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International audience; Understanding the evolutionary history of species is at the core of molecular evolution and is done using several inference methods. The critical issue is to quantify the uncertainty of the inference. The posterior probabilities in Bayesian phylogenetic inference and the bootstrap values in frequentist approaches measure the variability of the estimates due to the sampling of sites from genes and the sampling of genes from genomes. However, they do not measure the uncertainty due to taxon sampling. Taxa that experienced molecular homoplasy, recent selection, a spur of evolution, and so forth may disrupt the inference and cause incongruences in the estimated phylogeny. We define a taxon influence index to assess the influence of each taxon on the phylogeny. We found that although most taxa have a weak influence on the phylogeny, a small fraction of influential taxa strongly alter it even in clades only loosely related to them. We conclude that highly influential taxa should be given special attention and sampling them more thoroughly can lead to more dependable phylogenies.

The cellular energy produced by mitochondria is a fundamental currency of life. However, the extent to which mitochondrial (mt) performance (power and endurance) is adapted to habitats and life strategies of vertebrates is not well understood. A global analysis of mt genomes revealed that hydrophobicity (HYD) of mt membrane proteins (MMPs) is much lower in terrestrial vertebrates than in fishes and shows a strong negative correlation with serine/threonine composition (STC). Here, we present evidence that this systematic feature of MMPs was crucial for the evolution of large terrestrial vertebrates with high aerobic capacity. An Arrhenius-type equation gave positive correlations between STC and maximum life span (MLS) in terrestrial vertebrates (with a few exceptions relating to the lifestyle of small animals with a high resting metabolic rate [RMR]) and negative correlations in secondary marine vertebrates, such as cetaceans and alligators (which returned from land to water, utilizing buoyancy with increased body size). In particular, marked STC increases in primates (especially hominoids) among placentals were associated with very high MLS values. We connected these STC increases in MMPs with greater stability of respiratory complexes by estimating the degradation of the Arrhenius plot given by accelerating mtRMR up to mt maximum metabolic rate. Both mtRMR and HYD in terrestrial vertebrates decreased with increasing body mass. Decreases in mtRMR raise MMP stability when high mobility is not required, whereas decreased HYD may weaken this stability under the hydrophobic environment of lipid bilayer. High maximal metabolic rates (5-10 RMR), which we postulate require high MMP mobility, presumably render MMPs more unstable. A marked rise in STC may therefore be essential to stabilize MMPs, perhaps as dynamic supercomplexes, via hydrogen bonds associated with serine/threonine motifs.

This study deals with the problem of a change-point alternative in the estimation of fishing and natural mortality rates from tag recoveries. We consider some models of mortality rates, and estimate parameters by a maximum likelihood procedure. Taking the overdispersion of the recovery data into account, we employ the likelihood function of a normal approximation of Dirichlet compound multinomial distribution. In a case study of red sea bream Pagrus major in the Seto Inland Sea, we could not detect the change-point of the natural mortality rate. It was suggested that fluctuation in the recovery data substantially influenced the estimation of the changepoint mortality rates.

This paper considers the partial likelihood procedure for estimating fishing and natural mortality rates from tag recoveries. We consider the likelihood function of the multinomial model, and two models of mortality rates with a change-point against constant mortality are introduced. Explicit estimators of fishing mortality rates are derived. The asymptotic variances of total mortality rates and fishing mortality rates are also obtained explicitly, though a simple numerical solution is needed for estimating the total mortality rates. The procedure was applied to recovery data of red seabream Pagrus major in the Seto Inland Sea. The partial likelihood worked in the same way as the full one and was effective. It took about only four minutes to obtain estimates using partial likelihood, but it took about eight hours from the approach of full likelihood. Partial likelihood is powerful for analysis under the multinomial model.

In this study we evaluated the effectiveness of fish stock enhancement programs using a twostage random sampling survey of commercial landings. Estimators for the total number of fish landed, the ratio of the number of fish released to the total number of fish landed, the recovery rate, and the amount of income were formulated. Variance formulas for these estimators were derived. The tagging rate was also considered for these estimators. In a case study of the flounder fisheries off Fukushima Prefecture, we obtained a conservative estimate of 36, 982 recoveries from 246, 300 hatchery-reared fish over three years after release. The ratio of the recovery rate to the number of fish released was 0.15. The total income and benefit estimate were 32.6 and 7.9 million yen, respectively. We found that the stock enhacement program was economically profitable.

