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Improved estimation of macroevolutionary rates from fossil data using a Bayesian framework

  • Daniele Silvestro (a1), Nicolas Salamin (a2), Alexandre Antonelli (a3) and Xavier Meyer (a4)


The estimation of origination and extinction rates and their temporal variation is central to understanding diversity patterns and the evolutionary history of clades. The fossil record provides the only direct evidence of extinction and biodiversity changes through time and has long been used to infer the dynamics of diversity changes in deep time. The software PyRate implements a Bayesian framework to analyze fossil occurrence data to estimate the rates of preservation, origination, and extinction while incorporating several sources of uncertainty. Building upon this framework, we present a suite of methodological advances including more complex and realistic models of preservation and the first likelihood-based test to compare the fit across different models. Further, we develop a new reversible jump Markov chain Monte Carlo algorithm to estimate origination and extinction rates and their temporal variation, which provides more reliable results and includes an explicit estimation of the number and temporal placement of statistically significant rate changes. Finally, we implement a new C++ library that speeds up the analyses by orders of magnitude, therefore facilitating the application of the PyRate methods to large data sets. We demonstrate the new functionalities through extensive simulations and with the analysis of a large data set of Cenozoic marine mammals. We compare our analytical framework against two widely used alternative methods to infer origination and extinction rates, revealing that PyRate decisively outperforms them across a range of simulated data sets. Our analyses indicate that explicit statistical model testing, which is often neglected in fossil-based macroevolutionary analyses, is crucial to obtain accurate and robust results.

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Alroy, J. 1996. Constant extinction, constrained diversification, and uncoordinated stasis in North American mammals. Palaeogeography, Palaeoclimatology, Palaeoecology 127:285311.
Alroy, J. 2008. Dynamics of origination and extinction in the marine fossil record. Proceedings of the National Academy of Sciences USA 105:1153611542.
Alroy, J. 2014. Accurate and precise estimates of origination and extinction rates. Paleobiology 40:374397.
Alroy, J. 2015. A more precise speciation and extinction rate estimator. Paleobiology 41:633639.
Bapst, D. W., and Hopkins, M. J.. 2016. Comparing cal3 and other a posteriori time-scaling approaches in a case study with the pterocephaliid trilobites. Paleobiology 43:4967.
Benton, M. J., Forth, J., and Langer, M. C.. 2014. Models for the rise of the dinosaurs. Current Biology 24:R87R95.
Burin, G., Alencar, L. R. V., Chang, J., Alfaro, M. E., and Quental, T. B.. 2019. How well can we estimate diversity dynamics for clades in diversity decline? Systematic Biology 68:4762.
Burnham, K. P., and Anderson, D. A.. 2002. Model selection and multimodel inference: a practical information-theoretic approach, 2nd ed. Springer, New York.
Cantalapiedra, J. L., Fernández, M. H., Azanza, B., and Morales, J.. 2015. Congruent phylogenetic and fossil signatures of mammalian diversification dynamics driven by Tertiary abiotic change. Evolution 69:29412953. doi:10.1111/evo.12787.
Chang, J., Rabosky, D. L., Smith, S. A., and Alfaro, M. E.. 2019. An R package and online resource for macroevolutionary studies using the ray-finned fish tree of life. Methods in Ecology and Evolution 10:11181124.
Connolly, S. R., and Miller, A. I.. 2001. Joint estimation of sampling and turnover rates from fossil databases: capture-mark-recapture methods revisited. Paleobiology 27:751767.
Dib, L., Silvestro, D., and Salamin, N.. 2014. Evolutionary footprint of coevolving positions in genes. Bioinformatics 30:12411249.
Ezard, T. H. G., Aze, T., Pearson, P. N., and Purvis, A.. 2011. Interplay between changing climate and species’ ecology drives macroevolutionary dynamics. Science 332:349351.
Ezard, T. H., Quental, T. B., and Benton, M. J.. 2016. The challenges to inferring the regulators of biodiversity in deep time. Philosophical Transactions of the Royal Society of London B 371: 20150216. doi: 10.1098/rstb.2015.0216.
Foote, M. 2000. Origination and extinction components of taxonomic diversity: general problems. Paleobiology 26:74102.
Foote, M. 2001. Inferring temporal patterns of preservation, origination, and extinction from taxonomic survivorship analysis. Paleobiology 27:602630.
