The build-up of the present-day tropical diversity of tetrapods.

The extraordinary number of species in the tropics when compared to the extra-tropics is probably the most prominent and consistent pattern in biogeography, suggesting that overarching processes regulate this diversity gradient. A major challenge to characterizing which processes are at play relies on quantifying how the frequency and determinants of tropical and extra-tropical speciation, extinction, and dispersal events shaped evolutionary radiations. We address this question by developing and applying spatiotemporal phylogenetic and paleontological models of diversification for tetrapod species incorporating paleoenvironmental variation. Our phylogenetic model results show that area, energy, or species richness did not uniformly affect speciation rates across tetrapods and dispute expectations of a latitudinal gradient in speciation rates. Instead, both neontological and fossil evidence coincide in underscoring the role of extra-tropical extinctions and the outflow of tropical species in shaping biodiversity. These diversification dynamics accurately predict present-day levels of species richness across latitudes and uncover temporal idiosyncrasies but spatial generality across the major tetrapod radiations.

Bayesian inference of admixture graphs on Native American and Arctic populations.

Admixture graphs are mathematical structures that describe the ancestry of populations in terms of divergence and merging (admixing) of ancestral populations as a graph. An admixture graph consists of a graph topology, branch lengths, and admixture proportions. The branch lengths and admixture proportions can be estimated using numerous numerical optimization methods, but inferring the topology involves a combinatorial search for which no polynomial algorithm is known. In this paper, we present a reversible jump MCMC algorithm for sampling high-probability admixture graphs and show that this approach works well both as a heuristic search for a single best-fitting graph and for summarizing shared features extracted from posterior samples of graphs. We apply the method to 11 Native American and Siberian populations and exploit the shared structure of high-probability graphs to characterize the relationship between Saqqaq, Inuit, Koryaks, and Athabascans. Our analyses show that the Saqqaq is not a good proxy for the previously identified gene flow from Arctic people into the Na-Dene speaking Athabascans.

PhyloJunction: a computational framework for simulating, developing, and teaching evolutionary models.

We introduce PhyloJunction, a computational framework designed to facilitate the prototyping, test- ing, and characterization of evolutionary models. PhyloJunction is distributed as an open-source Python library that can be used to implement a variety of models, thanks to its flexible graphical modeling architecture and dedicated model specification language. Model design and use are exposed to users via command-line and graphical interfaces, which integrate the steps of simulating, summarizing, and visualizing data. This paper describes the features of PhyloJunction - which include, but are not limited to, a general implementation of a popular family of phylogenetic diversification models - and, moving forward, how it may be expanded to not only include new models, but to also become a platform for conducting and teaching statistical learning.

Deep Learning and Likelihood Approaches for Viral Phylogeography Converge on the Same Answers Whether the Inference Model Is Right or Wrong.

Analysis of phylogenetic trees has become an essential tool in epidemiology. Likelihood-based methods fit models to phylogenies to draw inferences about the phylodynamics and history of viral transmission. However, these methods are often computationally expensive, which limits the complexity and realism of phylodynamic models and makes them ill-suited for informing policy decisions in real-time during rapidly developing outbreaks. Likelihood-free methods using deep learning are pushing the boundaries of inference beyond these constraints. In this paper, we extend, compare, and contrast a recently developed deep learning method for likelihood-free inference from trees. We trained multiple deep neural networks using phylogenies from simulated outbreaks that spread among 5 locations and found they achieve close to the same levels of accuracy as Bayesian inference under the true simulation model. We compared robustness to model misspecification of a trained neural network to that of a Bayesian method. We found that both models had comparable performance, converging on similar biases. We also implemented a method of uncertainty quantification called conformalized quantile regression that we demonstrate has similar patterns of sensitivity to model misspecification as Bayesian highest posterior density (HPD) and greatly overlap with HPDs, but have lower precision (more conservative). Finally, we trained and tested a neural network against phylogeographic data from a recent study of the SARS-Cov-2 pandemic in Europe and obtained similar estimates of region-specific epidemiological parameters and the location of the common ancestor in Europe. Along with being as accurate and robust as likelihood-based methods, our trained neural networks are on average over 3 orders of magnitude faster after training. Our results support the notion that neural networks can be trained with simulated data to accurately mimic the good and bad statistical properties of the likelihood functions of generative phylogenetic models.

Phylogenetic inference of where species spread or split across barriers.