To evaluate the difference in quality of hatchery-reared fingerlings released into the same field at the same time, we propose simultaneous estimation of mortality rates taking the correlation between two series of recovery data into account. We consider the joint likelihood function as an extension of the bivariate normal distribution. For a test of mortality rates of two groups released, the likelihood ratio test is used. As an example, we applied this procedure to the case of red seabream Pagrus major in the Seto Inland Sea. We obtained maximum likelihood estimates for four models. The correlation coefficient was estimated to be over 0.9, and two models which assumed no correlation were rejected. For the two models of the correlation, the likelihood ratio test could not reject the hypothesis of no difference in the two groups. We also found that the X2 test of recovery rates under a contingency table is invalid for the overdispersion and correlation of recovery data.

Statistical models for the evolution of molecular sequences play an important role in the study of evolutionary processes. For the evolutionary analysis of protein-coding sequences, 3 types of evolutionary models are available: 1) nucleotide, 2) amino acid, and 3) codon substitution models. Selecting appropriate models can greatly improve the estimation of phylogenies and divergence times and the detection of positive selection. Although much attention has been paid to the comparisons among the same types of models, relatively little attention has been paid to the comparisons among the different types of models. Additionally, because such models have different data structures, comparison of those models using conventional model selection criteria such as Akaike information criterion (AIC) or Bayesian information criterion (BIC) is not straightforward. Here, we suggest new procedures to convert models of the above-mentioned 3 types to 64-dimensional models with nucleotide triplet substitution. These conversion procedures render it possible to statistically compare the models of these 3 types by using AIC or BIC. By analyzing divergent and conserved interspecific mammalian sequences and intraspecific human population data, we show the superiority of the codon substitution models and discuss the advantages and disadvantages of the models of the 3 types.

In this study, we evaluated the effectiveness of fish stock enhancement programs using a two-stage random sampling survey of commercial landings. Estimators for the total number of fish landed, the ratio of the number of fish released to the total number of fish landed, the recovery rate, and the amount of income were formulated. Variance formulas for these estimators were also derived. In a case study of the flounder fishery, we obtained the conservative estimate of 36 982 recoveries from 246 300 hatchery-reared fish over 3 yr after release. The ratio of the recovery rate to the number of fish released was 0.15. The total income and benefit estimate were $260 000 and $63 000 (U.S.), respectively. We found that the stock enhancement program was economically profitable. We also studied several sampling strategies. We recommend that as many markets as possible be surveyed for a minimum number of days because the variation in daily landings among markets was larger than that within markets. Stratification of markets should be conducted for accurate estimation.

The aim of this article is to consider methods for estimating of fishing and natural mortality rates from tag recoveries, where data are taken by research workers and no com-mercial fishing is operated. The log-linear model and the maximum likelihood approach were used for constant and unequal sampling effort models. We analyzed an example of red seabream Pagrus major where the sampling intensity was constant for every survey. By simulation studies, we found that the weighted least square method accompanied by successive approxi-mation using the EM algorithm is practical and gives proper estimates. For a case study where the sampling intensity varies in each survey, we analyzed the recovery data of the flounder Paralichthys olivaceus by the unequal effort model. We also replaced the recovery data by those per unit sampling effort, and estimated by use of the constant effort model. The constant effort model is invalid, and the maximum likelihood approach based on normal approximation should be applied.

Genetic bottlenecks facilitate the fixation and extinction of variants in populations, and viral populations are no exception to this theory. To examine the existence of genetic bottlenecks in cell-to-cell movement of plant RNA viruses, we prepared constructs for Soil-borne wheat mosaic virus RNA2 vectors carrying two different fluorescent proteins, yellow fluorescent protein (YFP) and cyan fluorescent protein (CFP). Coinoculation of host plant leaves with the two RNA2 vectors and the wild-type RNA1 showed separation of the two vector RNA2s, mostly within seven to nine cell-to-cell movements from individual initially coinfected cells. Our statistical analysis showed that the number of viral RNA genomes establishing infection in adjacent cells after the first cell-to-cell movement from an initially infected cell was 5.97 +/- 0.22 on average and 5.02 +/- 0.29 after the second cell-to-cell movement. These results indicate that plant RNA viruses may generally face narrow genetic bottlenecks in every cell-to-cell movement. Furthermore, our model suggests that, rather than suffering from fitness losses caused by the bottlenecks, the plant RNA viruses are utilizing the repeated genetic bottlenecks as an essential element of rapid selection of their adaptive variants in trans-acting genes or elements to respond to host shifting and changes in the growth conditions of the hosts.

