The phylogenetic mixed model

The phylogenetic mixed model is an application of the quantitative-genetic mixed model to interspecific data. Although this statistical framework provides a potentially unifying approach to quantitative-genetic and phylogenetic analysis, the model has been applied infrequently because of technical difficulties with parameter estimation. We recommend a reparameterization of the model that eliminates some of these difficulties, and we develop a new estimation algorithm for both the original maximum likelihood and new restricted maximum likelihood estimators. The phylogenetic mixed model is particularly rich in terms of the evolutionary insight that might be drawn from model parameters, so we also illustrate and discuss the interpretation of the model parameters in a specific comparative analysis.     

A mixed branch length model of heterotachy improves phylogenetic accuracy

Evolutionary relationships are typically inferred from molecular sequence data using a statistical model of the evolutionary process. When the model accurately reflects the underlying process, probabilistic phylogenetic methods recover the correct relationships with high accuracy. There is ample evidence, however, that models commonly used today do not adequately reflect real-world evolutionary dynamics. Virtually all contemporary models assume that relatively fast-evolving sites are fast across the entire tree, whereas slower sites always evolve at relatively slower rates. Many molecular sequences, however, exhibit site-specific changes in evolutionary rates, called "heterotachy." Here we examine the accuracy of 2 phylogenetic methods for incorporating heterotachy, the mixed branch length model--which incorporates site-specific rate changes by summing likelihoods over multiple sets of branch lengths on the same tree--and the covarion model, which uses a hidden Markov process to allow sites to switch between variable and invariable as they evolve. Under a variety of simple heterogeneous simulation conditions, the mixed model was dramatically more accurate than homotachous models, which were subject to topological biases as well as biases in branch length estimates. When data were simulated with strong versions of the types of heterotachy observed in real molecular sequences, the mixed branch length model was more accurate than homotachous techniques. Analyses of empirical data sets confirmed that the mixed branch length model can improve phylogenetic accuracy under conditions that cause homotachous models to fail. In contrast, the covarion model did not improve phylogenetic accuracy compared with homotachous models and was sometimes substantially less accurate. We conclude that a mixed branch length approach, although not the solution to all phylogenetic errors, is a valuable strategy for improving the accuracy of inferred trees.     

Implementation of a Markov model for phylogenetic trees

A recently developed mathematical model for the analysis of phylogenetic trees is applied to comparative data for 48 species. The model represents a return to fundamentals and makes no hypothesis with respect to the reversibility of the process. The species have been analysed in all subsets of three, and a measure of reliability of the results is provided. The numerical results of the computations on 17,296 triples of species are made available on the Internet. These results are discussed and the development of reliable tree structures for several species is illustrated. It is shown that, indeed, the Markov model is capable of considerably more interesting predictions than has been recognized to date.     

A phylogenetic model for understanding the effect of gene duplication on cancer progression

As biotechnology advances rapidly, a tremendous amount of cancer genetic data has become available, providing an unprecedented opportunity for understanding the genetic mechanisms of cancer. To understand the effects of duplications and deletions on cancer progression, two genomes (normal and tumor) were sequenced from each of five stomach cancer patients in different stages (I, II, III and IV). We developed a phylogenetic model for analyzing stomach cancer data. The model assumes that duplication and deletion occur in accordance with a continuous time Markov Chain along the branches of a phylogenetic tree attached with five extended branches leading to the tumor genomes. Moreover, coalescence times of the phylogenetic tree follow a coalescence process. The simulation study suggests that the maximum likelihood approach can accurately estimate parameters in the phylogenetic model. The phylogenetic model was applied to the stomach cancer data. We found that the expected number of changes (duplication and deletion) per gene for the tumor genomes is significantly higher than that for the normal genomes. The goodness-of-fit test suggests that the phylogenetic model with constant duplication and deletion rates can adequately fit the duplication data for the normal genomes. The analysis found nine duplicated genes that are significantly associated with stomach cancer.     

