Estimation of effective population size of HIV-1 within a host: a pseudomaximum-likelihood approach

Using pseudomaximum-likelihood approaches to phylogenetic inference and coalescent theory, we develop a computationally tractable method of estimating effective population size from serially sampled viral data. We show that the variance of the maximum-likelihood estimator of effective population size depends on the serial sampling design only because internal node times on a coalescent genealogy can be better estimated with some designs than with others. Given the internal node times and the number of sequences sampled, the variance of the maximum-likelihood estimator is independent of the serial sampling design. We then estimate the effective size of the HIV-1 population within nine hosts. If we assume that the mutation rate is 2.5 x 10(-5) substitutions/generation and is the same in all patients, estimated generation lengths vary from 0.73 to 2.43 days/generation and the mean (1.47) is similar to the generation lengths estimated by other researchers. If we assume that generation length is 1.47 days and is the same in all patients, mutation rate estimates vary from 1.52 x 10(-5) to 5.02 x 10(-5). Our results indicate that effective viral population size and evolutionary rate per year are negatively correlated among HIV-1 patients.     

The mutation rates of di-, tri- and tetranucleotide repeats in Drosophila melanogaster

In a recent study, we reported that the combined average mutation rate of 10 di-, 6 tri-, and 8 tetranucleotide repeats in Drosophila melanogaster was 6.3 x 10(-6) mutations per locus per generation, a rate substantially below that of microsatellite repeat units in mammals studied to date (range = 10(-2)-10(-5) per locus per generation). To obtain a more precise estimate of mutation rate for dinucleotide repeat motifs alone, we assayed 39 new dinucleotide repeat microsatellite loci in the mutation accumulation lines from our earlier study. Our estimate of mutation rate for a total of 49 dinucleotide repeats is 9.3 x 10(-6) per locus per generation, only slightly higher than the estimate from our earlier study. We also estimated the relative difference in microsatellite mutation rate among di-, tri-, and tetranucleotide repeats in the genome of D. melanogaster using a method based on population variation, and we found that tri- and tetranucleotide repeats mutate at rates 6.4 and 8.4 times slower than that of dinucleotide repeats, respectively. The slower mutation rates of tri- and tetranucleotide repeats appear to be associated with a relatively short repeat unit length of these repeat motifs in the genome of D. melanogaster. A positive correlation between repeat unit length and allelic variation suggests that mutation rate increases as the repeat unit lengths of microsatellites increase.      

A robust measure of HIV-1 population turnover within chronically infected individuals

A simple nonparameteric test for population structure was applied to temporally spaced samples of HIV-1 sequences from the gag-pol region within two chronically infected individuals. The results show that temporal structure can be detected for samples separated by about 22 months or more. The performance of the method, which was originally proposed to detect geographic structure, was tested for temporally spaced samples using neutral coalescent simulations. Simulations showed that the method is robust to variation in samples sizes and mutation rates, to the presence/absence of recombination, and that the power to detect temporal structure is high. By comparing levels of temporal structure in simulations to the levels observed in real data, we estimate the effective intra-individual population size of HIV-1 to be between 10(3) and 10(4) viruses, which is in agreement with some previous estimates. Using this estimate and a simple measure of sequence diversity, we estimate an effective neutral mutation rate of about 5 x 10(-6) per site per generation in the gag-pol region. The definition and interpretation of estimates of such "effective" population parameters are discussed.     

Population Genetics of Polymorphism and Divergence

Frequencies of mutant sites are modeled as a Poisson random field in two species that share a sufficiently recent common ancestor. The selective effect of the new alleles can be favorable, neutral, or detrimental. The model is applied to the sample configurations of nucleotides in the alcohol dehydrogenase gene (Adh) in Drosophila simulans and Drosophila yakuba. Assuming a synonymous mutation rate of 1.5 x 10(-8) per site per year and 10 generations per year, we obtain estimates for the effective population size (N(e) = 6.5 x 10(6)), the species divergence time (tdiv = 3.74 million years), and an average selection coefficient (sigma = 1.53 x 10(-6) per generation for advantageous or mildly detrimental replacements), although it is conceivable that only two of the amino acid replacements were selected and the rest neutral. The analysis, which includes a sampling theory for the independent infinite sites model with selection, also suggests the estimate that the number of amino acids in the enzyme that are susceptible to favorable mutation is in the range 2-23 at any one time. The approach provides a theoretical basis for the use of a 2 x 2 contingency table to compare fixed differences and polymorphic sites with silent sites and amino acid replacements.     

