Likelihood inference of non-constant diversification rates with incomplete taxon sampling

Fast Bayesian Inference of Phylogenies from Multiple Continuous Characters

Time-scaled phylogenetic trees are an ultimate goal of evolutionary biology and a necessary ingredient in comparative studies. The accumulation of genomic data has resolved the tree of life to a great extent, yet timing evolutionary events remain challenging if not impossible without external information such as fossil ages and morphological characters. Methods for incorporating morphology in tree estimation have lagged behind their molecular counterparts, especially in the case of continuous characters. Despite recent advances, such tools are still direly needed as we approach the limits of what molecules can teach us. Here, we implement a suite of state-of-the-art methods for leveraging continuous morphology in phylogenetics, and by conducting extensive simulation studies we thoroughly validate and explore our methods' properties. While retaining model generality and scalability, we make it possible to estimate absolute and relative divergence times from multiple continuous characters while accounting for uncertainty. We compile and analyze one of the most data-type diverse data sets to date, comprised of contemporaneous and ancient molecular sequences, and discrete and continuous morphological characters from living and extinct Carnivora taxa. We conclude by synthesizing lessons about our method's behavior, and suggest future research venues.

Scalable gradients enable Hamiltonian Monte Carlo sampling for phylodynamic inference under episodic birth-death-sampling models

Birth-death models play a key role in phylodynamic analysis for their interpretation in terms of key epidemiological parameters. In particular, models with piecewise-constant rates varying at different epochs in time, to which we refer as episodic birth-death-sampling (EBDS) models, are valuable for their reflection of changing transmission dynamics over time. A challenge, however, that persists with current time-varying model inference procedures is their lack of computational efficiency. This limitation hinders the full utilization of these models in large-scale phylodynamic analyses, especially when dealing with high-dimensional parameter vectors that exhibit strong correlations. We present here a linear-time algorithm to compute the gradient of the birth-death model sampling density with respect to all time-varying parameters, and we implement this algorithm within a gradient-based Hamiltonian Monte Carlo (HMC) sampler to alleviate the computational burden of conducting inference under a wide variety of structures of, as well as priors for, EBDS processes. We assess this approach using three different real world data examples, including the HIV epidemic in Odesa, Ukraine, seasonal influenza A/H3N2 virus dynamics in New York state, America, and Ebola outbreak in West Africa. HMC sampling exhibits a substantial efficiency boost, delivering a 10- to 200-fold increase in minimum effective sample size per unit-time, in comparison to a Metropolis-Hastings-based approach. Additionally, we show the robustness of our implementation in both allowing for flexible prior choices and in modeling the transmission dynamics of various pathogens by accurately capturing the changing trend of viral effective reproductive number.

Deep Learning from Phylogenies for Diversification Analyses

Birth-death (BD) models are widely used in combination with species phylogenies to study past diversification dynamics. Current inference approaches typically rely on likelihood-based methods. These methods are not generalizable, as a new likelihood formula must be established each time a new model is proposed; for some models, such a formula is not even tractable. Deep learning can bring solutions in such situations, as deep neural networks can be trained to learn the relation between simulations and parameter values as a regression problem. In this paper, we adapt a recently developed deep learning method from pathogen phylodynamics to the case of diversification inference, and we extend its applicability to the case of the inference of state-dependent diversification models from phylogenies associated with trait data. We demonstrate the accuracy and time efficiency of the approach for the time-constant homogeneous BD model and the Binary-State Speciation and Extinction model. Finally, we illustrate the use of the proposed inference machinery by reanalyzing a phylogeny of primates and their associated ecological role as seed dispersers. Deep learning inference provides at least the same accuracy as likelihood-based inference while being faster by several orders of magnitude, offering a promising new inference approach for the deployment of future models in the field.

