DOI: 10.5061/dryad.w0vt4b91q
title: Data from: Order matters: Autocorrelation of temperatures dictates extinction risk in populations with nonlinear thermal performance

description: Forecasting the risks caused by climate change often relies upon combining
 species' thermal performance curves with expected statistical
 distributions of experienced temperatures, without considering the order
 in which those temperatures occur. Such averaging approaches may obscure
 the disproportionate impacts that extreme events like heatwaves have on
 fitness and survival. In this study, we instead incorporate thermal
 performance curves with population dynamical modeling to elucidate the
 relationship between the sequence of temperature events -- driven by
 temporal autocorrelation -- and extinction risk. We show that the
 permutation of temperatures determines the extent of risk; as thermal
 regimes grow warmer, more variable, and more autocorrelated, the risk of
 extinction grows non-linearly and is driven by interactions between the
 thermal distribution and its temporal autocorrelation. Given that the
 mean, variance, and autocorrelation of temperatures are changing in
 nuanced ways across the globe, understanding these interactions is
 paramount for forecasting risk. Using empirical data from a benchmarked
 set of thermal performance curves, we demonstrate how extinction risk is
 impacted by interacting changes to temperature's distribution and
 autocorrelation level, while controlling for seasonal and diurnal cycling.
 Our results and modeling approach offer new tools for testing the
 robustness of thermal performance curves and emphasize the importance of
 looking beyond temporally-blind metrics, like mean population size or
 average thermal distributions, for forecasting impending extinction risks.
description: Included datasets (1) input data required to simulate extinction
 for 38 species with known thermal tolerances (arising from datasets
 compiled and used by Deutsch et al. 2008, Duffy et al. 2022, and Frazier
 et al. 2006) under two decades of observed climatic conditions at their
 collection locations (provided by Visual Crossings Corporation 2024); and
 (2) simulation outputs for several models which test extinction risk for
 species with different thermal tolerances, given variable thermal
 distributions and levels of autocorrelation, processed in Mathematica
 V.13.0.1 and as reported in the associated manuscript.
description: # Effects of temporal autocorrelation on extinction risk
 [https://doi.org/10.5061/dryad.w0vt4b91q](https://doi.org/10.5061/dryad.w0vt4b91q) This project utilized several models to test the impacts of varying the temporal autocorrelation of temperature time series on extinction risk, given a known organismal thermal tolerance. The first model (Model 1, 1.2) tests how varying different aspects of a thermal regime (mean, standard deviation, and autocorrelation of temperatures) alter different metrics of extinction risk for species with two idealized thermal performance curves (one generalist/temperate species and one specialist/tropical species); Model 1 examines how extinction risk and time to extinction vary across the full parameter space, while Model 1.2 examines the effects on population size across a narrower parameter set. Model 2 tests how varying the level of autocorrelation impacts more realistic scenarios by incorporating 38 empirical thermal performance curves with observed temperature data from the organisms' collection locations and varying the autocorrelation structure of the observed thermal regimes (while maintaining the observed seasonal and diurnal cycles). 
 
 ## 1 Description of the data and file structure The following is a list
 of files accessible after downloading and unzipping
 'AutocorrelationData.zip', which contains two folders
 ('Model Input Files' and 'Model Output Files'), along
 with a brief description of their contents and how to work with them. The
 workflow for recreating the results of the related manuscript is further
 described in the GitHub repository referenced below. All input data are
 provided as **.csv** files, spreadsheet files that can be viewed and
 manipulated in widely available programs like Microsoft Excel, Numbers, or
 Google Sheets. The **.csv** files alone are sufficient to recreate the
 results of this project. However, we additionally include some output
 files as **.m** file types, a binary code file best accessed using Wolfram
 Mathematica, for which they are the native export/import file type; code
 for reading and manipulating all such files is available in the Github
 repository. All **.m** files are made available for the convenience of
 recreating the exact plots generated in this project within Mathematica,
 but can be recreated (albeit with significant processing time) using the
 code provided in the Github repository. This description includes
 references to Mathematica code (**.nb**) files, all of which are not
 included in the Dryad repository but can be found in the GitHub repository
 (they are also available there as **.pdf** files for ease of reading for
 those without Mathematica access). ### 1.1 Model Input Files ##### 1.1.1
 'speciesparams.csv' This **.csv** files contains all necessary
 input parameters for running and plotting Model 2 (using
 'Model2.nb' and 'Model2_plotting.nb'). This file
 additional contains some of the output information from Model 2 for
 graphing purposes. Included variables are: 1. **species**: Abbreviated
 species names (short-hand for genus and full species; e.g., A.pisum),
 which is used in the .nb files to call the rest of the data. 2. **CTmax**,
 **Topt**, **sigma_p**: These are the thermal tolerance parameters for the
 fitted thermal performance curves (TPCs) of each species, provided by
 Deutsch et al. 2008 and Frazier et al. 2006. The curve parameterization
 follows Deutsch et al. 2008, such that CTmax is the critical thermal
 maximum (the right x-intercept), Topt is the thermal optimum (peak of the
 TPC), and sigma_p is a measure of breadth (such that sigma_p = (Topt -
 CTmin)/4). 3. **lat, long**: These provide the collection latitude and
 longitude of each species. 4. **H gamma, P gamma**: These denote the
 measured spectral exponent of the observed temperature time series in the
 historic (H) and recent (or present, P) time series. 5. **H P(Ext), P
 P(Ext):** These columns are the proportion of simulations that went
 extinct (or the probability of extinction P(Ext) ) at the measured
 spectral exponent of the temperature time series in the historic (H) and
 recent (P) time series. 6. **H mean, H stdev, P mean, P stdev:** These
 columns contain the measured mean and standard deviation (stdev) of the
 historic (H) and recent (P) temperature time series. 7. **Full species
 name:** This is the complete scientific name of each species. 8.