SignificanceGeography molds how species evolve in space. Strong geographical barriers to movement, for instance, both inhibit dispersal between regions and allow isolated populations to diverge as new species. Weak barriers, by contrast, permit species range expansion and persistence. These factors present a conundrum: How strong must a barrier be before between-region speciation outpaces dispersal? We designed a phylogenetic model of dispersal, extinction, and speciation that allows regional features to influence rates of biogeographic change and applied it to the neotropical radiation of Anolis lizards. Separation by water induces a threefold steeper barrier to movement than equivalent distances over land. Our model will help biologists detect relationships between evolutionary processes and the spatial contexts in which they operate.

A Diffusion-Based Approach for Simulating Forward-in-Time State-Dependent Speciation and Extinction Dynamics.

We establish a general framework using a diffusion approximation to simulate forward-in-time state counts or frequencies for cladogenetic state-dependent speciation-extinction (ClaSSE) models. We apply the framework to various two- and three-region geographic-state speciation-extinction (GeoSSE) models. We show that the species range state dynamics simulated under tree-based and diffusion-based processes are comparable. We derive a method to infer rate parameters that are compatible with given observed stationary state frequencies and obtain an analytical result to compute stationary state frequencies for a given set of rate parameters. We also describe a procedure to find the time to reach the stationary frequencies of a ClaSSE model using our diffusion-based approach, which we demonstrate using a worked example for a two-region GeoSSE model. Finally, we discuss how the diffusion framework can be applied to formalize relationships between evolutionary patterns and processes under state-dependent diversification scenarios.

Joint Phylogenetic Estimation of Geographic Movements and Biome Shifts during the Global Diversification of Viburnum.

Phylogeny, molecular sequences, fossils, biogeography, and biome occupancy are all lines of evidence that reflect the singular evolutionary history of a clade, but they are most often studied separately, by first inferring a fossil-dated molecular phylogeny, then mapping on ancestral ranges and biomes inferred from extant species. Here we jointly model the evolution of biogeographic ranges, biome affinities, and molecular sequences, while incorporating fossils to estimate a dated phylogeny for all of the 163 extant species of the woody plant clade Viburnum (Adoxaceae) that we currently recognize in our ongoing worldwide monographic treatment of the group. Our analyses indicate that while the major Viburnum lineages evolved in the Eocene, the majority of extant species originated since the Miocene. Viburnum radiated first in Asia, in warm, broad-leaved evergreen (lucidophyllous) forests. Within Asia, we infer several early shifts into more tropical forests, and multiple shifts into forests that experience prolonged freezing. From Asia, we infer two early movements into the New World. These two lineages probably first occupied warm temperate forests and adapted later to spreading cold climates. One of these lineages (Porphyrotinus) occupied cloud forests and moved south through the mountains of the Neotropics. Several other movements into North America took place more recently, facilitated by prior adaptations to freezing in the Old World. We also infer four disjunctions between Asia and Europe: the Tinus lineage is the oldest and probably occupied warm forests when it spread, whereas the other three were more recent and in cold-adapted lineages. These results variously contradict published accounts, especially the view that Viburnum radiated initially in cold forests and, accordingly, maintained vessel elements with scalariform perforations. We explored how the location and biome assignments of fossils affected our inference of ancestral areas and biome states. Our results are sensitive to, but not entirely dependent upon, the inclusion of fossil biome data. It will be critical to take advantage of all available lines of evidence to decipher events in the distant past. The joint estimation approach developed here provides cautious hope even when fossil evidence is limited. [Biogeography; biome; combined evidence; fossil pollen; phylogeny; Viburnum.].

Phylogenetic reconstruction of ancestral ecological networks through time for pierid butterflies and their host plants.

The study of herbivorous insects underpins much of the theory that concerns the evolution of species interactions. In particular, Pieridae butterflies and their host plants have served as a model system for studying evolutionary arms races. To learn more about the coevolution of these two clades, we reconstructed ancestral ecological networks using stochastic mappings that were generated by a phylogenetic model of host-repertoire evolution. We then measured if, when, and how two ecologically important structural features of the ancestral networks (modularity and nestedness) evolved over time. Our study shows that as pierids gained new hosts and formed new modules, a subset of them retained or recolonised the ancestral host(s), preserving connectivity to the original modules. Together, host-range expansions and recolonisations promoted a phase transition in network structure. Our results demonstrate the power of combining network analysis with Bayesian inference of host-repertoire evolution to understand changes in complex species interactions over time.

Interdependent Phenotypic and Biogeographic Evolution Driven by Biotic Interactions.

