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  • 1.
    Höhna, Sebastian
    Stockholm University, Faculty of Science, Department of Mathematics.
    Bayesian Phylogenetic Inference2011Licentiate thesis, comprehensive summary (Other academic)
    Abstract [en]

    In this thesis we consider two very different topics in Bayesian phylogenetic inference. The first paper, "Inferring speciation and extinction rates under different sampling schemes" by Sebastian Höhna, Tanja Stadler, Fredrik Ronquist and Tom Britton, focuses on estimating the rates of speciation and extinction of species when only a subsample of the present day species is available. The second paper "Burnin Estimation and Convergence Assessment" by Sebastian Höhna and Kristoffer Sahlin focuses on how to analyze the output of Markov chain Monte Carlo (MCMC) runs with respect to convergence to the stationary distribution and approximation of the posterior probability distribution.

    The birth-death process is used to describe the evolution of species diversity. Previous work enabled the estimation of speciation and extinction rates under the assumption of a constant rate birth-death process and complete sampling of all extant species. We extend the complete sampled birth-death process to incomplete sampling with three different types of sampling schemes: random sampling, diversified sampling and clustered sampling. On a set of empirical phylogenies with known sampling fraction we observe that taking the sampling fraction into account gives better fitting models, either by random sampling or diversified sampling.

    The current trend in Bayesian phylogenetic inference is to extend the available models by using more complex models and/or hierarchical models. This renders Bayesian inference by means of the MCMC algorithm very intricate. Performance of single or multiple MCMC runs need to be assessed. We investigate which methods are used in Bayesian phylogenetics to assess the performance of MCMC runs, which methods are available from other research areas and compile a strategy on how to assess convergence and how to estimate the burnin automatically in a statistically sound framework.

  • 2.
    Höhna, Sebastian
    Stockholm University, Faculty of Science, Department of Mathematics.
    Bayesian Phylogenetic Inference: Estimating Diversification Rates from Reconstructed Phylogenies2013Doctoral thesis, comprehensive summary (Other academic)
    Abstract [en]

    Phylogenetics is the study of the evolutionary relationship between species. Inference of phylogeny relies heavily on statistical models that have been extended and refined tremendously over the past years into very complex hierarchical models. Paper I introduces probabilistic graphical models to statistical phylogenetics and elaborates on the potential advantages a unified graphical model representation could have for the community, e.g., by facilitating communication and improving reproducibility of statistical analyses of phylogeny and evolution.

    Once the phylogeny is reconstructed it is possible to infer the rates of diversification (speciation and extinction). In this thesis I extend the birth-death process model, so that it can be applied to incompletely sampled phylogenies, that is, phylogenies of only a subsample of the presently living species from one group. Previous work only considered the case when every species had the same probability to be included and here I examine two alternative sampling schemes: diversified taxon sampling and cluster sampling. Paper II introduces these sampling schemes under a constant rate birth-death process and gives the probability density for reconstructed phylogenies. These models are extended in Paper IV to time-dependent diversification rates, again, under different sampling schemes and applied to empirical phylogenies. Paper III focuses on fast and unbiased simulations of reconstructed phylogenies. The efficiency is achieved by deriving the analytical distribution and density function of the speciation times in the reconstructed phylogeny.

  • 3.
    Höhna, Sebastian
    Stockholm University, Faculty of Science, Department of Mathematics.
    Fast simulation of reconstructed phylogenies under global time-dependent birth-death processes2013In: Bioinformatics, ISSN 1367-4803, E-ISSN 1367-4811, Vol. 29, no 11, p. 1367-1374Article in journal (Refereed)
    Abstract [en]

    Motivation: Diversification rates and patterns may be inferred from reconstructed phylogenies. Both the time-dependent and the diversity-dependent birthdeath process can produce the same observed patterns of diversity over time. To develop and test new models describing the macro-evolutionary process of diversification, generic and fast algorithms to simulate under these models are necessary. Simulations are not only important for testing and developing models but play an influential role in the assessment of model fit.

    Results: In the present article, I consider as the model a global time-dependent birthdeath process where each species has the same rates but rates may vary over time. For this model, I derive the likelihood of the speciation times from a reconstructed phylogenetic tree and show that each speciation event is independent and identically distributed. This fact can be used to simulate efficiently reconstructed phylogenetic trees when conditioning on the number of species, the time of the process or both. I show the usability of the simulation by approximating the posterior predictive distribution of a birthdeath process with decreasing diversification rates applied on a published bird phylogeny (family Cettiidae).

    Availability: The methods described in this manuscript are implemented in the R package TESS, available from the repository CRAN (http://cran.r-project.org/web/packages/TESS/).

  • 4.
    Höhna, Sebastian
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Drummond, Alexei J.
    Guided Tree Topology Proposals for Bayesian Phylogenetic Inference2012In: Systematic Biology, ISSN 1063-5157, E-ISSN 1076-836X, Vol. 61, no 1, p. 1-11Article in journal (Refereed)
    Abstract [en]

    Increasingly, large data sets pose a challenge for computationally intensive phylogenetic methods such as Bayesian Markov chain Monte Carlo (MCMC). Here, we investigate the performance of common MCMC proposal distributions in terms of median and variance of run time to convergence on 11 data sets. We introduce two new Metropolized Gibbs Samplers for moving through tree space. MCMC simulation using these new proposals shows faster average run time and dramatically improved predictability in performance, with a 20-fold reduction in the variance of the time to estimate the posterior distribution to a given accuracy. We also introduce conditional clade probabilities and demonstrate that they provide a superior means of approximating tree topology posterior probabilities from samples recorded during MCMC.