Estimation of the Amount of DNA Polymorphism When the Neutral Mutation Rate Varies among Sites

Knowing the amount of DNA polymorphism is essential to understand the mechanism of maintaining DNA polymorphism in a natural population. The amount of DNA polymorphism can be measured by the average number of nucleotide differences per site (π), the proportion of segregating (polymorphic) site (s) and the minimum number of mutations per site (s*). Since the latter two quantities depend on the sample size, θ is often used as a measure of the amount of DNA polymorphism, where θ = 4Nμ, N is the effective population size and μ is the neutral mutation rate per site per generation. It is known that θ estimated from π, s and s* under the infinite site model can be biased when the mutation rate varies among sites. We have therefore developed new methods for estimating θ under the finite site model. Using computer simulations, it has been shown that the new methods give almost unbiased estimates even when the mutation rate varies among sites substantially. Furthermore, we have also developed new statistics for testing neutrality by modifying Tajima's D statistic. Computer simulations suggest that the new test statistics can be used even when the mutation rate varies among sites.     

Estimating a nucleotide substitution rate for maize from polymorphism at a major domestication locus

To estimate a rate for single nucleotide substitutions for maize (Zea mays ssp. mays), we have taken advantage of data from genetic and archaeological studies of the domestication of maize from its wild ancestor, teosinte (Z. mays ssp. parviglumis). Genetic studies have shown that the teosinte branched1 (tb1) gene was a major target of human selection during maize domestication, and sequence diversity in the intergenic region 5' to the tb1-coding sequence is extraordinarily low. We show that polymorphism in this region is consistent with new mutation following fixation for a small number of tb1 haplotypes during domestication. Archeological studies suggest that maize was domesticated approximately 6,250-10,000 years ago and subsequently the size of the maize population is thought to have expanded rapidly. Using the observed number of mutations within the region of selection at tb1, the approximate age of maize domestication, and approximations for the maize genealogy, we have derived estimates for the nucleotide substitution rate for the tb1 intergenic region. Using two approaches, one of which is a coalescent approach, we obtain rate estimates of approximately 2.9 x 10(-8) and 3.3 x 10(-8) substitutions per site per year. We also show that the pattern of polymorphism in the tb1 intergenic region appears to have been strongly affected by the mutagenic effect of DNA methylation. Excluding target sites of symmetric DNA methylation (CG and CNG sites) from analysis, the mutation rate estimates are reduced by approximately 50%-60%, while the rates for CG and CNG sites are nearly an order of magnitude higher. We use rate estimates from the tb1 region to estimate the timing of expansion of transposable elements in the maize genome and suggest that this expansion occurred primarily within the last million years.     

Stochastic Simulations Suggest that HIV-1 Survives Close to Its Error Threshold

The use of mutagenic drugs to drive HIV-1 past its error threshold presents a novel intervention strategy, as suggested by the quasispecies theory, that may be less susceptible to failure via viral mutation-induced emergence of drug resistance than current strategies. The error threshold of HIV-1, , however, is not known. Application of the quasispecies theory to determine poses significant challenges: Whereas the quasispecies theory considers the asexual reproduction of an infinitely large population of haploid individuals, HIV-1 is diploid, undergoes recombination, and is estimated to have a small effective population size in vivo. We performed population genetics-based stochastic simulations of the within-host evolution of HIV-1 and estimated the structure of the HIV-1 quasispecies and . We found that with small mutation rates, the quasispecies was dominated by genomes with few mutations. Upon increasing the mutation rate, a sharp error catastrophe occurred where the quasispecies became delocalized in sequence space. Using parameter values that quantitatively captured data of viral diversification in HIV-1 patients, we estimated to be substitutions/site/replication, ∼2–6 fold higher than the natural mutation rate of HIV-1, suggesting that HIV-1 survives close to its error threshold and may be readily susceptible to mutagenic drugs. The latter estimate was weakly dependent on the within-host effective population size of HIV-1. With large population sizes and in the absence of recombination, our simulations converged to the quasispecies theory, bridging the gap between quasispecies theory and population genetics-based approaches to describing HIV-1 evolution. Further, increased with the recombination rate, rendering HIV-1 less susceptible to error catastrophe, thus elucidating an added benefit of recombination to HIV-1. Our estimate of may serve as a quantitative guideline for the use of mutagenic drugs against HIV-1.     