Scalable gradients enable Hamiltonian Monte Carlo sampling for phylodynamic inference under episodic birth-death-sampling models

Birth-death models play a key role in phylodynamic analysis for their interpretation in terms of key epidemiological parameters. In particular, models with piecewise-constant rates varying at different epochs in time, to which we refer as episodic birth-death-sampling (EBDS) models, are valuable for their reflection of changing transmission dynamics over time. A challenge, however, that persists with current time-varying model inference procedures is their lack of computational efficiency. This limitation hinders the full utilization of these models in large-scale phylodynamic analyses, especially when dealing with high-dimensional parameter vectors that exhibit strong correlations. We present here a linear-time algorithm to compute the gradient of the birth-death model sampling density with respect to all time-varying parameters, and we implement this algorithm within a gradient-based Hamiltonian Monte Carlo (HMC) sampler to alleviate the computational burden of conducting inference under a wide variety of structures of, as well as priors for, EBDS processes. We assess this approach using three different real world data examples, including the HIV epidemic in Odesa, Ukraine, seasonal influenza A/H3N2 virus dynamics in New York state, America, and Ebola outbreak in West Africa. HMC sampling exhibits a substantial efficiency boost, delivering a 10- to 200-fold increase in minimum effective sample size per unit-time, in comparison to a Metropolis-Hastings-based approach. Additionally, we show the robustness of our implementation in both allowing for flexible prior choices and in modeling the transmission dynamics of various pathogens by accurately capturing the changing trend of viral effective reproductive number.

Phylogenomics sheds new light on the drivers behind a long-lasting systematic riddle: the figwort family Scrophulariaceae

The figwort family, Scrophulariaceae, comprises c. 2000 species whose evolutionary relationships at the tribal level have proven difficult to resolve, hindering our ability to understand their origin and diversification. We designed a specific probe kit for Scrophulariaceae, targeting 849 nuclear loci and obtaining plastid regions as by-products. We sampled c. 87% of the genera described in the family and use the nuclear dataset to estimate evolutionary relationships, timing of diversification, and biogeographic patterns. Ten tribes, including two new tribes, Androyeae and Camptolomeae, are supported, and the phylogenetic positions of Androya, Camptoloma, and Phygelius are unveiled. Our study reveals a major diversification at c. 60 million yr ago in some Gondwanan landmasses, where two different lineages diversified, one of which gave rise to nearly 81% of extant species. A Southern African origin is estimated for most modern-day tribes, with two exceptions, the American Leucophylleae, and the mainly Australian Myoporeae. The rapid mid-Eocene diversification is aligned with geographic expansion within southern Africa in most tribes, followed by range expansion to tropical Africa and multiple dispersals out of Africa. Our robust phylogeny provides a framework for future studies aimed at understanding the role of macroevolutionary patterns and processes that generated Scrophulariaceae diversity.

Rapidly changing speciation and extinction rates can be inferred in spite of nonidentifiability

The birth-death model is commonly used to infer speciation and extinction rates by fitting the model to phylogenetic trees with exclusively extant taxa. Recently, it was demonstrated that speciation and extinction rates are not identifiable if the rates are allowed to vary freely over time. The group of birth-death models that have the same likelihood is called a congruence class, and there is no statistical evidence to favor one model over the other. This issue has led researchers to question if and what patterns can reliably be inferred from phylogenies of only extant taxa and whether time-variable birth-death models should be fitted at all. We explore the congruence class in the context of several empirical phylogenies as well as hypothetical scenarios. For these empirical phylogenies, we assume that we inferred the true congruence class. Thus, our conclusions apply to any empirical phylogeny for which we robustly inferred the true congruence class. When we summarize shared patterns in the congruence class, we show that strong directional trends in speciation and extinction rates are shared among most models. Therefore, we conclude that the inference of strong directional trends is robust. Conversely, estimates of constant rates or gentle slopes are not robust and must be treated with caution. Interestingly, the space of valid speciation rates is narrower and more limited in contrast to extinction rates, which are less constrained. These results provide further evidence and insights that speciation rates can be estimated more reliably than extinction rates.

Sequence Capture From Historical Museum Specimens: Maximizing Value for Population and Phylogenomic Studies

The application of high-throughput, short-read sequencing to degraded DNA has greatly increased the feasibility of generating genomic data from historical museum specimens. While many published studies report successful sequencing results from historical specimens; in reality, success and quality of sequence data can be highly variable. To examine predictors of sequencing quality, and methodological approaches to improving data accuracy, we generated and analyzed genomic sequence data from 115 historically collected museum specimens up to 180 years old. Data span both population genomic and phylogenomic scales, including historically collected specimens from 34 specimens of four species of Australian rock-wallabies (genus Petrogale) and 92 samples from 79 specimens of Australo-Papuan murine rodents (subfamily Murinae). For historical rodent specimens, where the focus was sampling for phylogenomics, we found that regardless of specimen age, DNA sequence libraries prepared from toe pad or bone subsamples performed significantly better than those taken from the skin (in terms of proportion of reads on target, number of loci captured, and data accuracy). In total, 93% of DNA libraries from toe pad or bone subsamples resulted in reliable data for phylogenetic inference, compared to 63% of skin subsamples. For skin subsamples, proportion of reads on target weakly correlated with collection year. Then using population genomic data from rock-wallaby skins as a test case, we found substantial improvement in final data quality by mapping to a high-quality “closest sister” de novo assembly from fresh tissues, compared to mapping to a sample-specific historical de novo assembly. Choice of mapping approach also affected final estimates of the number of segregating sites and Watterson's θ, both important parameters for population genomic inference. The incorporation of accurate and reliable sequence data from historical specimens has important outcomes for evolutionary studies at both population and phylogenomic scales. By assessing the outcomes of different approaches to specimen subsampling, library preparation and bioinformatic processing, our results provide a framework for increasing sequencing success for irreplaceable historical specimens.