Application of the secondary structure model of rRNA for phylogeny: D2-D3 expansion segments of the LSU gene of plant-parasitic nematodes from the family Hoplolaimidae Filipjev, 1934

Knowledge of rRNA structure is increasingly important to assist phylogenetic analysis through reconstructing optimal alignment, utilizing molecule features as an additional source of data and refining appropriate models of evolution of the molecule. We describe a procedure of optimization for alignment and a new coding method for nucleotide sequence data using secondary structure models of the D2 and D3 expansion fragments of the LSU-rRNA gene reconstructed for fifteen nematode species of the agriculturally important and diverse family Hoplolaimidae, order Tylenchida. Using secondary structure information we converted the original sequence data into twenty-eight symbol codes and submitted the transformed data to maximum parsimony analysis. We also applied the original sequence data set for Bayesian inference. This used the doublet model with sixteen states of nucleotide doublets for the stem region and the standard model of DNA substitution with four nucleotide states for loops and bulges. By this approach, we demonstrate that using structural information for phylogenetic analyses led to trees with lower resolved relationships between clades and likely eliminated some artefactual support for misinterpreted relationships, such as paraphyly of Helicotylenchus or Rotylenchus. This study as well as future phylogenetic analyses is herein supported by the development of an on-line database, NEMrRNA, for rRNA molecules in a structural format for nematodes. We also have developed a new computer program, RNAstat, for calculation of nucleotide statistics designed and proposed for phylogenetic studies.     

Modelling phylogenetic relationships using reticulated networks

Makarenkov, V., Legendre, P. & Desdevises, Y. (2004). Modelling phylogenetic relationships using reticulated networks. —  Zoologica Scripta , 33 , 89–96.
Most traditional methods of phylogenetic analysis assume that species evolution can be represented by means of a bifurcating tree model. In many phylogenetic situations, however, some of the evolutionary links between species are due to reticulate evolution. For instance, reticulate models can adequately describe such complicated mechanisms as lateral gene transfer in bacteria or species hybridization. The theoretical concepts of reticulate evolution developed in the 1980s and 1990s need to be supported by appropriate analytical tools and software. In this paper, we present the main features of a new distance-based method for modelling phylogenetic relationships among species by means of reticulated networks (RNs). The method uses the least-squares model to build a RN by gradually improving upon the solution provided by a phylogenetic tree. A computer program facilitating the reconstruction and visualization of reticulate phylogenies is made available to researchers. In the application section, we illustrate the usefulness of the method by studying the evolution of honeybees (genus Apis ). The method for reconstructing RNs has been included in the T-Rex ( Tree and Reticulogram Reconstruction ) package recently developed by the first-named author.     

Microsatellite Behavior with Range Constraints: Parameter Estimation and Improved Distances for Use in Phylogenetic Reconstruction

A symmetric stepwise mutation model with reflecting boundaries is employed to evaluate microsatellite evolution under range constraints. Methods of estimating range constraints and mutation rates under the assumptions of the model are developed. Least squares procedures are employed to improve molecular distance estimation for use in phylogenetic reconstruction in the case where range constraints and mutation rates vary across loci. The bias and accuracy of these methods are evaluated using computer simulations, and they are compared to previously existing methods which do not assume range constraints. Range constraints are seen to have a substantial impact on phylogenetic conclusions based on molecular distances, particularly for more divergent taxa. Results indicate that if range constraints are in effect, the methods developed here should be used in both the preliminary planning and final analysis of phylogenetic studies employing microsatellites. It is also seen that in order to make accurate phylogenetic inferences under range constraints, a larger number of loci are required than in their absence.     

