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The identifiability of tree topology for phylogenetic models, including covarion and mixture models.

For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter. We establish tree identifiability for a number of phylogenetic models, including a covarion model and a variety of mixture models with a limited number of classes. The proof is based on the introduction of a more general model, allowing more states at internal nodes of the tree than at leaves, and the study of the algebraic variety formed by the joint distributions to which it gives rise. Tree identifiability is first established for this general model through the use of certain phylogenetic invariants.

Computational Biology↗

Leaf structural and photosynthetic characteristics, and biomass allocation to foliage in relation to foliar nitrogen content and tree size in three Betula species.

Young trees 0.03-1.7 m high of three coexisting Betula species were investigated in four sites of varying soil fertility, but all in full daylight, to separate nutrient and plant size controls on leaf dry mass per unit area (MA), light-saturated foliar photosynthetic electron transport rate (J) and the fraction of plant biomass in foliage (F(L)). Because the site effect was generally non-significant in the analyses of variance with foliar nitrogen content per unit dry mass (N(M)) as a covariate, N(M) was used as an explaining variable of leaf structural and physiological characteristics. Average leaf area (S) and dry mass per leaf scaled positively with N(M) and total tree height (H) in all species. Leaf dry mass per unit area also increased with increasing H, but decreased with increasing N(M), whereas the effects were species-specific. Increases in plant size led to a lower and increases in N(M) to a greater FL and total plant foliar area per unit plant biomass (LAR). Thus, the self-shading probably increased with increasing N(M) and decreased with increasing H. Nevertheless, the whole-plant average M(A), as well as M(A) values of topmost fully exposed leaves, correlated with N(M) and H in a similar manner, indicating that scaling of MA with N(M) and H did not necessarily result from the modified degree of within-plant shading. The rate of photosynthetic electron transport per unit dry mass (J(M)) scaled positively with N(M), but decreased with increasing H and M(A). Thus, increases in M(A) with tree height and decreasing nitrogen content not only resulted in a lower plant foliar area (LAR = F(L)/M(A)), but also led to lower physiological activity of unit foliar biomass. The leaf parameters (J(M), N(M) and M(A)) varied threefold, but the whole-plant characteristic FL varied 20-fold and LAR 30-fold, indicating that the biomass allocation was more plastically adjusted to different plant internal nitrogen contents and to tree height than the foliar variables. Our results demonstrate that: (1) tree height and N(M) may independently control foliar structure and physiology, and have an even greater impact on biomass allocation; and (2) the modified within-plant light availabilities alone do not explain the observed patterns. Although there were interspecific differences with respect to the statistical significance of the relationships, all species generally fit common regressions. However, these differences were consistent, and suggested that more competitive species with inherently larger growth rates also more plastically respond to N and H.

Betula↗

Sex change towards female in dying Acer rufinerve trees.

BACKGROUND AND AIMS: Sex changes within the genus Acer (Aceraceae) may occur because of associations of sex expression and plant health. In this study, a natural population of Acer rufinerve was monitored to clarify the sex change patterns, the relationship between sex expression and plant health, and the causal environmental conditions that precede sex changes. METHODS: Sex expression, growth rate and mortality of A. rufinerve trees in a natural population were monitored from 1992 to 1997. KEY RESULTS: Three types of sex expression were observed among A. rufinerve: male, female and bisexual. Among the three types of sex expression, sex changes occurred in all directions. In the growing season of 1994, precipitation was reduced. Stem growth rate decreased and mortality was high in 1994. In the spring of 1995, a drastic sex change from male to female or to bisexual occurred. As a result, the sex ratio became female-biased in 1995, although it had been male-biased from 1992 to 1994. In 1996 and 1997, the proportion of males in the population increased, partly as a result of female mortality and partly as a result of female-to-male sex changes. Sex expression of A. rufinerve was associated with their growth rate and mortality. The growth rate decreased for trees whose sex changed from male to female or to bisexual, and increased for trees whose sex changed from female to male or to bisexual. Dead trees reproduced as females before they died, except for those that died as males in 1994. CONCLUSIONS: One explanation for the sex change towards increasing femaleness for this A. rufinerve population in 1995 was the deterioration of plant health in the previous growing season, because of reduced precipitation. Sex changes of unhealthy and dying A. rufinerve towards femaleness may facilitate re-occupancy by offspring in gaps created by the death of A. rufinerve trees.