Foote, M. 2003. Origination and extinction through the Phanerozoic: a new approach. Journal of Geology 111:125148.
Foote, M. 2007. Extinction and quiescence in marine animal genera. Paleobiology 33:261272.
Foote, M., and Miller, A. I.. 2007. Principles of paleontology. Freeman, New York.
Foote, M., and Raup, D. M.. 1996. Fossil preservation and the stratigraphic ranges of taxa. Paleobiology 22:121140.
Foote, M., Crampton, J. S., Beu, A. G., Marshall, B. A., Cooper, R. A., Maxwell, P. A., and Matcham, I.. 2007. Rise and fall of species occupancy in Cenozoic fossil mollusks. Science 318:11311134.
Foote, M., Crampton, J. S., Beu, A. G., and Nelson, C. S.. 2015. Aragonite bias, and lack of bias, in the fossil record: lithological, environmental, and ecological controls. Paleobiology 41:245265.
Gelman, A., Carlin, J. B., Stern, H. S., and Rubin, D. B.. 2013. Bayesian data analysis, 3rd ed. Chapman & Hall/CRC Texts in Statistical Science, London.
Gernhard, T. 2008. The conditioned reconstructed process. Journal of Theoretical Biology 253:769778.
Green, P. J. 1995. Reversible jump Markov chain Monte Carlo and Bayesian model determination. Biometrika 82:711732.
Hagen, O., Andermann, T., Quental, B. T., Antonelli, A., and Silvestro, D.. 2017. Estimating age-dependent extinction: contrasting evidence from fossil and phylogenies. Systematic Biology 67:458474. doi:10.1093/sysbio/syx082.
Heath, T. A., Hulsenbeck, J. P., and Stadler, T.. 2014. The fossilized birth–death process for coherent calibration of divergence-time estimates. Proceedings of the National Academy of Sciences USA 111:29572966.
Jetz, W., Thomas, G. H., Joy, J. B., Hartmann, K., and Mooers, A. O.. 2012. The global diversity of birds in space and time. Nature 491:444448.
Kass, R. E., and Raftery, A. E.. 1995. Bayes factors. Journal of the American Statistical Association 90:773795.
Keiding, N. 1975. Maximum likelihood estimation in the birth-death process. Annals of Statistics 3:363372.
Kendall, D. G. 1948. On the generalized birth-and-death process. Annals of Mathematical Statistics 19:115.
Kocsis, A. T., Reddin, C. J., Alroy, J., and Kiessling, W.. 2019. The R package divdyn for quantifying diversity dynamics using fossil sampling data. Methods in Ecology and Evolution 10:735743.
Kurtén, B. 1954. Population dynamics: a new method in paleontology. Journal of Paleontology 28:286292.
Lartillot, N., and Philippe, H.. 2006. Computing Bayes factors using thermodynamic integration. Systematic Biology 55:195207.
Lehtonen, S., Silvestro, D., Karger, D. N., Scotese, C., Tuomisto, H., Kessler, M., Peña, C., Wahlberg, N., and Antonelli, A.. 2017. Environmentally driven extinction and opportunistic origination explain fern diversification patterns. Scientific Reports 7:ar4831.
Liow, L. H., and Finarelli, J. A.. 2014. A dynamic global equilibrium in carnivoran diversification over 20 million years. Proceedings of the Royal Society of London B 281:20132312.
Liow, L. H., and Nichols, J. D.. 2010. Estimating rates and probabilities of origination and extinction using taxonomic occurrence data: capture-recapture approaches. In Hunt, G. and Alroy, J., eds. Short Courses in Paleontology 16:81–94. Yale University Printing and Publishing, New Haven, Conn.
Liow, L. H., Fortelius, M., Bingham, E., Lintulaakso, K., Mannila, H., Flynn, L., and Stenseth, N. C.. 2008. Higher origination and extinction rates in larger mammals. Proceedings of the National Academy of Sciences USA 105:60976102.
Liow, L., Quental, T., and Marshall, C.. 2010a. When can decreasing diversification rates be detected with molecular phylogenies and the fossil record? Systematic Biology 59:646659.
Liow, L. H., Skaug, H., Ergon, T., and Schweder, T.. 2010b. Global occurrence trajectories of microfossils: environmental volatility and the rise and fall of individual species. Paleobiology 36:224252.