Mixed state on a sparsely encoded associative memory model

 We analyzed symmetric mixed states corresponding to the so-called concept formation on a sparsely encoded associative memory model with 0–1 neurons. Three types of mixed states – OR, AND, and a majority decision – are described as typical examples. Each element of the OR mixed state is composed of corresponding memory pattern elements by means of the OR operation. The other two types are similarly defined. By analyzing their equilibrium properties through self-consistent signal-to-noise analysis and computer simulation, we found that the storage capacity of the OR mixed state diverges in a sparse limit, but that the other states do not diverge. In addition, we found that the optimal threshold values, which maximize the storage capacity for the memory pattern and the OR mixed state, coincide with each other in the spare limit. We conclude that the OR mixed state is a reasonable representative of mixed state in the sparse limit. Received: 10 November 1999 / Accepted in revised form: 5 April 2001     

The statistical analysis of fluctuating asymmetry: REML estimation of a mixed regression model

The unbiased estimation of fluctuating asymmetry (FA) requires independent repeated measurements on both sides. The statistical analysis of such data is currently performed by a two-way mixed ANOVA analysis. Although this approach produces unbiased estimates of FA, many studies do not utilize this method. This may be attributed in part to the fact that the complete analysis of FA is very cumbersome and cannot be performed automatically with standard statistical software. Therefore, further elaboration of the statistical tools to analyse FA should focus on the usefulness of the method, in order for the correct statistical approaches to be applied more regularly. In this paper we propose a mixed regression model with restricted maximum likelihood (REML) parameter estimation to model FA. This routine yields exactly the same estimates of FA as the two-way mixed ANOVA . Yet the advantages of this approach are that it allows (a) testing the statistical significance of FA, (b) modelling and testing heterogeneity in both FA and measurement error (ME) among samples, (c) testing for nonzero directional asymmetry and (d) obtaining unbiased estimates of individual FA levels. The switch from a mixed two-way ANOVA to a mixed regression model was made to avoid overparametrization. Two simulation studies are presented. The first shows that a previously proposed method to test the significance of FA is incorrect, contrary to our mixed regression approach. In the second simulation study we show that a traditionally applied measure of individual FA [abs(left – right)] is biased by ME. The proposed mixed regression method, however, produces unbiased estimates of individual FA after modelling heterogeneity in ME. The applicability of this method is illustrated with two analyses.     

Use of a multilocus variable-number tandem repeat analysis method for molecular subtyping and phylogenetic analysis of Neisseria meningitidis isolates

Background  

The multilocus variable-number tandem repeat (VNTR) analysis (MLVA) technique has been developed for fine typing of many bacterial species. The genomic sequences of Neisseria meningitidis strains Z2491, MC58 and FAM18 have been available for searching potential VNTR loci by computer software. In this study, we developed and evaluated a MLVA method for molecular subtyping and phylogenetic analysis of N. meningitidis strains.     

Selecting the best-fit model of nucleotide substitution

Despite the relevant role of models of nucleotide substitution in phylogenetics, choosing among different models remains a problem. Several statistical methods for selecting the model that best fits the data at hand have been proposed, but their absolute and relative performance has not yet been characterized. In this study, we compare under various conditions the performance of different hierarchical and dynamic likelihood ratio tests, and of Akaike and Bayesian information methods, for selecting best-fit models of nucleotide substitution. We specifically examine the role of the topology used to estimate the likelihood of the different models and the importance of the order in which hypotheses are tested. We do this by simulating DNA sequences under a known model of nucleotide substitution and recording how often this true model is recovered by the different methods. Our results suggest that model selection is reasonably accurate and indicate that some likelihood ratio test methods perform overall better than the Akaike or Bayesian information criteria. The tree used to estimate the likelihood scores does not influence model selection unless it is a randomly chosen tree. The order in which hypotheses are tested, and the complexity of the initial model in the sequence of tests, influence model selection in some cases. Model fitting in phylogenetics has been suggested for many years, yet many authors still arbitrarily choose their models, often using the default models implemented in standard computer programs for phylogenetic estimation. We show here that a best-fit model can be readily identified. Consequently, given the relevance of models, model fitting should be routine in any phylogenetic analysis that uses models of evolution.     