Direct estimation of the mitochondrial DNA mutation rate in Drosophila melanogaster

Mitochondrial DNA (mtDNA) variants are widely used in evolutionary genetics as markers for population history and to estimate divergence times among taxa. Inferences of species history are generally based on phylogenetic comparisons, which assume that molecular evolution is clock-like. Between-species comparisons have also been used to estimate the mutation rate, using sites that are thought to evolve neutrally. We directly estimated the mtDNA mutation rate by scanning the mitochondrial genome of Drosophila melanogaster lines that had undergone approximately 200 generations of spontaneous mutation accumulation (MA). We detected a total of 28 point mutations and eight insertion-deletion (indel) mutations, yielding an estimate for the single-nucleotide mutation rate of 6.2 × 10⁻⁸ per site per fly generation. Most mutations were heteroplasmic within a line, and their frequency distribution suggests that the effective number of mitochondrial genomes transmitted per female per generation is about 30. We observed repeated occurrences of some indel mutations, suggesting that indel mutational hotspots are common. Among the point mutations, there is a large excess of G→A mutations on the major strand (the sense strand for the majority of mitochondrial genes). These mutations tend to occur at nonsynonymous sites of protein-coding genes, and they are expected to be deleterious, so do not become fixed between species. The overall mtDNA mutation rate per base pair per fly generation in Drosophila is estimated to be about 10× higher than the nuclear mutation rate, but the mitochondrial major strand G→A mutation rate is about 70× higher than the nuclear rate. Silent sites are substantially more strongly biased towards A and T than nonsynonymous sites, consistent with the extreme mutation bias towards A+T. Strand-asymmetric mutation bias, coupled with selection to maintain specific nonsynonymous bases, therefore provides an explanation for the extreme base composition of the mitochondrial genome of Drosophila.     

Factors Influencing Ascertainment Bias of Microsatellite Allele Sizes: Impact on Estimates of Mutation Rates

Microsatellite loci play an important role as markers for identification, disease gene mapping, and evolutionary studies. Mutation rate, which is of fundamental importance, can be obtained from interspecies comparisons, which, however, are subject to ascertainment bias. This bias arises, for example, when a locus is selected on the basis of its large allele size in one species (cognate species 1), in which it is first discovered. This bias is reflected in average allele length in any noncognate species 2 being smaller than that in species 1. This phenomenon was observed in various pairs of species, including comparisons of allele sizes in human and chimpanzee. Various mechanisms were proposed to explain observed differences in mean allele lengths between two species. Here, we examine the framework of a single-step asymmetric and unrestricted stepwise mutation model with genetic drift. Analysis is based on coalescent theory. Analytical results are confirmed by simulations using the simuPOP software. The mechanism of ascertainment bias in this model is a tighter correlation of allele sizes within a cognate species 1 than of allele sizes in two different species 1 and 2. We present computations of the expected average allele size difference, given the mutation rate, population sizes of species 1 and 2, time of separation of species 1 and 2, and the age of the allele. We show that when the past demographic histories of the cognate and noncognate taxa are different, the rate and directionality of mutations affect the allele sizes in the two taxa differently from the simple effect of ascertainment bias. This effect may exaggerate or reverse the effect of difference in mutation rates. We reanalyze literature data, which indicate that despite the bias, the microsatellite mutation rate estimate in the ancestral population is consistently greater than that in either human or chimpanzee and the mutation rate estimate in human exceeds or equals that in chimpanzee with the rate of allele length expansion in human being greater than that in chimpanzee. We also demonstrate that population bottlenecks and expansions in the recent human history have little impact on our conclusions.     

