Sepkoski, J. J. A factor analytic description of the phanerozoic marine fossil record. Paleobiology 7, 36–53 (1981).
Google Scholar
Quental, T. B. & Marshall, C. R. Diversity dynamics: molecular phylogenies need the fossil record. Trends Ecol. Evol. 25, 434–441 (2010).
Google Scholar
Ezard, T. H., Aze, T., Pearson, P. N. & Purvis, A. Interplay between changing climate and species’ ecology drives macroevolutionary dynamics. Science 332, 349–351 (2011).
Google Scholar
Benton, M. J. Exploring macroevolution using modern and fossil data. Proc. R. Soc. B: Biol. Sci. 282, 20150569 (2015).
Google Scholar
Niklas, K. J. Measuring the tempo of plant death and birth. N. Phytol. 207, 254–256 (2015).
Google Scholar
Rabosky, D. L. & Hurlbert, A. H. Species richness at continental scales is dominated by ecological limits. Am. Nat. 185, 572–583 (2015).
Google Scholar
Harmon, L. J. & Harrison, S. Species diversity is dynamic and unbounded at local and continental scales. Am. Nat. 185, 584–593 (2015).
Google Scholar
Sepkoski Jr, J. Phanerozoic overview of mass extinction. In Patterns and Processes in the History of Life: Report of the Dahlem Workshop on Patterns and Processes in the History of Life Berlin 1985, June 16–21, 277–295 (Springer, 1986).
Benton, M. J. & Emerson, B. C. How did life become so diverse? the dynamics of diversification according to the fossil record and molecular phylogenetics. Palaeontology 50, 23–40 (2007).
Google Scholar
Alroy, J. Geographical, environmental and intrinsic biotic controls on phanerozoic marine diversification. Palaeontology 53, 1211–1235 (2010).
Google Scholar
Weber, M. G., Wagner, C. E., Best, R. J., Harmon, L. J. & Matthews, B. Evolution in a community context: on integrating ecological interactions and macroevolution. Trends Ecol. Evol. 32, 291–304 (2017).
Google Scholar
Niklas, K. J., Tiffney, B. H. & Knoll, A. H. Patterns in vascular land plant diversification. Nature 303, 614 – 616 (1983).
Google Scholar
Foote, M., Miller, A., Raup, D. & Stanley, S.Principles of Paleontology (W. H. Freeman, 2007). https://books.google.ch/books?id=8TsDC2OOvbYC
Close, R., Benson, R., Saupe, E., Clapham, M. & Butler, R. The spatial structure of phanerozoic marine animal diversity. Science 368, 420–424 (2020).
Google Scholar
Raja, N. B. et al. Colonial history and global economics distort our understanding of deep-time biodiversity. Nat. Ecol. Evol. 6, 145–154 (2022).
Google Scholar
Smith, A. B. & McGowan, A. J. The ties linking rock and fossil records and why they are important for palaeobiodiversity studies. Geol. Soc. Lond. Spec. Publ. 358, 1–7 (2011).
Google Scholar
Benson, R., Butler, R., Close, R., Saupe, E. & Rabosky, D. Biodiversity across space and time in the fossil record. Curr. Biol. 31, R1225–R1236 (2021).
Google Scholar
Smith, A. B. Large–scale heterogeneity of the fossil record: implications for phanerozoic biodiversity studies. Philos. Trans. R. Soc. Lond. Ser. B: Biol. Sci. 356, 351–367 (2001).
Google Scholar
Alroy, J. Fair sampling of taxonomic richness and unbiased estimation of origination and extinction rates. Paleontol. Soc. Pap. 16, 55–80 (2010).
Google Scholar
Chao, A. & Jost, L. Coverage-based rarefaction and extrapolation: standardizing samples by completeness rather than size. Ecology 93, 2533–2547 (2012).
Google Scholar
Raup, D. Taxonomic diversity estimation using rarefaction. Paleobiology 1, 333–342 (1975).
Google Scholar
Alroy, J. et al. Effects of sampling standardization on estimates of phanerozoic marine diversification. Proc. Natl Acad. Sci. 98, 6261–6266 (2001).