We present a methodology for quantifying biodiversity at the sequence level by developing the probability theory on a set of strings. Further, we apply our methodology to the problem of quantifying the population diversity of microorganisms in several extreme environments and digestive organs and reveal the relation between microbial diversity and various environmental parameters.

To get reliable information of the age structure of whale population, Japan conducted a feasibility study of scientific research in the Antarctic in 1987/88. Though the sample was not large enough, it was the first data free from the problem of selectivity and whaling ground bias. From the analysis, it was found that the biological characteristics are highly heterogeneous spatially or other ways. Considering this, we recognize that the survey should be designed to collect the sample from the whole research area uniformly to obtain unbiased estimates of population characteristics. However, in an actual biological field survey, it is difficult to keep the sampling fractions thecisely the same for each sampling units. Therefore, it is important to detect the heterogeneity in the sample, and poststratify the data corresponding to the heterogeneity. The methodology of the estimation and model evaluation presented here will be useful for the development of biological field survey in general.

The amino acid sequences of the largest subunits of the RNA polymerases I, II, and III from eukaryotes were compared with those of archaebacterial and eubacterial homologs, and their evolutionary relationships were analyzed in detail by a recently developed tree-making method, the likelihood method of protein phylogeny, as well as by the neighbor-joining method and the parsimony method, together with bootstrap analyses. It was shown that the best tree topologies predicted by the first two methods are identical, whereas the last one predicts a distinct tree. The maximum likelihood tree revealed that, after the separation from archaebacteria, the three eukaryotic RNA polymerases diverged from an ancestral precursor in the eukaryotic lineage. This result is contrasted with the published result showing multiple origins for the three eukaryotic polymerases. It was shown that eukaryotic RNA polymerase I evolved much more rapidly than RNA polymerases II and III: The N-terminal half of RNA polymerase I shows an extraordinarily high evolutionary rate, possibly due to relaxed functional constraints. In contrast the evolutionary rate of archaebacterial RNA polymerase is remarkably limited. In addition, including the second largest subunit of the RNA polymerase, a detailed analysis for the branching pattern of the three major groups of archaebacteria was carried out by the maximum likelihood method. It was shown that the three major groups of archaebacteria are likely to form a single cluster; that is, archaebacteria are likely to be monophyletic as originally proposed by Woese and his colleagues.

Anopheles dirus and Anopheles baimaii are closely related species which feed on primates, particularly humans, and transmit malaria in the tropical forests of mainland Southeast Asia. Here, we report an in-depth phylogeographic picture based on 269 individuals from 21 populations from mainland Southeast Asia. Analysis of 1537 bp of mtDNA sequence revealed that the population history of A. baimaii is far more complex than previously thought. An old expansion (pre-300 kyr BP) was inferred in northern India/Bangladesh with a wave of south-eastwards expansion arriving at the Thai border (ca 135-173 kyr BP) followed by leptokurtic dispersal very recently (ca 16 kyr BP) into peninsular Thailand. The long and complex population history of these anthropophilic species suggests their expansions are not in response to the relatively recent (ca 40 kyr BP) human expansions in mainland Southeast Asia but, rather, fit well with our understanding of Pleistocene climatic change there.

Codon-and amino acid-substitution models are widely used for the evolutionary analysis of protein-coding DNA sequences. Using codon models, the amounts of both nonsynonymous and synonymous DNA substitutions can be estimated. The ratio of these amounts represents the strength of selective pressure. Using amino acid models, the amount of nonsynonymous substitutions is estimated, but that of synonymous substitutions is ignored. Although amino acid models lose any information regarding synonymous substitutions, they explicitly incorporate the information for amino acid replacement, which is empirically derived from databases. It is often presumed that when the protein-coding sequences are highly divergent, synonymous substitutions might be saturated and the evolutionary analysis may be hampered by synonymous noise. However, there exists no quantitative procedure to verify whether synonymous substitutions can be ignored; therefore, amino acid models have been arbitrarily selected. In this study, we investigate the issue of a statistical comparison between codon-and amino acid-substitution models. For this purpose, we propose a new procedure to transform a 20-dimensional amino acid model to a 61-dimensional codon model. This transformation reveals that amino acid models belong to a subset of the codon models and enables us to test whether synonymous substitutions can be ignored by using the likelihood ratio. Our theoretical results and analyses of real data indicate that synonymous substitutions are very informative and substantially improve evolutionary inference, even when the sequences are highly divergent. Therefore, we note that amino acid models should be adopted only after carefully investigating and discarding the possibility that synonymous substitutions can reveal important evolutionary information.