 **Region:** This is the broad region of the world the coordinates for the
 species fall into, as categorized by Duffy et al. 2022 (SHEX for Southern
 Hemisphere, NHEX for Northern Hemisphere, and TROP for the tropics). #####
 1.1.2 'VisualCrossingData.zip' Once unzipped, this file contains
 two **.csv** files per species. Each file is labeled by the shortened
 species name, the geographic coordinates, and the date range (either
 historic or recent) for which it contains the daily minimum and maximum
 temperatures (e.g.,
 'A.citricola_34.98,138.4_1994-01-01to2003-12-31.csv'). Each file
 contains four columns: 'datetime' is the collection date,
 'tempmax' and 'tempmin' are the maximum and minimum
 temperatures observed that day, and 'source' indicates the type
 of data (options are 'obs' = observation historical weather
 station datapoints and 'stat' = statistically inferred
 datapoints). All temperatures are reported in Kelvin. Details of exactly
 how this data was retrieved from Visual Crossings Weather and processed
 are available in Appendix S4 (and see below). 'Model2.nb' will
 automatically retrieve the correct **.csv** files for any chosen species
 and time range from this folder. ### 1.2 Model Output Files ##### 1.2.1
 'Model1_outputs.zip' Access this file by unzipping it. It
 contains two zipped **.m** files, which were generated (and can be
 recreated by) running 'Model1.nb'. 1.
 ***extTime_tmax2000_dims21,7,7,1000.m.zip***: Access this file by first
 unzipping it, then using code in 'Model1.nb'. This file contains
 the calculated extinction times generated for the generic
 generalist/temperate species for the range of mean, standard deviation,
 and autocorrelation temperature scenarios utilized in Model 1, and can be
 used to re-create Fig 4 by running 'Model1_plotting.nb'. This
 file can be recreated by running 'Model1.nb' but does require
 significant computing time and is thus included here for the convenience
 of the reader. The naming scheme is output variable (extTime), number of
 time steps (tmax = 2000), and dimensions of the output vector (21
 autocorrelation levels, 7 mean temperate treatments, 7 standard deviation
 of temperature treatments, 1000 iterations). 2.
 ***extTime_trop_tmax2000_dims21,7,7,1000.m.zip***: Access this file by
 first unzipping it, then using code in 'Model1_plotting.nb'.
 This file contains the calculated extinction times generated for the
 generic specialist/tropical species for the range of mean, standard
 deviation, and autocorrelation temperature scenarios utilized and Model1,
 and can be used to re-create Fig 4 by running
 'Model1_plotting.nb'. This file can be recreated by running
 'Model1.nb' but does require significant computing time and is
 thus included here for the convenience of the reader. The naming scheme is
 output variable (extTime), TPC used (tropical), number of time steps (tmax
 = 2000), and dimensions of the output vector (21 autocorrelation levels, 7
 mean temperate treatments, 7 standard deviation of temperature treatments,
 1000 iterations). ##### 1.2.2 'Model1.2_outputs.zip' Access this
 file by unzipping it. It contains three **.m** files, which were generated
 (and can be recreated by) running 'Model1.2_abundance.nb'. 1.
 ***extMetrics8_extTime_tmax2000_dims21,4,1,1000.m***: The calculated
 extinction times for the generalist/temperate TPC across 1000 runs of 2000
 time steps, tested across 21 autocorrelation levels, 4 mean temperature
 treatments, and 1 standard deviation of temperature treatment, using the
 file 'Model1.2_abundance.nb'. This file is plotted in Fig 3b
 using 'Model1.2_abundance_plotting.nb'. 2.
 ***extMetrics8_popsize_tmax2000_dims21,4,1,1000.m***: The calculated
 population sizes at each time step across the simulations for the
 generalist/temperate TPC across 1000 runs of 2000 time steps, tested
 across 21 autocorrelation levels, 4 mean temperature treatments, and 1
 standard deviation of temperature treatment, using the file
 'Model1.2_abundance.nb'. This file is plotted in Fig 3a using
 'Model1.2_abundance_plotting.nb'. 3.