Google Scholar
Starrfelt, J. & Liow, L. H. How many dinosaur species were there? fossil bias and true richness estimated using a poisson sampling model. Philos. Trans. R. Soc. B: Biol. Sci. 371, 20150219 (2016).
Google Scholar
Flannery-Sutherland, J. T., Silvestro, D. & Benton, M. J. Global diversity dynamics in the fossil record are regionally heterogeneous. Nat. Commun. 13, 1–17 (2022).
Google Scholar
Chao, A. Estimating the population size for capture-recapture data with unequal catchability. Biometrics 43, 783–791 (1987).
Alroy, J. Limits to species richness in terrestrial communities. Ecol. Lett. 21, 1781–1789 (2018).
Google Scholar
Alroy, J. On four measures of taxonomic richness. Paleobiology 46, 158–175 (2020).
Google Scholar
Close, R., Evers, S., Alroy, J. & Butler, R. How should we estimate diversity in the fossil record? testing richness estimators using sampling-standardised discovery curves. Methods Ecol. Evol. 9, 1386–1400 (2018).
Google Scholar
Close, R. et al. The apparent exponential radiation of phanerozoic land vertebrates is an artefact of spatial sampling biases. Proc. R. Soc. B 287, 20200372 (2020).
Google Scholar
Antell, G. T., Benson, R. B. & Saupe, E. E. Spatial standardization of taxon occurrence data—a call to action. Paleobiology https://doi.org/10.1017/pab.2023.36 (2024).
Dunne, E. M., Thompson, S. E., Butler, R. J., Rosindell, J. & Close, R. A. Mechanistic neutral models show that sampling biases drive the apparent explosion of early tetrapod diversity. Nat. Ecol. Evol. 7, 1480–1489 (2023).
Google Scholar
Hauffe, T., Pires, M. M., Quental, T. B., Wilke, T. & Silvestro, D. A quantitative framework to infer the effect of traits, diversity and environment on dispersal and extinction rates from fossils. Methods Ecol. Evol. 13, 1201–1213 (2022).
Google Scholar
Cermeño, P. et al. Post-extinction recovery of the phanerozoic oceans and biodiversity hotspots. Nature 607, 507–511 (2022).
Google Scholar
Hagen, O. et al. gen3sis: a general engine for eco-evolutionary simulations of the processes that shape earth’s biodiversity. PLoS Biol. 19, e3001340 (2021).
Google Scholar
Hagen, O., Skeels, A., Onstein, R. E., Jetz, W. & Pellissier, L. Earth history events shaped the evolution of uneven biodiversity across tropical moist forests. Proc. Natl Acad. Sci. 118, e2026347118 (2021).
Google Scholar
Vilhena, D. A. & Smith, A. B. Spatial bias in the marine fossil record. PLoS One 8, e74470 (2013).
Google Scholar
Raup, D. M. Taxonomic diversity during the phanerozoic: the increase in the number of marine species since the paleozoic may be more apparent than real. Science 177, 1065–1071 (1972).
Google Scholar
Raup, D. M. Species diversity in the phanerozoic: a tabulation. Paleobiology 2, 279–288 (1976).
Google Scholar
Foote, M., Crampton, J. S., Beu, A. G. & Nelson, C. S. Aragonite bias, and lack of bias, in the fossil record: lithological, environmental, and ecological controls. Paleobiology 41, 245–265 (2015).
Google Scholar
Silvestro, D., Salamin, N. & Schnitzler, J. Pyrate: a new program to estimate speciation and extinction rates from incomplete fossil data. Methods Ecol. Evol. 5, 1126–1131 (2014).
Google Scholar
Cantalapiedra, J. L. et al. The rise and fall of proboscidean ecological diversity. Nat. Ecol. Evol. 5, 1266–1272 (2021).
Google Scholar
Rumelhart, D. E., Hinton, G. E. & Williams, R. J. Learning representations by back-propagating errors. Nature 323, 533–536 (1986).
Google Scholar
Hochreiter, S. & Schmidhuber, J. Long short-term memory. Neural Comput. 9, 1735–1780 (1997).
