s41558-022-01490-7.pdf

Nature Climate Change | Volume 12 | November 2022 | 1037–1044 1037 nature climate change https://doi.org/10.1038/s41558-022-01490-7 Article Climate-mediated shifts in temperature fluctuations promote extinction risk Kate Duffy   1,2,3 , Tarik C. Gouhier   4 & Auroop R. Ganguly1,5 Climate-mediated changes in thermal stress can destabilize animal populations and promote extinction risk. However, risk assessments often focus on changes in mean temperatures and thus ignore the role of temporal variability or structure. Using Earth System Model projections, we show that significant regional differences in the statistical distribution of temperature will emerge over time and give rise to shifts in the mean, variability and persistence of thermal stress. Integrating these trends into mathematical models that simulate the dynamical and cumulative effects of thermal stress on the performance of 38 globally distributed ectotherm species revealed complex regional changes in population stability over the twenty-first century, with temperate species facing higher risk. Yet despite their idiosyncratic effects on stability, projected temperatures universally increased extinction risk. Overall, these results show that the effects of climate change may be more extensive than previously predicted on the basis of the statistical relationship between biological performance and average temperature. Biodiversity loss has been recognized as one of the top global risks by the World Economic Forum because it could erode or eliminate key ecosystem functions and services1. Climate change is expected to surpass habitat loss as the leading threat to global biodiversity by the middle of the twenty-first century2. Observed changes in the distri- bution and phenology of species have already been linked to climate fluctuations in numerous studies3. Although conservation actions may ameliorate potential biodiversity loss, the success of these efforts depends on our ability to predict the response of ecological systems to environmental changes. Most ecological impact studies so far have relied on statistical models, such as bioclimate envelope approaches, to determine how cli- mate change will impact ecological populations4–7. Bioclimate envelope models are typically constructed by either mapping the geographical distribution of species to co-located temperature records via regres- sion techniques or by building species’ thermal profiles via empirical assessments of their performance across a range of temperatures (that is, thermal performance curves or TPCs)4,8. These relationships between organisms and temperature are then used to predict the dis- tribution of species under future thermal conditions projected under various climate change scenarios. Despite the power and popularity of TPCs, these statistical approaches can yield inaccurate predictions because they typically rely on mean annual conditions and thus ignore the influence of the temporal structure of temperature fluctuations at finer scales. This is problematic because the nonlinear relationship between tempera - ture and most metrics of biological performance essentially guaran - tees that the average organismal response will not be equivalent to their response to the average condition 9–12. Specifically, when an organism is exposed to a sequence of temperatures x, its performance at the average temperature f ( ̄x) will differ from the average of its performance f (x) . T emporal variation in temperature will either magnify (f (x) > f ( ̄x)) or dampen (f (x) < f ( ̄x)) the effects of its mean on organismal performance depending on the curvature of f (that is, whether f is accelerating or decelerating9). In many cases, changes in temperature variability can be as or more important than changes in Received: 2 March 2022 Accepted: 31 August 2022 Published online: 20 October 2022 Check for updates 1Sustainability and Data Sciences Laboratory, Department of Civil and Environmental Engineering, Northeastern University, Boston, MA, USA. 2NASA Ames Research Center, Moffett Field, CA, USA. 3Bay Area Environmental Research Institute, Moffett Field, CA, USA. 4Department of Marine and Environmental Sciences, Marine Science Center, Northeastern University, Nahant, MA, USA. 5Pacific Northwest National Laboratory, Richland, WA, USA.  e-mail: [email protected] Nature Climate Change | Volume 12 | November 2022 | 1037–1044 1038 Article https://doi.org/10.1038/s41558-022-01490-7 temperatures (that is, across quantiles ranging from τ = 2.5% at the low end to τ = 97.5% at the high end) in the Northern Hemisphere Extra-tropics (NHEX, 30° N to 90° N), the Southern Hemisphere Extra-tropics (SHEX, 90° S to 30° S), and the Tropics (TROP, 30° S to 30° N). When averaging trends across regions, we found asymmetrical but uniformly positive trends across all quantiles, indicating that the entire temperature distribution is shifting upwards but at rates that vary systematically across the distribution. In NHEX, the lowest quan- tile of the distribution (τ = 2.5%, 0.33 K per decade) is warming at twice the rate of the uppermost quantile (τ = 97.5%, 0.16 K per decade). The SHEX exhibits a similar pattern of disproportionate warming for the low quantiles (τ = 2.5%, 0.15 K per decade; τ = 97.5%, 0.10 K per decade). Conversely, in the tropics, the upper quantiles of temperature are warm- ing faster ( τ = 97.5%, 0.14 K per decade) than the lower quantiles (τ = 2.5%, 0.10 K per decade). The magnitude of trends is greater in NHEX than in SHEX or TROP. The more pronounced extra-tropical decrease in the incidence of cold events may benefit cold-limited spe- cies; however, quantile trends also indicate increased positive skewness of the NHEX temperature distribution, which has been associated with declines in long-term ecological performance15. Across all eight CMIP6 models that we analysed and in all three latitudinal regions, trends in the tails of the distributions differ from the trends in the central ten- dencies, thus highlighting the importance of moving beyond mean temperature when predicting organismal performance. Trends in the variability of temperature between 1850 and 2100 are predicted to exhibit similarly complex regional patterns (Fig. 2c).
