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Impacts of speciation and extinction measured by an evolutionary decay clock

A Publisher Correction to this article was published on 13 January 2021

This article has been updated


The hypothesis that destructive mass extinctions enable creative evolutionary radiations (creative destruction) is central to classic concepts of macroevolution1,2. However, the relative impacts of extinction and radiation on the co-occurrence of species have not been directly quantitatively compared across the Phanerozoic eon. Here we apply machine learning to generate a spatial embedding (multidimensional ordination) of the temporal co-occurrence structure of the Phanerozoic fossil record, covering 1,273,254 occurrences in the Paleobiology Database for 171,231 embedded species. This facilitates the simultaneous comparison of macroevolutionary disruptions, using measures independent of secular diversity trends. Among the 5% most significant periods of disruption, we identify the ‘big five’ mass extinction events2, seven additional mass extinctions, two combined mass extinction–radiation events and 15 mass radiations. In contrast to narratives that emphasize post-extinction radiations1,3, we find that the proportionally most comparable mass radiations and extinctions (such as the Cambrian explosion and the end-Permian mass extinction) are typically decoupled in time, refuting any direct causal relationship between them. Moreover, in addition to extinctions4, evolutionary radiations themselves cause evolutionary decay (modelled co-occurrence probability and shared fraction of species between times approaching zero), a concept that we describe as destructive creation. A direct test of the time to over-threshold macroevolutionary decay4 (shared fraction of species between two times ≤ 0.1), counted by the decay clock, reveals saw-toothed fluctuations around a Phanerozoic mean of 18.6 million years. As the Quaternary period began at a below-average decay-clock time of 11 million years, modern extinctions further increase life’s decay-clock debt.

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Fig. 1: Time structure of the fossil record.
Fig. 2: Macroevolutionary decay.
Fig. 3: Balance between mass radiation and extinction.

Data availability

Raw data are publicly available in the Paleobiology Database at Additional source data for Figs. 13 are provided in the Dryad data repository ( Additional data are provided as Extended Data Figs. 17.

Code availability

Custom computer code is provided as Supplementary Computer Code Code 16.

Change history

  • 13 January 2021

    A Correction to this paper has been published:


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This research was supported by funding from an IADS Research Fellowship (J.F.H.C.), EON Research Fellowship (J.F.H.C.) at the Tokyo Institute of Technology (supported by a grant from the John Templeton Foundation), Earth–Life Science Institute Research Interactions Committee Visitor Fund (N.G. and J.F.H.C.) and Swedish Research Council (VR grant no. 2015-04726, G.E.B.). We thank S. Newman and L. Schalkwyk for computing time and support, S. Conway Morris and E. Mitchell for highly constructive comments on the manuscript.

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Authors and Affiliations



J.F.H.C., N.G and G.E.B. designed research, N.G. and J.F.H.C. wrote computer code and performed analyses and J.F.H.C. wrote the paper with input from all authors.

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Correspondence to Jennifer F. Hoyal Cuthill.

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The authors declare no competing interests.

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Peer review information Nature thanks Emily Mitchell 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 Methods graphical summary and effects of computer simulated diversity increases.

a, Graphical summary of the ML method. bg, Computer simulations of secular variation in diversity, testing effects on measures of co-occurrence structure used in this study. bg, Linear (bd) and exponential (eg) diversity increases (Supplementary Computer Code 3). b, e, Heatmaps visualizing the machine learnt spatial embedding distance between mean species locations at different times: yellow, closest; purple, farthest. c, f, Plot of embedding distances between successive times. d, g, Plot of first two principal component axes from the 16-dimensional spatial embedding. ML training times were 3,000 training epochs.

Extended Data Fig. 2 Bootstrap data-resampling results and shared fraction of species between successive times versus mean embedding distance.

a, Bootstrap data-resampling results: differences in embedding distances for 60 reference fossils, compared within 20 A, B, C triplets over 18 technical replicates of bootstrap data re-sampling and ML embedding training. Error bars, s.d. of the distance absolute(A–B) – absolute(A–C): mean 0.77. We expect the embedding distances to be comparatively stable within the time range over which co-occurrence probability is within the evolutionary decay range (observed to be mean 30 Myr for co-occurrence probability to reach 0.1 in the complete data set). b, d, Fraction of species shared between successive times, calculated exhaustively from raw species time ranges (histogram, Extended Data Fig. 6a). c, e, Distance in the ML spatial embedding between mean species locations at successive times. Compared times are at increments of 1 Myr. b, c, Complete fossil occurrence data set. d, e, Taxonomically screened data set. Vertical lines indicate the 5% most significant times of fractional species turnover (Fig. 3, Extended Data Fig. 4): mass extinctions (red), mass radiations (blue) and mixed mass extinction–radiations (magenta).