  • 5.
    Höhna, Sebastian
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Heath, Tracy A.
    University of California, Berkeley.
    Boussau, Bastien
    University of California, Berkeley .
    Landis, Michael J.
    University of California, Berkeley .
    Ronquist, Fredrik
    Swedish Museum of Natural History.
    Huelsenbeck, John P.
    University of California, Berkeley .
    Probabilistic Graphical Model Representation in PhylogeneticsManuscript (preprint) (Other academic)
    Abstract [en]

    Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to model representation and software development. Clear communication and representation of the chosen model is crucial for: (1) reproducibility of an analysis, (2) model development and (3) software design. Moreover, a unified, clear and understandable framework formodel representation lowers the barrier for beginning scientists and non-specialists to grasp the model including the assumptions and parameter/variable dependencies.

    Graphical models is such a unifying framework that has gained in popularity in the statistical literature in recent years. The core idea isto break complex models into conditionally independent distributions and the strength lies in, amongst others: comprehensibility, flexibility, adaptability and computational algorithms. Graphical models can be used to teach statistical models, to facilitate communication among phylogeneticists and in the development of generic software for simulation and statistical inference.

    Here, we provide an introduction to graphical models for phylogeneticists and extend the standard graphical model representation to the realm of phylogenetics. We introduce a new graphical model component, tree plates, to capture the changing structure of the subgraph corresponding to a phylogenetic tree. We describe a range of phylogenetic models using the graphical model framework and built these into separate, interchangeable modules. Phylogenetic model graphs can be readily used in simulation, maximum likelihood inference, and Bayesian inference using either Metropolis-Hastings or Gibbs sampling of the posterior distribution.

  • 6.
    Höhna, Sebastian
    et al.
    Stockholm University, Faculty of Science, Department of Mathematics.
    Sahlin, Kristoffer
    Royal Institute of Technology (KTH).
    Burnin Estimation and Convergence AssessmentManuscript (preprint) (Other academic)
    Abstract [en]

    Estimating the burnin length and assessing convergence purely from the output of an MCMC run is increasingly important in Bayesian phylogenetic inference. Previously, methods for estimating the burnin and assessing convergence have been ad-hoc, such as the minimum number of effective samples or the deviation in split frequencies. In this paper we compare the currently used methods to convergence assessment methods from the mathematical literature, namely the Geweke test and the Heidelberger-Welch test. The latter two show strong advantages in being statistically consistent and unbiased. Statistical consistency and unbiasedness was verified on simulated data with known posterior distributions. Both methods consider convergence as the Null hypothesis. The Null hypothesis is rejected based on standard p-values, which are easier to interpret than a threshold as used by the eeffective sample size. We extend these convergence assessment methods for single and multiple chains. Furthermore, we test the performance of the convergence assessment methods on an empirical dataset and conclude that tests for convergence to the same stationary distribution from independent runs are most adequate. Additionally,we developed an automatic procedure that finds the optimal burnin in the cases we studied. All methods we tested are implemented in the open source software RevBayes (http://www.revbayes.net/).

  • 7. Ronquist, Fredrik
    et al.
    Teslenko, Maxim
    van der Mark, Paul
    Ayres, Daniel L.
    Darling, Aaron
    Höhna, Sebastian
    Stockholm University, Faculty of Science, Department of Mathematics.
    Larget, Bret
    Liu, Liang
    Suchard, Marc A.
    Huelsenbeck, John P.
    MrBayes 3.2: Efficient Bayesian Phylogenetic Inference and Model Choice Across a Large Model Space2012In: Systematic Biology, ISSN 1063-5157, E-ISSN 1076-836X, Vol. 61, no 3, p. 539-542Article in journal (Refereed)
    Abstract [en]

    Since its introduction in 2001, MrBayes has grown in popularity as a software package for Bayesian phylogenetic inference using Markov chain Monte Carlo (MCMC) methods. With this note, we announce the release of version 3.2, a major upgrade to the latest official release presented in 2003. The new version provides convergence diagnostics and allows multiple analyses to be run in parallel with convergence progress monitored on the fly. The introduction of new proposals and automatic optimization of tuning parameters has improved convergence for many problems. The new version also sports significantly faster likelihood calculations through streaming single-instruction-multiple-data extensions (SSE) and support of the BEAGLE library, allowing likelihood calculations to be delegated to graphics processing units (GPUs) on compatible hardware. Speedup factors range from around 2 with SSE code to more than 50 with BEAGLE for codon problems. Checkpointing across all models allows long runs to be completed even when an analysis is prematurely terminated. New models include relaxed clocks, dating, model averaging across time-reversible substitution models, and support for hard, negative, and partial (backbone) tree constraints. Inference of species trees from gene trees is supported by full incorporation of the Bayesian estimation of species trees (BEST) algorithms. Marginal model likelihoods for Bayes factor tests can be estimated accurately across the entire model space using the stepping stone method. The new version provides more output options than previously, including samples of ancestral states, site rates, site d(N)/d(S) rations, branch rates, and node dates. A wide range of statistics on tree parameters can also be output for visualization in FigTree and compatible software.

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