The low evolutionary rate of human T-cell lymphotropic virus type-1 confirmed by analysis of vertical transmission chains

The evolutionary rate of the human T-cell lymphotropic virus type-1 (HTLV-1) is considered to be very low, in strong contrast to the related human retrovirus HIV. However, current estimates of the HTLV-1 rate rely on the anthropological calibration of phylogenies using assumed dates of human migration events. To obtain an independent rate estimate, we analyzed two variable regions of the HTLV-1 genome (LTR and env) from eight infected families. Remarkable genetic stability was observed, as only two mutations in LTR (756 bp) and three mutations in env (522 bp) occurred within the 16 vertical transmission chains, including one ambiguous position in each region. The evolutionary rate in HTLV-1 was then calculated using a maximum-likelihood approach that used the highest and lowest possible times of HTLV-1 shared ancestry, given the known transmission histories. The rates for the LTR and env regions were 9.58 x 10(-8)-1.25 x 10(-5) and 7.84 x 10(-7) -2.33 x 10(-5)nucleotide substitutions per site per year, respectively. A more precise estimate was obtained for the combined LTR-env data set, which was 7.06 x 10(-7)-1.38 x 10(-5)substitutions per site per year. We also note an interesting correlation between the occurrence of mutations in HTLV-1 and the age of the individual infected.     

A Coalescent Estimator of the Population Recombination Rate

Population genetic models often use a population recombination parameter 4Nc, where N is the effective population size and c is the recombination rate per generation. In many ways 4Nc is comparable to 4Nu, the population mutation rate. Both combine genome level and population level processes, and together they describe the rate of production of genetic variation in a population. However, 4Nc is more difficult to estimate. For a population sample of DNA sequences, historical recombination can only be detected if polymorphisms exist, and even then most recombination events are not detectable. This paper describes an estimator of 4Nc, hereafter designated γ (gamma), that was developed using a coalescent model for a sample of four DNA sequences with recombination. The reliability of γ was assessed using multiple coalescent simulations. In general γ has low to moderate bias, and the reliability of γ is comparable, though less, than that for a widely used estimator of 4Nu. If there exists an independent estimate of the recombination rate (per generation, per base pair), γ can be used to estimate the effective population size or the neutral mutation rate.     

Direct estimate of the spontaneous germ line mutation rate in African green monkeys

Here, I provide the first direct estimate of the spontaneous mutation rate in an Old World monkey, using a seven individual, three‐generation pedigree of African green monkeys. Eight de novo mutations were identified within ～1.5 Gbp of accessible genome, corresponding to an estimated point mutation rate of 0.94 × 10^?8 per site per generation, suggesting an effective population size of ～12000 for the species. This estimation represents a significant improvement in our knowledge of the population genetics of the African green monkey, one of the most important nonhuman primate models in biomedical research. Furthermore, by comparing mutation rates in Old World monkeys with the only other direct estimates in primates to date–humans and chimpanzees–it is possible to uniquely address how mutation rates have evolved over longer time scales. While the estimated spontaneous mutation rate for African green monkeys is slightly lower than the rate of 1.2 × 10^?8 per base pair per generation reported in chimpanzees, it is similar to the lower range of rates of 0.96 × 10^?8–1.28 × 10^?8 per base pair per generation recently estimated from whole genome pedigrees in humans. This result suggests a long‐term constraint on mutation rate that is quite different from similar evidence pertaining to recombination rate evolution in primates.     

Telomere dynamics in HIV-1 infected and uninfected chimpanzees measured by an improved method based on high-resolution two-dimensional calibration of DNA sizes

We developed an improved method for accurately measuring telomere lengths based on two-dimensional calibration of DNA sizes combined with pulsed field electrophoresis and quantitative analysis of high-resolution gel images. This method was used to quantify the length of telomeres in longitudinal samples of peripheral blood mononuclear cells (PBMCs) from five chimpanzees infected with human immunodeficiency virus type 1 (HIV-1) and three uninfected animals, 14 to 27 years of age. The average length of the telomere restriction fragments (TRF) of infected and uninfected chimpanzees were 11.7 ± 0.25 kbp, and 11.6 ± 0.61 kbp, respectively, and were about 1 kbp and 3 kbp longer than those of human infants and 30 year old adults, respectively. There was a trend of a slight decrease (30–60 bp per year) in the TRF of two HIV infected chimpanzees over 30–35 months, while the TRF of one naive chimpanzee slightly increased over 20 months. Although the number of chimpanzees in this study is small and no statistically significant linear dependencies on time were observed, it appears that in chimpanzees, rates of shortening of the TRF are comparable or smaller than in adult humans and are not significantly affected by HIV-1 infection, which may be related to the inability of HIV-1 to cause disease in these animals.     