Acer↗

GeneTree: comparing gene and species phylogenies using reconciled trees.

SUMMARY: GeneTree is a program for comparing gene and species trees using reconciled trees. The program can compute the cost of embedding a gene tree within a species tree, visually display the location and number of gene duplications and losses, and search for optimal species trees. AVAILABILITY: The program is free and is available at ((http://taxonomy.zoology.gla.ac. uk/rod/genetree/genetree.html)).

Algorithms↗

RadCon: phylogenetic tree comparison and consensus.

SUMMARY: RadCon is a Macintosh program for manipulating and analysing phylogenetic trees. The program can determine the Cladistic Information Content of individual trees, the stability of leaves across a set of bootstrap trees, produce the strict basic Reduced Cladistic Consensus profile of a set of trees and convert a set of trees into its matrix representation for supertree construction. AVAILABILITY: The program is free and available at http://taxonomy.zoology.gla.ac.uk/ approximately jthorley/radcon/radcon.html.

Phylogeny↗

MacT: Apple Macintosh programs for constructing phylogenetic trees.

MacT is a set of programs for the Apple Macintosh to construct and evaluate unrooted trees derived from amino acid sequences using a distance matrix method. Programs are designed on a 'one program--one task' basis for (i) determining the branching order in trees consisting of four or five species and calculating various statistical measures, (ii) calculating statistical measures for all possible topologies of unrooted trees and (iii) generating and evaluating trees derived from bootstrapped samples. With four auxiliary programs unrooted trees can be built for maximal 26 species, and the robustness of topologies be tested by bootstrapping.

Algorithms↗

Bayesian gene/species tree reconciliation and orthology analysis using MCMC.

MOTIVATION: Comparative genomics in general and orthology analysis in particular are becoming increasingly important parts of gene function prediction. Previously, orthology analysis and reconciliation has been performed only with respect to the parsimony model. This discards many plausible solutions and sometimes precludes finding the correct one. In many other areas in bioinformatics probabilistic models have proven to be both more realistic and powerful than parsimony models. For instance, they allow for assessing solution reliability and consideration of alternative solutions in a uniform way. There is also an added benefit in making model assumptions explicit and therefore making model comparisons possible. For orthology analysis, uncertainty has recently been addressed using parsimonious reconciliation combined with bootstrap techniques. However, until now no probabilistic methods have been available. RESULTS: We introduce a probabilistic gene evolution model based on a birth-death process in which a gene tree evolves 'inside' a species tree. Based on this model, we develop a tool with the capacity to perform practical orthology analysis, based on Fitch's original definition, and more generally for reconciling pairs of gene and species trees. Our gene evolution model is biologically sound (Nei et al., 1997) and intuitively attractive. We develop a Bayesian analysis based on MCMC which facilitates approximation of an a posteriori distribution for reconciliations. That is, we can find the most probable reconciliations and estimate the probability of any reconciliation, given the observed gene tree. This also gives a way to estimate the probability that a pair of genes are orthologs. The main algorithmic contribution presented here consists of an algorithm for computing the likelihood of a given reconciliation. To the best of our knowledge, this is the first successful introduction of this type of probabilistic methods, which flourish in phylogeny analysis, into reconciliation and orthology analysis. The MCMC algorithm has been implemented and, although not yet being in its final form, tests show that it performs very well on synthetic as well as biological data. Using standard correspondences, our results carry over to allele trees as well as biogeography.

Algorithms↗

Regression trees for regulatory element identification.

MOTIVATION: The transcription of a gene is largely determined by short sequence motifs that serve as binding sites for transcription factors. Recent findings suggest direct relationships between the motifs and gene expression levels. In this work, we present a method for identifying regulatory motifs. Our method makes use of tree-based techniques for recovering the relationships between motifs and gene expression levels. RESULTS: We treat regulatory motifs and gene expression levels as predictor variables and responses, respectively, and use a regression tree model to identify the structural relationships between them. The regression tree methodology is extended to handle responses from multiple experiments by modifying the split function. The significance of regulatory elements is determined by analyzing tree structures and using a variable importance measure. When applied to two data sets of the yeast Saccharomyces cerevisiae, the method successfully identifies most of the regulatory motifs that are known to control gene transcription under the given experimental conditions, and suggests several new putative motifs. Analysis of the tree structures also reconfirms several pairs of motifs that are known to regulate gene transcription in combination. AVAILABILITY: http://if.kaist.ac.kr/~phuong/RegTree

Algorithms↗

Phylogenetic trees based on gene content.