Biotic interactions are hypothesized to be one of the main processes shaping trait and biogeographic evolution during lineage diversification. Theoretical and empirical evidence suggests that species with similar ecological requirements either spatially exclude each other, by preventing the colonization of competitors or by driving coexisting populations to extinction, or show niche divergence when in sympatry. However, the extent and generality of the effect of interspecific competition in trait and biogeographic evolution has been limited by a dearth of appropriate process-generating models to directly test the effect of biotic interactions. Here, we formulate a phylogenetic parametric model that allows interdependence between trait and biogeographic evolution, thus enabling a direct test of central hypotheses on how biotic interactions shape these evolutionary processes. We adopt a Bayesian data augmentation approach to estimate the joint posterior distribution of trait histories, range histories, and coevolutionary process parameters under this analytically intractable model. Through simulations, we show that our model is capable of distinguishing alternative scenarios of biotic interactions. We apply our model to the radiation of Darwin's finches-a classic example of adaptive divergence-and find limited support for in situ trait divergence in beak size, but stronger evidence for convergence in traits such as beak shape and tarsus length and for competitive exclusion throughout their evolutionary history. These findings are more consistent with presympatric, rather than postsympatric, niche divergence. Our modeling framework opens new possibilities for testing more complex hypotheses about the processes underlying lineage diversification. More generally, it provides a robust probabilistic methodology to model correlated evolution of continuous and discrete characters. [Bayesian; biotic interactions; competition; data augmentation; historical biogeography; trait evolution.].

Bayesian Inference of Ancestral Host-Parasite Interactions under a Phylogenetic Model of Host Repertoire Evolution.

Intimate ecological interactions, such as those between parasites and their hosts, may persist over long time spans, coupling the evolutionary histories of the lineages involved. Most methods that reconstruct the coevolutionary history of such interactions make the simplifying assumption that parasites have a single host. Many methods also focus on congruence between host and parasite phylogenies, using cospeciation as the null model. However, there is an increasing body of evidence suggesting that the host ranges of parasites are more complex: that host ranges often include more than one host and evolve via gains and losses of hosts rather than through cospeciation alone. Here, we develop a Bayesian approach for inferring coevolutionary history based on a model accommodating these complexities. Specifically, a parasite is assumed to have a host repertoire, which includes both potential hosts and one or more actual hosts. Over time, potential hosts can be added or lost, and potential hosts can develop into actual hosts or vice versa. Thus, host colonization is modeled as a two-step process that may potentially be influenced by host relatedness. We first explore the statistical behavior of our model by simulating evolution of host-parasite interactions under a range of parameter values. We then use our approach, implemented in the program RevBayes, to infer the coevolutionary history between 34 Nymphalini butterfly species and 25 angiosperm families. Our analysis suggests that host relatedness among angiosperm families influences how easily Nymphalini lineages gain new hosts. [Ancestral hosts; coevolution; herbivorous insects; probabilistic modeling.].

Pulsed evolution shaped modern vertebrate body sizes.

The relative importance of different modes of evolution in shaping phenotypic diversity remains a hotly debated question. Fossil data suggest that stasis may be a common mode of evolution, while modern data suggest some lineages experience very fast rates of evolution. One way to reconcile these observations is to imagine that evolution proceeds in pulses, rather than in increments, on geological timescales. To test this hypothesis, we developed a maximum-likelihood framework for fitting Lévy processes to comparative morphological data. This class of stochastic processes includes both an incremental and a pulsed component. We found that a plurality of modern vertebrate clades examined are best fitted by pulsed processes over models of incremental change, stationarity, and adaptive radiation. When we compare our results to theoretical expectations of the rate and speed of regime shifts for models that detail fitness landscape dynamics, we find that our quantitative results are broadly compatible with both microevolutionary models and observations from the fossil record.

Sterile marginal flowers increase visitation and fruit set in the hobblebush (Viburnum lantanoides, Adoxaceae) at multiple spatial scales.

Background and Aims: Enlarged sterile flowers on the periphery of inflorescences increase the attractiveness of floral displays, and previous studies have generally demonstrated that these have positive effects on insect visitation and/or reproductive success. However, experiments have not specifically been designed to examine the benefits of sterile flowers under conditions that reflect the early stages in their evolution, i.e. when plants that produce sterile flowers are at low frequency. Methods: Over three years, three experiments were performed in natural populations of Viburnum lantanoides, which produces sterile marginal flowers (SMFs). The first experiment established that fruit production in V. lantanoides increases with the receipt of outcross pollen. The second tested the role of SMFs under extant conditions, comparing fruit production in two populations composed entirely of intact plants or entirely of plants with the SMFs removed. The third was designed to mimic the presumed context in which SMFs first evolved; here, SMFs were removed from all but a few plants in a population, and rates of insect visitation and fruit set were compared between plants with intact and denuded SMFs. Key Results: In comparing whole populations, the presence of SMFs nearly doubled fruit set. Under simulated 'ancestral' conditions within a population, plants with intact SMFs received double the insect visits and produced significantly more fruits than denuded plants. There was no significant effect of the number of inflorescences or fertile flowers on insect visitation or fruit set, indicating that the presence of SMFs accounted for these differences. Conclusions: The presence of SMFs significantly increased pollinator attraction and female reproductive success both in contemporary and simulated ancestral contexts, indicating that stabilizing selection is responsible for their maintenance, and directional selection likely drove their evolution when they first appeared. This study demonstrates a novel approach to incorporating historically relevant scenarios into experimental studies of floral evolution.

