Mitochondrial mismatch analysis is insensitive to the mutational process

Mismatch distributions are histograms showing the pattern of nucleotide (or restriction) site differences between pairs of individuals in a sample. They can be used to test hypotheses about the history of population size and subdivision (if selective neutrality is assumed) or about selection (if a constant population size is assumed). Previous work has assumed that mutations never strike the same site twice, an assumption that is called the model of infinite sites. Fortunately, the results are surprisingly robust even when this assumption is violated. We show here that (1) confidence regions inferred using the infinite- sites model differ little from those inferred using a model of finite sites with uniform site-specific mutation rates, and (2) even when site- specific mutation rates follow a gamma distribution, confidence regions are little changed until the gamma shape parameter falls well below its plausible range, to roughly 0.01. In addition, we evaluate and reject the proposition that mismatch waves are produced by pooling data from several subdivisions of a structured population.      

Mathematische Modelle in der Populationsgenetik

In mathematical population genetics, the influence of selection and mutation on the evolution of a population is modelled. Because all populations and particularly the samples used for their analysis are finite, the stochastic nature of these models plays an important role. Relevant genetic models include the Wright–Fisher model and the coalescence model for the genealogy of samples, as well as the infinite alleles model and the infinite sites model for the mutation processes superimposed upon these genealogies.     

Sequence-Dependent Gene Conversion: Can Duplicated Genes Diverge Fast Enough to Escape Conversion?

Conversion between duplicated genes limits their independent evolution. Models in which conversion frequencies decrease as genes diverge are examined to determine conditions under which genes can "escape" further conversion and hence escape from a gene family. A review of results from various recombination systems suggests two classes of sequence-dependence models: (1) the "k-hit" model in which conversion is completely inactivated by a few (k) mutational events, such as the insertion of a mobile element, and (2) more general models where conversion frequency gradually declines as genes diverge through the accumulation of point mutants. Exact analysis of the k-hit model is given and an approximate analysis of a more general sequence-dependent model is developed and verified by computer simulation. If mu is the per nucleotide mutation rate, then neutral duplicated genes diverging through point mutants are likely to escape conversion provided 2 mu/lambda much greater than 0.1, where lambda is the conversion rate between identical genes. If 2 mu/lambda much less than 0.1, the expected number of conversions before escape increases exponentially so that, for biological purposes, the genes never escape conversion. For single mutational events sufficient to block further conversions, occurring at rate nu per copy per generation, many conversions are expected if 2 nu/lambda much less than 1, while the genes essentially evolve independently if 2 nu/lambda much greater than 1. Implications of these results for both models of concerted evolution and the evolution of new gene functions via gene duplication are discussed.     

EVOLUTION AND EXTINCTION IN A CHANGING ENVIRONMENT: A QUANTITATIVE-GENETIC ANALYSIS

Because of the ubiquity of genetic variation for quantitative traits, virtually all populations have some capacity to respond evolutionarily to selective challenges. However, natural selection imposes demographic costs on a population, and if these costs are sufficiently large, the likelihood of extinction will be high. We consider how the mean time to extinction depends on selective pressures (rate and stochasticity of environmental change, and strength of selection), population parameters (carrying capacity, and reproductive capacity), and genetics (rate of polygenic mutation). We assume that in a randomly mating, finite population subject to density-dependent population growth, individual fitness is determined by a single quantitative-genetic character under Gaussian stabilizing selection with the optimum phenotype exhibiting directional change, or random fluctuations, or both. The quantitative trait is determined by a finite number of freely recombining, mutationally equivalent, additive loci. The dynamics of evolution and extinction are investigated, assuming that the population is initially under mutation-selection-drift balance. Under this model, in a directionally changing environment, the mean phenotype lags behind the optimum, but on the average evolves parallel to it. The magnitude of the lag determines the vulnerability to extinction. In finite populations, stochastic variation in the genetic variance can be quite pronounced, and bottlenecks in the genetic variance temporarily can impair the population's adaptive capacity enough to cause extinction when it would otherwise be unlikely in an effectively infinite population. We find that maximum sustainable rates of evolution or, equivalently, critical rates of environmental change, may be considerably less than 10% of a phenotypic standard deviation per generation.     