A method for quantification of absolute amounts of nucleic acids by (RT)-PCR and a new mathematical model for data analysis

Accurate quantification of nucleic acids by competitive (RT)-PCR requires a valid internal standard, a reference for data normalization and an adequate mathematical model for data analysis. We report here an effective procedure for the generation of homologous RNA internal standards and a strategy for synthesizing and using a reference target RNA in quantification of absolute amounts of nucleic acids. Further, a new mathematical model describing the general kinetic features of competitive PCR was developed. The model extends the validity of quantitative competitive (RT)-PCR beyond the exponential phase. The new method eliminates the errors arising from different amplification efficiencies of the co-amplified sequences and from heteroduplex formation in the system. The high accuracy (relative error <2%) is comparable to the recently developed real time detection 5'-nuclease PCR. Also, corresponding computer software has been devised for practical data analysis.     

A structurally relevant coarse-grained model for cholesterol

Detailed atomistic computer simulations are now widely used to study biological membranes, including increasingly mixed lipid systems that involve, for example, cholesterol, which is a key membrane lipid. Typically, simulations of these systems start from a preassembled bilayer because the timescale on which self-assembly occurs in mixed lipid systems is beyond the practical abilities of fully atomistic simulations. To overcome this limitation and study bilayer self-assembly, coarse-grained models have been developed. Although there are several coarse-grained models for cholesterol reported in the literature, these generally fail to account explicitly for the unique molecular features of cholesterol that relate to its function and role as a membrane lipid. In this work, we propose a new coarse-grained model for cholesterol that retains the molecule's unique features and, as a result, can be used to study crystalline structures of cholesterol. In the development of the model, two levels of coarse-graining are explored and the importance of retaining key molecular features in the coarse-grained model that are relevant to structural properties is investigated.     

TaxMan: a taxonomic database manager

Background  

Phylogenetic analysis of large, multiple-gene datasets, assembled from public sequence databases, is rapidly becoming a popular way to approach difficult phylogenetic problems. Supermatrices (concatenated multiple sequence alignments of multiple genes) can yield more phylogenetic signal than individual genes. However, manually assembling such datasets for a large taxonomic group is time-consuming and error-prone. Additionally, sequence curation, alignment and assessment of the results of phylogenetic analysis are made particularly difficult by the potential for a given gene in a given species to be unrepresented, or to be represented by multiple or partial sequences. We have developed a software package, TaxMan, that largely automates the processes of sequence acquisition, consensus building, alignment and taxon selection to facilitate this type of phylogenetic study.     

Effect of site-specific heterogeneous evolution on phylogenetic reconstruction: a simple evaluation

Recent studies have shown that heterogeneous evolution may mislead phylogenetic analysis, which has been neglected for a long time. We evaluate the effect of heterogeneous evolution on phylogenetic analysis, using 18 fish mitogenomic coding sequences as an example. Using the software DIVERGE, we identify 198 amino acid sites that have experienced heterogeneous evolution. After removing these sites, the rest of sites are shown to be virtually homogeneous in the evolutionary rate. There are some differences between phylogenetic trees built with heterogeneous sites ("before tree") and without heterogeneous sites ("after tree"). Our study demonstrates that for phylogenetic reconstruction, an effective approach is to identify and remove sites with heterogeneous evolution, and suggests that researchers can use the software DIVERGE to remove the influence of heterogeneous evolution before reconstructing phylogenetic trees.     