 ***extMetrics8_trop_extTime_tmax2000_dims21,4,1,1000.m***: The calculated
 extinction times for the specialist/tropical TPC across 1000 runs of 2000
 time steps, tested across 21 autocorrelation levels, 4 mean temperature
 treatments, and 1 standard deviation of temperature treatment, using the
 file 'Model1.2_abundance.nb'. This file is plotted in Appendix
 S5 using 'Model1.2_abundance_plotting.nb'. 4.
 ***extMetrics8_trop_popsize_tmax2000_dims21,4,1,1000.m***: The calculated
 population sizes at each time step across the simulations for the
 generalist/temperate TPC across 1000 runs of 2000 time steps, tested
 across 21 autocorrelation levels, 4 mean temperature treatments, and 1
 standard deviation of temperature treatment, using the file
 'Model1.2_abundance.nb'. This file is plotted in Appendix S5
 using 'Model1.2_abundance_plotting.nb'. ##### 1.2.3
 'Model2_VCOutputs.zip' Access this file by unzipping it; it
 contains all results generated from 'Model2.nb'. Each file
 contains the simulated extinction time for each species in either the
 historical (1994-01-01to2003-12-31) or recent (2014-01-01to2023-12-31)
 time period, using an extinction threshold of one individual, across all
 tested autocorrelation levels (e.g.,
 'model3.3.2_A.pisum_1994-01-01to2003-12-31_ext1.m'). There is an
 additional subfolder ('minpop') containing the simulated minimum
 population size observed in each time period for each species that never
 went extinct (e.g.,
 'model3.3.3_minPop_A.pisum_1994-01-01to2003-12-31_ext1.m').
 These files are used to generate information in 'points.zip', as
 well as creating Fig 5 and extended figures with
 'Model2_plotting.nb'. This file also contains one subfolder
 named 'points', which contains 5 **.csv** files with plotting
 information for supplemental figures. Each file has five columns: Species
 (with the species name), H_gamma (the spectral exponent observed in the
 historical temperature time series), H_ExtTime (the average time to
 extinction across simulations at the historical spectral exponent),
 P_gamma (the spectral exponent observed in the recent temperature time
 series), and P__ExtTime (the average time to extinction across simulations
 at the recent spectral exponent). They are divvied up into separate files
 purely for plotting purposes; 'Model2_plotting.nb'
 automattically collects the appropriate data for each species and plot. 1.
 ***allpoints.csv*** contains this information for every tested species. 2.
 ***fullextinctpoints.csv*** contains this information for all species that
 went extinct 100% of the time. 3. ***fullpersistpoints.csv*** contains
 this information for all species that went extinct 0% of the time. 4.
 ***usefulpoints.csv*** contains this information for all species that went
 extinct some, but not all, of the time. 5. ***uselesspoints.csv***
 contains the complied information for species that went extinct either 0%
 or 100% of the time (i.e., fullextinctpoints and fullpersistpoints). 
 
 ## 2 Sharing/Access information The temperature time series data in
 VisualCrossingData.zip was downloaded from Visual Crossings Corporation
 using their Weather Query Builder. Files included in this dataset have
 been cleaned (checked for missing data, leap years removed), but raw data
 is accessible via their website by entering the coordinates and time range
 for each species (see Appendix S4). *
 [https://www.visualcrossing.com/weather/weather-data-services#](https://www.visualcrossing.com/weather/weather-data-services#) Species data was derived from datasets compiled and analyzed by the following sources: * Frazier, M. R., Huey, R., and Berrigan, D. (2006). Thermodynamics Constrains the Evolution of Insect Population Growth Rates: “Warmer Is Better.” The American Naturalist, 168(4): 512–520. Publisher: The University of Chicago Press. * Deutsch, C. A., Tewksbury, J. J., Huey, R. B., Sheldon, K. S., Ghalambor, C. K., Haak, D. C., and Martin, P. R. (2008). Impacts of climate warming on terrestrial ectotherms across latitude. Proceedings of the National Academy of Sciences, 105(18):6668–6672. Publisher: National Acad Sciences * Duffy, K., Gouhier, T. C., and Ganguly, A. R. (2022). Climate-mediated shifts in temperature fluctuations promote extinction risk. Nature Climate Change, 12(11):1037–1044. Publisher: Springer Science and Business Media LLC 
 
 ## 3 Code/Software All code is available
 at [github.com/arobey63/autocorrelation](https://github.com/arobey63/autocorrelation) (DOI: [10.5281/zenodo.17728683](https://doi.org/10.5281/zenodo.17728683)), including files for generating and plotting all outputs found in the paper. Each 'Model#' code must be run prior to each 'Model#_plotting' code, or the outputs required for plots must be downloaded from here. Most code requires no manual adjustments except for selecting the TPC or species on which to perform simulations and selecting the appropriate import and export locations, as noted in comments within code files. All code was run using Mathematica V.13.0.1.