The island model with stochastic migration

The island model with stochastically variable migration rate and immigrant gene frequency is investigated. It is supposed that the migration rate and the immigrant gene frequency are independent of each other in each generation, and each of them is independently and identically distributed in every generation. The treatment is confined to a single diallelic locus without mutation. If the diploid population is infinite, selection is absent and the immigrant gene frequency is fixed, then the gene frequency on the island converges to the immigrant frequency, and the logarithm of the absolute value of its deviation from it is asymptotically normally distributed. Assuming only neutrality, the evolution of the exact mean and variance of the gene frequency are derived for an island with finite population. Selection is included in the diffusion approximation: if all evolutionary forces have comparable roles, the gene frequency will be normally distributed at all times. All results in the paper are completely explicit.     

Computer simulation of different types of evolutionary process

The computer model of two alternative variants of biological evolution is proposed. The first variant supposes random while the second--directed change of individual features, thus corresponding to the Darwinian and non-Darwinian evolution. The evolution of fish communities in fresh waters serves as a particular example. The model is executed using object-oriented method of programming and mathematical apparatus of fuzzy logics. The investigation of the model showed that process of Darwinian evolution is connected with significantly greater species diversity and variability of evolutionary process trajectories than non-Darwinian one. On the other hand, non-Darwinian type of evolution provides fast achievement of high individual fitness, especially under conditions of constant environment. Non-Darwinian type evolution failed in big evolutionary alteration (for example, transition to predation); while the Darwinian evolution under the same conditions can produce such alterations though it took more time and many extinct species. Phylogenetic tree of Darwinian evolution is always more complex than of non-Darwinian one under the same conditions.     

Molecular Evolution in a Multisite Nearly Neutral Mutation Model

A simple nearly neutral mutation model of protein evolution was studied using computer simulation assuming a constant population size. In this model, a gene consists of a finite number of codons and there is no recombination within a gene. Each codon has two replacement and one silent sites. The fitness of a gene was determined multiplicatively by amino acids specified by codons (the independent multicodon model). Nucleotide diversity at replacement sites decreases as selection becomes stronger. A reduction of nucleotide diversity at silent sites also occurs as selection intensifies but the magnitude of the reduction is not a monotone function of the intensity of selection. The dispersion index is close to one. The average value of Tajima's and Fu and Li's statistics are negative and their absolute values increases as selection intensifies. However, their powers of detecting selection under the present model were not high unless the number of sites is large or mutation rate is high. The MK test was shown to detect intermediate selection fairly well. For comparison, the house-of-cards model was also investigated and its behavior was shown to be more sensitive to changes of population size than that of the independent multicodon model. The relevance of the present model for explaining protein evolution was discussed comparing its prediction and recent DNA data. Received: 24 May 1999 / Accepted: 17 August 1999     

Models of nearly neutral mutations with particular implications for nonrandom usage of synonymous codons

Summary The population dynamics of nearly neutral mutations are studied using a single-site and a multisite model. In the latter model, the nucleotides in a sequence are completely linked and the selection schemes employed are additive, multiplicative, and additive with a threshold. Although the third selection scheme is very different from the first two, the three schemes produce identical results for a wide range of parameter values. Thus the present study provides a general theory for the population dynamics of nearly neutral mutations because the results can also be used to draw inferences about other selection schemes such as stabilizing selection and synergistic selection. It is shown that the number of slightly deleterious mutations accumulated in a sequence can be considerably larger under the multisite model than under the single-site model, particularly if the sequence is long or if the mutation rate per site is high. The results show that even a very slight selective difference between synonymous codons can produce a strong bias in codon usage. Three alternative explanations for the strong bias in codon usage in bacterial and yeast genes are considered. The implications of the present results for molecular evolution are discussed.     