Background The mitochondrial (mt) gene tree of placental mammals reveals a very strong acceleration of the amino acid (AA) replacement rate and a change in AA compositional bias in the lineage leading to the higher primates (simians), in contrast to the nuclear gene tree. Whether this acceleration and compositional bias were caused by adaptive evolution at the AA level or directional mutation pressure at the DNA level has been vigorously debated. Methodology/Principal Findings Our phylogenetic analysis indicates that the rate acceleration in the simian lineage is accompanied by a marked increase in threonine (Thr) residues in the transmembrane helix regions of mt DNA-encoded proteins. This Thr increase involved the replacement of hydrophobic AAs in the membrane interior. Even after accounting for lack of independence due to phylogeny, a regression analysis reveals a statistical significant positive correlation between Thr composition and longevity in primates. Conclusion/Significance Because crucial roles of Thr and Ser in membrane proteins have been proposed to be the formation of hydrogen bonds enhancing helix-helix interactions, the Thr increase detected in the higher primates might be adaptive by serving to reinforce stability of mt proteins in the inner membrane. The correlation between Thr composition in the membrane interior and the longevity of animals is striking, especially because some mt functions are thought to be involved in aging.

We consider the inference of which of two alleles is ancestral when the alleles have a single nonsynonymous difference and when natural selection acts via protein tertiary structure. Whereas the probability that an allele is ancestral under neutrality is equal to its frequency, under selection this probability depends on allele frequency and on the magnitude and direction of selection pressure. Although allele frequencies can be well estimated from intraspecific data, small fitness differences have a large evolutionary impact but can be difficult to estimate with only intraspecific data. Methods for predicting aspects of phenotype from genotype can supplement intraspecific sequence data. Recently developed statistical techniques can assess effects of phenotypes, such as protein tertiary structure on molecular evolution. While these techniques were initially designed for comparing protein-coding genes from different species, the resulting interspecific inferences can be assigned population genetic interpretations to assess the effect of selection pressure, and we use them here along with intraspecific allele frequency data to estimate the probability that an allele is ancestral. We focus on 140 nonsynonymous single nucleotide polymorphisms of humans that are in proteins with known tertiary structures. We find that our technique for employing protein tertiary structure information yields some biologically plausible results but that it does not substantially improve the inference of ancestral human allele types.

In Taiwan, conserved areas represent more than 20% of the current jurisdiction, which is about twice that of the proportion of protected land worldwide. In this study, we explored the spatial distribution of bird assemblages in Taiwan. By analysing functional and phylogenetic diversity relative to elevational gradient, we assessed the network of bird protected areas. Hotspots of species richness were located at the coastal areas of northern and western Taiwan, although hotspots for protected bird species were located in the mountain areas. We found that phylogenetically close birds have similar trait values, and the protected species were evenly distributed in the functional and phylogenetic trees. The assemblages in higher-elevation areas were more phylogenetically clumped than those in lower-elevation areas, indicating that, in addition to elevational gradient, phylogenetic constraint may be a crucial factor that influences bird distribution in Taiwan. However, the current bird protected areas in Taiwan may overly depend on species richness and overlook the importance of the overall phylogenetic diversity.

A maximum likelihood method for inferring protein phylogeny was developed. It is based on a Markov model that takes into account the unequal transition probabilities among pairs of amino acids and does not assume constancy of rate among different lineages. Therefore, this method is expected to be powerful in inferring phylogeny among distantly related proteins, either orthologous or parallogous, where the evolutionary rate may deviate from constancy. Not only amino acid substitutions but also insertion/deletion events during evolution were incorporated into the Markov model. A simple method for estimating a bootstrap probability for the maximum likelihood tree among alternatives without performing a maximum likelihood estimation for each resampled data set was developed. These methods were applied to amino acid sequence data of a photosynthetic membrane protein,psbA, from photosystem II, and the phylogeny of this protein was discussed in relation to the origin of chloroplasts.

To investigate the evolutionary impact of protein structure, the experimentally determined tertiary structure and the protein-coding DNA sequence were collected for each of 1,195 genes. These genes were studied via a model of sequence change that explicitly incorporates effects on evolutionary rates due to protein tertiary structure. In the model, these effects act via the solvent accessibility environments and pairwise amino acid interactions that are induced by tertiary structure. To compare the hypotheses that structure does and does not have a strong influence on evolution, Bayes factors were estimated for each of the 1,195 sequences. Most of the Bayes factors strongly support the hypothesis that protein structure affects protein evolution. Furthermore, both solvent accessibility and pairwise interactions among amino acids are inferred to have important roles in protein evolution. Our results also indicate that the strength of the relationship between tertiary structure and evolution has a weak but real correlation to the annotation information in the Gene Ontology database. Although their influences on rates of evolution vary among protein families, we find that the mean impacts of solvent accessibility and pairwise interactions are about the same.

