Empirical evaluation of a prior for Bayesian phylogenetic inference

The Bayesian method of phylogenetic inference often produces high posterior probabilities (PPs) for trees or clades, even when the trees are clearly incorrect. The problem appears to be mainly due to large sizes of molecular datasets and to the large-sample properties of Bayesian model selection and its sensitivity to the prior when several of the models under comparison are nearly equally correct (or nearly equally wrong) and are of the same dimension. A previous suggestion to alleviate the problem is to let the internal branch lengths in the tree become increasingly small in the prior with the increase in the data size so that the bifurcating trees are increasingly star-like. In particular, if the internal branch lengths are assigned the exponential prior, the prior mean mu0 should approach zero faster than 1/square root n but more slowly than 1/n, where n is the sequence length. This paper examines the usefulness of this data size-dependent prior using a dataset of the mitochondrial protein-coding genes from the baleen whales, with the prior mean fixed at mu0=0.1n(-2/3). In this dataset, phylogeny reconstruction is sensitive to the assumed evolutionary model, species sampling and the type of data (DNA or protein sequences), but Bayesian inference using the default prior attaches high PPs for conflicting phylogenetic relationships. The data size-dependent prior alleviates the problem to some extent, giving weaker support for unstable relationships. This prior may be useful in reducing apparent conflicts in the results of Bayesian analysis or in making the method less sensitive to model violations.     

Borders,paradox and power

Border studies have grappled with, on the one hand, the need for the use of common themes or concepts while, on the other, the need for contextual specificity. Borders are sites that embody different potentialities: division and contact, conflict and cooperation, security and anxiety, creativity and oppression, among others. In short, they are sites of the paradoxical. Paradox, it is argued, is the common overarching conceptual characteristic of borders but which specific potentialities are embodied in a border and what prevails as a result of the ensuing power struggles requires contextual specificity. Cyprus, a divided island lying on various border lines, partly inside and partly outside the EU, presents a useful socio-political space in order to illustrate this argument by outlining the specific paradoxical aspects of its own border and the results of the ensuing power struggles.     

Condition-dependence,genotype-by-environment interactions and the lek paradox

The lek paradox states that maintaining genetic variation necessary for 'indirect benefit' models of female choice is difficult, and two interrelated solutions have been proposed. 'Genic capture' assumes condition-dependence of sexual traits, while genotype-by-environment interactions (GEIs) offer an additional way to maintain diversity. However, condition-dependence, particularly with GEIs, implies that environmental variation can blur the relationship between male displays and offspring fitness. These issues have been treated separately in the past. Here we combine them in a population genetic model, and show that predictions change not only in magnitude but also in direction when the timing of dispersal between environments relative to the life cycle is changed. GEIs can dramatically improve the evolution of costly female preferences, but also hamper it if much dispersal occurs between the life history stage where condition is determined and mating. This situation also arises if selection or mutation rates are too high. In general, our results highlight that when evaluating any mechanism promoted as a potential resolution of the lek paradox, it is not sufficient to focus on its effects on genetic variation. It also has to be assessed to what extent the proposed mechanism blurs the association between male attractiveness and offspring fitness; the net balance of these two effects can be positive or negative, and often strongly context-dependent.     

Condition-dependence, genotype-by-environment interactions and the lek paradox

The lek paradox states that maintaining genetic variation necessary for ‘indirect benefit’ models of female choice is difficult, and two interrelated solutions have been proposed. ‘Genic capture’ assumes condition-dependence of sexual traits, while genotype-by-environment interactions (GEIs) offer an additional way to maintain diversity. However, condition-dependence, particularly with GEIs, implies that environmental variation can blur the relationship between male displays and offspring fitness. These issues have been treated separately in the past. Here we combine them in a population genetic model, and show that predictions change not only in magnitude but also in direction when the timing of dispersal between environments relative to the life cycle is changed. GEIs can dramatically improve the evolution of costly female preferences, but also hamper it if much dispersal occurs between the life history stage where condition is determined and mating. This situation also arises if selection or mutation rates are too high. In general, our results highlight that when evaluating any mechanism promoted as a potential resolution of the lek paradox, it is not sufficient to focus on its effects on genetic variation. It also has to be assessed to what extent the proposed mechanism blurs the association between male attractiveness and offspring fitness; the net balance of these two effects can be positive or negative, and often strongly context-dependent.     