Google Scholar
Gers, F., Schmidhuber, J. & Cummins, F. Learning to forget: continual prediction with lstm. Neural Comput. 12, 2451–2471 (2000).
Google Scholar
Gal, Y. & Ghahramani, Z. A theoretically grounded application of dropout in recurrent neural networks. Adv. Neural Inform. Process. Syst. 29, 1–9 (2016).
Gal, Y. & Ghahramani, Z. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. In International Conference on Machine Learning 48, 1050–1059 (PMLR, 2016).
Silvestro, D. & Andermann, T. Prior choice affects ability of bayesian neural networks to identify unknowns. arXiv preprint arXiv:2005.04987 (2020).
Brusatte, S. L. et al. The extinction of the dinosaurs. Biol. Rev. 90, 628–642 (2015).
Google Scholar
Dunne, E. M., Farnsworth, A., Greene, S. E., Lunt, D. J. & Butler, R. J. Climatic drivers of latitudinal variation in late triassic tetrapod diversity. Palaeontology 64, 101–117 (2021).
Google Scholar
De Celis, A., Narváez, I., Arcucci, A. & Ortega, F. Lagerstätte effect drives notosuchian palaeodiversity (crocodyliformes, notosuchia). Historical Biol. 33, 3031–3040 (2021).
Google Scholar
Cleary, T. J., Benson, R. B., Holroyd, P. A. & Barrett, P. M. Tracing the patterns of non-marine turtle richness from the triassic to the palaeogene: from origin to global spread. Palaeontology 63, 753–774 (2020).
Google Scholar
Silvestro, D. et al. Fossil data support a pre-Cretaceous origin of flowering plants. Nat. Ecol. Evol. 5, 449–457 (2021).
Leuenberger, C. & Wegmann, D. Bayesian computation and model selection without likelihoods. Genetics 184, 243–252 (2010).
Google Scholar
Marjoram, P., Molitor, J., Plagnol, V. & Tavaré, S. Markov chain monte carlo without likelihoods. Proc. Natl Acad. Sci. 100, 15324–15328 (2003).
Google Scholar
Tavaré, S., Balding, D. J., Griffiths, R. C. & Donnelly, P. Inferring coalescence times from dna sequence data. Genetics 145, 505–518 (1997).
Google Scholar
Goodfellow, I., Bengio, Y. & Courville, A. Deep Learning (MIT, 2016).
Edler, D., Guedes, T., Zizka, A., Rosvall, M. & Antonelli, A. Infomap Bioregions: interactive mapping of biogeographical regions from species distributions. Syst. Biol. 66, 197–204 (2016).
Google Scholar
Vilhena, D. A. & Antonelli, A. A network approach for identifying and delimiting biogeographical regions. Nat. Commun. 6, 6848 (2015).
Google Scholar
Hoyal Cuthill, J. F., Guttenberg, N. & Budd, G. E. Impacts of speciation and extinction measured by an evolutionary decay clock. Nature 588, 636–641 (2020).
Google Scholar
Foster, W. J. et al. How predictable are mass extinction events? R. Soc. Open Sci. 10, 221507 (2023).
Google Scholar
Foster, W. J. et al. Machine learning identifies ecological selectivity patterns across the end-permian mass extinction. Paleobiology 48, 357–371 (2022).
Google Scholar
Tietje, M. & Rödel, M.-O. Evaluating the predicted extinction risk of living amphibian species with the fossil record. Ecol. Lett. 21, 1135–1142 (2018).
Google Scholar
Finnegan, S. et al. Paleontological baselines for evaluating extinction risk in the modern oceans. Science 348, 567–570 (2015).
Google Scholar
Raja, N. B. et al. Morphological traits of reef corals predict extinction risk but not conservation status. Glob. Ecol. Biogeogr. 30, 1597–1608 (2021).
Google Scholar
Fricke, E. C. et al. Collapse of terrestrial mammal food webs since the late pleistocene. Science 377, 1008–1011 (2022).