Cyphoderia ampulla (Cyphoderiidae: Rhizaria), a tale of freshwater sailors. The causes and consequences of ecological transitions through the salinity barrier in a family of benthic protists

The salinity barrier that separates marine and freshwater biomes is probably the most important division in biodiversity on Earth. Those organisms that successfully performed this transition had access to new ecosystems while undergoing changes in selective pressure, which often led to major shifts in diversification rates. While these transitions have been extensively investigated in animals, the tempo, mode, and outcome of crossing the salinity barrier have been scarcely studied in other eukaryotes. Here, we reconstructed the evolutionary history of the species complex Cyphoderia ampulla (Euglyphida: Cercozoa: Rhizaria) based on DNA sequences from the nuclear SSU rRNA gene and the mitochondrial cytochrome oxidase subunit I gene, obtained from publicly available environmental DNA data (GeneBank, EukBank) and isolated organisms. A tree calibrated with euglyphid fossils showed that four independent transitions towards freshwater systems occurred from the Mid Miocene onwards, coincident with important fluctuations in sea level. Ancestral trait reconstructions indicated that the whole family Cyphoderiidae had a marine origin and suggest that ancestors of the freshwater forms were euryhaline and lived in environments with fluctuating salinity. Diversification rates did not show any obvious increase concomitant with ecological transitions, but morphometric analyses indicated that species increased in size and homogenized their morphology after colonizing the new environments. This suggests adaptation to changes in selective pressure exerted by life in freshwater sediments.

The rise of grasslands is linked to atmospheric CO2 decline in the late Palaeogene

Grasslands are predicted to experience a major biodiversity change by the year 2100. A better understanding of how grasslands have responded to past environmental changes will help predict the outcome of current and future environmental changes. Here, we explore the relationship between past atmospheric CO₂ and temperature fluctuations and the shifts in diversification rate of Poaceae (grasses) and Asteraceae (daisies), two exceptionally species-rich grassland families (~11,000 and ~23,000 species, respectively). To this end, we develop a Bayesian approach that simultaneously estimates diversification rates through time from time-calibrated phylogenies and correlations between environmental variables and diversification rates. Additionally, we present a statistical approach that incorporates the information of the distribution of missing species in the phylogeny. We find strong evidence supporting a simultaneous increase in diversification rates for grasses and daisies after the most significant reduction of atmospheric CO₂ in the Cenozoic (~34 Mya). The fluctuations of paleo-temperatures, however, appear not to have had a significant relationship with the diversification of these grassland families. Overall, our results shed new light on our understanding of the origin of grasslands in the context of past environmental changes.

A better understanding of how grasslands have responded to past environmental changes will help predict the outcomes of future changes. This study explores past climatic fluctuations and shifts in the diversification rate of grasses and daisies, finding strong evidence for a simultaneous increase in their diversification rates following a reduction of atmospheric CO₂ in the Cenozoic.

Parallel power posterior analyses for fast computation of marginal likelihoods in phylogenetics

In Bayesian phylogenetic inference, marginal likelihoods can be estimated using several different methods, including the path-sampling or stepping-stone-sampling algorithms. Both algorithms are computationally demanding because they require a series of power posterior Markov chain Monte Carlo (MCMC) simulations. Here we introduce a general parallelization strategy that distributes the power posterior MCMC simulations and the likelihood computations over available CPUs. Our parallelization strategy can easily be applied to any statistical model despite our primary focus on molecular substitution models in this study. Using two phylogenetic example datasets, we demonstrate that the runtime of the marginal likelihood estimation can be reduced significantly even if only two CPUs are available (an average performance increase of 1.96x). The performance increase is nearly linear with the number of available CPUs. We record a performance increase of 13.3x for cluster nodes with 16 CPUs, representing a substantial reduction to the runtime of marginal likelihood estimations. Hence, our parallelization strategy enables the estimation of marginal likelihoods to complete in a feasible amount of time which previously needed days, weeks or even months. The methods described here are implemented in our open-source software RevBayes which is available from http://www.RevBayes.com.