Extended Data Fig. 3 Proportions of species originating versus going extinct.

1-Myr increments from 600 to 0 Ma with a threshold of 30% species entry/exit threshold, grey square. This threshold highlights the top 66 times of turnover from 222 total turnover times identified among 600 times included in the analysis. Red, mass extinctions; blue, mass radiations; magenta, mixed mass extinction–radiations.

Extended Data Fig. 4 Times of greatest fractional species turnover in the Phanerozoic fossil record.

Top 5% most significant proportionate extinction or origination times (corresponding to the 30 labelled and coloured times in Fig. 3, > 42% species entry/exit threshold). Drill plots for focal times (key, top left) comparing stratigraphic ranges of all species occurring within 1 Myr of the focal time, vertically sorted into originations, extinctions and crossing ranges. Colours indicate over threshold mass extinctions (red), mass radiations (blue) and mixed mass extinction–radiations (magenta). Relevant stratigraphic unit names, dates and corresponding references are those used in the PBDB (*ref. 30; **refs. 31,32).

Extended Data Fig. 5 Breakdown by phylum of species extinctions and originations at the top 5% of evolutionary disruption times.

Associated with Fig. 3, Extended Data Fig. 4. Proportions of species entering (dark blue) or exiting (dark red) the fossil record are shown for the 19 most prevalent phyla in the data set (taxonomically screened data set).

Extended Data Fig. 6 Raw species time ranges and diversity counts and examples of the decay in probability of temporal co-occurrence.

a, Raw species time ranges: time ranges (maximum occurrence – minimum occurrence) for 137,779 fossil species (taxonomically screened data set). Taxonomically screened Phanerozoic data set (535–0 Ma): median = 6.5 Myr, mean = 9.95 Myr, s.d. = 12.86. Complete data set: median 7 Myr, mean 14.4 s.d. = 28.1 Myr. b, Raw diversity counts: sampled-in-bin taxonomic diversity of genera (grey dashed line) and families (black line) for the complete data set, output by the PBDB within the default time bin of geological ages (at maximum Ma). cf, Examples of decays in co-occurrence probability (c, e) or in shared fraction of species (d, f), from base times 1 Myr before versus after major evolutionary disturbance events. Grey dashed lines indicate a value of 0.1. c, d, End-Permian mass extinction at 252 Ma. e, f, Carboniferous mass radiation at 358 Ma. Following a disturbance event, co-occurrence probabilities and shared fractions of species fall more rapidly to low levels because comparatively few living species co-occur with any species that were present in the past.

Extended Data Fig. 7 Conceptual diagram comparing measures of macroevolutionary decay, decay-clock detail focusing on the last 40 Myr and statistical relationships between measures of macroevolutionary disturbance and time.

a, Set representation of the shared fraction of species between compared times (for example, times t1 and t2). This measure is used in this study and is closely conceptually related to the co-occurrence probability calculated using the ML spatial embedding (see Methods for further details). b, Fraction of surviving species, a core concept of standard methods of survivor analysis for example4. These measures (a, b) will be equal if no new species have originated by time t2 (scenario in c). Where new species have instead originated by time t2, their effect will be picked up by the measures used in this study (a), whereas the impact of new species would not be considered by measures only of the fraction of survivors from t1 (b). d, Vertical lines indicate times of evolutionary disturbance (blue, mass radiations; red, mass extinctions, corresponding to Fig. 3; grey, turnover events below the mass-event threshold). e, (1), measures of disturbance to co-occurrence structure calculated between consecutive time windows are largely independent of Phanerozoic time (over which there have been secular trends in raw diversity20). The shared fraction of species shows no significant relationship with time (taxonomically screened data set). The embedding distance (complete data set) shows a weak relationship across the whole Phanerozoic that is removed when Cenozoic data are excluded (data excluded in order to isolate hypothesized effect after initial data analysis), consistent with a weak effect on Cenozoic embedding distance from fossils with ranges extending to 0 Ma (which are particularly abundant in the data set). (2), proportions of species exiting or entering the fossil record within 1 Myr of a given time show no significant relationship with time (taxonomically screened data set). All statistical tests are two-tailed.

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This zip folder contains Supplementary Computer Code 1-6, with Python program files supplied in py or ipynb file format and in pdf format. Descriptions of each code are included in an accompanying text file.

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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).

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