UNLABELLED: Comparing gene content between species can be a useful approach for reconstructing phylogenetic trees. In this paper, we derive a maximum-likelihood estimation of evolutionary distance between species under a simple model of gene genesis and gene loss. Using simulated data on a biological tree with 107 taxa (and on a number of randomly generated trees), we compare the accuracy of tree reconstruction using this ML distance measure to an earlier ad hoc distance. We then compare these distance-based approaches to a character-based tree reconstruction method (Dollo parsimony) which seems well suited to the analysis of gene content data. To simplify simulations, we give a formal proof of the well-known 'fact' that the Dollo parsimony score is independent of the choice of root. Our results show a consistent trend, with the character-based method and ML distance measure outperforming the earlier ad hoc distance method. AVAILABILITY: http://www.ab.informatik.uni-tuebingen.de/software/genecontent/welcome_en.html

Algorithms↗

Predicting protein-protein interaction by searching evolutionary tree automorphism space.

MOTIVATION: Uncovering the protein-protein interaction network is a fundamental step in the quest to understand the molecular machinery of a cell. This motivates the search for efficient computational methods for predicting such interactions. Among the available predictors are those that are based on the co-evolution hypothesis "evolutionary trees of protein families (that are known to interact) are expected to have similar topologies". Many of these methods are limited by the fact that they can handle only a small number of protein sequences. Also, details on evolutionary tree topology are missing as they use similarity matrices in lieu of the trees. RESULTS: We introduce MORPH, a new algorithm for predicting protein interaction partners between members of two protein families that are known to interact. Our approach can also be seen as a new method for searching the best superposition of the corresponding evolutionary trees based on tree automorphism group. We discuss relevant facts related to the predictability of protein-protein interaction based on their co-evolution. When compared with related computational approaches, our method reduces the search space by approximately 3 x 10(5)-fold and at the same time increases the accuracy of predicting correct binding partners.

Algorithms↗

Pair stochastic tree adjoining grammars for aligning and predicting pseudoknot RNA structures.

MOTIVATION: Since the whole genome sequences of many species have been determined, computational prediction of RNA secondary structures and computational identification of those non-coding RNA regions by comparative genomics become important. Therefore, more advanced alignment methods are required. Recently, an approach of structural alignment for RNA sequences has been introduced to solve these problems. Pair hidden Markov models on tree structures (PHMMTSs) proposed by Sakakibara are efficient automata-theoretic models for structural alignment of RNA secondary structures, although PHMMTSs are incapable of handling pseudoknots. On the other hand, tree adjoining grammars (TAGs), a subclass of context-sensitive grammars, are suitable for modeling pseudoknots. Our goal is to extend PHMMTSs by incorporating TAGs to be able to handle pseudoknots. RESULTS: We propose pair stochastic TAGs (PSTAGs) for aligning and predicting RNA secondary structures including a simple type of pseudoknot which can represent most known pseudoknot structures. First, we extend PHMMTSs defined on alignment of 'trees' to PSTAGs defined on alignment of 'TAG trees' which represent derivation processes of TAGs and are functionally equivalent to derived trees of TAGs. Then, we develop an efficient dynamic programming algorithm of PSTAGs for obtaining an optimal structural alignment including pseudoknots. We implement the PSTAG algorithm and demonstrate the properties of the algorithm by using it to align and predict several small pseudoknot structures. We believe that our implemented program based on PSTAGs is the first grammar-based and practically executable software for comparative analyses of RNA pseudoknot structures, and, further, non-coding RNAs.

Algorithms↗

Mutation parameters from DNA sequence data using graph theoretic measures on lineage trees.