Biogeographic Dating of Speciation Times Using Paleogeographically Informed Processes.

Standard models of molecular evolution cannot estimate absolute speciation times alone, and require external calibrations to do so, such as fossils. Because fossil calibration methods rely on the incomplete fossil record, a great number of nodes in the tree of life cannot be dated precisely. However, many major paleogeographical events are dated, and since biogeographic processes depend on paleogeographical conditions, biogeographic dating may be used as an alternative or complementary method to fossil dating. I demonstrate how a time-stratified biogeographic stochastic process may be used to estimate absolute divergence times by conditioning on dated paleogeographical events. Informed by the current paleogeographical literature, I construct an empirical dispersal graph using 25 areas and 26 epochs for the past 540 Ma of Earth's history. Simulations indicate biogeographic dating performs well so long as paleogeography imposes constraint on biogeographic character evolution. To gauge whether biogeographic dating may be of practical use, I analyzed the well-studied turtle clade (Testudines) to assess how well biogeographic dating fares when compared to fossil-calibrated dating estimates reported in the literature. Fossil-free biogeographic dating estimated the age of the most recent common ancestor of extant turtles to be from the Late Triassic, which is consistent with fossil-based estimates. Dating precision improves further when including a root node fossil calibration. The described model, paleogeographical dispersal graph, and analysis scripts are available for use with RevBayes.

RevBayes: Bayesian Phylogenetic Inference Using Graphical Models and an Interactive Model-Specification Language.

Programs for Bayesian inference of phylogeny currently implement a unique and fixed suite of models. Consequently, users of these software packages are simultaneously forced to use a number of programs for a given study, while also lacking the freedom to explore models that have not been implemented by the developers of those programs. We developed a new open-source software package, RevBayes, to address these problems. RevBayes is entirely based on probabilistic graphical models, a powerful generic framework for specifying and analyzing statistical models. Phylogenetic-graphical models can be specified interactively in RevBayes, piece by piece, using a new succinct and intuitive language called Rev. Rev is similar to the R language and the BUGS model-specification language, and should be easy to learn for most users. The strength of RevBayes is the simplicity with which one can design, specify, and implement new and complex models. Fortunately, this tremendous flexibility does not come at the cost of slower computation; as we demonstrate, RevBayes outperforms competing software for several standard analyses. Compared with other programs, RevBayes has fewer black-box elements. Users need to explicitly specify each part of the model and analysis. Although this explicitness may initially be unfamiliar, we are convinced that this transparency will improve understanding of phylogenetic models in our field. Moreover, it will motivate the search for improvements to existing methods by brazenly exposing the model choices that we make to critical scrutiny. RevBayes is freely available at http://www.RevBayes.com [Bayesian inference; Graphical models; MCMC; statistical phylogenetics.].

Phylowood: interactive web-based animations of biogeographic and phylogeographic histories.

SUMMARY: Phylowood is a web service that uses JavaScript to generate in-browser animations of biogeographic and phylogeographic histories from annotated phylogenetic input. The animations are interactive, allowing the user to adjust spatial and temporal resolution, and highlight phylogenetic lineages of interest. AVAILABILITY AND IMPLEMENTATION: All documentation and source code for Phylowood is freely available at https://github.com/mlandis/phylowood, and a live web application is available at https://mlandis.github.io/phylowood.

Sensitivity of quantitative traits to mutational effects and number of loci.

