Source-linked AI summary
Automatic detection of key innovations, rate shifts, and diversity-dependence on phylogenetic trees
Daniel L. Rabosky
TL;DR
Existing methods do not provide a general framework for delineating heterogeneous diversification processes within single phylogenies. This paper develops BAMM, which usually identifies the true number of processes across six simulated macroevolutionary scenarios, while its cetacean results do not rule out ocean restructuring as an alternative explanation.
Problem
Existing methods have limited ability to accommodate diversification-rate variation through time and among lineages within single phylogenies.
Method
The method uses a compound Poisson process and reversible-jump Markov chain Monte Carlo to identify changing diversification processes without prespecifying their locations.
Results
Across six distinct macroevolutionary scenarios, BAMM usually identified the true number of processes in the generating model.
Takeaways & Limitations
BAMM supports exploration of heterogeneous macroevolutionary dynamics involving distinct diversification processes.
Takeaways & Limitations
The cetacean results do not rule out ocean restructuring as a contributor to the dolphin clade’s clade-specific speciation-rate burst and slowdown.
Abstract
from arXiv · showhide
A number of methods have been developed to infer differential rates of species diversification through time and among clades using time-calibrated phylogenetic trees. However, we lack a general framework that can delineate and quantify heterogeneous mixtures of dynamic processes within single phylogenies. I developed a method that can identify arbitrary numbers of time-varying diversification processes on phylogenies without specifying their locations in advance. The method uses reversible-jump Markov Chain Monte Carlo to move between model subspaces that vary in the number of distinct diversification regimes. The model assumes that changes in evolutionary regimes occur across the branches of phylogenetic trees under a compound Poisson process and explicitly accounts for rate variation through time and among lineages. Using simulated datasets, I demonstrate that the method can be used to quantify complex mixtures of time-dependent, diversity-dependent, and constant-rate diversification processes. I compared the performance of the method to the MEDUSA model of rate variation among lineages. As an empirical example, I analyzed the history of speciation and extinction during the radiation of modern whales. The method described here will greatly facilitate the exploration of macroevolutionary dynamics across large phylogenetic trees, which may have been shaped by heterogeneous mixtures of distinct evolutionary processes.
Introduction · Materials and Methods · Compound Poisson process model of diversification rate variation 105
The paper introduces a Bayesian framework for identifying heterogeneous, time-varying diversification regimes on phylogenies without pre-specifying their number or locations. It models regime shifts with a compound Poisson process and uses reversible-jump MCMC to compare models with different numbers of processes.
- Introduction: The framework addresses the lack of methods jointly accommodating diversification-rate variation through time and among lineages, which can otherwise bias parameter estimates and interpretations.
- Introduction: It represents phylogenies as heterogeneous mixtures of distinct evolutionary processes, including combinations of diversity-dependent and constant-rate diversification.
- Introduction: The Bayesian analysis provides marginal distributions of speciation and extinction rates for every phylogenetic branch while automatically exploring a broad candidate-model space.
- Compound Poisson process model of diversification rate variation 105: Regime shifts occur across tree branches under a compound Poisson process, with each transition initiating a process inherited by downstream nodes until another transition or terminal branches.
- Compound Poisson process model of diversification rate variation 105: The model permits any number of transitions, including a single root process or multiple independent time-varying processes governing different parts of the tree.
- Compound Poisson process model of diversification rate variation 105: Each process has time-varying speciation and constant background extinction, with exponential speciation change also approximating diversity-dependent diversification.
Bayesian implementation
The Bayesian implementation uses reversible-jump MCMC to estimate the number of distinct evolutionary regimes and their diversification parameters across phylogenetic trees. It combines within-model parameter updates with transdimensional transition additions and deletions under a compound Poisson framework.
- Bayesian implementation: Reversible-jump MCMC moves between models by adding or deleting transitions, while updating transition locations, rates, and other current-model parameters.The chain supports moves between Mk and Mk+1 or Mk-1, plus updates to Λ, ξi, λ0,i, zi, and µi.
- Bayesian implementation: Likelihoods are computed on branches using a discretized constant-rate birth-death model that approximates time-dependent and diversity-dependent rates.Transition locations have a uniform (0, T) prior, while λ and µ use relatively flat exponential priors and z uses a normal prior with mean 0 and variance 0.05.