MOTIVATION: B cells responding to antigenic stimulation can fine-tune their binding properties through a process of affinity maturation composed of somatic hypermutation, affinity-selection and clonal expansion. The mutation rate of the B cell receptor DNA sequence, and the effect of these mutations on affinity and specificity, are of critical importance for understanding immune and autoimmune processes. Unbiased estimates of these properties are currently lacking due to the short time-scales involved and the small numbers of sequences available. RESULTS: We have developed a bioinformatic method based on a maximum likelihood analysis of phylogenetic lineage trees to estimate the parameters of a B cell clonal expansion model, which includes somatic hypermutation with the possibility of lethal mutations. Lineage trees are created from clonally related B cell receptor DNA sequences. Important links between tree shapes and underlying model parameters are identified using mutual information. Parameters are estimated using a likelihood function based on the joint distribution of several tree shapes, without requiring a priori knowledge of the number of generations in the clone (which is not available for rapidly dividing populations in vivo). A systematic validation on synthetic trees produced by a mutating birth-death process simulation shows that our estimates are precise and robust to several underlying assumptions. These methods are applied to experimental data from autoimmune mice to demonstrate the existence of hypermutating B cells in an unexpected location in the spleen.

Algorithms↗

Gene genealogy in three related populations: consistency probability between gene and population trees.

A genealogical relationship among genes at a locus (gene tree) sampled from three related populations was examined with special reference to population relatedness (population tree). A phylogenetically informative event in a gene tree constructed from nucleotide differences consists of interspecific coalescences of genes in each of which two genes sampled from different populations are descended from a common ancestor. The consistency probability between gene and population trees in which they are topologically identical was formulated in terms of interspecific coalescences. It was found that the consistency probability thus derived substantially increases as the sample size of genes increases, unless the divergence time of populations is very long compared to population sizes. Hence, there are cases where large samples at a locus are very useful in inferring a population tree.

Diploidy↗

Similarities and gradients in growth unit branching patterns during ontogeny in "Fuji" apple trees: a stochastic approach.

This study aims to explore and model the changes in growth unit (GU) branching patterns during tree ontogeny. The question was addressed in apple trees cv. "Fuji", by analysing the relative impact of GU length and within-tree position. The development of two 6-year-old trees was recorded over 6 years. The fate of axillary buds along each GU was represented as a sequence of symbols corresponding to five types of lateral growth: latent buds, short, medium, long, and floral lateral GUs. Based on an exploratory analysis of data and a priori hypotheses, a hidden semi-Markov chain was estimated from all of these GU sequences. This model was composed of six transient states representing successive branching zones along the GUs. The accuracy of this global model was a posteriori assessed by fitting the characteristic distributions computed from model parameters to the corresponding empirical characteristic distributions extracted from the observed sequences. The observed sequences were then grouped hierarchically according to the GU length, year of growth, and branching order. Comparing model parameters between these sub-groups revealed similarities between GUs. These similarities were based on particular branching zones whose composition and relative position within the GUs remained invariant across the subgroups: the latent zones, floral zone, and short-lateral zone. The probability of occurrence of the floral zone varied with the year, showing the alternate fruiting of "Fuji". It is shown that, during tree ontogeny, as GU length decreases, branching patterns tend to progressively simplify due to the disappearance of the most central zones and a progressive reduction in the length of the floral zone.

Malus↗

Root of the Eukaryota tree as inferred from combined maximum likelihood analyses of multiple molecular sequence data.

Extensive studies aiming to establish the structure and root of the Eukaryota tree by phylogenetic analyses of molecular sequences have thus far not resulted in a generally accepted tree. To re-examine the eukaryotic phylogeny using alternative genes, and to obtain a more robust inference for the root of the tree as well as the relationship among major eukaryotic groups, we sequenced the genes encoding isoleucyl-tRNA and valyl-tRNA synthetases, cytosolic-type heat shock protein 90, and the largest subunit of RNA polymerase II from several protists. Combined maximum likelihood analyses of 22 protein-coding genes including the above four genes clearly demonstrated that Diplomonadida and Parabasala shared a common ancestor in the rooted tree of Eukaryota, but only when the fast-evolving sites were excluded from the original data sets. The combined analyses, together with recent findings on the distribution of a fused dihydrofolate reductase-thymidylate synthetase gene, narrowed the possible position of the root of the Eukaryota tree on the branch leading to Opisthokonta or to the common ancestor of Diplomonadida/Parabasala. However, the analyses did not agree with the position of the root located on the common ancestor of Opisthokonta and Amoebozoa, which was argued by Stechmann and Cavalier-Smith [Curr. Biol. 13:R665-666, 2003] based on the presence or absence of a three-gene fusion of the pyrimidine biosynthetic pathway: carbamoyl-phosphate synthetase II, dihydroorotase, and aspartate carbamoyltransferase. The presence of the three-gene fusion recently found in the Cyanidioschyzon merolae (Rhodophyta) genome sequence data supported our analyses against the Stechmann and Cavalier-Smith-rooting in 2003.

