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Extant timetrees are consistent with a myriad of diversification histories

Abstract

Time-calibrated phylogenies of extant species (referred to here as ‘extant timetrees’) are widely used for estimating diversification dynamics1. However, there has been considerable debate surrounding the reliability of these inferences2,3,4,5 and, to date, this critical question remains unresolved. Here we clarify the precise information that can be extracted from extant timetrees under the generalized birth–death model, which underlies most existing methods of estimation. We prove that, for any diversification scenario, there exists an infinite number of alternative diversification scenarios that are equally likely to have generated any given extant timetree. These ‘congruent’ scenarios cannot possibly be distinguished using extant timetrees alone, even in the presence of infinite data. Importantly, congruent diversification scenarios can exhibit markedly different and yet similarly plausible dynamics, which suggests that many previous studies may have over-interpreted phylogenetic evidence. We introduce identifiable and easily interpretable variables that contain all available information about past diversification dynamics, and demonstrate that these can be estimated from extant timetrees. We suggest that measuring and modelling these identifiable variables offers a more robust way to study historical diversification dynamics. Our findings also make it clear that palaeontological data will continue to be crucial for answering some macroevolutionary questions.

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Fig. 1: Illustration of congruent birth–death processes (simulations).
Fig. 2: Illustration of congruent birth–death processes (real data).
Fig. 3: Conceptual implications.

Data availability

No new data were generated for this manuscript. All phylogenetic datasets used as examples have previously been published previously, and are cited where appropriate.

Code availability

Computational methods used for this article—including functions for simulating birth–death models, for constructing models within a given congruence class, for calculating the likelihood of a congruence class and for directly fitting congruence classes (either in terms of λp or in terms of rp and ρλo) to extant timetrees—are implemented in the R package castor v.1.5.5, which is available from The Comprehensive R Archive Network at https://cran.r-project.org/package=castor.

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Acknowledgements

S.L. was supported by a start-up grant by the University of Oregon. M.W.P. was supported by an NSERC Discovery Grant. We thank L. Harmon, S. Otto, A. MacPherson, D. Schluter, T. J. Davies, M. Whitlock, L. F. Henao Diaz, K. Kaur, J. Uyeda, D. Caetano, J. Rolland, L. Parfrey and A. Mooers for insightful comments on this work.

Author information

Affiliations

Authors

Contributions

S.L. performed the mathematical calculations and computational analyses. S.L. and M.W.P. conceived the project and contributed to the writing of the manuscript.

Corresponding authors

Correspondence to Stilianos Louca or Matthew W. Pennell.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Lee Hsiang Liow, Antonis Rokas, Mike Steel and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Pulled speciation and diversification rates.

a, b, Pulled speciation rate (a) and pulled diversification rate (b) of the four congruent models shown in Fig. 1.

Extended Data Fig. 2 Illustration of congruent birth–death processes (fossil data).

a, Origination and extinction rates of marine invertebrate genera, estimated from fossil data. b, Congruent scenario to that in a, obtained by reversing the linear trend of μ (that is, fitting a linear curve to the original μ, and then subtracting that curve twice) and adjusting λ according to equation (2). c, Congruent scenario to that in a, assuming an extinction rate of zero. Further details are provided in Supplementary Information section S.10.

Extended Data Fig. 3 Previous studies are likely to have over-interpreted phylogenetic data.

Time-dependent birth–death model fitted to a nearly complete extant timetree of the Cetacea, under the assumption of extinction rates of zero (μ = 0), compared to a congruent model in which the extinction rate is close to the speciation rate (μ = 0.9λ). a, LTT of the tree, compared to the dLTT predicted by the two models. b, Speciation rates (λ) and extinction rates (μ) of the two models. c, Net diversification rates (r = λ − μ) of the two models. Further details are provided in Supplementary Information section S.4.

Extended Data Fig. 4 Additional examples of congruent birth–death processes.

ac, Example of two congruent—yet markedly different—birth–death models. Both models exhibit a temporary spike in the extinction rate and a temporary spike in the speciation rate; however, the timings of these events differ substantially between the two models. Both models exhibit the same dLTT and the same pulled diversification rate (rp) and would yield identical likelihoods for any given extant timetree. a, Speciation rates (λ and λ*) and extinction rates (μ and μ*) of the two models, plotted over time. Continuous curves correspond to the first model, and dashed curves correspond to the second model. b, Net diversification rates (r and r*) and pulled diversification rate (rp) of the two models. c, dLTT and deterministic total diversities (N and N*) predicted by the two models. df, Another example of two congruent models. In the first model, the speciation and extinction rates both decrease exponentially over time, whereas in the second model the extinction rate increases exponentially over time and the speciation rate exhibits variable directions of change over time. In all models, the sampling fraction is ρ = 0.5.