A central goal of computational biology is the prediction of phenotype from DNA and protein sequence data. Recent models of sequence change use in silico prediction systems to incorporate the effects of phenotype on evolutionary rates. These models have been designed for analyzing sequence data from different species and have been accompanied by statistical techniques for estimating model parameters when the incorporation of phenotype induces dependent change among sequence positions. A difficulty with these efforts to link phenotype and interspecific evolution is that evolution occurs within populations, and parameters of interspecific models should have population genetic interpretations. We show, with two examples, how population genetic interpretations can be assigned to evolutionary models. The first example considers the impact of RNA secondary structure on sequence change, and the second reflects the tendency for protein tertiary structure to influence nonsynonymous substitution rates. We argue that statistical fit to data should not be the sole criterion for assessing models of sequence change. A good interspecific model should also yield a clear and biologically plausible population genetic interpretation.

BACKGROUND:Molecular studies have reported divergence times of modern placental orders long before the Cretaceous-Tertiary boundary and far older than paleontological data. However, this discrepancy may not be real, but rather appear because of the violation of implicit assumptions in the estimation procedures, such as non-gradual change of evolutionary rate and failure to correct for convergent evolution. METHODOLOGY/PRINCIPAL FINDINGS:New procedures for divergence-time estimation robust to abrupt changes in the rate of molecular evolution are described. We used a variant of the multidimensional vector space (MVS) procedure to take account of possible convergent evolution. Numerical simulations of abrupt rate change and convergent evolution showed good performance of the new procedures in contrast to current methods. Application to complete mitochondrial genomes identified marked rate accelerations and decelerations, which are not obtained with current methods. The root of placental mammals is estimated to be approximately 18 million years more recent than when assuming a log Brownian motion model. Correcting the pairwise distances for convergent evolution using MVS lowers the age of the root about another 20 million years compared to using standard maximum likelihood tree branch lengths. These two procedures combined revise the root time of placental mammals from around 122 million years ago to close to 84 million years ago. As a result, the estimated distribution of molecular divergence times is broadly consistent with quantitative analysis of the North American fossil record and traditional morphological views. CONCLUSIONS/SIGNIFICANCE:By including the dual effects of abrupt rate change and directly accounting for convergent evolution at the molecular level, these estimates provide congruence between the molecular results, paleontological analyses and morphological expectations. The programs developed here are provided along with sample data that reproduce the results of this study and are especially applicable studies using genome-scale sequence lengths.

Detecting protein-protein interactions and assigning proteins to functional complexes are key challenges of modern biology. The rise of genomics has lead to evidence that correlated patterns of presence/absence and/or fusing of proteins in any organism suggest these proteins interact. Unfortunately, methods based on such data work best with divergent genomes, whereas major sequencing efforts in vertebrates, for example, are yielding alignments of the same set of proteins sampled from the same set of taxa (species). Using vertebrate mitochondrial genomes to illustrate a novel method, we associate proteins based on vectors of their evolutionary tree edge (branch or internode) lengths. This approach is based on the expectation that molecular coevolution is greatest between proteins that interact in some way. Mitochondrial DNA-encoded proteins are associated into groups largely consistent with the complexes they come from. This association is apparently not due to the tree structure or mutation processes, leaving coevolution as the best explanation. We show that it is important that the tree used to derive the edge-length vector is estimated accurately in terms of both topology and edge lengths. Although more complex substitution models reduce systematic error, they also inflate stochastic error. This makes the use of less complex substitution models preferable in some circumstances. We describe a method to estimate correlations of pairwise evolutionary distances, which adjusts for non-independent correlations due to shared evolutionary history. Associations of proteins based on their edge-length vectors are visualized and assessed using a variety of hierarchical clustering and multidimensional scaling methods. New formula for estimating the fit of data to model, including the average percent standard deviation of distances on least squares trees, are presented. Use of edge-length vectors is compared and contrasted with correlated distance methods, correlated rates methods, and site-specific evidence of coevolution.