PEAS V1.0: a package for elementary analysis of SNP data

We have developed a software package named PEAS to facilitate analyses of large data sets of single nucleotide polymorphisms (SNPs) for population genetics and molecular phylogenetics studies. PEAS reads SNP data in various formats as input and is versatile in data formatting; using PEAS, it is easy to create input files for many popular packages, such as STRUCTURE, frappe, Arlequin, Haploview, LDhat, PLINK, EIGENSOFT, PHASE, fastPHASE, MEGA and PHYLIP. In addition, PEAS fills up several analysis gaps in currently available computer programs in population genetics and molecular phylogenetics. Notably, (i) It calculates genetic distance matrices with bootstrapping for both individuals and populations from genome-wide high-density SNP data, and the output can be streamlined to MEGA and PHYLIP programs for further processing; (ii) It calculates genetic distances from STRUCTURE output and generates MEGA file to reconstruct component trees; (iii) It provides tools to conduct haplotype sharing analysis for phylogenetic studies based on high-density SNP data. To our knowledge, these analyses are not available in any other computer program. PEAS for Windows is freely available for academic users from http://www.picb.ac.cn/~xushua/index.files/Download_PEAS.htm.     

The finite polygenic mixed model: An alternative formulation for the mixed model of inheritance

This paper presents a mixed model of inheritance with a finite number of polygenic loci. This model leads to a likelihood that can be calculated using efficient algorithms developed for oligogenic models. For comparison, likelihood profiles were obtained for the finite polygenic mixed model, the usual mixed model, with exact and approximate calculations, and for a class D regressive model. The profiles for the finite polygenic mixed model were closest to the profiles for the usual mixed model with exact calculations.     

From a phylogenetic tree to a reticulated network.

In many phylogenetic problems, assuming that species have evolved from a common ancestor by a simple branching process is unrealistic. Reticulate phylogenetic models, however, have been largely neglected because the concept of reticulate evolution have not been supported by using appropriate analytical tools and software. The reticulate model can adequately describe such complicated mechanisms as hybridization between species or lateral gene transfer in bacteria. In this paper, we describe a new algorithm for inferring reticulate phylogenies from evolutionary distances among species. The algorithm is capable of detecting contradictory signals encompassed in a phylogenetic tree and identifying possible reticulate events that may have occurred during evolution. The algorithm produces a reticulate phylogeny by gradually improving upon the initial solution provided by a phylogenetic tree model. The new algorithm is compared to the popular SplitsGraph method in a reanalysis of the evolution of photosynthetic organisms. A computer program to construct and visualize reticulate phylogenies, called T-Rex (Tree and Reticulogram Reconstruction), is available to researchers at the following URL: www.fas.umontreal.ca/biol/casgrain/en/labo/t-rex.     

Computer aided analysis for biosensing and screening

Biosensors with animal and microbial cells immobilized close to the tip of a membrane electrode have been developed for chemical and drug testing. Our experimental results show that biosensors can be used for drug screening and to provide useful information about various cell-chemical interactions. A computer aided analysis (CAA) software package is being developed here using the biosensor for various screening purposes. This software package enables us to use a computer to analyze the biosensor dynamic responses. Computer simulation and parameter estimation techniques are used to select the best model and to describe the biochemical and pharmacologic effects of various chemicals and drugs on different cell lines.     

General quantitative genetic methods for comparative biology: phylogenies,taxonomies and multi‐trait models for continuous and categorical characters

Although many of the statistical techniques used in comparative biology were originally developed in quantitative genetics, subsequent development of comparative techniques has progressed in relative isolation. Consequently, many of the new and planned developments in comparative analysis already have well‐tested solutions in quantitative genetics. In this paper, we take three recent publications that develop phylogenetic meta‐analysis, either implicitly or explicitly, and show how they can be considered as quantitative genetic models. We highlight some of the difficulties with the proposed solutions, and demonstrate that standard quantitative genetic theory and software offer solutions. We also show how results from Bayesian quantitative genetics can be used to create efficient Markov chain Monte Carlo algorithms for phylogenetic mixed models, thereby extending their generality to non‐Gaussian data. Of particular utility is the development of multinomial models for analysing the evolution of discrete traits, and the development of multi‐trait models in which traits can follow different distributions. Meta‐analyses often include a nonrandom collection of species for which the full phylogenetic tree has only been partly resolved. Using missing data theory, we show how the presented models can be used to correct for nonrandom sampling and show how taxonomies and phylogenies can be combined to give a flexible framework with which to model dependence.