Extended Data Fig. 5 Identifiability issues persist in large trees.

ac, Diversification analysis of a timetree (about 114,000 tips) simulated from a birth–death process that exhibits a mass extinction event at around 5 Myr before present. a, LTT of the generated tree (long-dashed curve), dLTT of the true model that generated the tree (continuous curve) and dLTT of a maximum-likelihood fitted model (short-dashed curve) are shown. The fitted dLTT is practically identical to the true dLTT and thus is covered by the latter. b, True speciation and extinction rates (continuous curves), compared to fitted speciation and extinction rates (dashed curves). There is considerable disagreement between the fitted and true λ and μ, despite the fact that the allowed model set could—in principle—approximate the true rates reasonably well. c, Pulled diversification rate (PDR) of the true model (continuous curve), compared to the pulled diversification rate of the fitted model (dashed curve). df, Diversification analysis of a timetree (about 785,000 tips) simulated from a birth–death process that exhibits a rapid radiation event at around 5 Myr before present and a mass extinction event at around 2 Myr before present. df are analogous to ac. There is considerable disagreement between the fitted and true λ and μ, despite the fact that the allowed model set could—in principle—approximate the true rates reasonably well. Extended Data Figure 7 provides the fitting results when μ is fixed to its true value. gi, Diversification analyses of an extant timetree of 79,874 seed plant species, performed either by fitting λ and μ on a grid of discrete time points or by fitting the parameters of generic polynomial or exponential functions for λ and μ. g, LTT of the tree, dLTT of the grid-fitted model and dLTT of the fitted parametric model. h, Speciation and extinction rates predicted by the grid-fitted model or the fitted parametric model. i, Pulled diversification rate predicted by the grid-fitted model and the fitted parametric model. Further details are provided in Supplementary Information sections S.10 and S.11.

Extended Data Fig. 6 Identifiability issues cannot be resolved with the Akaike information criterion.

Maximum-likelihood birth–death models fitted to a tree comprising 1,000,000 tips, simulated on the basis of the origination and extinction rates of marine invertebrate genera estimated from fossil data. Top row, maximum-likelihood-fitted piecewise constant model (also known as birth–death–shift model), with grid size (n = 11) chosen by minimizing the Akaike information criterion (AIC). Bottom row, maximum-likelihood-fitted piecewise linear model, with grid size (n = 12) chosen by minimizing the AIC. Left column, dLTTs of the fitted models compared to the true dLTT and the LTT of the tree. Right column, fitted speciation and extinction rates, compared to the true rates used to generate the tree. In both cases, the maximum-likelihood models poorly reflect the true rates despite a near-perfect match of the LTT, even when the complexity of the models was optimized on the basis of the AIC. For further details, see Supplementary Information sections S.2 and S.10.

Extended Data Fig. 7 Estimating λ when μ and ρ are fixed or known.

ac, Example analysis of a simulated extant timetree (about 114,000 tips) that exhibits a mass extinction event at around 5 Myr before present. A birth–death model was fitted while fixing μ and ρ to their true values; λ was fitted at 15 discrete time points. a, LTT of the generated tree (long-dashed curve), dLTT of the true model that generated the tree (continuous curve) and dLTT of a maximum-likelihood fitted model (short-dashed curve). The fitted dLTT is practically identical to the true dLTT, and is thus covered by the latter. b, True speciation and extinction rates (continuous curves), along with the fitted speciation rate and fixed extinction rate (dashed curves). c, Pulled diversification rate of the true model (rp, continuous curve), compared to the pulled diversification rate of the fitted model (dashed curve). df, Example analysis of a simulated extant timetree (about 785,000 tips) that exhibits a rapid radiation event at about 5 Myr before present and a mass extinction event at about 2 Myr before present. A birth–death model was fitted similarly to the example shown in ac, and df are analogous to ac. In both cases, rate estimation was restricted to ages at which the LTT included at least 500 lineages. Further details are provided in Supplementary Information section S.10.

Extended Data Fig. 8 Fitting congruence classes instead of models.

Analysis of an extant timetree generated by a birth–death model that exhibits a temporary rapid radiation event about 5 Myr before present and a mass extinction event about 2 Myr before present. A congruence class was fitted to the timetree either in terms of the pulled diversification rate (rp) and the product ρλo, or in terms of the pulled speciation rate (PSR) (λp). a, LTT of the tree (long-dashed curve), together with the dLTT of the true model (continuous curve) and the dLTT of the fitted congruence classes (short-dashed curve); in both cases, the fitted dLTT was almost identical to the true dLTT, and is thus completely covered by the latter. b, Pulled diversification rate of the true model (continuous curve), compared to the fitted pulled diversification rate (short-dashed curve). c, Pulled speciation rate of the true model (continuous curve), compared to the fitted pulled speciation rate (short-dashed curve). The pulled diversification rate and pulled speciation rate were fitted via maximum-likelihood methods, allowing the pulled diversification rate or pulled speciation rate to vary freely at 15 discrete equidistant time points. Further details are provided in in Supplementary Information section S.9.

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This file contains Supplementary Text S.1-S.11.

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Louca, S., Pennell, M.W. Extant timetrees are consistent with a myriad of diversification histories. Nature 580, 502–505 (2020). https://doi.org/10.1038/s41586-020-2176-1

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