Persistence, spread and the drift paradox

We derive conditions for persistence and spread of a population where individuals are either immobile or dispersing by advection and diffusion through a one-dimensional medium with a unidirectional flow. Reproduction occurs only in the stationary phase. Examples of such systems are found in rivers and streams, marine currents, and areas with prevalent wind direction. In streams, a long-standing question, dubbed 'the drift paradox', asks why aquatic insects faced with downstream drift are able to persist in upper stream reaches. For our two-phase model, persistence of the population is guaranteed if, at low population densities, the local growth rate of the stationary component of the population exceeds the rate of entry of individuals into the drift. Otherwise the persistence condition involves all the model parameters, and persistence requires a critical (minimum) domain size. We calculate the rate at which invasion fronts propagate up- and downstream, and show that persistence and ability to spread are closely connected: if the population cannot advance upstream against the flow, it also cannot persist on any finite spatial domain. By studying two limiting cases of our model, we show that residence in the immobile state always enhances population persistence. We use our findings to evaluate a number of mechanisms previously proposed in the ecological literature as resolutions of the drift paradox.     

Bayesian model adequacy and choice in phylogenetics

Bayesian inference is becoming a common statistical approach to phylogenetic estimation because, among other reasons, it allows for rapid analysis of large data sets with complex evolutionary models. Conveniently, Bayesian phylogenetic methods use currently available stochastic models of sequence evolution. However, as with other model-based approaches, the results of Bayesian inference are conditional on the assumed model of evolution: inadequate models (models that poorly fit the data) may result in erroneous inferences. In this article, I present a Bayesian phylogenetic method that evaluates the adequacy of evolutionary models using posterior predictive distributions. By evaluating a model's posterior predictive performance, an adequate model can be selected for a Bayesian phylogenetic study. Although I present a single test statistic that assesses the overall (global) performance of a phylogenetic model, a variety of test statistics can be tailored to evaluate specific features (local performance) of evolutionary models to identify sources failure. The method presented here, unlike the likelihood-ratio test and parametric bootstrap, accounts for uncertainty in the phylogeny and model parameters.     

The Gibbs paradox and unidirectional fluxes

The Gibbs paradox is introduced by means of a particular example: the interdiffusion of two molecular species through a membrane. In the limit when passing from the interdiffusion of two distinct species to that of identical species, the equation for dissipation (or, equivalently, entropy production) fails catastrophically. In the case of an equilibrium system, one finds the paradoxical situation of a zero net flux in conjunction with nonzero dissipation. A general analysis of the problem is given in terms of a metrical theory of irreversible thermodynamics. Its mathematical structure provides a criterion for identity sufficient to resolve the paradox. Metrical aspects of the Principle of Superposition are examined. The paper ends with a discussion of the conceptual and physical difficulties that the Gibbs paradox poses for the idea of unidirectional fluxes. In particular, it is demonstrated that the commonly held notion that net flux is a superposition of an inward and an outward flux violates the Second Law.     

缺失数据和贝叶斯系统发育分析精确度之探索

The effect of missing data on phylogenetic methods is a potentially important issue in our attempts to reconstruct the Tree of Life. If missing data are truly problematic, then it may be unwise to include species in an analysis that lack data for some characters (incomplete taxa) or to include characters that lack data for some species. Given the difficulty of obtaining data from all characters for all taxa (e.g., fossils), missing data might seriously impede efforts to reconstruct a comprehensive phylogeny that includes all species. Fortunately, recent simulations and empirical analyses suggest that missing data cells are not themselves problematic, and that incomplete taxa can be accurately placed as long as the overall number of characters in the analysis is large. However, these studies have so far only been conducted on parsimony, likelihood, and neighbor-joining methods. Although Bayesian phylogenetic methods have become widely used in recent years, the effects of missing data on Bayesian analysis have not been adequately studied. Here, we conduct simulations to test whether Bayesian analyses can accurately place incomplete taxa despite extensive missing data. In agreement with previous studies of other methods, we find that Bayesian analyses can accurately reconstruct the position of highly incomplete taxa (i.e., 95% missing data), as long as the overall number of characters in the analysis is large. These results suggest that highly incomplete taxa can be safely included in many Bayesian phylogenetic analyses.     