The aim of this article is to develop an integrated-likelihood (IL) approach to estimate the genetic differentiation between populations. The conventional maximum-likelihood (ML) and pseudolikelihood (PL) methods that use sample counts of alleles may cause severe underestimations of FST, which means overestimations of θ = 4Nm, when the number of sampling localities is small. To reduce such bias in the estimation of genetic differentiation, we propose an IL method in which the mean allele frequencies over populations are regarded as nuisance parameters and are eliminated by integration. To maximize the IL function, we have developed two algorithms, a Monte Carlo EM algorithm and a Laplace approximation. Our simulation studies show that the method proposed here outperforms the conventional ML and PL methods in terms of unbiasedness and precision. The IL method was applied to real data for Pacific herring and African elephants.

“A comparison of the structures of homologous proteins (i.e., proteins with the same kinds of biological activity or function) from different species is important, therefore, for two reasons. First, the similarities found give a measure of the minimum structure for biological function. Second, the differences found may give us important clues to the rate at which successful mutations have occurred throughout evolutionary time and may also serve as an additional basis for establishing phylogenetic relationships.”

The impact of the biological network structures on the divergence between the two copies of one duplicate gene pair involved in the networks has not been documented on a genome scale. Having analyzed the most recently updated Database of Interacting Proteins (DIP) by incorporating the information for duplicate genes of the same age in yeast, we find that there was a highly significantly positive correlation between the level of connectivity of ancient genes and the number of shared partners of their duplicates in the protein-protein interaction networks. This suggests that duplicate genes with a low ancestral connectivity tend to provide raw materials for functional novelty, whereas those duplicate genes with a high ancestral connectivity tend to create functional redundancy for a genome during the same evolutionary period. Moreover, the difference in the number of partners between two copies of a duplicate pair was found to follow a power-law distribution. This suggests that loss and gain of interacting partners for most duplicate genes with a lower level of ancestral connectivity is largely symmetrical, whereas the "hub duplicate genes" with a higher level of ancient connectivity display an asymmetrical divergence pattern in protein-protein interactions. Thus, it is clear that the protein-protein interaction network structures affect the divergence pattern of duplicate genes. Our findings also provide insights into the origin and development of biological networks.

The rate of molecular evolution can vary among lineages. Sources of this variation have differential effects on synonymous and nonsynonymous substitution rates. Changes in effective population size or patterns of natural selection will mainly alter nonsynonymous substitution rates. Changes in generation length or mutation rates are likely to have an impact on both synonymous and nonsynonymous substitution rates. By comparing changes in synonymous and nonsynonymous rates, the relative contributions of the driving forces of evolution can be better characterized. Here, we introduce a procedure for estimating the chronological rates of synonymous and nonsynonymous substitutions on the branches of an evolutionary tree. Because the widely used ratio of nonsynonymous and synonymous rates is not designed to detect simultaneous increases or simultaneous decreases in synonymous and nonsynonymous rates, the estimation of these rates rather than their ratio can improve characterization of the evolutionary process. With our Bayesian approach, we analyze cytochrome oxidase subunit I evolution in primates and infer that nonsynonymous rates have a greater tendency to change over time than do synonymous rates. Our analysis of these data also suggests that rates have been positively correlated.

Evolutionary trees sit at the core of all realistic models describing a set of related sequences, including alignment, homology search, ancestral protein reconstruction and 2D/3D structural change. It is important to assess the stochastic error when estimating a tree, including models using the most realistic likelihood-based optimizations, yet computation times may be many days or weeks. If so, the bootstrap is computationally prohibitive. Here we show that the extremely fast "resampling of estimated log likelihoods" or RELL method behaves well under more general circumstances than previously examined. RELL approximates the bootstrap (BP) proportions of trees better that some bootstrap methods that rely on fast heuristics to search the tree space. The BIC approximation of the Bayesian posterior probability (BPP) of trees is made more accurate by including an additional term related to the determinant of the information matrix (which may also be obtained as a product of gradient or score vectors). Such estimates are shown to be very close to MCMC chain values. Our analysis of mammalian mitochondrial amino acid sequences suggest that when model breakdown occurs, as it typically does for sequences separated by more than a few million years, the BPP values are far too peaked and the real fluctuations in the likelihood of the data are many times larger than expected. Accordingly, several ways to incorporate the bootstrap and other types of direct resampling with MCMC procedures are outlined. Genes evolve by a process which involves some sites following a tree close to, but not identical with, the species tree. It is seen that under such a likelihood model BP (bootstrap proportions) and BPP estimates may still be reasonable estimates of the species tree. Since many of the methods studied are very fast computationally, there is no reason to ignore stochastic error even with the slowest ML or likelihood based methods.