Causes and Consequences of Apparent Timescaling Across All Estimated Evolutionary Rates

Evolutionary rates play a central role in connecting micro- and macroevolution. All evolutionary rate estimates, including rates of molecular evolution, trait evolution, and lineage diversification, share a similar scaling pattern with time: The highest rates are those measured over the shortest time interval. This creates a disconnect between micro- and macroevolution, although the pattern is the opposite of what some might expect: Patterns of change over short timescales predict that evolution has tremendous potential to create variation and that potential is barely tapped by macroevolution. In this review, we discuss this shared scaling pattern across evolutionary rates. We break down possible explanations for scaling into two categories, estimation error and model misspecification, and discuss how both apply to each type of rate. We also discuss the consequences of this ubiquitous pattern, which can lead to unexpected results when comparing ratesover different timescales. Finally, after addressing purely statistical concerns, we explore a few possibilities for a shared unifying explanation across the three types of rates that results from a failure to fully understand and account for how biological processes scale over time.

The implications of interrelated assumptions on estimates of divergence times and rates of diversification

Phylogenies are increasingly being used as a basis to provide insight into macroevolutionary history. Here, we use simulation experiments and empirical analyses to evaluate methods that use phylogenies as a basis to make estimates of divergence times and rates of diversification. This is the first study to present a comprehensive assessment of the key variables that underpin analyses in this field - including substitution rates, speciation rates, and extinction, plus character sampling and taxon sampling. We show that in unrealistically simplistic cases (where substitution rates and speciation rates are constant, and where there is no extinction), increased character and taxon sampling lead to more accurate and precise parameter estimates. By contrast, in more complex but realistic cases (where substitution rates, speciation rates, and extinction rates vary), gains in accuracy and precision from increased character and taxon sampling are far more limited. The lack of accuracy and precision even occurs when using methods that are designed to account for more complex cases, such as relaxed clocks, fossil calibrations, and models that allow speciation rates and extinction rates to vary. The problem also persists when analysing genomic scale datasets. These results suggest two interrelated problems that occur when the processes that generated the data are more complex. First, methodological assumptions are more likely to be violated. Second, limitations in the information content of the data become more important.

Macroevolutionary dynamics of parasite diversification: A reality check

Parasitism is often invoked as a factor explaining the variation in diversification rates across the tree of life, while also representing up to half of Earth's diversity. Yet, patterns and processes of parasite diversification remain mostly unknown. In this study, we assess the patterns of parasite diversification and specifically determine the role of life-history traits (i.e. life cycle complexity and host range) and major coevolutionary events in driving diversification across eight phylogenetic datasets spanning taxonomically different parasite groups. Aware of the degree of incomplete sampling among all parasite phylogenies, we also tested the impact of sampling bias on estimates of diversification. We show that the patterns and rates of parasite diversification differ among taxa according to life cycle complexity and to some extent major host transitions. Only directly transmitted parasites were found to be influenced by an effect of major host transitions on diversification rates. Although parasitism may be a main factor responsible for heterogeneity in diversification among the tree of life, the high degree of incomplete parasite phylogenies remains an obstacle when modelling diversification dynamics. Nevertheless, we provide the first comparative test of parasite diversification, revealing some consistent patterns and insight into the processes that shape it.

Locally adaptive Bayesian birth-death model successfully detects slow and rapid rate shifts