Google Scholar
He, Y. et al. Challenges and opportunities in applying AI to evolutionary morphology. ecoevorXiv preprint DOI:10.32942/x2s315 (2024).
Tetard, M. et al. A new automated radiolarian image acquisition, stacking, processing, segmentation, and identification workflow. Clim. Discuss. 2020, 1–23 (2020).
Edie, S. M., Collins, K. S. & Jablonski, D. High-throughput micro-ct scanning and deep learning segmentation workflow for analyses of shelly invertebrates and their fossils: examples from marine bivalvia. Front. Ecol. Evol. 11, 1127756 (2023).
Google Scholar
Andermann, T., Strömberg, C. A., Antonelli, A. & Silvestro, D. The origin and evolution of open habitats in North America inferred by Bayesian deep learning models. Nat. Commun. 13, 4833 (2022).
Google Scholar
Kane, M. J., Price, N., Scotch, M. & Rabinowitz, P. Comparison of Arima and random forest time series models for prediction of avian influenza h5n1 outbreaks. BMC Bioinforma. 15, 1–9 (2014).
Google Scholar
Simpson, G. L. Modelling palaeoecological time series using generalised additive models. Front. Ecol. Evol. 6, 149 (2018).
Google Scholar
Close, R. A., Evers, S. W., Alroy, J. & Butler, R. J. How should we estimate diversity in the fossil record? testing richness estimators using sampling-standardised discovery curves. Methods Ecol. Evol. 9, 1386–1400 (2018).
Google Scholar
Silvestro, D. et al. A 450 million years long latitudinal gradient in age-dependent extinction. Ecol. Lett. 23, 439–446 (2020).
Google Scholar
Chan, J. et al. A likelihood-free inference framework for population genetic data using exchangeable neural networks. Adv. Neural Inform. Process. Syst. 31, 8594–8605 (2018).
Schrider, D. R. & Kern, A. D. Supervised machine learning for population genetics: a new paradigm. Trends Genet. 34, 301–312 (2018).
Google Scholar
Lajaaiti, I., Lambert, S., Voznica, J., Morlon, H. & Hartig, F. A comparison of deep learning architectures for inferring parameters of diversification models from extant phylogenies. Preprint at bioRxiv https://doi.org/10.1101/2023.03.03.530992 (2023).
Chen, Z.-Q. & Benton, M. J. The timing and pattern of biotic recovery following the end-permian mass extinction. Nat. Geosci. 5, 375–383 (2012).
Google Scholar
Stanley, S. M. Estimates of the magnitudes of major marine mass extinctions in earth history. Proc. Natl Acad. Sci. 113, E6325–E6334 (2016).
Google Scholar
Knoll, A. H., Bambach, R. K., Payne, J. L., Pruss, S. & Fischer, W. W. Paleophysiology and end-permian mass extinction. Earth Planet. Sci. Lett. 256, 295–313 (2007).
Google Scholar
Sepkoski Jr, J. J. A compendium of fossil marine animal genera. Bull. Am. Paleontol. 363, 1–560 (2002).
Dunhill, A. M., Foster, W. J., Sciberras, J. & Twitchett, R. J. Impact of the late triassic mass extinction on functional diversity and composition of marine ecosystems. Palaeontology 61, 133–148 (2018).
Google Scholar
Raup, D. M. & Sepkoski Jr, J. J. Mass extinctions in the marine fossil record. Science 215, 1501–1503 (1982).
Google Scholar
Muscente, A. et al. Quantifying ecological impacts of mass extinctions with network analysis of fossil communities. Proc. Natl Acad. Sci. 115, 5217–5222 (2018).
Google Scholar
Žliobaitė, I. & Fortelius, M. On calibrating the completometer for the mammalian fossil record. Paleobiology 48, 1–11 (2022).
Google Scholar
Harzhauser, M. et al. Biogeographic responses to geodynamics: a key study all around the oligo–miocene tethyan seaway. Zool. Anz.-A J. Comp. Zool. 246, 241–256 (2007).