- Bayesian implementation: The method estimates the number of distinct evolutionary regimes across phylogenetic trees and marginal distributions of speciation and diversification parameters.The full model includes transition locations and diversification parameters for each transition, alongside the overall transition rate Λ.
Analysis of simulated datasets
The study evaluated BAMM on 3,000 simulated datasets spanning six diversification scenarios, including constant-rate, time-varying, and diversity-dependent processes. Performance was assessed using model selection, branch-specific rate recovery, and proportional error.
- Analysis of simulated datasets: The simulations covered six diversification scenarios, including constant-rate birth-death, pure-birth-to-exponential-change, and diversity-dependent multiprocess models.The diversity-dependent models included one through four shifts to independent, decoupled speciation-extinction processes, with 500 simulations per scenario.
- Analysis of simulated datasets: Simulated multiprocess trees introduced rate shifts at randomly selected times and lineages, then simulated descendant subtrees under newly sampled process parameters.Shift times were sampled between 40 and 95 time units, and subtrees were required to contain at least 25 and fewer than 1000 terminal taxa.
- Analysis of simulated datasets: The analysis compared BAMM’s branch-specific speciation and extinction estimates with the true evolutionary rates using OLS regression and proportional error.Proportional error was defined as a weighted average of proportional rate differences across phylogenetic branches; a value of 2 indicates estimates twice the true rate.
Comparison with MEDUSA
BAMM was compared with MEDUSA, which identifies lineage-specific rate shifts but typically assumes diversification rates remain constant through time within rate classes. The comparison used simulated datasets to assess process-count recovery and branch-specific rate error, while a separate BAMM analysis examined cetacean diversification.
- Comparison with MEDUSA: MEDUSA incrementally adds rate shifts from a constant-rate birth-death model using stepwise AIC until additional partitions no longer improve fit.
- Comparison with MEDUSA: MEDUSA typically assumes diversification rates are constant through time within rate classes, but the consequences of violating this assumption remain unresolved.
- Comparison with MEDUSA: The study analyzed 500 datasets under each of six diversification models, evaluating MEDUSA’s process-count recovery and branch-specific speciation-rate proportional error.
- Empirical example: cetacean radiation: For cetaceans, BAMM analyzed diversification across a time-calibrated tree of 87 of 89 extant whale and dolphin species using compound-Poisson rate variation.
Results
Simulations showed that BAMM generally recovered the number and values of diversification processes, outperforming MEDUSA for time- and diversity-dependent rates. Applied to cetaceans, BAMM supported a two-process model with elevated speciation in the ancestral Delphinidae lineage.
- Analysis of simulated datasets: Across five heterogeneous-rate scenarios, BAMM’s MAP model was no more complex than the generating model in more than 95% of simulations.Power decreased for the most complex DD3–DD5 models, but model overfitting was not a problem.
- Analysis of simulated datasets: BAMM speciation-rate estimates closely tracked generating rates, with mean proportional error near 1.0 across all simulation scenarios.A small number of weak correlations reflected underfitting, while extinction-rate estimates were generally biased upward and explained little variance.
- Analysis of simulated datasets: BAMM correctly identified the true number of processes in 90% of DD2 datasets, versus 40.2% for MEDUSA.For DD5, BAMM identified the generating model in 38.4% of simulations, compared with fewer than 5% for MEDUSA.
- Analysis of simulated datasets: MEDUSA branch-specific speciation estimates were extremely poor, with slope modes of zero in four of five scenarios, whereas BAMM estimates were closer to 1.0.MEDUSA explained little rate variance and generally underestimated time- or diversity-dependent speciation rates.
- Analysis of the time-calibrated cetacean phylogeny: Cetacean analyses strongly supported a two-process model: the one-process model had p = 0.017, with posterior odds of 44.6 favoring two processes.The supported shift indicated substantially elevated speciation in the ancestral lineage leading to Delphinidae, with probability greater than 0.975.
- Analysis of the time-calibrated cetacean phylogeny: Whale speciation showed an overall background decline with a Miocene spike driven by Delphinidae, while mean relative extinction was 0.36.Additional cetacean processes received little support, and extinction estimates remained low under all priors.
Discussion
The method models phylogenetic trees as mixtures of dynamic evolutionary processes, detecting rate shifts, key innovations, time dependence, and diversity dependence. It performed well in simulations, but extinction estimates remain unreliable despite accurate diversity-dependent inference and fast likelihood calculations.