Birth-death processes have given biologists a model-based framework to answer questions about changes in the birth and death rates of lineages in a phylogenetic tree. Therefore birth-death models are central to macroevolutionary as well as phylodynamic analyses. Early approaches to studying temporal variation in birth and death rates using birth-death models faced difficulties due to the restrictive choices of birth and death rate curves through time. Sufficiently flexible time-varying birth-death models are still lacking. We use a piecewise-constant birth-death model, combined with both Gaussian Markov random field (GMRF) and horseshoe Markov random field (HSMRF) prior distributions, to approximate arbitrary changes in birth rate through time. We implement these models in the widely used statistical phylogenetic software platform RevBayes, allowing us to jointly estimate birth-death process parameters, phylogeny, and nuisance parameters in a Bayesian framework. We test both GMRF-based and HSMRF-based models on a variety of simulated diversification scenarios, and then apply them to both a macroevolutionary and an epidemiological dataset. We find that both models are capable of inferring variable birth rates and correctly rejecting variable models in favor of effectively constant models. In general the HSMRF-based model has higher precision than its GMRF counterpart, with little to no loss of accuracy. Applied to a macroevolutionary dataset of the Australian gecko family Pygopodidae (where birth rates are interpretable as speciation rates), the GMRF-based model detects a slow decrease whereas the HSMRF-based model detects a rapid speciation-rate decrease in the last 12 million years. Applied to an infectious disease phylodynamic dataset of sequences from HIV subtype A in Russia and Ukraine (where birth rates are interpretable as the rate of accumulation of new infections), our models detect a strongly elevated rate of infection in the 1990s.

Estimating rates and patterns of diversification with incomplete sampling: a case study in the rosids

PREMISE

Recent advances in generating large-scale phylogenies enable broad-scale estimation of species diversification. These now common approaches typically are characterized by (1) incomplete species coverage without explicit sampling methodologies and/or (2) sparse backbone representation, and usually rely on presumed phylogenetic placements to account for species without molecular data. We used empirical examples to examine the effects of incomplete sampling on diversification estimation and provide constructive suggestions to ecologists and evolutionary biologists based on those results.

METHODS

We used a supermatrix for rosids and one well-sampled subclade (Cucurbitaceae) as empirical case studies. We compared results using these large phylogenies with those based on a previously inferred, smaller supermatrix and on a synthetic tree resource with complete taxonomic coverage. Finally, we simulated random and representative taxon sampling and explored the impact of sampling on three commonly used methods, both parametric (RPANDA and BAMM) and semiparametric (DR).

RESULTS

We found that the impact of sampling on diversification estimates was idiosyncratic and often strong. Compared to full empirical sampling, representative and random sampling schemes either depressed or inflated speciation rates, depending on methods and sampling schemes. No method was entirely robust to poor sampling, but BAMM was least sensitive to moderate levels of missing taxa.

CONCLUSIONS

We suggest caution against uncritical modeling of missing taxa using taxonomic data for poorly sampled trees and in the use of summary backbone trees and other data sets with high representative bias, and we stress the importance of explicit sampling methodologies in macroevolutionary studies.

Increased diversification rates are coupled with higher rates of climate space exploration in Australian Acacia (Caesalpinioideae)

Australia is an excellent setting to explore relationships between climate change and diversification dynamics. Aridification since the Eocene has resulted in spectacular radiations within one or more Australian biomes. Acacia is the largest plant genus on the Australian continent, with around 1000 species, and is present in all biomes. We investigated the macroevolutionary dynamics of Acacia within climate space. We analysed phylogenetic and climatic data for 503 Acacia species to estimate a time-calibrated phylogeny and central climatic tendencies for BioClim layers from 132 000 herbarium specimens. Diversification rate heterogeneity and rates of climate space exploration were tested. We inferred two diversification rate increases, both associated with significantly higher rates of climate space exploration. Observed spikes in climate disparity within the Pleistocene correspond with onset of Pleistocene glacial-interglacial cycling. Positive time dependency in environmental disparity applies in the basal grade of Acacia, though climate space exploration rates were lower. Incongruence between rates of climate space exploration and disparity suggests different Acacia lineages have experienced different macroevolutionary processes. The second diversification rate increase is associated with a south-east Australian mesic lineage, suggesting adaptations to progressively aridifying environments and ability to transition into mesic environments contributed to Acacia's dominance across Australia.

A Cambrian-Ordovician Terrestrialization of Arachnids

Understanding the temporal context of terrestrialization in chelicerates depends on whether terrestrial groups, the traditional Arachnida, have a single origin and whether or not horseshoe crabs are primitively or secondarily marine. Molecular dating on a phylogenomic tree that recovers arachnid monophyly, constrained by 27 rigorously vetted fossil calibrations, estimates that Arachnida originated during the Cambrian or Ordovician. After the common ancestor colonized the land, the main lineages appear to have rapidly radiated in the Cambrian-Ordovician boundary interval, coinciding with high rates of molecular evolution. The highest rates of arachnid diversification are detected between the Permian and Early Cretaceous. A pattern of ancient divergence estimates for terrestrial arthropod groups in the Cambrian while the oldest fossils are Silurian (seen in both myriapods and arachnids) is mirrored in the molecular and fossil records of land plants. We suggest the discrepancy between molecular and fossil evidence for terrestrialization is likely driven by the extreme sparseness of terrestrial sediments in the rock record before the late Silurian.

