Alexei J. Drummond

Climbing grades are used to classify a climbing route based on its perceived difficulty, and have come to play a central role in the sport of rock climbing. Recently, the first statistically rigorous method for estimating climbing grades from whole-history ascent data was described (Scarff, D. (2020). Estimation of climbing route difficulty using whole-history rating. arXiv preprint arXiv:2001.05388 ), based on the dynamic Bradley–Terry model for games between players of time-varying ability. In this paper, we implement inference under the whole-history rating model using Markov chain Monte Carlo and apply the method to a curated data set made up of climbers who climb regularly. We use these data to get an estimate of the model’s fundamental scale parameter m , which defines the proportional increase in difficulty associated with an increment of grade. We show that the data conform to assumptions that the climbing grade scale is a logarithmic scale of difficulty, like decibels or stellar magnitude. We estimate that an increment in Ewbank, French and UIAA climbing grade systems corresponds to 2.10, 2.09 and 2.13 times increase in difficulty respectively, assuming a logistic model of probability of success as a function of grade. Whereas we find that the Vermin scale for bouldering (V-grade scale) corresponds to a 3.17 increase in difficulty per grade increment. In addition, we highlight potential connections between the logarithmic properties of climbing grade scales and the psychophysical laws of Weber and Fechner.

Conditioning the inference of a Bayesian phylogenetic time tree on a single molecular clock model treats clock choice as fixed, even when support among plausible clock families is uncertain. When that assumption is wrong, estimated timescales and their uncertainty can be distorted. Existing practice usually addresses this by fitting strict, uncorrelated lognormal relaxed (UCLN), and autocorrelated clocks separately and comparing their marginal likelihoods, but this requires multiple computationally expensive model selection analyses. Here we introduce a hierarchical clock-mixture framework, implemented as the open-source RelaxClockAveraging package for BEAST 2, that separates two questions that are often conflated in clock comparison: whether branch-specific rate variation is needed at all, and, if it is, whether that variation is better described as uncorrelated or autocorrelated. The method averages analytically between strict and relaxed clocks at the top level and then compares UCLN and autocorrelated models within the relaxed class on a shared branch-rate vector, returning posterior probabilities for all three clock families together with model-averaged summaries for parameters shared across them. In stratified simulations, the generating clock family was retained in the 95% posterior model set in all replicates, while model-averaged estimates of the overall substitution rate, root age, and tree length remained accurate. On a DENV-4 benchmark, the mixture reproduced the higher-effort nested-sampling ranking of clock families while avoiding the extreme run-to-run variability of independent marginal-likelihood estimates. On empirical benchmarks, the method recovered strong support for the autocorrelated clock on the classical 31-taxon chloroplast rbcL data set. On an RSV-A G-gene data set it concentrated virtually all posterior support on UCLN while preserving the established RSV-A timescale. On a 245-taxon structured-coalescent H3N2 dataset it assigned most posterior mass to the relaxed-clock class, with support within that class concentrated on the autocorrelated family, and the inferred timescale remained consistent with the published estimate. These results show that clock-model support and downstream timescale sensitivity are related but not identical. Single-clock dating analyses can still be adequate, but fixing a clock model should be justified by posterior support rather than treated as a default assumption.

Credible intervals and credible sets, such as highest posterior density (HPD) intervals, form an integral statistical tool in Bayesian phylogenetics, both for phylogenetic analyses and for development. Readily available for continuous parameters such as base frequencies and clock rates, the vast and complex space of tree topologies poses significant challenges for defining analogous credible sets. Traditional frequency-based approaches are inadequate for diffuse posteriors where sampled trees are often unique. To address this, we introduce novel and efficient methods for estimating the credible level of individual tree topologies using tractable tree distributions, specifically Conditional Clade Distribution (CCD). Furthermore, we propose a new concept called α credible CCD, which encapsulates a CCD whose trees collectively make up α probability. We present algorithms to compute these credible CCDs efficiently and to determine credible levels of tree topologies as well as of subtrees. We evaluate the accuracy of these credible set methods leveraging simulated and real datasets. Furthermore, to demonstrate the utility of our methods, we use well-calibrated simulation studies to evaluate the performance of different CCD models. In particular, we show how the credible set methods can be used to conduct rank-uniformity validation and produce Empirical Cumulative Distribution Function (ECDF) plots, supplementing standard coverage analyses for continuous parameters.

Navigating the mysterious space of evolutionary histories

Bayesian phylogenetic inference uses Markov chain Monte Carlo sampling to estimate the posterior distribution of phylogenetic trees. However, the complex geometry of treespace makes these distributions difficult to characterise. Traditional approaches often summarise posterior samples into a single point estimate, discarding much of the information contained in the full distribution. Conditional clade distributions (CCDs) address this by providing a tractable model of the full tree distribution, but existing parameterisations exhibit complementary strengths. We introduce a new family of models called regularised conditional clade distributions (regCCD), which apply regularisation to balance sample fidelity against overfitting, thereby combining the strengths of existing parameterisations. We show that regCCD outperforms existing models in capturing the posterior distribution and provides better point estimates than its underlying model. Furthermore, we provide an efficient procedure for selecting the optimal regularisation parameter for a given posterior tree set. Finally, we demonstrate the application of regCCD in assessing whether different phylogenetic models or data produce statistically distinguishable tree distributions.