Molecular Characterization of Ambiguous Mutations in HIV-1 Polymerase Gene: Implications for Monitoring HIV Infection Status and Drug Resistance

Detection of recent HIV infections is a prerequisite for reliable estimations of transmitted HIV drug resistance (t-HIVDR) and incidence. However, accurately identifying recent HIV infection is challenging due partially to the limitations of current serological tests. Ambiguous nucleotides are newly emerged mutations in quasispecies, and accumulate by time of viral infection. We utilized ambiguous mutations to establish a measurement for detecting recent HIV infection and monitoring early HIVDR development. Ambiguous nucleotides were extracted from HIV-1 pol-gene sequences in the datasets of recent (HIVDR threshold surveys [HIVDR-TS] in 7 countries; n=416) and established infections (1 HIVDR monitoring survey at baseline; n=271). An ambiguous mutation index of 2.04×10^-3 nts/site was detected in HIV-1 recent infections which is equivalent to the HIV-1 substitution rate (2×10^-3 nts/site/year) reported before. However, significantly higher index (14.41×10^-3 nts/site) was revealed with established infections. Using this substitution rate, 75.2% subjects in HIVDR-TS with the exception of the Vietnam dataset and 3.3% those in HIVDR-baseline were classified as recent infection within one year. We also calculated mutation scores at amino acid level at HIVDR sites based on ambiguous or fitted mutations. The overall mutation scores caused by ambiguous mutations increased (0.54×10^-23.48×10^-2/DR-site) whereas those caused by fitted mutations remained stable (7.50-7.89×10^-2/DR-site) in both recent and established infections, indicating that t-HIVDR exists in drug-naïve populations regardless of infection status in which new HIVDR continues to emerge. Our findings suggest that characterization of ambiguous mutations in HIV may serve as an additional tool to differentiate recent from established infections and to monitor HIVDR emergence.     

Extremely rapid spread of human immunodeficiency virus type 1 BF recombinants in Argentina

The epidemic of human immunodeficiency virus type 1 (HIV-1) in Argentina is distinctive in that many infections are caused by subtype BF recombinant viruses. To determine their demographic history, we estimated the evolutionary rate, mode of population growth, and age of genetic diversity among 40 BF vpu sequences. This revealed one of the highest substitution rates reported for HIV-1, at 10.793 x 10(-3) substitutions per site per year, and a very rapid rate of population growth, with an initial mean epidemic doubling time of 3.72 months. This rapid population growth is compatible with an elevated fitness for subtype BF compared to that for "pure" B and F viruses.     

High mutation rates in the mitochondrial genomes of Daphnia pulex

Despite the great utility of mitochondrial DNA (mtDNA) sequence data in population genetics and phylogenetics, key parameters describing the process of mitochondrial mutation (e.g., the rate and spectrum of mutational change) are based on few direct estimates. Furthermore, the variation in the mtDNA mutation process within species or between lineages with contrasting reproductive strategies remains poorly understood. In this study, we directly estimate the mtDNA mutation rate and spectrum using Daphnia pulex mutation-accumulation (MA) lines derived from sexual (cyclically parthenogenetic) and asexual (obligately parthenogenetic) lineages. The nearly complete mitochondrial genome sequences of 82 sexual and 47 asexual MA lines reveal high mtDNA mutation rate of 1.37 × 10(-7) and 1.73 × 10(-7) per nucleotide per generation, respectively. The Daphnia mtDNA mutation rate is among the highest in eukaryotes, and its spectrum is dominated by insertions and deletions (70%), largely due to the presence of mutational hotspots at homopolymeric nucleotide stretches. Maximum likelihood estimates of the Daphnia mitochondrial effective population size reveal that between five and ten copies of mitochondrial genomes are transmitted per female per generation. Comparison between sexual and asexual lineages reveals no statistically different mutation rates and highly similar mutation spectra.     

