Maximum parsimony on subsets of taxa

In this paper we investigate mathematical questions concerning the reliability (reconstruction accuracy) of Fitch's maximum parsimony algorithm for reconstructing the ancestral state given a phylogenetic tree and a character. In particular, we consider the question whether the maximum parsimony method applied to a subset of taxa can reconstruct the ancestral state of the root more accurately than when applied to all taxa, and we give an example showing that this indeed is possible. A surprising feature of our example is that ignoring a taxon closer to the root improves the reliability of the method. On the other hand, in the case of the two-state symmetric substitution model, we answer affirmatively a conjecture of Li, Steel and Zhang which states that under a molecular clock the probability that the state at a single taxon is a correct guess of the ancestral state is a lower bound on the reconstruction accuracy of Fitch's method applied to all taxa.     

Root location in random trees: A polarity property of all sampling consistent phylogenetic models except one

Neutral macroevolutionary models, such as the Yule model, give rise to a probability distribution on the set of discrete rooted binary trees over a given leaf set. Such models can provide a signal as to the approximate location of the root when only the unrooted phylogenetic tree is known, and this signal becomes relatively more significant as the number of leaves grows. In this short note, we show that among models that treat all taxa equally, and are sampling consistent (i.e. the distribution on trees is not affected by taxa yet to be included), all such models, except one (the so-called PDA model), convey some information as to the location of the ancestral root in an unrooted tree.     

A method for measuring support for synapomorphy using character state distributions on phylogenetic trees

Synapomorphies are fundamental to phylogenetic systematics as they offer empirical evidence of monophyletic groups. However, no method exists to directly measure synapomorphy. Here, we propose a method that quantifies synapomorphy using the pattern of character state distribution over a cladogram separately for each character and for each clade. We define a fully synapomorphic character state as one shared by all of a clade’s terminal taxa and at the same time completely absent from all terminal taxa outside that clade. The extent to which this condition is met corresponds to the support for the character state being synapomorphic or, in short, support for synapomorphy. It is calculated as the probability of randomly selecting, by multi‐stage sampling following the topology of the tree, two terminals from inside a clade sharing the same character state and one terminal from outside the clade bearing a different character state. The method is independent of tree inference and free of transformational assumptions, and so can be applied to any tree and used for any type of discrete character. By measuring synapomorphy, the method offers a potential tool for determining diagnostic character states for taxa on different hierarchical levels, for evaluating alternative systems of character coding, and for evaluating clade support. We show how the method differs from ancestral character state reconstruction methods and goodness‐of‐fit indices. We demonstrate the behaviour of our method with several hypothetical scenarios and its potential use with two real‐life examples.     

A two-stage pruning algorithm for likelihood computation for a population tree

We have developed a pruning algorithm for likelihood estimation of a tree of populations. This algorithm enables us to compute the likelihood for large trees. Thus, it gives an efficient way of obtaining the maximum-likelihood estimate (MLE) for a given tree topology. Our method utilizes the differences accumulated by random genetic drift in allele count data from single-nucleotide polymorphisms (SNPs), ignoring the effect of mutation after divergence from the common ancestral population. The computation of the maximum-likelihood tree involves both maximizing likelihood over branch lengths of a given topology and comparing the maximum-likelihood across topologies. Here our focus is the maximization of likelihood over branch lengths of a given topology. The pruning algorithm computes arrays of probabilities at the root of the tree from the data at the tips of the tree; at the root, the arrays determine the likelihood. The arrays consist of probabilities related to the number of coalescences and allele counts for the partially coalesced lineages. Computing these probabilities requires an unusual two-stage algorithm. Our computation is exact and avoids time-consuming Monte Carlo methods. We can also correct for ascertainment bias.     

