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1. Practical guidelines for Bayesian phylogenetic inference using Markov Chain Monte Carlo (MCMC)

   Barido-Sottani, J; Schwery, O; Warnock, RCM; Zhang, C; Wright, AM (June 2024, Open research Europe)

   Phylogenetic estimation is, and has always been, a complex endeavor. Estimating a phylogenetic tree involves evaluating many possible solutions and possible evolutionary histories that could explain a set of observed data, typically by using a model of evolution. Modern statistical methods involve not just the estimation of a tree, but also solutions to more complex models involving fossil record information and other data sources. Markov Chain Monte Carlo (MCMC) is a leading method for approximating the posterior distribution of parameters in a mathematical model. It is deployed in all Bayesian phylogenetic tree estimation software. While many researchers use MCMC in phylogenetic analyses, interpreting results and diagnosing problems with MCMC remain vexing issues to many biologists. In this manuscript, we will offer an overview of how MCMC is used in Bayesian phylogenetic inference, with a particular emphasis on complex hierarchical models, such as the fossilized birth-death (FBD) model. We will discuss strategies to diagnose common MCMC problems and troubleshoot difficult analyses, in particular convergence issues. We will show how the study design, the choice of models and priors, but also technical features of the inference tools themselves can all be adjusted to obtain the best results. Finally, we will also discuss the unique challenges created by the incorporation of fossil information in phylogenetic inference, and present tips to address them. 

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2. Multimodal parameter spaces of a complex multi-channel neuron model

   https://doi.org/10.3389/fnsys.2022.999531  

   Wang, Y. Curtis; Rudi, Johann; Velasco, James; Sinha, Nirvik; Idumah, Gideon; Powers, Randall K.; Heckman, Charles J.; Chardon, Matthieu K. (October 2022, Frontiers in Systems Neuroscience)

   One of the most common types of models that helps us to understand neuron behavior is based on the Hodgkin–Huxley ion channel formulation (HH model). A major challenge with inferring parameters in HH models is non-uniqueness: many different sets of ion channel parameter values produce similar outputs for the same input stimulus. Such phenomena result in an objective function that exhibits multiple modes (i.e., multiple local minima). This non-uniqueness of local optimality poses challenges for parameter estimation with many algorithmic optimization techniques. HH models additionally have severe non-linearities resulting in further challenges for inferring parameters in an algorithmic fashion. To address these challenges with a tractable method in high-dimensional parameter spaces, we propose using a particular Markov chain Monte Carlo (MCMC) algorithm, which has the advantage of inferring parameters in a Bayesian framework. The Bayesian approach is designed to be suitable for multimodal solutions to inverse problems. We introduce and demonstrate the method using a three-channel HH model. We then focus on the inference of nine parameters in an eight-channel HH model, which we analyze in detail. We explore how the MCMC algorithm can uncover complex relationships between inferred parameters using five injected current levels. The MCMC method provides as a result a nine-dimensional posterior distribution, which we analyze visually with solution maps or landscapes of the possible parameter sets. The visualized solution maps show new complex structures of the multimodal posteriors, and they allow for selection of locally and globally optimal value sets, and they visually expose parameter sensitivities and regions of higher model robustness. We envision these solution maps as enabling experimentalists to improve the design of future experiments, increase scientific productivity and improve on model structure and ideation when the MCMC algorithm is applied to experimental data. 

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3. Properties of Markov Chain Monte Carlo Performance across Many Empirical Alignments

   https://doi.org/10.1093/molbev/msaa295  

   Harrington, Sean M; Wishingrad, Van; Thomson, Robert C (November 2020, Molecular Biology and Evolution)

   Pupko, Tal (Ed.)