- Methodological contribution: The compound Poisson framework treats trees as mixtures of dynamic processes and detects rate shifts, key innovations, time-dependent speciation, and diversity dependence within single trees.BAMM output includes process-number and model-posterior estimates, process locations, parameter estimates, and branch-specific speciation and extinction rates.
- Simulation performance: Branch-specific rate estimates remained strong for the most complex DD5 scenario, with an observed mean slope of 0.95 and lower variance than other scenarios.The observed DD5 slope was closer to 1.0 than slopes from simulations with only two processes.
- Limitations: Extinction-rate estimates were potentially biased and showed low confidence, with accuracy likely worsening when real phylogenies violate model assumptions.The estimates remained correlated with true rates, but confidence was low and model-assumption violations may further reduce accuracy.
- Diversity dependence and computation: BAMM inferred diversity-dependent dynamics across simulation scenarios using an exponential speciation-change function, while enabling extremely fast likelihood calculations on large trees.The exponential approximation improves computational efficiency relative to more demanding full diversity-dependent models with extinction.
Comparison to existing methods
Compared with BAMM, MEDUSA underestimated the number of diversification processes and poorly estimated speciation rates when diversification rates varied through time. These shortcomings reflect MEDUSA’s assumption of time-constant rates, a limitation increasingly consequential for larger, heterogeneous phylogenies.
- Comparison to existing methods: MEDUSA was not robust to violations of its assumption that diversification rates remain constant through time, unlike BAMM’s explicit modeling of temporal and lineage rate variation.The method implementations differ in whether they account for rate variation through time and among lineages.
- Comparison to existing methods: BAMM often estimated the true number of generating processes, whereas MEDUSA consistently underestimated them, with larger errors as model complexity increased.The comparison is shown in Figures 4 and 7.
- Comparison to existing methods: MEDUSA’s estimated speciation rates were especially poor and showed little overall correspondence with the true rates in simulations.This result is reported in Figure 8.
- Comparison to existing methods: Rate-heterogeneity challenges are likely to intensify for larger phylogenies because they are more likely to combine distinct evolutionary processes.This complexity motivated the proposed method.
Cetacean macroevolutionary dynamics
Cetacean diversification shows a relatively flat lineage-accumulation curve but strong support for two distinct evolutionary rate regimes. One regime involves weak root-level slowdown, while another features an explosive Delphinidae burst followed by slowdown.
- Cetacean macroevolutionary dynamics: The overall cetacean lineage-accumulation curve is relatively flat, suggesting relatively little variation in speciation rates through time.This result complements previous studies of cetacean diversification through time.
- Cetacean macroevolutionary dynamics: Strong support identifies two distinct cetacean evolutionary rate regimes: weak root-level speciation slowdown and an explosive Delphinidae burst followed by slowdown.The root process involves a weak slowdown through time, whereas the Delphinidae process is associated with an explosive burst and subsequent slowdown.
- Cetacean macroevolutionary dynamics: Speciation increased from 13 Ma to 4 Ma, likely reflecting rapid diversification of the dolphin clade.This pattern may reflect independent evolutionary dynamics of delphinid and non-delphinid lineages.
- Cetacean macroevolutionary dynamics: Ocean restructuring may have contributed to the clade-specific burst and slowdown, but acceleration during this interval could equally reflect another process.The results do not rule out ocean restructuring, while also presenting an alternative explanation for the acceleration in rates.
of a key evolutionary innovation early in the history of the dolphins.
The framework is designed for extensions that add alternative diversification models and account for uncertainty in phylogenetic trees. Future work could also jointly analyze paleontological and neontological data, although suitable datasets remain elusive.
- of a key evolutionary innovation early in the history of the dolphins.: Future extensions could add alternative functional models for speciation and extinction-rate variation through time.The computational machinery for adding, moving, and deleting processes is described as flexible.
- of a key evolutionary innovation early in the history of the dolphins.: BAMM currently simulates posterior distributions across a fixed topology, so inferred parameter intervals exclude uncertainty in topology and branch lengths.Credible intervals currently reflect only parametric uncertainty from the diversification model and would presumably increase when tree uncertainty is included.