Non-hereditary Maximum Parsimony trees

In this paper, we investigate a conjecture by Arndt von Haeseler concerning the Maximum Parsimony method for phylogenetic estimation, which was published by the Newton Institute in Cambridge on a list of open phylogenetic problems in 2007. This conjecture deals with the question whether Maximum Parsimony trees are hereditary. The conjecture suggests that a Maximum Parsimony tree for a particular (DNA) alignment necessarily has subtrees of all possible sizes which are most parsimonious for the corresponding subalignments. We answer the conjecture affirmatively for binary alignments on 5 taxa but also show how to construct examples for which Maximum Parsimony trees are not hereditary. Apart from showing that a most parsimonious tree cannot generally be reduced to a most parsimonious tree on fewer taxa, we also show that compatible most parsimonious quartets do not have to provide a most parsimonious supertree. Last, we show that our results can be generalized to Maximum Likelihood for certain nucleotide substitution models.     

Ancestral state reconstruction of body size in the Caniformia (Carnivora, Mammalia): the effects of incorporating data from the fossil record

A recent molecular phylogeny of the mammalian order Carnivora implied large body size as the ancestral condition for the caniform subclade Arctoidea using the distribution of species mean body sizes among living taxa. "Extant taxa-only" approaches such as these discount character state observations for fossil members of living clades and completely ignore data from extinct lineages. To more rigorously reconstruct body sizes of ancestral forms within the Caniformia, body size and first appearance data were collected for 149 extant and 367 extinct taxa. Body sizes were reconstructed for four ancestral nodes using weighted squared-change parsimony on log-transformed body mass data. Reconstructions based on extant taxa alone favored large body sizes (on the order of 10 to 50 kg) for the last common ancestors of both the Caniformia and Arctoidea. In contrast, reconstructions incorporating fossil data support small body sizes (< 5 kg) for the ancestors of those clades. When the temporal information associated with fossil data was discarded, body size reconstructions became ambiguous, demonstrating that incorporating both character state and temporal information from fossil taxa unambiguously supports a small ancestral body size, thereby falsifying hypotheses derived from extant taxa alone. Body size reconstructions for Caniformia, Arctoidea, and Musteloidea were not sensitive to potential errors introduced by uncertainty in the position of extinct lineages relative to the molecular topology, or to missing body size data for extinct members of an entire major clade (the aquatic Pinnipedia). Incorporating character state observations and temporal information from the fossil record into hypothesis testing has a significant impact on the ability to reconstruct ancestral characters and constrains the range of potential hypotheses of character evolution. Fossil data here provide the evidence to reliably document trends of both increasing and decreasing body size in several caniform clades. More generally, including fossils in such analyses incorporates evidence of directional trends, thereby yielding more reliable ancestral character state reconstructions.     

The relative contribution of band number to phylogenetic accuracy in AFLP data sets

We examined the effect of increasing the number of sampled amplified fragment length polymorphism (AFLP) bands to reconstruct an accurate and well-supported AFLP-based phylogeny. In silico AFLP was performed using simulated DNA sequences evolving along balanced and unbalanced model trees with recent, uniform and ancient radiations and average branch lengths (from the most internal node to the tip) ranging from 0.02 to 0.05 substitutions per site. Trees were estimated by minimum evolution (ME) and maximum parsimony (MP) methods from both DNA sequences and virtual AFLP fingerprints. The comparison of the true tree with the estimated AFLP trees suggests that moderate numbers of AFLP bands are necessary to recover the correct topology with high bootstrap support values (i.e. >70%). Fewer numbers of bands are necessary for shorter tree lengths and for balanced than for unbalanced tree topologies. However, branch length estimation was rather unreliable and did not improve substantially after a certain number of bands were sampled. These results hold for different levels of genome coverage and number of taxa analysed. In silico AFLP using bacterial genomic DNA sequences recovered a well-supported tree topology that mirrored an empirical phylogeny based on a set of 31 orthologous gene sequences when as few as 263 AFLP bands were scored. These results suggest that AFLPs may be an efficient alternative to traditional DNA sequencing for accurate topology reconstruction of shallow trees when not very short ancestral branches exist.     

