s41558-022-01490-7.pdf

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Nature Climate Change Article https://doi.org/10.1038/s41558-022-01490-7 Extended Data Fig. 1 | T emperature variation at multiple timescales contributes to trends in overall variance. a-b T emporal trends in the power of variation at sub-annual to annual periodicities (3-days to 2-years) (a) and multi-annual periodicities (2-30 years) (b). Trends represent the slope obtained by regressing wavelet power at each geographical location against time. Countervailing trends are found in the Arctic, where the power of short term, high-frequency fluctuations is decreasing and the power of more persistent,
low-frequency fluctuations is increasing. Nature Climate Change Article https://doi.org/10.1038/s41558-022-01490-7 Extended Data Fig. 2 | Drivers of changes in stability (analysis includes both pre- and post-extinction period). Kernel density plots illustrate the relationships between population mean and population standard deviation in the historical period and the future climate change period. The grey 1:1 line divides the more stable regime (high-mean/low-variance; below line), and the less stable regime (low-mean/high-variance; above line). Bimodal distributions emerge in the extra-tropics, with some species at low abundance and standard deviation, and a larger cluster of species at high abundance and standard deviation.

Nature Climate Change Article https://doi.org/10.1038/s41558-022-01490-7 Extended Data Fig. 3 | Drivers of changes in stability (analysis only includes pre-extinction period). When only pre-extinction dynamics are analyzed, significant changes in population abundance persist in the extra-tropics; changes in population standard deviation become significant for NHEX and TROP and remain non- significant for SHEX.

Nature Climate Change Article https://doi.org/10.1038/s41558-022-01490-7 Extended Data Fig. 4 | Scaling of the intrinsic growth rate has moderate effects on temperature-driven impacts on population stability and extinction risk. Results exhibited limited sensitivity to the choice of smaller (scaling factor = 0.1; a,b) and larger (scaling factor = 10.0; e,f) intrinsic growth rates. Although larger growth rates were more strongly associated with deceased stability and increased extinction risk than smaller growth rates, the latitudinal patterns and effect sizes were consistent with the changes in population stability, c, and extinction probability, d, observed under normalized growth rates.

Nature Climate Change Article https://doi.org/10.1038/s41558-022-01490-7 Extended Data Fig. 5 | T emperature-driven effects on population stability and extinction risk are robust to the degree of population self-regulation. Results exhibited limited sensitivity to strong (α = 1; Fig. 4) and weak (α = 0.1; above) self-regulation in the form of crowding effects. Latitudinal patterns and effect sizes were consistent for changes in population stability, a, and extinction probability, b. Nature Climate Change Article https://doi.org/10.1038/s41558-022-01490-7 Extended Data Fig. 6 | Patterns of species risk are sensitive to treatment of high-temperature performance. Change in the average fitness (growth rate) driven by daily temperature between the historical period (1950-2000) and future period (2050-2100) when allowing negative growth rates above CTmax as in Vasseur et al. 2014 (a) and when performance values are bounded by 0 above CTmax as in Deutsch et al. 2008 (b). Change in the average fitness (growth rate) driven by monthly mean temperature between the historical period and future period when allowing negative growth rates above CTmax (c) and when performance values are bounded by 0 above CTmax (d).

Nature Climate Change Article https://doi.org/10.1038/s41558-022-01490-7 Extended Data Fig. 7 | Increased stability is negatively related to extinction probability. Regression relationships in our simulations are presented a, when considering only the pre-extinction time period and b, when taking into account the full 50-year periods. Regardless of largely positive (b) or mixed (a) changes in stability, there is generally a weak but significant negative relationship between stability and extinction probability globally (p-value < 0.05).

