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Clustered versus catastrophic global vertebrate declines

Matters Arising to this article was published on 26 January 2022

Matters Arising to this article was published on 26 January 2022

Matters Arising to this article was published on 26 January 2022

Matters Arising to this article was published on 26 January 2022

An Author Correction to this article was published on 18 January 2021

This article has been updated


Recent analyses have reported catastrophic global declines in vertebrate populations1,2. However, the distillation of many trends into a global mean index obscures the variation that can inform conservation measures and can be sensitive to analytical decisions. For example, previous analyses have estimated a mean vertebrate decline of more than 50% since 1970 (Living Planet Index2). Here we show, however, that this estimate is driven by less than 3% of vertebrate populations; if these extremely declining populations are excluded, the global trend switches to an increase. The sensitivity of global mean trends to outliers suggests that more informative indices are needed. We propose an alternative approach, which identifies clusters of extreme decline (or increase) that differ statistically from the majority of population trends. We show that, of taxonomic–geographic systems in the Living Planet Index, 16 systems contain clusters of extreme decline (comprising around 1% of populations; these extreme declines occur disproportionately in larger animals) and 7 contain extreme increases (around 0.4% of populations). The remaining 98.6% of populations across all systems showed no mean global trend. However, when analysed separately, three systems were declining strongly with high certainty (all in the Indo-Pacific region) and seven were declining strongly but with less certainty (mostly reptile and amphibian groups). Accounting for extreme clusters fundamentally alters the interpretation of global vertebrate trends and should be used to help to prioritize conservation efforts.

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Fig. 1: Stylized patterns of system-wide growth rates.
Fig. 2: Effect of extreme populations on the global growth index.
Fig. 3: Population trends by taxonomic groups and realms.
Fig. 4: Effect of the size of the time series.
Fig. 5: Populations in the primary clusters across all systems, after removal of extreme clusters.

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Data availability

Data can be obtained from the LPI database (, AmphiBio30 (, FishBase ( and life-history traits can be obtained from the amniote life-history database27 (

Code availability

Code for the BHM model is available at:

Change history


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We thank E. Hudgins, D. Nguyen, S. Varadarajan and A. Jones for discussions, T. Coulson for comments and S. Varadarajan and F. Moyes for help creating the figures. This work was supported by a Natural Sciences and Engineering Research Council (NSERC) Discovery grant to B.L.

Author information

Authors and Affiliations



Authors are listed in order of their contributions. B.L. formulated the BHM model, conducted analyses and wrote the majority of the paper. A.L.H. discussed and clarified the ideas and had a central role in the writing of the paper. D.A.G. discussed and clarified the ideas, synthesized the data and contributed to the writing of the paper. B.M. discussed and clarified the ideas, and commented on the manuscript. M.D. discussed and clarified the ideas, commented on and improved the presentation of the manuscript. R.F. discussed and clarified the ideas, and provided insight into the LPI data and analyses.

Corresponding author

Correspondence to Brian Leung.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature thanks Tim Coulson 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 Theoretical analyses of BHM model.

The pp plots show that the posterior distributions for each estimated parameter are unbiased and largely follow a 1:1 line for each hyper parameter (σ, τ) as well as the fraction in each cluster (f1, f2 = 1 − f1). The 1:1 line is the theoretic expectation, indicating that the true parameter value falls below the 0.01 quantile 1% of the time, the 0.02 quantile 2% of the time, and so on.

Extended Data Fig. 2 Sensitivity analyses of primary cluster trends.

The trends of the primary clusters (θ1), for the main analysis (x axis) versus the sensitivity analysis (y axis) for the threshold for extreme clusters (top) and the offset when n = 0 was observed (bottom).

Extended Data Fig. 3 Effect of small time series on primary cluster trends.

Each point represents a trend estimate for the primary cluster of a system, with the full dataset (x axis) versus data excluding time series with less than 10 data points (y axis). The red dot indicates the freshwater Indo-Pacific mammals, which was reduced from 22 populations (full) to 2 populations (only data with at least 10 data points).

Extended Data Fig. 4 Mean trends of primary clusters across systems calculated using the BHM model.

Top, all species (14,700 populations). Middle, only large species (9,596 populations). Bottom, only small species (5,103 populations). The small species appear to be declining more than large species, although this finding needs to be interpreted with caution, as most primary distributions did not significantly deviate from zero for small species.

Extended Data Fig. 5 Histograms of observed growth rates and output of the BHM model for systems 1–16.

Blue line, primary cluster; red line, extreme cluster(s) from the model. Grey vertical lines show the range of observed values. In comparing the model output to the data we show the following. (1) The variation of the BHM primary cluster (blue line) is much lower than the raw data, because the BHM separates variation in among-population trends from variation due to within-population fluctuations. (2) The BHM model identifies evidence for extreme clusters in both directions (for example, terrestrial Indo-Pacific birds) or only one direction (for example, terrestrial Neotropical mammals), but not for other apparent clusters (for example, terrestrial Indo-Pacific herps). The BHM integrates the magnitude of within-population fluctuations, time-series sizes, number of populations, among-population variance, and the magnitude and frequency of the extreme populations in determining whether additional (extreme) clusters are needed to account for the observations.

Extended Data Fig. 6 Histograms of observed growth rates and output of the BHM model for systems 17–32.

Blue line, primary cluster; red line, extreme cluster(s) from the model. Grey vertical lines show the range of observed values. For further information, see Extended Data Fig. 5.

Extended Data Fig. 7 Histograms of observed growth rates and output of the BHM model for systems 33–48.

Blue line, primary cluster; red line, extreme cluster(s) from the model. Grey vertical lines show the range of observed values. For further information, see Extended Data Fig. 5.

Extended Data Fig. 8 Histograms of observed growth rates and output of the BHM model for systems 49–57.

Blue line, primary cluster; red line, extreme cluster(s) from the model. Grey vertical lines show the range of observed values. For further information, see Extended Data Fig. 5.

Supplementary information

Supplementary Information

This file contains Supplementary Methods, Supplementary Results, Supplementary Discussion: Effect of small time-series on extreme clusters and Supplementary Tables.

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Leung, B., Hargreaves, A.L., Greenberg, D.A. et al. Clustered versus catastrophic global vertebrate declines. Nature 588, 267–271 (2020).

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