and there is even a low rate of invasion, horizontally acquired sequences can be fixed in the population or at least persist for a long time in a substantial fraction of individuals in the population even when they are neutral or slightly deleterious. The available biological data strongly suggest that intense within-population and even between-populations gene flows are realistic for at least some prokaryotic species and environments. Therefore, our modeling results are compatible with the notion of a pivotal role of horizontal gene transfer in the evolution of prokaryotes.     

Effects of Mitochondrial DNA Rate Variation on Reconstruction of Pleistocene Demographic History in a Social Avian Species,Pomatostomus superciliosus

Mitochondrial sequence data is often used to reconstruct the demographic history of Pleistocene populations in an effort to understand how species have responded to past climate change events. However, departures from neutral equilibrium conditions can confound evolutionary inference in species with structured populations or those that have experienced periods of population expansion or decline. Selection can affect patterns of mitochondrial DNA variation and variable mutation rates among mitochondrial genes can compromise inferences drawn from single markers. We investigated the contribution of these factors to patterns of mitochondrial variation and estimates of time to most recent common ancestor (T_MRCA) for two clades in a co-operatively breeding avian species, the white-browed babbler Pomatostomus superciliosus. Both the protein-coding ND3 gene and hypervariable domain I control region sequences showed departures from neutral expectations within the superciliosus clade, and a two-fold difference in T_MRCA estimates. Bayesian phylogenetic analysis provided evidence of departure from a strict clock model of molecular evolution in domain I, leading to an over-estimation of T_MRCA for the superciliosus clade at this marker. Our results suggest mitochondrial studies that attempt to reconstruct Pleistocene demographic histories should rigorously evaluate data for departures from neutral equilibrium expectations, including variation in evolutionary rates across multiple markers. Failure to do so can lead to serious errors in the estimation of evolutionary parameters and subsequent demographic inferences concerning the role of climate as a driver of evolutionary change. These effects may be especially pronounced in species with complex social structures occupying heterogeneous environments. We propose that environmentally driven differences in social structure may explain observed differences in evolutionary rate of domain I sequences, resulting from longer than expected retention times for matriarchal lineages in the superciliosus clade.     

Extinction in relation to demographic and environmental stochasticity in age-structured models

The demographic variance of an age-structured population is defined. This parameter is further split into components generated by demographic stochasticity in each vital rate. The applicability of these parameters are investigated by checking how an age-structured population process can be approximated by a diffusion with only three parameters. These are the deterministic growth rate computed from the expected projection matrix and the environmental and demographic variances. We also consider age-structured populations where the fecundity at any stage is either zero or one, and there is neither environmental stochasticity nor dependence between individual fecundity and survival. In this case the demographic variance is uniquely determined by the vital rates defining the projection matrix. The demographic variance for a long-lived bird species, the wandering albatross in the southwestern part of the Indian Ocean, is estimated. We also compute estimates of the age-specific contributions to the total demographic variance from survival, fecundity and the covariance between survival and fecundity.     

Effects of metabolic rate on protein evolution

Since the modern evolutionary synthesis was first proposed early in the twentieth century, attention has focused on assessing the relative contribution of mutation versus natural selection on protein evolution. Here we test a model that yields general quantitative predictions on rates of protein evolution by combining principles of individual energetics with Kimura's neutral theory. The model successfully predicts much of the heterogeneity in rates of protein evolution for diverse eukaryotes (i.e. fishes, amphibians, reptiles, birds, mammals) from different thermal environments. Data also show that the ratio of non-synonymous to synonymous nucleotide substitution is independent of body size, and thus presumably of effective population size. These findings indicate that rates of protein evolution are largely controlled by mutation rates, which in turn are strongly influenced by individual metabolic rate.