The estimation of diversification rates is one of the most vividly debated topics in modern systematics, with considerable controversy surrounding the power of phylogenetic and fossil-based approaches in estimating extinction. Van Valen’s seminal work from 1973 proposed the “Law of constant extinction” which states that the probability of extinction of taxa is not dependent on their age. This assumption of age-independent extinction has prevailed for decades with its assessment based on survivorship curves, which, however, do not directly account for the incompleteness of the fossil record, and have rarely been applied at the species level. Here, we present a Bayesian framework to estimate extinction rates from the fossil record accounting for age-dependent extinction (ADE). Our approach, unlike previous implementations, explicitly models unobserved species and accounts for the effects of fossil preservation on the observed longevity of sampled lineages. We assess the performance and robustness of our method through extensive simulations and apply it to a fossil data set of terrestrial Carnivora spanning the past 40 Myr. We find strong evidence of ADE, as we detect the extinction rate to be highest in young species and declining with increasing species age. For comparison, we apply a recently developed analogous ADE model to a dated phylogeny of extant Carnivora. Although the phylogeny-based analysis also infers age-dependent extinction, it indicates that the extinction rate, instead, increases with increasing taxon age. The estimated mean species longevity also differs substantially, with the fossil-based analyses estimating 2.0 Myr, in contrast to 9.8 Myr derived from the phylogeny-based inference. Scrutinizing these discrepancies, we find that both fossil and phylogeny-based ADE models are prone to high error rates when speciation and extinction rates increase or decrease through time. However, analyses of simulated and empirical data show that fossil-based inferences are more robust. This study shows that an accurate estimation of ADE from incomplete fossil data is possible when the effects of preservation are jointly modeled, thus allowing for a reassessment of Van Valen’s model as a general rule in macroevolution.
Supplementary Material including Figures and Table.
Carnivora Fossil and Pylogenetic Empirical Data
The folder “empirical_data” contains the empirical data used for estimating age-dependent extinction processes.
The folder “fossil_ Pires_et_al_2015” stores fossil data of Carnivora from the Northern Hemisphere compiled and cleansed by Pires et al. (2015). Inside the folder, “all_carnivora_SpeciesList.txt” provides a species list with extinct or extant status. The file “all_carnivora.py” is a ready for PyRate input file of the fossil data set, for more information please refer to PyRate help literature provided at https://github.com/dsilvestro/PyRate/wiki. The files “all_carnivora_combined_10_files.log” and “all_carnivora_Neogene_combined_10_files.log” are the outputs from the PyRate runs of the 10 replicated data sets for the entire fossil data set and the data set for the fossils found during the Neogene (see Fig2 for a schematic workflow).
The folder “phylogenetic_Nyakatura_Bininda-Emonds_2012” stores the dated phylogeny of 286 species extant carnivores, with crown age at about 65 Ma build by Nyakatura and Bininda-Emonds (2012)
- Pires M.M., Silvestro D., Quental T.B. 2015. Continental faunal exchange and the asymmetrical radiation of carnivores. Proc. R. Soc. Biol. Sci. Ser. B 282.
- Nyakatura K., Bininda-Emonds O.R.P. 2012. Updating the evolutionary history of carnivora (mammalia): A new species-level supertree complete with divergence time estimates. Bmc Biol 10.
The folder “fossil_simulations” contains the R and Python scripts used for the fossils simulation study.
The folder “1.simulators” contains the R scripts adapted from (Hagen and Stadler 2014) used to simulate the initial complete phylogenies. “SimulatorScenarioIandII_ConstantOverTime.R” was used for simulating scenarios I and II, “SimulatorScenarioIII_2TimeBin.R” was used for simulating scenario III and “SimulatorScenarioIV_2TimeBin_BIGDROP.R” was used for simulating scenario IV. Please note that these files require the parameters given at “parametersage.csv” and generated by the scripts “Parametersage_Generator.R” found respectively inside each scenario folder. Please change the working directories before running the scripts.
To generate fossil data from the phylogenies the script “2.FossilSamplerRunOverFolder.py” was run, evoking “fossil_sampler.py” for all fossils inside the respective scenario. The script “3.GetPyRateEstimatesRunOverFolders.py” automates a PyRate estimation while “4.PlottingScenarios.R” is used for visualizing the result. “SummarySimulations.RData” summarizes the results and analysis conducted. Each scenario folder also contains a “summary_ScenarioX.csv” file recording the number of: sampled species, singletons, simulated extinct species, simulated extant species, fossil occurrences and several other returned values from PyRate.
- Hagen O., Hartmann K., Steel M., Stadler T. 2015. Age-Dependent Speciation Can Explain the Shape of Empirical Phylogenies. Syst Biol. 64 (3): 432-440. doi: 10.1093/sysbio/syv001.
- Hagen O., Stadler T. 2017. Treesimgm: Simulating phylogenetic trees under general bellman harris models with lineage-specific shifts of speciation and extinction in r. Methods Ecol. Evol. in press.
Simulation of Morphospecies
Script used to measure the effect of anagenesis on the estimation of true ADE shape parameter (Supplementary Material Fig. S6).