Life history,immunity, Peto's paradox and tumours in birds

Cancer and tumours may evolve in response to life‐history trade‐offs between growth and duration of development on one hand, and between growth and maintenance of immune function on the other. Here, we tested whether (i) bird species with slow developmental rates for their body size experience low incidence of tumours because slow development allows for detection of rapid proliferation of cell lineages. We also test whether (ii) species with stronger immune response during development are more efficient at detecting tumour cells and hence suffer lower incidence of tumours. Finally, we tested Peto's paradox, that there is a positive relationship between tumour incidence and body mass. We used information on developmental rates and body mass from the literature and of tumour incidence (8468 birds) and size of the bursa of Fabricius for 7659 birds brought to a taxidermist in Denmark. We found evidence of the expected negative relationship between incidence of tumours and developmental rates and immunity after controlling for the positive association between tumour incidence and body size. These results suggest that evolution has modified the incidence of tumours in response to life history and that Peto's paradox may be explained by covariation between body mass, developmental rates and immunity.     

Bayesian phylogenetics with BEAUti and the BEAST 1.7

Computational evolutionary biology, statistical phylogenetics and coalescent-based population genetics are becoming increasingly central to the analysis and understanding of molecular sequence data. We present the Bayesian Evolutionary Analysis by Sampling Trees (BEAST) software package version 1.7, which implements a family of Markov chain Monte Carlo (MCMC) algorithms for Bayesian phylogenetic inference, divergence time dating, coalescent analysis, phylogeography and related molecular evolutionary analyses. This package includes an enhanced graphical user interface program called Bayesian Evolutionary Analysis Utility (BEAUti) that enables access to advanced models for molecular sequence and phenotypic trait evolution that were previously available to developers only. The package also provides new tools for visualizing and summarizing multispecies coalescent and phylogeographic analyses. BEAUti and BEAST 1.7 are open source under the GNU lesser general public license and available at http://beast-mcmc.googlecode.com and http://beast.bio.ed.ac.uk.     

Model parameterization, prior distributions, and the general time-reversible model in Bayesian phylogenetics

Bayesian phylogenetic methods require the selection of prior probability distributions for all parameters of the model of evolution. These distributions allow one to incorporate prior information into a Bayesian analysis, but even in the absence of meaningful prior information, a prior distribution must be chosen. In such situations, researchers typically seek to choose a prior that will have little effect on the posterior estimates produced by an analysis, allowing the data to dominate. Sometimes a prior that is uniform (assigning equal prior probability density to all points within some range) is chosen for this purpose. In reality, the appropriate prior depends on the parameterization chosen for the model of evolution, a choice that is largely arbitrary. There is an extensive Bayesian literature on appropriate prior choice, and it has long been appreciated that there are parameterizations for which uniform priors can have a strong influence on posterior estimates. We here discuss the relationship between model parameterization and prior specification, using the general time-reversible model of nucleotide evolution as an example. We present Bayesian analyses of 10 simulated data sets obtained using a variety of prior distributions and parameterizations of the general time-reversible model. Uniform priors can produce biased parameter estimates under realistic conditions, and a variety of alternative priors avoid this bias.     

Combined data, Bayesian phylogenetics, and the origin of the New Zealand cicada genera

We have applied Bayesian and maximum likelihood methods of phylogenetic estimation to data from four mitochondrial genes (COI, COII, 12S, and 16S) and a single nuclear gene (EF1alpha) from several genera of New Zealand, Australian, and New Caledonian cicada taxa. We specifically focused on the heterogeneity of phylogenetic signal among the different data partitions and the biogeographic origins of the New Zealand cicada fauna. The Bayesian analyses circumvent many of the problems associated with other statistical tests for comparing data partitions. We took an information-theoretic approach to model selection based on the Akaike Information Criterion (AIC). This approach indicated that there was considerable uncertainty in identifying the best-fit model for some of the partitions. Additionally, a large amount of uncertainty was associated with many parameter estimates from the substitution model. However, a sensitivity analysis on the combined dataset indicated that the model selection uncertainty had little effect on estimates of topology because these estimates were largely insensitive to changes in the assumed model. This outcome suggests strong signal in our data. Our analyses support a New Caledonian affiliation of the New Zealand cicada genera Maoricicada, Kikihia, and Rhodopsalta and Australian affinities for the genera Amphipsalta and Notopsalta. This result was surprising, given that previous cicada biologists suspected a close relationship between Amphipsalta, Notopsalta, and Rhodopsalta based on genitalic characters. Relationships among the closely related genera Maoricicada, Kikihia, and Rhodopsalta were poorly resolved, the mitochondrial data and the EF1alpha data favoring different arrangements within this clade.     