In some Drosophila species, there are two types of greatly diverged amylase (Amy) genes (Amy clusters 1 and 2), each encoding active amylase isozymes. Cluster 1 is located at the middle of its chromosomal arm, and the region has a normal local recombination rate. However, cluster 2 is near the centromere, and this region is known to have a reduced recombination rate. Although nonsynonymous substitutions follow a molecular clock, synonymous substitutions were accelerated in cluster 2 after gene duplications. This resulted in a higher GC content at the third codon position (GC3) and codon usage bias in cluster 1, and lower GC3 content and codon usage bias in the cluster 2. However, no systematic difference in GC content was observed in the first and second codon positions or the 3'-flanking regions. Therefore, differences in local recombination rate rather than mutation bias might explain the divergence at synonymous sites between the two Amy clusters within species (Hill-Robertson effect). Alternatively, the different patterns and levels of expression between the two clusters may imply that the reduced expression level in cluster 2 caused by chromatin potentiation decreased the codon bias. Both of these hypotheses imply the importance of the genomic background as a driving force of divergence between non-tandemly duplicated genes.

Markovian models of protein evolution that relax the assumption of independent change among codons are considered. With this comparatively realistic framework, an evolutionary rate at a site can depend both on the state of the site and on the states of surrounding sites. By allowing a relatively general dependence structure among sites, models of evolution can reflect attributes of tertiary structure. To quantify the impact of protein structure on protein evolution, we analyze protein-coding DNA sequence pairs with an evolutionary model that incorporates effects of solvent accessibility and pairwise interactions among amino acid residues. By explicitly considering the relationship between nonsynonymous substitution rates and protein structure, this approach can lead to refined detection and characterization of positive selection. Analyses of simulated sequence pairs indicate that parameters in this evolutionary model can be well estimated. Analyses of lysozyme c and annexin V sequence pairs yield the biologically reasonable result that amino acid replacement rates are higher when the replacements lead to energetically favorable proteins than when they destabilize the proteins. Although the focus here is evolutionary dependence among codons that is associated with protein structure, the statistical approach is quite general and could be applied to diverse cases of evolutionary dependence where surrogates for sequence fitness can be measured or modeled.

Bayesian methods for estimating evolutionary divergence times are extended to multigene data sets, and a technique is described for detecting correlated changes in evolutionary rates among genes. Simulations are employed to explore the effect of multigene data on divergence time estimation, and the methodology is illustrated with a previously published data set representing diverse plant taxa. The fact that evolutionary rates and times are confounded when sequence data are compared is emphasized and the importance of fossil information for disentangling rates and times is stressed.

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 × 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 × 10−5 to 5.02 × 10−5. Our results indicate that effective viral population size and evolutionary rate per year are negatively correlated among HIV-1 patients.

The existence of a quantitative trait locus (QTL) is usually tested using the likelihood of the quantitative trait on the basis of phenotypic character data plus the recombination fraction between QTL and flanking markers. When doing this, the likelihood is calculated for all possible locations on the linkage map. When multiple QTL are suspected close by, it is impractical to calculate the likelihood for all possible combinations of numbers and locations of QTL. Here, we propose a genetic algorithm (GA) for the heuristic solution of this problem. GA can globally search the optimum by improving the “genotype” with alterations called “recombination” and “mutation.” The “genotype” of our GA is the number and location of QTL. The “fitness” is a function based on the likelihood plus Akaike’s information criterion (AIC), which helps avoid false-positive QTL. A simulation study comparing the new method with existing QTL mapping packages shows the advantage of the new GA. The GA reliably distinguishes multiple QTL located in a single marker interval.

We developed an empirical Bayes procedure to estimate genetic distances between populations using allele frequencies. This procedure makes it possible to describe the skewness of the genetic distance while taking full account of the uncertainty of the sample allele frequencies. Dirichlet priors of the allele frequencies are specified, and the posterior distributions of the various composite parameters are obtained by Monte Carlo simulation. To avoid overdependence on subjective priors, we adopt a hierarchical model and estimate hyperparameters by maximizing the joint marginal-likelihood function. Taking advantage of the empirical Bayesian procedure, we extend the method to estimate the effective population size using temporal changes in allele frequencies. The method is applied to data sets on red sea bream, herring, northern pike, and ayu broodstock. It is shown that overdispersion overestimates the genetic distance and underestimates the effective population size, if it is not taken into account during the analysis. The joint marginal-likelihood function also estimates the rate of gene flow into island populations.