Liow, L. H., Reitan, T., and Harnik, P. G.. 2015. Ecological interactions on macroevolutionary time scales: clams and brachiopods are more than ships that pass in the night. Ecology Letters 18:10301039.
Marshall, C. R. 2017. Five paleobiological laws needed to understand the evolution of the living biota. Nature Ecology and Evolution 1:165.
May, M. R., Höhna, S., and Moore, B. R.. 2016. A Bayesian approach for detecting the impact of mass-extinction events on molecular phylogenies when rates of lineage diversification may vary. Methods in Ecology and Evolution 7:947959.
Miller, A. I., and Foote, M.. 2003. Increased longevities of post-Paleozoic marine genera after mass extinctions. Science 302:10301032.
Neal, R. M. 2000. Markov chain sampling methods for Dirichlet process mixture models. Journal of Computational and Graphical Statistics 9:249265.
Nee, S. 2006. Birth-death models in macroevolution. Annual Review of Ecology, Evolution, and Systematics 37:117.
Nee, S., May, R. M., and Harvey, P. H.. 1994. The reconstructed evolutionary process. Philosophical Transactions of the Royal Society of London B 344:305311.
Pennell, M. W., Eastman, J. M., Slater, G. J., Brown, J. W., Uyeda, J. C., FitzJohn, R. G., Alfaro, M. E., and Harmon, L. J.. 2014. geiger v2.0: an expanded suite of methods for fitting macroevolutionary models to phylogenetic trees. Bioinformatics 30:22162218.
Perez-Escobar, O. A., Chomicki, G., Condamine, F. L., Karremans, A. P., Bogarin, D., Matzke, N. J., Silvestro, D., and Antonelli, A.. 2017. Recent origin and rapid speciation of neotropical orchids in the world's richest plant biodiversity hotspot. New Phytologist 215:891905.
Peters, S. E. 2008. Environmental determinants of extinction selectivity in the fossil record. Nature 454:626638.
Pimiento, C., Griffin, J. N., Clements, C. F., Silvestro, D., Varela, S., Uhen, M. D., and Jaramillo, C.. 2017. The Pliocene marine megafauna extinction and its impact on functional diversity. Nature Ecology and Evolution 1:11001106.
Piras, P., Silvestro, D., Carotenuto, F., Castiglione, S., Kotsakis, A., Maiorino, L., Melchionna, M., Mondanaro, A., Sansalone, G., Serio, C., Vero, V. A., and Raia, P.. 2018. Evolution of the sabertooth mandible: a deadly ecomorphological specialization. Palaeogeography, Palaeoclimatology, Palaeoecology 496:166174.
Pires, M. M., Silvestro, D., and Quental, T. B.. 2017. Interactions within and between clades shaped the diversification of terrestrial carnivores. Evolution 71:18551864.
Quental, T., and Marshall, C. R.. 2010. Diversity dynamics: Molecular phylogenies need the fossil record. Trends in Ecology and Evolution 25:434441.
Quental, T. B., and Marshall, C. R.. 2013. How the Red Queen drives terrestrial mammals to extinction. Science 341:290292.
Raia, P., Carotenuto, F., Mondanaro, A., Castiglione, S., Passaro, F., Saggese, F., Melchionna, M., Serio, C., Alessio, L., Silvestro, D., and Fortelius, M.. 2016. Progress to extinction: increased specialisation causes the demise of animal clades. Scientific Reports 6:30965.
Raup, D. M. 1986. Biological extinction in earth history. Science 231:15281533.
Raup, D. M., and Sepkoski, J. J.. 1982. Mass extinctions in the marine fossil record. Science 215:15011503.
Raup, D. M., and Sepkoski, J. J.. 1984. Periodicity of extinctions in the geologic past. Proceedings of the National Academy of Sciences USA 81:801805.
Rolland, J., Silvestro, D., Schluter, D., Guisan, A., Broennimann, O., and Salamin, N.. 2018. The impact of endothermy on the climatic niche evolution and the distribution of vertebrate diversity. Nature Ecology and Evolution 2:459464.
Sadler, P. M., Kemple, W. G., and Kooser, M. A.. 2008. CONOP9 programs for solving the stratigraphic correlation and seriation problems as constrained optimization. Springer, Netherlands, 461462.