The Amount of DNA Polymorphism Maintained in a Finite Population When the Neutral Mutation Rate Varies among Sites

The expectations of the average number of nucleotide differences per site (π), the proportion of segregating site (s), the minimum number of mutations per site (s*) and some other quantities were derived under the finite site models with and without rate variation among sites, where the finite site models include Jukes and Cantor's model, the equal-input model and Kimura's model. As a model of rate variation, the gamma distribution was used. The results indicate that if distribution parameter α is small, the effect of rate variation on these quantities are substantial, so that the estimates of θ based on the infinite site model are substantially underestimated, where θ = 4Nv, N is the effective population size and v is the mutation rate per site per generation. New methods for estimating θ are also presented, which are based on the finite site models with and without rate variation. Using these methods, underestimation can be corrected.     

Pairwise Comparisons of Mitochondrial DNA Sequences in Stable and Exponentially Growing Populations

We consider the distribution of pairwise sequence differences of mitochondrial DNA or of other nonrecombining portions of the genome in a population that has been of constant size and in a population that has been growing in size exponentially for a long time. We show that, in a population of constant size, the sample distribution of pairwise differences will typically deviate substantially from the geometric distribution expected, because the history of coalescent events in a single sample of genes imposes a substantial correlation on pairwise differences. Consequently, a goodness-of-fit test of observed pairwise differences to the geometric distribution, which assumes that each pairwise comparison is independent, is not a valid test of the hypothesis that the genes were sampled from a panmictic population of constant size. In an exponentially growing population in which the product of the current population size and the growth rate is substantially larger than one, our analytical and simulation results show that most coalescent events occur relatively early and in a restricted range of times. Hence, the "gene tree" will be nearly a "star phylogeny" and the distribution of pairwise differences will be nearly a Poisson distribution. In that case, it is possible to estimate r, the population growth rate, if the mutation rate, mu, and current population size, N0, are assumed known. The estimate of r is the solution to ri/mu = ln(N0r) - gamma, where i is the average pairwise difference and gamma approximately 0.577 is Euler's constant.     

The evolution of stress-induced hypermutation in asexual populations

Numerous empirical studies show that stress of various kinds induces a state of hypermutation in bacteria via multiple mechanisms, but theoretical treatment of this intriguing phenomenon is lacking. We used deterministic and stochastic models to study the evolution of stress-induced hypermutation in infinite and finite-size populations of bacteria undergoing selection, mutation, and random genetic drift in constant environments and in changing ones. Our results suggest that if beneficial mutations occur, even rarely, then stress-induced hypermutation is advantageous for bacteria at both the individual and the population levels and that it is likely to evolve in populations of bacteria in a wide range of conditions because it is favored by selection. These results imply that mutations are not, as the current view holds, uniformly distributed in populations, but rather that mutations are more common in stressed individuals and populations. Because mutation is the raw material of evolution, these results have a profound impact on broad aspects of evolution and biology.     

The effect of selection on esterase allozymes in a barley population

Changes in gene and genotypic frequencies at four esterase loci were monitored over 25 generations in Composite Cross V, an experimental population of barley, to obtain experimental evidence concerning the balance of forces responsible for: (1) the marked differences in allelic frequencies among barleys from different ecogeographical regions of the world; and (2) the extensive allelic variation found within local populations of barley. Analyses of the highly significant changes in allelic frequencies which occurred in CCV showed they were due to directional selection favoring particular alleles and not to mutation, migration or genetic drift. The results show that intense balancing selection, featuring consistent excesses of heterozygotes, also occurred in CCV. It is concluded that among the factors of neo-Darwinian evolution, natural selection plays the predominant role in determining the observed patterns of allelic variation in the barley species as a whole.     

拉马克的归来—对达尔文主义的再审视

适应性突变（adaptive mutation）和表观遗传学（epigenetics）的新进展为拉马克主张的＂获得性遗传＂提供了越来越多的证据,暗示它在生物进化中所起的作用可能远比我们之前想象的要大的多。这虽然与新达尔文主义相左,但却在一定程度上符合经典达尔文主义：作为＂自然选择＂的重要补充,＂获得性遗传＂至少应视作一个辅助的机制而纳入＂达尔文框架＂中。这种建立在多元论基础上的进化观正是达尔文留给后人最重要的遗产。     

Natural selection and the evolution of neutralism

The efficiency of evolutionary search increases as the density of acceptable proteins in a protein space increases. Populations caught in regions whose density is too low to support evolution can be pulled into high density regions by hitchhiking selection. As they move into such regions, the action of natural selection becomes more effective, yet these populations will satisfy conditions which lead to predictions made by neutral, so-called non-Darwinian models.     