Estimating density dependence from population time series using demographic theory and life-history data

For populations with a density-dependent life history reproducing at discrete annual intervals, we analyze small or moderate fluctuations in population size around a stable equilibrium, which is applicable to many vertebrate populations. Using a life history having age at maturity alpha, with stochasticity and density dependence in adult recruitment and mortality, we derive a linearized autoregressive equation with time lags from 1 to alpha yr. Contrary to current interpretations, the coefficients corresponding to different time lags in the autoregressive dynamics are not simply measures of delayed density dependence but also depend on life-history parameters. The theory indicates that the total density dependence in a life history, D, should be defined as the negative elasticity of population growth rate per generation with respect to change in population size, [Formula: see text], where lambda is the asymptotic multiplicative growth rate per year, T is the generation time, and N is adult population size. The total density dependence in the life history, D, can be estimated from the sum of the autoregression coefficients. We estimate D in populations of seven vertebrate species for which life-history studies and unusually long time series of complete population censuses are available. Estimates of D were statistically significant and large, on the order of 1 or higher, indicating strong density dependence in five of the seven species. We also show that life history can explain the qualitative features of population autocorrelation functions and power spectra and observations of increasing empirical variance in population size with increasing length of time series.     

Mutation accumulation and the effect of copia insertions in Drosophila melanogaster

Repeated efforts to estimate the genomic deleterious mutation rate per generation (U) in Drosophila melanogaster have yielded inconsistent estimates ranging from 0.01 to nearly 1. We carried out a mutation-accumulation experiment with a cryopreserved control population in hopes of resolving some of the uncertainties raised by these estimates. Mutation accumulation (MA) was carried out by brother sister mating of 150 sublines derived from two inbred lines. Fitness was measured under conditions chosen to mimic the ancestral laboratory environment of these genotypes. We monitored the insertions of a transposable element, copia, that proved to accumulate at the unusually high rate of 0.24 per genome per generation in one of our MA lines. Mutational variance in fitness increased at a rate consistent with previous studies, yielding a mutational coefficient of variation greater than 3%. The performance of the cryopreserved control relative to the MA lines was inconsistent, so estimates of mutation rate by the Bateman-Mukai method are suspect. Taken at face value, these data suggest a modest decline in fitness of about 0.3% per generation. The element number of copia was a significant predictor of fitness within generations; on average, insertions caused a 0.76% loss in fitness, although the confidence limits on this estimate are wide.     

Estimate of the mutation rate per nucleotide in humans

Many previous estimates of the mutation rate in humans have relied on screens of visible mutants. We investigated the rate and pattern of mutations at the nucleotide level by comparing pseudogenes in humans and chimpanzees to (i) provide an estimate of the average mutation rate per nucleotide, (ii) assess heterogeneity of mutation rate at different sites and for different types of mutations, (iii) test the hypothesis that the X chromosome has a lower mutation rate than autosomes, and (iv) estimate the deleterious mutation rate. Eighteen processed pseudogenes were sequenced, including 12 on autosomes and 6 on the X chromosome. The average mutation rate was estimated to be approximately 2.5 x 10(-8) mutations per nucleotide site or 175 mutations per diploid genome per generation. Rates of mutation for both transitions and transversions at CpG dinucleotides are one order of magnitude higher than mutation rates at other sites. Single nucleotide substitutions are 10 times more frequent than length mutations. Comparison of rates of evolution for X-linked and autosomal pseudogenes suggests that the male mutation rate is 4 times the female mutation rate, but provides no evidence for a reduction in mutation rate that is specific to the X chromosome. Using conservative calculations of the proportion of the genome subject to purifying selection, we estimate that the genomic deleterious mutation rate (U) is at least 3. This high rate is difficult to reconcile with multiplicative fitness effects of individual mutations and suggests that synergistic epistasis among harmful mutations may be common.