Sepkoski, J. J. 1998. Rates of speciation in the fossil record. Philosophical Transactions of the Royal Society of London B 353:315326.
Silvestro, D., Salamin, N., and Schnitzler, J.. 2014a. PyRate: a new program to estimate speciation and extinction rates from incomplete fossil data. Methods in Ecology and Evolution 5:11261131.
Silvestro, D., Schnitzler, J., Li, L. H., Antonelli, A., and Salamin, N.. 2014b. Bayesian estimation of speciation and extinction from incomplete fossil occurrence data. Systematic Biology 63:349367.
Silvestro, D., Antonelli, A., Salamin, N., and Quental, T. B.. 2015a. The role of clade competition in the diversification of North American canids. Proceedings of the National Academy of Sciences USA 112:86848689.
Silvestro, D., Cascales-Miñana, B., Bacon, C. D., and Antonelli, A.. 2015b. Revisiting the origin and diversification of vascular plants through a comprehensive Bayesian analysis of the fossil record. New Phytologist 207:425436. doi:10.1111/nph.13247.
Silvestro, D., Zizka, A., Bacon, C. D., Cascales-Miñana, B., Salamin, N., and Antonelli, A.. 2016. Fossil biogeography: a new model to infer dispersal, extinction and sampling from palaeontological data. Philosophical Transactions of the Royal Society of London B 371:20150225.
Silvestro, D., Pires, M. M., Quental, T. B., and Salamin, N.. 2017. Bayesian estimation of multiple clade competition from fossil data. Evolutionary Ecology Research 18:4159.
Silvestro, D., Warnock, R. C. M., Gavryushkina, A., and Stadler, T.. 2018. Closing the gap between palaeontological and neontological speciation and extinction rate estimates. Nature Communications 9: 5237. doi: 10.1038/s41467-018-07622-y.
Smiley, T. M. 2018. Detecting diversification rates in relation to preservation and tectonic history from simulated fossil records. Paleobiology 44:124.
Stadler, T. 2009. On incomplete sampling under birth-death models and connections to the sampling-based coalescent. Journal of Theoretical Biology 261:5866.
Stadler, T. 2013. Recovering speciation and extinction dynamics based on phylogenies. Journal of Evolutionary Biology 26:12031219.
Stephens, M. 2000. Bayesian analysis of mixture models with an unknown number of components—an alternative to reversible jump methods. Annals of Statistics 28:4074.
Van Valen, L., and Sloan, R. E.. 1966. The extinction of the multituberculates. Systematic Zoology 15:261278.
Vrba, E. S. 1985. Environment and evolution: alternative causes of the temporal distribution of evolutionary events. South African Journal of Science 81:229236.
Wagner, P. J., and Marcot, J.. 2013. Modelling distributions of fossil sampling rates over time, space and taxa: assessment and implications for macroevolutionary studies. Methods in Ecology and Evolution 4:703713.
Warnock, R. C. M., Parham, J. F., Joyce, W. G., Lyson, T. R., and Donoghue, P. C. J.. 2015. Calibration uncertainty in molecular dating analyses: there is no substitute for the prior evaluation of time priors. Proceedings of the Royal Society of London B 282:20141013.
Yang, Z. 1994. Maximum likelihood phylogenetic estimation from DNA sequences with variable rates over sites: Approximate methods. Journal of Molecular Evolution 39:306314.
Zanne, A. E., Tank, D. C., Cornwell, W. K., Eastman, J. M., Smith, S. A., FitzJohn, R. G., McGlinn, D. J., O'Meara, B. C., Moles, A. T., Reich, P. B., Royer, D. L., Soltis, D. E., Stevens, P. F., Westoby, M., Wright, I. J., Aarssen, L., Bertin, R. I., Calaminus, A., Govaerts, R., Hemmings, F., Leishman, M. R., Oleksyn, J., Soltis, P. S., Swenson, N. G., Warman, L., and Beaulieu, J. M.. 2014. Three keys to the radiation of angiosperms into freezing environments. Nature 506:394394.
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Improved estimation of macroevolutionary rates from fossil data using a Bayesian framework

  • Daniele Silvestro (a1), Nicolas Salamin (a2), Alexandre Antonelli (a3) and Xavier Meyer (a4)


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