Estimating mutation parameters,population history and genealogy simultaneously from temporally spaced sequence data

Molecular sequences obtained at different sampling times from populations of rapidly evolving pathogens and from ancient subfossil and fossil sources are increasingly available with modern sequencing technology. Here, we present a Bayesian statistical inference approach to the joint estimation of mutation rate and population size that incorporates the uncertainty in the genealogy of such temporally spaced sequences by using Markov chain Monte Carlo (MCMC) integration. The Kingman coalescent model is used to describe the time structure of the ancestral tree. We recover information about the unknown true ancestral coalescent tree, population size, and the overall mutation rate from temporally spaced data, that is, from nucleotide sequences gathered at different times, from different individuals, in an evolving haploid population. We briefly discuss the methodological implications and show what can be inferred, in various practically relevant states of prior knowledge. We develop extensions for exponentially growing population size and joint estimation of substitution model parameters. We illustrate some of the important features of this approach on a genealogy of HIV-1 envelope (env) partial sequences.     

The probability of correctly resolving a split as an experimental design criterion in phylogenetics

We illustrate how recently developed large sequence-length approximations to probabilities of correct phylogenetic reconstruction for maximum likelihood estimation can be used to evaluate experimental design strategies. The specific criterion of interest is the probability of correctly resolving an a priori defined split of interest in a phylogenetic tree. Design strategies considered include increased taxon sampling and increasing sequence length. Our analyses of specific examples strongly suggest that it is better to sample taxa that connect as close as possible to the split of interest. Assuming this can be done, these examples suggest it is better to sample additional taxa than to add a comparable number of sites for the existing taxa. If the rates of evolution in the added taxa are slow, it is better to choose taxa connecting to a long edge, but if rates are comparable to a sister lineage, it is not necessarily the best strategy to sample taxa connected to a long edge. We also examined deleting taxa while increasing the number of sites. Although deleting a small number of taxa distant from the split of interest can be beneficial, deleting too many or making poor choices as to what should be deleted can lead to smaller probabilities of correct reconstruction than for the original sequence data.     

Bayes estimation of species divergence times and ancestral population sizes using DNA sequences from multiple loci

The effective population sizes of ancestral as well as modern species are important parameters in models of population genetics and human evolution. The commonly used method for estimating ancestral population sizes, based on counting mismatches between the species tree and the inferred gene trees, is highly biased as it ignores uncertainties in gene tree reconstruction. In this article, we develop a Bayes method for simultaneous estimation of the species divergence times and current and ancestral population sizes. The method uses DNA sequence data from multiple loci and extracts information about conflicts among gene tree topologies and coalescent times to estimate ancestral population sizes. The topology of the species tree is assumed known. A Markov chain Monte Carlo algorithm is implemented to integrate over uncertain gene trees and branch lengths (or coalescence times) at each locus as well as species divergence times. The method can handle any species tree and allows different numbers of sequences at different loci. We apply the method to published noncoding DNA sequences from the human and the great apes. There are strong correlations between posterior estimates of speciation times and ancestral population sizes. With the use of an informative prior for the human-chimpanzee divergence date, the population size of the common ancestor of the two species is estimated to be approximately 20,000, with a 95% credibility interval (8000, 40,000). Our estimates, however, are affected by model assumptions as well as data quality. We suggest that reliable estimates have yet to await more data and more realistic models.     

Estimation of evolutionary parameters with phylogenetic trees

An important issue in the phylogenetic analysis of nucleotide sequence data using the maximum likelihood (ML) method is the underlying evolutionary model employed. We consider the problem of simultaneously estimating the tree topology and the parameters in the underlying substitution model and of obtaining estimates of the standard errors of these parameter estimates. Given a fixed tree topology and corresponding set of branch lengths, the ML estimates of standard evolutionary model parameters are asymptotically efficient, in the sense that their joint distribution is asymptotically normal with the variance–covariance matrix given by the inverse of the Fisher information matrix. We propose a new estimate of this conditional variance based on estimation of the expected information using a Monte Carlo sampling (MCS) method. Simulations are used to compare this conditional variance estimate to the standard technique of using the observed information under a variety of experimental conditions. In the case in which one wishes to estimate simultaneously the tree and parameters, we provide a bootstrapping approach that can be used in conjunction with the MCS method to estimate the unconditional standard error. The methods developed are applied to a real data set consisting of 30 papillomavirus sequences. This overall method is easily incorporated into standard bootstrapping procedures to allow for proper variance estimation.     