Google Scholar
Flower, B. P. & Kennett, J. P. The middle miocene climatic transition: East antarctic ice sheet development, deep ocean circulation and global carbon cycling. Palaeogeogr. Palaeoclimatol. Palaeoecol. 108, 537–555 (1994).
Google Scholar
Zachos, J., Pagani, M., Sloan, L., Thomas, E. & Billups, K. Trends, rhythms, and aberrations in global climate 65 ma to present. Science 292, 686–693 (2001).
Google Scholar
Andermann, T., Faurby, S., Turvey, S. T., Antonelli, A. & Silvestro, D. The past and future human impact on mammalian diversity. Sci. Adv. 6, eabb2313 (2020).
Google Scholar
Westerhold, T. et al. An astronomically dated record of earth’s climate and its predictability over the last 66 million years. Science 369, 1383–1387 (2020).
Google Scholar
Faith, J. T., Rowan, J., Du, A. & Koch, P. L. Plio-pleistocene decline of African megaherbivores: no evidence for ancient hominin impacts. Science 362, 938–941 (2018).
Google Scholar
Stuart, A. J. Late quaternary megafaunal extinctions on the continents: a short review. Geol. J. 50, 338–363 (2015).
Google Scholar
Jukar, A., Lyons, S., Wagner, P. & Uhen, M. Late quaternary extinctions in the Indian subcontinent. Palaeogeogr. Palaeoclimatol. Palaeoecol. 562, 110137 (2021).
Google Scholar
Fisher, D. C. Paleobiology of pleistocene proboscideans. Annu. Rev. Earth Planet. Sci. 46, 229–260 (2018).
Google Scholar
Kendall, D. G. On the generalized birth-and-death process. Ann. Math. Stat. 19, 1 – 15 (1948).
Google Scholar
Raup, D. M. Mathematical models of cladogenesis. Paleobiology 11, 42–52 (1985).
Google Scholar
Silvestro, D., Antonelli, A., Salamin, N. & Quental, T. B. The role of clade competition in the diversification of North American canids. Proc. Natl Acad. Sci. USA 112, 8684–8689 (2015).
Google Scholar
Liow, L. H. & Finarelli, J. A. A dynamic global equilibrium in carnivoran diversification over 20 million years. Proc. R. Soc. B: Biol. Sci. 281, 20132312–20132312 (2014).
Google Scholar
Jones, L. A., Dean, C. D., Mannion, P. D., Farnsworth, A. & Allison, P. A. Spatial sampling heterogeneity limits the detectability of deep time latitudinal biodiversity gradients. Proc. R. Soc. B 288, 20202762 (2021).
Google Scholar
Szandała, T. Review and Comparison of Commonly Used Activation Functions for Deep Neural Networks, 203–224 (Springer Singapore, Singapore, 2021). https://doi.org/10.1007/978-981-15-5495-7_11.
Kingma, D. P. & Ba, J. Adam: a method for stochastic optimization. arXiv preprint arXiv 1412.6980 (2014).
Kocsis, A., Reddin, C., Alroy, J. & Kiessling, W. The r package divdyn for quantifying diversity dynamics using fossil sampling data. Methods Ecol. Evol. 10, 735–743 (2019).
Google Scholar
R Core Team. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2013).
Etienne, R. S. et al. Diversity-dependence brings molecular phylogenies closer to agreement with the fossil record. Proc. R. Soc. B: Biol. Sci. 279, 1300–1309 (2012).
Google Scholar
Song, H. et al. Flat latitudinal diversity gradient caused by the permian–triassic mass extinction. Proc. Natl Acad. Sci. 117, 17578–17583 (2020).
Google Scholar
Song, H. et al. Data from: flat latitudinal diversity gradient caused by the permian–triassic mass extinction. Dryad https://doi.org/10.5061/dryad.41ns1rn9z (2020).
Carrillo, J. D. et al. Disproportionate extinction of South American mammals drove the asymmetry of the great American biotic interchange. Proc. Natl Acad. Sci. 117, 26281–26287 (2020).
Google Scholar
Abadi, M. et al. TensorFlow: large-scale machine learning on heterogeneous systems. https://www.tensorflow.org/ (2015).