Selective Sampling of Species and Fossils Influences Age Estimates Under the Fossilized Birth-Death Model

The fossilized birth-death (FBD) model allows the estimation of species divergence times from molecular and fossil information in a coherent framework of diversification and fossil sampling. Some assumptions of the FBD model, however, are difficult to meet in phylogenetic analyses of highly diverse groups. Here, I use simulations to assess the impact of extreme model violations, including diversified sampling of species and the exclusive use of the oldest fossils per clade, on divergence times estimated with the FBD model. My results demonstrate that selective sampling of fossils can produce dramatically overestimated divergence times when the FBD model is used for inference, due to an interplay of underestimates for the model parameters net diversification rate, turnover, and fossil-sampling proportion. In contrast, divergence times estimated with CladeAge, a method that uses information about the oldest fossils per clade together with estimates of sampling and diversification rates, are accurate under these conditions. Practitioners of Bayesian divergence-time estimation should therefore ensure that the dataset conforms to the expectations of the FBD model, or estimates of sampling and diversification rates should be obtained a priori so that CladeAge can be used for the inference.

Exploring the power of Bayesian birth-death skyline models to detect mass extinction events from phylogenies with only extant taxa

Mass extinction events (MEEs), defined as significant losses of species diversity in significantly short time periods, have attracted the attention of biologists because of their link to major environmental change. MEEs have traditionally been studied through the fossil record, but the development of birth-death models has made it possible to detect their signature based on extant-taxa phylogenies. Most birth-death models consider MEEs as instantaneous events where a high proportion of species are simultaneously removed from the tree ("single pulse" approach), in contrast to the paleontological record, where MEEs have a time duration. Here, we explore the power of a Bayesian Birth-Death Skyline (BDSKY) model to detect the signature of MEEs through changes in extinction rates under a "time-slice" approach. In this approach, MEEs are time intervals where the extinction rate is greater than the speciation rate. Results showed BDSKY can detect and locate MEEs but that precision and accuracy depend on the phylogeny's size and MEE intensity. Comparisons of BDSKY with the single-pulse Bayesian model, CoMET, showed a similar frequency of Type II error and neither model exhibited Type I error. However, while CoMET performed better in detecting and locating MEEs for smaller phylogenies, BDSKY showed higher accuracy in estimating extinction and speciation rates.

Macroevolutionary diversification rates show time dependency

For centuries, biologists have been captivated by the vast disparity in species richness between different groups of organisms. Variation in diversity is widely attributed to differences between groups in how fast they speciate or go extinct. Such macroevolutionary rates have been estimated for thousands of groups and have been correlated with an incredible variety of organismal traits. Here we analyze a large collection of phylogenetic trees and fossil time series and describe a hidden generality among these seemingly idiosyncratic results: speciation and extinction rates follow a scaling law in which both depend on the age of the group in which they are measured, with the fastest rates in the youngest clades. Using a series of simulations and sensitivity analyses, we demonstrate that the time dependency is unlikely to be a result of simple statistical artifacts. As such, this time scaling is likely a genuine feature of the tree of life, hinting that the dynamics of biodiversity over deep time may be driven in part by surprisingly simple and general principles.

The choice of tree prior and molecular clock does not substantially affect phylogenetic inferences of diversification rates

Comparative methods allow researchers to make inferences about evolutionary processes and patterns from phylogenetic trees. In Bayesian phylogenetics, estimating a phylogeny requires specifying priors on parameters characterizing the branching process and rates of substitution among lineages, in addition to others. Accordingly, characterizing the effect of prior selection on phylogenies is an active area of research. The choice of priors may systematically bias phylogenetic reconstruction and, subsequently, affect conclusions drawn from the resulting phylogeny. Here, we focus on the impact of priors in Bayesian phylogenetic inference and evaluate how they affect the estimation of parameters in macroevolutionary models of lineage diversification. Specifically, we simulate trees under combinations of tree priors and molecular clocks, simulate sequence data, estimate trees, and estimate diversification parameters (e.g., speciation and extinction rates) from these trees. When substitution rate heterogeneity is large, diversification rate estimates deviate substantially from those estimated under the simulation conditions when not captured by an appropriate choice of relaxed molecular clock. However, in general, we find that the choice of tree prior and molecular clock has relatively little impact on the estimation of diversification rates insofar as the sequence data are sufficiently informative and substitution rate heterogeneity among lineages is low-to-moderate.