We show how to make appropriate likelihood ratio tests for evolutionary tree models when parameters such as edge (internodes or branches) lengths have nonnegativity constraints. In such cases, under the null model of an edge length being zero, the marginal distribution of this parameter is proven to be a "half-normal", that is, 50% zero values and 50% the positive half of a normal distribution. Other constrained parameters, such as the proportion of invariant sites, give similar results. To make likelihood ratio tests between nested models, e.g., H(0): homogeneous site rates, and H(1): site rates follow a gamma distribution with variance 1/k, then asymptotically as sequence length increases, the distribution under H(0) becomes a mixture of chi distributions, in this case 50% chi(0), and 50% chi(1) (where the subscript denotes degrees of freedom, i.e. , not the usually assumed 100% chi(1); which leads to a conservative test). Such mixtures are sometimes called distributions. Simulations show that even with sequences as short as 125 sites, some parameters, including the proportion of invariant sites, fit asymptotic distributions closely.

Two simple methods have been proposed by Kishino et al. for estimating bootstrap probabilities of alternative trees from a maximum-likelihood analysis without performing maximum-likelihood estimation for each resampled data set; i.e., a resampling estimated log-likelihood method and a multivariate normal distribution method. To examine the extent to which these two methods provide good approximations, bootstrap probabilities estimated by these methods from real data were compared with those estimated by repeated bootstrap resampling and maximum-likelihood estimation. It turned out that both of these simple methods are good approximations to the computationally intensive bootstrap method. This finding should motivate people in this field to use the maximumlikelihood method when inferring molecular evolutionary trees.

Widely used methods for phylogenetic inference, both those that require and those that produce alignments, share certain weaknesses. These weaknesses are discussed, and a method that lacks them is introduced. For each pair of sequences in the data set, the method utilizes both insertion-deletion and amino acid replacement information to estimate a pairwise evolutionary distance. It is also possible to allow regional heterogeneity of replacement rates. Because a likelihood framework is adopted, the standard deviation of each pairwise distance can be estimated. The distance matrix and standard error estimates are used to infer a phylogenetic tree. As an example, this method is used on 10 widely diverged sequences of the second largest RNA polymerase subunit. A pseudo-bootstrap technique is devised to assess the validity of the inferred phylogenetic tree.

Our previous evolutionary model is generalized to permit approximate treatment of multiple-base insertions and deletions as well as regional heterogeneity of substitution rates. Parameter estimation and alignment procedures that incorporate these generalizations are developed. Simulations are used to assess the accuracy of the parameter estimation procedure and an example of an inferred alignment is included.

Background Small heat shock proteins (sHSPs) are products of heat shock response and of other stress responses, and ubiquitous in all three domains of life, archaea, bacteria, and eukarya. They mainly function as molecular chaperones to protect proteins from being denatured in extreme conditions. Study on insect sHSPs could provide some insights into evolution of insects that have adapted to diverse niches in the world. Results Taking advantage of the newly assembled genome sequence, we performed a genome-wide analysis of the candidate sHSP genes in the silkworm, Bombyx mori. Based on known silkworm sHSP sequences, we identified 16 silkworm sHSP genes. Most of them are distributed on two silkworm chromosomes 5 and 27, respectively. 15 of 16 silkworm sHSPs have expression evidence. The comparative analysis of insect sHSPs from B. mori, Drosophila melanogaster, Apis mellifera, Tribolium castaneum, and Anopheles gambiae revealed that there is only one orthologous cluster whereas remaining clusters are species-specific on the phylogenetic tree. This suggested that most of sHSPs might have diverged in function across insects investigated. In addition, the data presented in this study also revealed that sHSPs in the insect orthologous cluster are highly conserved in both sequence and expression pattern. In sum, insect sHSPs show a completely different evolutionary pattern from that found in vertebrate sHSPs. Conclusion B. mori has the largest number of insect sHSP genes characterized to date, including 16 genes. The inference that most species-specific sHSPs might have diverged in function across insects investigated will help us understand the adaptability of these insects to diverse environments.

Most algorithms for the alignment of biological sequences are not derived from an evolutionary model. Consequently, these alignment algorithms lack a strong statistical basis. A maximum likelihood method for the alignment of two DNA sequences is presented. This method is based upon a statistical model of DNA sequence evolution for which we have obtained explicit transition probabilities. The evolutionary model can also be used as the basis of procedures that estimate the evolutionary parameters relevant to a pair of unaligned DNA sequences. A parameter-estimation approach which takes into account all possible alignments between two sequences is introduced; the danger of estimating evolutionary parameters from a single alignment is discussed.