A population genetical model for sequence evolution under multiple types of mutation

DNA sequencing and restriction mapping provide us with information on DNA sequence evolution within populations, from which the phylogenetic relationships among the sequences can be inferred. Mutations such as base substitutions, deletions, insertions and transposable element insertions can be identified in each sequence. Theoretical study of this type of sequence evolution has been initiated recently. In this paper, population genetical models for sequence evolution under multiple types of mutation are developed. Models of infinite population size with neutral mutation, infinite population size with deleterious mutation and finite population size with neutral mutation are considered.     

The evolution of bet-hedging adaptations to rare scenarios

When faced with a variable environment, organisms may switch between different strategies according to some probabilistic rule. In an infinite population, evolution is expected to favor the rule that maximizes geometric mean fitness. If some environments are encountered only rarely, selection may not be strong enough for optimal switching probabilities to evolve. Here we calculate the evolution of switching probabilities in a finite population by analyzing fixation probabilities of alleles specifying switching rules. We calculate the conditions required for the evolution of phenotypic switching as a form of bet-hedging as a function of the population size N, the rate theta at which a rare environment is encountered, and the selective advantage s associated with switching in the rare environment. We consider a simplified model in which environmental switching and phenotypic switching are one-way processes, and mutation is symmetric and rare with respect to the timescale of fixation events. In this case, the approximate requirements for bet-hedging to be favored by a ratio of at least R are that sN>log(R) and thetaN>square root R .     

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.     

ANTIBODY SELECTION AND AMINO ACID REVERSIONS

Pathogens adapt to antibody surveillance through amino acid replacements in targeted protein regions, or epitopes, that interfere with antibody binding. However, such escape mutations may exact a fitness cost due to impaired protein function. Here, it is hypothesized that the recurring generation of specific neutralizing antibodies to an epitope region as it evolves in response to antibody selection will cause amino acid reversions by releasing early escape mutations from immune selection. The plausibility of this hypothesis was tested with stochastic simulation of adaptation at the molecular sequence level in finite populations. Under the conditions of strong selection and weak mutation, the rates of allele fixation and amino acid reversion increased with population size and selection coefficients. These rates decreased with population size, however, if mutation became strong, because clonal interference reduced the rate of adaptation. The model successfully predicts the rate of reversion per allele fixation for an important human immunodeficiency virus type 1 (HIV‐1) antibody epitope region. Therefore, antibody selection may generate complex adaptive dynamics.     

Selection for mutational robustness in finite populations

We investigate the evolutionary dynamics of a finite population of RNA sequences replicating on a neutral network. Despite the lack of differential fitness between viable sequences, we observe typical properties of adaptive evolution, such as increase of mean fitness over time and punctuated-equilibrium transitions, after initial mutation-selection balance has been reached. We find that a product of population size and mutation rate of approximately 30 or larger is sufficient to generate selection pressure for mutational robustness, even if the population size is orders of magnitude smaller than the neutral network on which the population resides. Our results show that quasispecies effects and neutral drift can occur concurrently, and that the relative importance of each is determined by the product of population size and mutation rate.     

Near-periodic substitution and the genetic variance induced by environmental change

We investigate a model that describes the evolution of a diploid sexual population in a changing environment. Individuals have discrete generations and are subject to selection on the phenotypic value of a quantitative trait, which is controlled by a finite number of bialleic loci. Environmental change is taken to lead to a uniformly changing optimal phenotypic value. The population continually adapts to the changing environment, by allelic substitution, at the loci controlling the trait. We investigate the detailed interrelation between the process of allelic substitution and the adaptation and variation of the population, via infinite population calculations and finite population simulations. We find a simple relation between the substitution rate and the rate of change of the optimal phenotypic value.