Post-Cretaceous bursts of evolution along the benthic-pelagic axis in marine fishes

Ecological opportunity arising in the aftermath of mass extinction events is thought to be a powerful driver of evolutionary radiations. Here, we assessed how the wake of the Cretaceous-Palaeogene (K-Pg) mass extinction shaped diversification dynamics in a clade of mostly marine fishes (Carangaria), which comprises a disparate array of benthic and pelagic dwellers including some of the most astonishing fish forms (e.g. flatfishes, billfishes, remoras, archerfishes). Analyses of lineage diversification show time-heterogeneous rates of lineage diversification in carangarians, with highest rates reached during the Palaeocene. Likewise, a remarkable proportion of Carangaria's morphological variation originated early in the history of the group and in tandem with a marked incidence of habitat shifts. Taken together, these results suggest that all major lineages and body plans in Carangaria originated in an early burst shortly after the K-Pg mass extinction, which ultimately allowed the occupation of newly released niches along the benthic-pelagic habitat axis.

How Well Can We Detect Lineage-Specific Diversification-Rate Shifts? A Simulation Study of Sequential AIC Methods

Evolutionary biologists have long been fascinated by the extreme differences in species numbers across branches of the Tree of Life. This has motivated the development of statistical methods for detecting shifts in the rate of lineage diversification across the branches of phylogenic trees. One of the most frequently used methods, MEDUSA, explores a set of diversification-rate models, where each model assigns branches of the phylogeny to a set of diversification-rate categories. Each model is first fit to the data, and the Akaike information criterion (AIC) is then used to identify the optimal diversification model. Surprisingly, the statistical behavior of this popular method is uncharacterized, which is a concern in light of: (1) the poor performance of the AIC as a means of choosing among models in other phylogenetic contexts; (2) the ad hoc algorithm used to visit diversification models, and; (3) errors that we reveal in the likelihood function used to fit diversification models to the phylogenetic data. Here, we perform an extensive simulation study demonstrating that MEDUSA (1) has a high false-discovery rate (on average, spurious diversification-rate shifts are identified ≈30% of the time), and (2) provides biased estimates of diversification-rate parameters. Understanding the statistical behavior of MEDUSA is critical both to empirical researchers—in order to clarify whether these methods can make reliable inferences from empirical datasets—and to theoretical biologists—in order to clarify the specific problems that need to be solved in order to develop more reliable approaches for detecting shifts in the rate of lineage diversification. [Akaike information criterion; extinction; lineage-specific diversification rates; phylogenetic model selection; speciation.]

A generalized birth and death process for modeling the fates of gene duplication

Background

Accurately estimating the timing and mode of gene duplications along the evolutionary history of species can provide invaluable information about underlying mechanisms by which the genomes of organisms evolved and the genes with novel functions arose. Mechanistic models have previously been introduced that allow for probabilistic inference of the evolutionary mechanism for duplicate gene retention based upon the average rate of loss over time of the duplicate. However, there is currently no probabilistic model embedded in a birth-death modeling framework that can take into account the effects of different evolutionary mechanisms of gene retention when analyzing gene family data.

Results

In this study, we describe a generalized birth-death process for modeling the fates of gene duplication. Use of mechanistic models in a phylogenetic framework requires an age-dependent birth-death process. Starting with a single population corresponding to the lineage of a phylogenetic tree and with an assumption of a clock that starts ticking for each duplicate at its birth, an age-dependent birth-death process is developed by extending the results from the time-dependent birth-death process. The implementation of such models in a full phylogenetic framework is expected to enable large scale probabilistic analysis of duplicates in comparative genomic studies.

Conclusions

We develop an age-dependent birth-death model for understanding the mechanisms of gene retention, which allows a gene loss rate dependent on each duplication event. Simulation results indicate that different mechanisms of gene retentions produce distinct likelihood functions, which can be used with genomic data to quantitatively distinguish those mechanisms.

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. [Computation; graphical models; inference; modularization; statistical phylogenetics; tree plate.]