When models of quantitative genetic variation are built from population genetic first principles, several assumptions are often made. One of the most important assumptions is that traits are controlled by many genes of small effect. This leads to a prediction of a Gaussian trait distribution in the population, via the Central Limit Theorem. Since these biological assumptions are often unknown or untrue, we characterized how finite numbers of loci or large mutational effects can impact the sampling distribution of a quantitative trait. To do so, we developed a neutral coalescent-based framework, allowing us to gain a detailed understanding of how number of loci and the underlying mutational model impacts the distribution of a quantitative trait. Through both analytical theory and simulation we found the normality assumption was highly sensitive to the details of the mutational process, with the greatest discrepancies arising when the number of loci was small or the mutational kernel was heavy-tailed. In particular, skewed mutational effects will produce skewed trait distributions and fat-tailed mutational kernels result in multimodal sampling distributions, even for traits controlled by a large number of loci. Since selection models and robust neutral models may produce qualitatively similar sampling distributions, we advise extra caution should be taken when interpreting model-based results for poorly understood systems of quantitative traits.

Probabilistic graphical model representation in phylogenetics.

Recent years have seen a rapid expansion of the model space explored in statistical phylogenetics, emphasizing the need for new approaches to statistical model representation and software development. Clear communication and representation of the chosen model is crucial for: (i) reproducibility of an analysis, (ii) model development, and (iii) software design. Moreover, a unified, clear and understandable framework for model representation lowers the barrier for beginners and nonspecialists to grasp complex phylogenetic models, including their assumptions and parameter/variable dependencies. Graphical modeling is a unifying framework that has gained in popularity in the statistical literature in recent years. The core idea is to break complex models into conditionally independent distributions. The strength lies in the comprehensibility, flexibility, and adaptability of this formalism, and the large body of computational work based on it. Graphical models are well-suited 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 introduce modules to simplify the representation of standard components in large and complex models. Phylogenetic model graphs can be readily used in simulation, maximum likelihood inference, and Bayesian inference using, for example, Metropolis-Hastings or Gibbs sampling of the posterior distribution.

Phylogenetic analysis using Lévy processes: finding jumps in the evolution of continuous traits.

Gaussian processes, a class of stochastic processes including Brownian motion and the Ornstein-Uhlenbeck process, are widely used to model continuous trait evolution in statistical phylogenetics. Under such processes, observations at the tips of a phylogenetic tree have a multivariate Gaussian distribution, which may lead to suboptimal model specification under certain evolutionary conditions, as supposed in models of punctuated equilibrium or adaptive radiation. To consider non-normally distributed continuous trait evolution, we introduce a method to compute posterior probabilities when modeling continuous trait evolution as a Lévy process. Through data simulation and model testing, we establish that single-rate Brownian motion (BM) and Lévy processes with jumps generate distinct patterns in comparative data. We then analyzed body mass and endocranial volume measurements for 126 primates. We rejected single-rate BM in favor of a Lévy process with jumps for each trait, with the lineage leading to most recent common ancestor of great apes showing particularly strong evidence against single-rate BM.

Bayesian analysis of biogeography when the number of areas is large.

Historical biogeography is increasingly studied from an explicitly statistical perspective, using stochastic models to describe the evolution of species range as a continuous-time Markov process of dispersal between and extinction within a set of discrete geographic areas. The main constraint of these methods is the computational limit on the number of areas that can be specified. We propose a Bayesian approach for inferring biogeographic history that extends the application of biogeographic models to the analysis of more realistic problems that involve a large number of areas. Our solution is based on a "data-augmentation" approach, in which we first populate the tree with a history of biogeographic events that is consistent with the observed species ranges at the tips of the tree. We then calculate the likelihood of a given history by adopting a mechanistic interpretation of the instantaneous-rate matrix, which specifies both the exponential waiting times between biogeographic events and the relative probabilities of each biogeographic change. We develop this approach in a Bayesian framework, marginalizing over all possible biogeographic histories using Markov chain Monte Carlo (MCMC). Besides dramatically increasing the number of areas that can be accommodated in a biogeographic analysis, our method allows the parameters of a given biogeographic model to be estimated and different biogeographic models to be objectively compared. Our approach is implemented in the program, BayArea.

phyddle: software for phylogenetic model exploration with deep learning.

Many realistic phylogenetic models lack tractable likelihood functions, prohibiting their use with standard inference methods. We present phyddle, a pipeline-based toolkit for performing phylogenetic modeling tasks using likelihood-free deep learning approaches. phyddle coordinates modeling tasks through five analysis steps (Simulate, Format, Train, Estimate, and Plot) that transform raw phylogenetic datasets as input into numerical and visualized model-based output. Benchmarks show that phyddle accurately performs a range of inference tasks, such as estimating macroevolutionary parameters, selecting among continuous trait evolution models, and passing coverage tests for epidemiological models, even for models that lack tractable likelihoods. phyddle has a flexible command-line interface, making it easy to integrate deep learning approaches for phylogenetics into research workflows. Learn more about phyddle at https://phyddle.org.