Bayesian design of noninferiority trials for medical devices using historical data

Summary We develop a new Bayesian approach of sample size determination (SSD) for the design of noninferiority clinical trials. We extend the fitting and sampling priors of Wang and Gelfand (2002, Statistical Science 17 , 193–208) to Bayesian SSD with a focus on controlling the type I error and power. Historical data are incorporated via a hierarchical modeling approach as well as the power prior approach of Ibrahim and Chen (2000, Statistical Science 15 , 46–60). Various properties of the proposed Bayesian SSD methodology are examined and a simulation‐based computational algorithm is developed. The proposed methodology is applied to the design of a noninferiority medical device clinical trial with historical data from previous trials.     

Bayesian shrinkage analysis of QTLs under shape-adaptive shrinkage priors, and accurate re-estimation of genetic effects

The successful implementation of Bayesian shrinkage analysis of high-dimensional regression models, as often encountered in quantitative trait locus (QTL) mapping, is contingent upon the choice of suitable sparsity-inducing priors. In practice, the shape (that is, the rate of tail decay) of such priors is typically preset, with no regard for the range of plausible alternatives and the fact that the most appropriate shape may depend on the data at hand. This study is presumably the first attempt to tackle this oversight through the shape-adaptive shrinkage prior (SASP) approach, with a focus on the mapping of QTLs in experimental crosses. Simulation results showed that the separation between genuine QTL effects and spurious ones can be made clearer using the SASP-based approach as compared with existing competitors. This feature makes our new method a promising approach to QTL mapping, where good separation is the ultimate goal. We also discuss a re-estimation procedure intended to improve the accuracy of the estimated genetic effects of detected QTLs with regard to shrinkage-induced bias, which may be particularly important in large-scale models with collinear predictors. The re-estimation procedure is relevant to any shrinkage method, and is potentially valuable for many scientific disciplines such as bioinformatics and quantitative genetics, where oversaturated models are booming.     

Reliability of Bayesian posterior probabilities and bootstrap frequencies in phylogenetics

Many empirical studies have revealed considerable differences between nonparametric bootstrapping and Bayesian posterior probabilities in terms of the support values for branches, despite claimed predictions about their approximate equivalence. We investigated this problem by simulating data, which were then analyzed by maximum likelihood bootstrapping and Bayesian phylogenetic analysis using identical models and reoptimization of parameter values. We show that Bayesian posterior probabilities are significantly higher than corresponding nonparametric bootstrap frequencies for true clades, but also that erroneous conclusions will be made more often. These errors are strongly accentuated when the models used for analyses are underparameterized. When data are analyzed under the correct model, nonparametric bootstrapping is conservative. Bayesian posterior probabilities are also conservative in this respect, but less so.     

A solution to the human paradox: fundamental ontogenies and heterochronies

Solving the human paradox means explaining how a genetic difference of a mere 1% can be consistent with 5 million years of anatomical transformation from great apes to present-dayHomo sapiens. The solution proposed here is that of the internal history of ontogenetic change. A concept of “fundamental ontogeny” is developed and deduced from comparison between living and fossil primates. The fossil human lineage can be summarized into five fundamental ontogenies corresponding to successive skull plans (bauplans) resulting from five major phases of craniofacial contraction: prosimians (adapiforms), monkey apes (propliopithecidae), great apes (dryopithecidae), australopithecines andHomo. The morphological areas defined by these skull plans include more-or-less numerous species. This concept leads to renewed debate about (i) the relationship between speciation and bauplans, and (ii) the mechanisms involved in the successive steps of cranio-facial contraction and the correlated morphological changes. It is suggested that, from great apes to modern man, numerous heterochronies (hypermorphosis, hypomorphosis and post-displacements) have occurred during ontogeny, allowing the acquisition of permanent bipedalism inAustralopithecus andHomo, the increased cranial capacity of primitive forms ofHomo, and the disappearance of simian characters associated with renewed increase in cranial capacity inH. sapiens.