Animals↗

Accounting for uncertainty in the tree topology has little effect on the decision-theoretic approach to model selection in phylogeny estimation.

Currently available methods for model selection used in phylogenetic analysis are based on an initial fixed-tree topology. Once a model is picked based on this topology, a rigorous search of the tree space is run under that model to find the maximum-likelihood estimate of the tree (topology and branch lengths) and the maximum-likelihood estimates of the model parameters. In this paper, we propose two extensions to the decision-theoretic (DT) approach that relax the fixed-topology restriction. We also relax the fixed-topology restriction for the Bayesian information criterion (BIC) and the Akaike information criterion (AIC) methods. We compare the performance of the different methods (the relaxed, restricted, and the likelihood-ratio test [LRT]) using simulated data. This comparison is done by evaluating the relative complexity of the models resulting from each method and by comparing the performance of the chosen models in estimating the true tree. We also compare the methods relative to one another by measuring the closeness of the estimated trees corresponding to the different chosen models under these methods. We show that varying the topology does not have a major impact on model choice. We also show that the outcome of the two proposed extensions is identical and is comparable to that of the BIC, Extended-BIC, and DT. Hence, using the simpler methods in choosing a model for analyzing the data is more computationally feasible, with results comparable to the more computationally intensive methods. Another outcome of this study is that earlier conclusions about the DT approach are reinforced. That is, LRT, Extended-AIC, and AIC result in more complicated models that do not contribute to the performance of the phylogenetic inference, yet cause a significant increase in the time required for data analysis.

Computational Biology↗

When is it safe to use an oversimplified substitution model in tree-making?

The choice of an "optimal" mathematical model for computing evolutionary distances from real sequences is not currently supported by easy-to-use software applicable to large data sets, and an investigator frequently selects one of the simplest models available. Here we study properties of the observed proportion of differences (p-distance) between sequences as an estimator of evolutionary distance for tree-making. We show that p-distances allow for consistent tree-making with any of the popular methods working with evolutionary distances if evolution of sequences obeys a "molecular clock" (more precisely, if it follows a stationary time-reversible Markov model of nucleotide substitution). Next, we show that p-distances seem to be efficient in recovering the correct tree topology under a "molecular clock," but produce "statistically supported" wrong trees when substitutions rates vary among evolutionary lineages. Finally, we outline a practical approach for selecting an "optimal" model of nucleotide substitution in a real data analysis, and obtain a crude estimate of a "prior" distribution of the expected tree branch lengths under the Jukes-Cantor model. We conclude that the use of a model that is obviously oversimplified is inadvisable unless it is justified by a preliminary analysis of the real sequences.

Base Sequence↗

Multiple maxima of likelihood in phylogenetic trees: an analytic approach.

Maximum likelihood (ML) is a widely used criterion for selecting optimal evolutionary trees. However, the nature of the likelihood surface for trees is still not sufficiently understood, especially with regard to the frequency of multiple optima. Here, we initiate an analytic study for identifying sequences that generate multiple optima. We concentrate on the problem of optimizing edge weights for a given tree or trees (as opposed to searching through the space of all trees). We report a new approach to computing ML directly, which we have used to find large families of sequences that have multiple optima, including sequences with a continuum of optimal points. Such data sets are best supported by different (two or more) phylogenies that vary significantly in their timings of evolutionary events. Some standard biological processes can lead to data with multiple optima, and consequently the field needs further investigation. Our results imply that hill-climbing techniques as currently implemented in various software packages cannot guarantee that one will find the global ML point, even if it is unique.

Evolution, Molecular↗