- of a key evolutionary innovation early in the history of the dolphins.: Joint inference from paleontological and neontological data is a further goal because the two data types are frequently in conflict.The objective is facilitated by theoretical advances for estimating evolutionary rates from fossils and molecular phylogenies, but suitable datasets remain elusive.
Summary · 3. Mittelbach GG, Schemske DW, Cornell HV, Allen AP, Brown JM, et al. (2007) · 9. Wagner CE, Harmon LJ, Seehausen O (2012) Ecological opportunity and sexual
The paper presents a reversible-jump MCMC framework for inferring heterogeneous mixtures of time-constant and time-varying evolutionary processes on phylogenetic trees. By relaxing time-homogeneous diversification assumptions, it broadens the description of evolutionary dynamics and may extend to other phylogenetic applications.
- Summary: The framework models phylogenies as collections of dynamic processes, greatly extending the ability to describe evolutionary dynamics.It infers mixtures of processes that have influenced phylogenetic-tree structure.
- Summary: By relaxing time-homogeneous diversification, the model describes complex mixtures of time-constant and time-varying processes.This directly addresses the limitation that previous transdimensional phylogenetic MCMC studies generally assumed constant dynamics within component processes.
- Summary: Reversible-jump MCMC fitting of time-inhomogeneous multiprocess models to phylogenetic data may support applications beyond those described here.Suggested areas include DNA sequence evolution, phenotypic evolution, and phylogeography.
- 3. Mittelbach GG, Schemske DW, Cornell HV, Allen AP, Brown JM, et al. (2007): The cited literature includes work on latitudinal diversity gradients, community diversity, adaptive radiation, and reconciling molecular phylogenies with the fossil record.These references frame diversification, biogeographic, and macroevolutionary questions related to the framework.
- 3. Mittelbach GG, Schemske DW, Cornell HV, Allen AP, Brown JM, et al. (2007): Additional cited studies address time-dependent speciation and extinction and the estimation of diversification rates from phylogenetic information.These references are presented as related work on diversification-rate inference.
- 9. Wagner CE, Harmon LJ, Seehausen O (2012) Ecological opportunity and sexual: The bibliography also cites research linking adaptive radiation to ecological opportunity and sexual selection, alongside studies of origination, extinction, reconstructed evolutionary processes, and diversity dependence.The cited diversity-dependence work concerns agreement between molecular phylogenies and the fossil record.
14. Rabosky DL, Lovette IJ (2008) Explosive evolutionary radiations: Decreasing
This section cites prior work on diversification-rate shifts, changing speciation or extinction, and ecological dynamics of clade diversification.
- Rabosky and Lovette examine explosive evolutionary radiations through decreasing speciation or increasing extinction through time.
- Stadler reports recent diversification-rate shifts revealed by mammalian phylogeny.
- McPeek addresses ecological dynamics of clade diversification and community assembly.
20. Alfaro ME, Santini F, Brock C, Alamillo H, Dornburg A, et al. (2009) Nine
The section lists prior studies on vertebrate diversification, stochastic diversity patterns, quantitative traits, and trait effects on speciation and extinction.
- Alfaro et al. (2009) examined exceptional radiations and high turnover as explanations for species diversity in jawed vertebrates.
- The cited literature includes methods for testing stochastic diversity patterns and quantifying relationships between traits and diversification.
- Additional studies addressed binary-character effects on speciation and extinction, adaptive zones, insect diversification, and equilibrium dynamics in island lizards.
27. Rabosky DL (2010) Extinction rates should not be estimated from molecular
The study evaluates a multi-process diversification model that can recover mixtures of evolutionary regimes, outperform MEDUSA when speciation rates vary through time, and characterize diversification in cetaceans. Results also show robust speciation estimates but greater prior sensitivity for extinction.
- Simulation results: The true number of diversification-process transitions was recovered only when time-constant speciation was not imposed.The simulated generating model contained three processes and two transitions.
- Comparison with MEDUSA: MEDUSA consistently underestimated the true number of processes when speciation rates varied through time, whereas BAMM produced comparable analyses under the same datasets.
- Cetacean application: In cetaceans, a massive spike in mean speciation rates at 7.5 Ma corresponded to the early radiation of the group.
- Cetacean application: Cetacean speciation-rate estimates were remarkably robust to prior choice, whereas extinction estimates were more prior-sensitive but low overall.The comparison included γ = 10 and γ = 0.1 priors.