Increased taxon sampling greatly reduces phylogenetic error

Several authors have argued recently that extensive taxon sampling has a positive and important effect on the accuracy of phylogenetic estimates. However, other authors have argued that there is little benefit of extensive taxon sampling, and so phylogenetic problems can or should be reduced to a few exemplar taxa as a means of reducing the computational complexity of the phylogenetic analysis. In this paper we examined five aspects of study design that may have led to these different perspectives. First, we considered the measurement of phylogenetic error across a wide range of taxon sample sizes, and conclude that the expected error based on randomly selecting trees (which varies by taxon sample size) must be considered in evaluating error in studies of the effects of taxon sampling. Second, we addressed the scope of the phylogenetic problems defined by different samples of taxa, and argue that phylogenetic scope needs to be considered in evaluating the importance of taxon-sampling strategies. Third, we examined the claim that fast and simple tree searches are as effective as more thorough searches at finding near-optimal trees that minimize error. We show that a more complete search of tree space reduces phylogenetic error, especially as the taxon sample size increases. Fourth, we examined the effects of simple versus complex simulation models on taxonomic sampling studies. Although benefits of taxon sampling are apparent for all models, data generated under more complex models of evolution produce higher overall levels of error and show greater positive effects of increased taxon sampling. Fifth, we asked if different phylogenetic optimality criteria show different effects of taxon sampling. Although we found strong differences in effectiveness of different optimality criteria as a function of taxon sample size, increased taxon sampling improved the results from all the common optimality criteria. Nonetheless, the method that showed the lowest overall performance (minimum evolution) also showed the least improvement from increased taxon sampling. Taking each of these results into account re-enforces the conclusion that increased sampling of taxa is one of the most important ways to increase overall phylogenetic accuracy.     

Experimental design in phylogenetics: testing predictions from expected information

Taxon and character sampling are central to phylogenetic experimental design; yet, we lack general rules. Goldman introduced a method to construct efficient sampling designs in phylogenetics, based on the calculation of expected Fisher information given a probabilistic model of sequence evolution. The considerable potential of this approach remains largely unexplored. In an earlier study, we applied Goldman's method to a problem in the phylogenetics of caecilian amphibians and made an a priori evaluation and testable predictions of which taxon additions would increase information about a particular weakly supported branch of the caecilian phylogeny by the greatest amount. We have now gathered mitogenomic and rag1 sequences (some newly determined for this study) from additional caecilian species and studied how information (both expected and observed) and bootstrap support vary as each new taxon is individually added to our previous data set. This provides the first empirical test of specific predictions made using Goldman's method for phylogenetic experimental design. Our results empirically validate the top 3 (more intuitive) taxon addition predictions made in our previous study, but only information results validate unambiguously the 4th (less intuitive) prediction. This highlights a complex relationship between information and support, reflecting that each measures different things: Information is related to the ability to estimate branch length accurately and support to the ability to estimate the tree topology accurately. Thus, an increase in information may be correlated with but does not necessitate an increase in support. Our results also provide the first empirical validation of the widely held intuition that additional taxa that join the tree proximal to poorly supported internal branches are more informative and enhance support more than additional taxa that join the tree more distally. Our work supports the view that adding more data for a single (well chosen) taxon may increase phylogenetic resolution and support in weakly supported parts of the tree without adding more characters/genes. Altogether our results corroborate that, although still underexplored, Goldman's method offers a powerful tool for experimental design in molecular phylogenetic studies. However, there are still several drawbacks to overcome, and further assessment of the method is needed in order to make it better understood, more accessible, and able to assess the addition of multiple taxa.     

氮添加对树木根系特性的影响

大气氮沉降对植物个体及整个生态系统都具有复杂的影响.本文共搜集39篇(16篇英文、23篇中文)已发表期刊论文的数据,通过整合分析方法分析了氮添加对树木根系特性的影响,并对比了发表在中、英文期刊上的结果差异.结果表明: 氮添加显著增加了细根直径(+6.7%)、细根氮含量(+8.9%)和细根呼吸速率(+17.5%),对细根生物量、细根长度、比根长、细根碳含量以及细根碳氮比的影响并不显著.不同的气候带类型和肥料类型对试验结果也具有不同的影响.另外,发表于英文期刊的试验结果的显著性普通高于发表在中文期刊上的结果.本文总结了氮添加对树木根系特性影响的普适性规律,以此分析了氮添加对森林生态系统碳循环影响的主要机理.     