Bayesian phylodynamic models have become essential for reconstructing population history from genetic data, yet their accuracy depends crucially on choosing appropriate demographic models. To address uncertainty in model choice, we introduce a Bayesian model averaging (BMA) framework that integrates multiple parametric coalescent models—including constant, exponential, logistic, and Gompertz growth—along with their “expansion” variants that account for non-zero ancestral populations. Implemented in a Bayesian setting with Metropolis-coupled Markov chain Monte Carlo, this approach allows the sampler to switch among candidate growth functions, thereby capturing demographic histories without having to pre-specify a single model. Simulation studies verify that the logistic and Gompertz models may require specialized sampling strategies such as adaptive multivariate proposals to achieve robust mixing. We demonstrate the performance of these models on datasets simulated under different substitution models, and show that joint inference of genealogy and population parameters is well-calibrated when properly incorporating correlated-move operators and BMA. We then apply this method to two real-world datasets. Analysis of Egyptian Hepatitis C virus sequences indicates that models with a founder population followed by a rapid expansion are well supported, with a slight preference for Gompertz-like expansions. Our analysis of a metastatic colorectal cancer single-cell dataset suggests that exponential-like growth is plausible even for an advanced stage cancer patient. We believe this highlights that tumor subclones may retain substantial proliferative capacity into the later stages of the disease. Overall, our unified BMA framework reduces the need for restrictive model selection procedures and can also provide deeper biological insights into epidemic spread and tumor evolution. By systematically integrating multiple growth hypotheses within a standard Bayesian setting, this approach naturally avoids overfitting and offers a powerful tool for inferring population histories across diverse biological domains.

Here we present the open-source and cross-platform BEAST X software that combines molecular phylogenetic reconstruction with complex trait evolution, divergence-time dating and coalescent demographics in an efficient statistical inference engine. BEAST X significantly advances the flexibility and scalability of evolutionary models supported. Novel clock and substitution models leverage a large variety of evolutionary processes; discrete, continuous and mixed traits with missingness and measurement errors; and fast, gradient-informed integration techniques that rapidly traverse high-dimensional parameter spaces.

Bayesian phylodynamic models have become essential for reconstructing population history from genetic data, yet their accuracy depends crucially on choosing appropriate demographic models. To address uncertainty in model choice, we introduce a Bayesian Model Averaging (BMA) framework that integrates multiple parametric coalescent models--including constant, exponential, logistic, and Gompertz growth--along with their ''expansion'' variants that account for non-zero ancestral populations. Implemented in a Bayesian setting with Metropolis-coupled MCMC, this approach allows the sampler to switch among candidate growth functions, thereby capturing demographic histories without having to pre-specify a single model. Simulation studies verify that the logistic and Gompertz models may require specialised sampling strategies such as adaptive multivariate proposals to achieve robust mixing. We demonstrate the performance of these models on datasets simulated under different substitution models, and show that joint inference of genealogy and population parameters is well-calibrated when properly incorporating correlated-move operators and BMA. We then apply this method to two real-world datasets. Analysis of Egyptian Hepatitis C virus (HCV) sequences indicates that models with a founder population followed by a rapid expansion are well supported, with a slight preference for Gompertz-like expansions. Our analysis of a single metastatic colorectal cancer (CRC) single-cell dataset suggests that exponential-like growth is plausible even for an advanced stage cancer patient. We believe this highlights that tumour subclones may retain substantial proliferative capacity into the later stages of the disease. Overall, our unified BMA framework reduces the need for restrictive model selection procedures and can also provide deeper biological insights into epidemic spread and tumour evolution. By systematically integrating multiple growth hypotheses within a standard Bayesian setting, this approach naturally avoids overfitting and offers a powerful tool for inferring population histories across diverse biological domains.

Bayesian phylogenetic analysis with MCMC algorithms generates an estimate of the posterior distribution of phylogenetic trees in the form of a sample of phylogenetic trees and related parameters. The high dimensionality and non-Euclidean nature of tree space complicates summarizing the central tendency and variance of the posterior distribution in tree space. Here we introduce a new tractable tree distribution and associated point estimator that can be constructed from a posterior sample of trees. Through simulation studies we show that this point estimator performs at least as well and often better than standard methods of producing Bayesian posterior summary trees. We also show that the method of summary that performs best depends on the sample size and dimensionality of the problem in non-trivial ways.

In a phylogenetic analysis, rogue taxa and clades are those that, due to their uncertain placement, contribute disproportionally to the variance in a set of phylogenetics trees. They can obscure clear evolutionary relationships and complicate the interpretation of results. While existing rogue detection algorithms focus on improving the consensus tree for a set of trees, we introduce algorithms based on phylogenetic entropy to improve the analysis in a Bayesian framework. In particular, we introduce a tool that extracts a skeleton distribution of the posterior tree distribution that contains the core relationships by removing a minimal subset of rogues. Additionally, we enable detailed analyses of rogues at both the taxon and clade levels, including the visualisation of different rogue placements.