   Abstract Nearly all current Bayesian phylogenetic applications rely on Markov chain Monte Carlo (MCMC) methods to approximate the posterior distribution for trees and other parameters of the model. These approximations are only reliable if Markov chains adequately converge and sample from the joint posterior distribution. Although several studies of phylogenetic MCMC convergence exist, these have focused on simulated data sets or select empirical examples. Therefore, much that is considered common knowledge about MCMC in empirical systems derives from a relatively small family of analyses under ideal conditions. To address this, we present an overview of commonly applied phylogenetic MCMC diagnostics and an assessment of patterns of these diagnostics across more than 18,000 empirical analyses. Many analyses appeared to perform well and failures in convergence were most likely to be detected using the average standard deviation of split frequencies, a diagnostic that compares topologies among independent chains. Different diagnostics yielded different information about failed convergence, demonstrating that multiple diagnostics must be employed to reliably detect problems. The number of taxa and average branch lengths in analyses have clear impacts on MCMC performance, with more taxa and shorter branches leading to more difficult convergence. We show that the usage of models that include both Γ-distributed among-site rate variation and a proportion of invariable sites is not broadly problematic for MCMC convergence but is also unnecessary. Changes to heating and the usage of model-averaged substitution models can both offer improved convergence in some cases, but neither are a panacea. 

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4. Handling Logical Character Dependency in Phylogenetic Inference: Extensive Performance Testing of Assumptions and Solutions Using Simulated and Empirical Data

   https://doi.org/10.1093/sysbio/syad006  

   Simões, TR; Vernygora, OV; and de Medeiros, BAS (April 2023, Systematic biology)

   Liliana Davalos (Ed.)

   Logical character dependency is a major conceptual and methodological problem in phylogenetic inference of morphological data sets, as it violates the assumption of character independence that is common to all phylogenetic methods. It is more frequently observed in higher-level phylogenies or in data sets characterizing major evolutionary transitions, as these represent parts of the tree of life where (primary) anatomical characters either originate or disappear entirely. As a result, secondary traits related to these primary characters become “inapplicable” across all sampled taxa in which that character is absent. Various solutions have been explored over the last three decades to handle character dependency, such as alternative character coding schemes and, more recently, new algorithmic implementations. However, the accuracy of the proposed solutions, or the impact of character dependency across distinct optimality criteria, has never been directly tested using standard performance measures. Here, we utilize simple and complex simulated morphological data sets analyzed under different maximum parsimony optimization procedures and Bayesian inference to test the accuracy of various coding and algorithmic solutions to character dependency. This is complemented by empirical analyses using a recoded data set on palaeognathid birds. We find that in small, simulated data sets, absent coding performs better than other popular coding strategies available (contingent and multistate), whereas in more complex simulations (larger data sets controlled for different tree structure and character distribution models) contingent coding is favored more frequently. Under contingent coding, a recently proposed weighting algorithm produces the most accurate results for maximum parsimony. However, Bayesian inference outperforms all parsimony-based solutions to handle character dependency due to fundamental differences in their optimization procedures—a simple alternative that has been long overlooked. Yet, we show that the more primary characters bearing secondary (dependent) traits there are in a data set, the harder it is to estimate the true phylogenetic tree, regardless of the optimality criterion, owing to a considerable expansion of the tree parameter space. 

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5. The Impact of Model Misspecification on Phylogenetic Network Inference

   https://doi.org/10.18061/bssb.v3i1.9553  

   Cao, Zhen; Li, Meng; Ogilvie, Huw; Nakhleh, Luay (July 2024, Bulletin of the Society of Systematic Biologists)

   The development of statistical methods to infer species phylogenies with reticulations (species networks) has led to many discoveries of gene flow between distinct species. These methods typically assume only incomplete lineage sorting and introgression. Given that phylogenetic networks can be arbitrarily complex, these methods might compensate for model misspecification by increasing the number of dimensions beyond the true value. Herein, we explore the effect of potential model misspecification, including the negligence of gene tree estimation error (GTEE) and assumption of a single substitution rate for all genomic loci, on the accuracy of phylogenetic network inference using both simulated and biological data. In particular, we assess the accuracy of estimated phylogenetic networks as well as test statistics for determining whether a network is the correct evolutionary history, as opposed to the simpler model that is a tree.We found that while GTEE negatively impacts the performance of test statistics to determine the “treeness” of the evolutionary history of a data set, running those tests on triplets of taxa and correcting for multiple-testing significantly ameliorates the problem. We also found that accounting for substitution rate heterogeneity improves the reliability of full Bayesian inference methods of phylogenetic networks, whereas summary statistic methods are robust to GTEE and rate heterogeneity, though currently require manual inspection to determine the network complexity. 

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