Effects of taxon sampling and tree reconstruction methods on phylodiversity metrics

相似文献   

Sensitivity of phylogeny estimation to taxonomic sampling

Recent studies have shown that addition or deletion of taxa from a data matrix can change the estimate of phylogeny. I used 29 data sets from the literature to examine the effect of taxon sampling on phylogeny estimation within data sets. I then used multiple regression to assess the effect of number of taxa, number of characters, homoplasy, strength of support, and tree symmetry on the sensitivity of data sets to taxonomic sampling. Sensitivity to sampling was measured by mapping characters from a matrix of culled taxa onto optimal trees for that reduced matrix and onto the pruned optimal tree for the entire matrix, then comparing the length of the reduced tree to the length of the pruned complete tree. Within-data-set patterns can be described by a second-order equation relating fraction of taxa sampled to sensitivity to sampling. Multiple regression analyses found number of taxa to be a significant predictor of sensitivity to sampling; retention index, number of informative characters, total support index, and tree symmetry were nonsignificant predictors. I derived a predictive regression equation relating fraction of taxa sampled and number of taxa potentially sampled to sensitivity to taxonomic sampling and calculated values for this equation within the bounds of the variables examined. The length difference between the complete tree and a subsampled tree was generally small (average difference of 0-2.9 steps), indicating that subsampling taxa is probably not an important problem for most phylogenetic analyses using up to 20 taxa.     

Bayesian phylogenetic inference using DNA sequences: a Markov Chain Monte Carlo Method

An improved Bayesian method is presented for estimating phylogenetic trees using DNA sequence data. The birth-death process with species sampling is used to specify the prior distribution of phylogenies and ancestral speciation times, and the posterior probabilities of phylogenies are used to estimate the maximum posterior probability (MAP) tree. Monte Carlo integration is used to integrate over the ancestral speciation times for particular trees. A Markov Chain Monte Carlo method is used to generate the set of trees with the highest posterior probabilities. Methods are described for an empirical Bayesian analysis, in which estimates of the speciation and extinction rates are used in calculating the posterior probabilities, and a hierarchical Bayesian analysis, in which these parameters are removed from the model by an additional integration. The Markov Chain Monte Carlo method avoids the requirement of our earlier method for calculating MAP trees to sum over all possible topologies (which limited the number of taxa in an analysis to about five). The methods are applied to analyze DNA sequences for nine species of primates, and the MAP tree, which is identical to a maximum-likelihood estimate of topology, has a probability of approximately 95%.      

Evolutionary history of vegetative reproduction in Porpidia s.L. (Lichen-forming ascomycota)

The evolutionary history of gains and losses of vegetative reproductive propagules (soredia) in Porpidia s.l., a group of lichen-forming ascomycetes, was clarified using Bayesian Markov chain Monte Carlo (MCMC) approaches to monophyly tests and a combined MCMC and maximum likelihood approach to ancestral character state reconstructions. The MCMC framework provided confidence estimates for the reconstructions of relationships and ancestral character states, which formed the basis for tests of evolutionary hypotheses. Monophyly tests rejected all hypotheses that predicted any clustering of reproductive modes in extant taxa. In addition, a nearest-neighbor statistic could not reject the hypothesis that the vegetative reproductive mode is randomly distributed throughout the group. These results show that transitions between presence and absence of the vegetative reproductive mode within Porpidia s.l. occurred several times and independently of each other. Likelihood reconstructions of ancestral character states at selected nodes suggest that--contrary to previous thought--the ancestor to Porpidia s.l. already possessed the vegetative reproductive mode. Furthermore, transition rates are reconstructed asymmetrically with the vegetative reproductive mode being gained at a much lower rate than it is lost. A cautious note has to be added, because a simulation study showed that the ancestral character state reconstructions were highly dependent on taxon sampling. However, our central conclusions, particularly the higher rate of change from vegetative reproductive mode present to absent than vice versa within Porpidia s.l., were found to be broadly independent of taxon sampling.