1 nature portfolio | reporting summary March 2021 Corresponding author(s): Kate Duffy Last updated by author(s): Aug 23, 2022 Reporting Summary Nature Portfolio wishes to improve the reproducibility of the work that we publish. This form provides structure for consistency and transparency in reporting. For further information on Nature Portfolio policies, see our Editorial Policies and the Editorial Policy Checklist. Statistics For all statistical analyses, confirm that the following items are present in the figure legend, table legend, main text, or Methods section. n/a Confirmed The exact sample size (n) for each experimental group/condition, given as a discrete number and unit of measurement A statement on whether measurements were taken from distinct samples or whether the same sample was measured repeatedly The statistical test(s) used AND whether they are one- or two-sided Only common tests should be described solely by name; describe more complex techniques in the Methods section. A description of all covariates tested A description of any assumptions or corrections, such as tests of normality and adjustment for multiple comparisons A full description of the statistical parameters including central tendency (e.g. means) or other basic estimates (e.g. regression coefficient) AND variation (e.g. standard deviation) or associated estimates of uncertainty (e.g. confidence intervals) For null hypothesis testing, the test statistic (e.g. F, t, r) with confidence intervals, effect sizes, degrees of freedom and P value noted Give P values as exact values whenever suitable. For Bayesian analysis, information on the choice of priors and Markov chain Monte Carlo settings For hierarchical and complex designs, identification of the appropriate level for tests and full reporting of outcomes Estimates of effect sizes (e.g. Cohen's d, Pearson's r), indicating how they were calculated Our web collection on statistics for biologists contains articles on many of the points above. Software and code Policy information about availability of computer code Data collection No software was used for data collection in this study. Data analysis Open source codes were used to analyze the data, including R package quantreg v5.88 and R package biwavelet v0.02.21. Custom codes for analysis are available in our public GitHub repository at https://github.com/KateDuffy/climate-change-ecology For manuscripts utilizing custom algorithms or software that are central to the research but not yet described in published literature, software must be made available to editors and reviewers. We strongly encourage code deposition in a community repository (e.g. GitHub). See the Nature Portfolio guidelines for submitting code & software for further information. Data Policy information about availability of data All manuscripts must include a data availability statement. This statement should provide the following information, where applicable:

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The CMIP6 simulation data used in this paper is available via the data portal https://esgf-node.llnl.gov/search/cmip6/. The ecology data is available for download at https://doi.org/10.1073/pnas.0709472105.

2 nature portfolio | reporting summary March 2021 Human research participants Policy information about studies involving human research participants and Sex and Gender in Research. Reporting on sex and gender Not applicable Population characteristics Not applicable Recruitment Not applicable Ethics oversight Not applicable Note that full information on the approval of the study protocol must also be provided in the manuscript. Field-specific reporting Please select the one below that is the best fit for your research. If you are not sure, read the appropriate sections before making your selection. Life sciences Behavioural & social sciences Ecological, evolutionary & environmental sciences For a reference copy of the document with all sections, see nature.com/documents/nr-reporting-summary-flat.pdf Ecological, evolutionary & environmental sciences study design All studies must disclose on these points even when the disclosure is negative. Study description Using simulations from the latest generation of earth system models, we applied quantile, spectral, and wavelet analyses of temperature projections to study the way that temperatures will increase over time. We integrated temperature projections into
empirically-parameterized mathematical models that simulate the dynamical and cumulative effects of thermal stress on the performance of 38 global ectotherm species. Research sample We obtained experimentally derived thermal tolerance parameters for a set of terrestrial ectotherms of the phylum arthropoda (n = 38) published by Deutsch et al. (2008). Deutsch gathered data from 31 previously published thermal performance studies, which were published between 1974 and 2003 based on a collection of insects from 35 different locations. For each species, experimental intrinsic growth rates at multiple temperatures were used to fit a thermal performance curve yielding least-squares estimates of the the curve's parameters. This dataset was selected to represent a globally distributed set of arthropod species. Sampling strategy Not applicable to study. We analyzed existing data as described in the data availability statement. Data collection Not applicable to study. We analyzed existing data as described in the data availability statement. Timing and spatial scale Not applicable to study. We analyzed existing data as described in the data availability statement. Data exclusions No data were excluded from the analysis. Reproducibility Our study consists of fully reproducible data analysis. Randomization Not applicable. Blinding Not relevant to study. Did the study involve field work? Yes No Reporting for specific materials, systems and methods We require information from authors about some types of materials, experimental systems and methods used in many studies. Here, indicate whether each material, system or method listed is relevant to your study. If you are not sure if a list item applies to your research, read the appropriate section before selecting a response.

3 nature portfolio | reporting summary March 2021 Materials & experimental systems n/a Involved in the study Antibodies Eukaryotic cell lines Palaeontology and archaeology Animals and other organisms Clinical data Dual use research of concern Methods n/a Involved in the study ChIP-seq Flow cytometry MRI-based neuroimaging

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