Variance will generally increase across temperate and tropical land areas below 45° N, with regional exceptions including Asia. The strong- est increases in variance are in the northern mid latitudes, including northern Africa, southern Europe, the Middle East and the western United States. Variance is decreasing most rapidly in the high northern latitudes, especially in Canada and Russia25. The concurrent decrease in variability at high latitudes and its increase at other latitudes sug - gests that temperature variation, similar to mean temperature, is becoming more spatially homogeneous in a warming world. These findings are generally consistent with studies of the previous genera- tion of climate models, which suggested increasing temperature vari- ability in tropical countries26 and decreasing variability in the northern mid to high latitudes 27. Trends at the regional level are congruent with quantile trends (Fig. 2a), which indicate a widening temperature distribution (increasing variance) in TROP, and a narrowing tempera- ture distribution (decreasing variance) in NHEX and SHEX, as well as large-scale changes in physical climate processes 26–28. The effects of these trends in temperature variation on ecological systems will depend on the geographical location and physiological properties of each species, with increasing variability either promoting or reducing performance on the basis of its position relative to the inflection point of an organism’s TPC9. Frequency-resolved temperature changes T o better understand these spatiotemporal patterns, we used time-frequency decomposition via the wavelet transform to resolve changes in the variability of temperature at sub-annual to annual time- scales (between 2 d and 2 yr) and multi-annual timescales (between 2 yr and 30 yr; Extended Data Fig. 1). Wavelet transforms resolve a signal in both the time and frequency domains to describe how each frequency or period in the time series contributes to variation over time. We found countervailing trends in scale-specific variability in the mid to high northern latitudes. The magnitude of short-term variability is decreas- ing, while the magnitude of long-term variability is increasing. Arctic amplification, which is detectable in both observational data and cli- mate simulations, has previously been suggested as the main driver of decreasing sub-seasonal variability at these latitudes27. Meanwhile at the mid latitudes, variation in both annual and multi-annual timescales is increasing, consistent with increasing variance at all periodicities. the mean value 13,14. In one study, climate-mediated changes in mean temperature alone were found to broadly promote organismal per- formance in ectotherms, but accounting for the temporal variability of temperature dampened this effect and led to most species suffering a performance loss 15. Although the temporal structure of temperature can theoretically be incorporated into bioclimate envelope models by using finer tem- poral scale data, accounting for its dynamical effects on organisms is much more difficult because of the ‘static’ nature of these methods and their general inability to account for the cumulative effects of previous temperatures on organismal performance. However, theory has shown that such carryover effects associated with the temporal structure or autocorrelation of temperature can interact with the magnitude of temperature variability to determine population persistence 16. Specifically, temporally autocorrelated variation tends to reduce extinction risk by decreasing the likelihood of catastrophic conditions under strong variation, whereas temporally autocorrelated variation tends to promote extinction risk under weak variation by increasing the likelihood that organisms will experience long stretches of poor conditions16. Prolonged exposure to temperatures above the species’ critical thermal maximum is particularly destabilizing as it can reduce population fitness below the replacement rate17. Analyses of historical observations and projections from previous generation climate models have found strong temporal trends in the variability and autocorrela- tion of temperature18–21, suggesting the potential for a larger impact on ecological populations in the future. Overall, these empirical and theoretical results highlight the importance of quantifying changes in the mean, variability and autocorrelation of temperature projected under climate change to predict their joint influence on ecological systems over the course of the twenty-first century. However, dispari- ties in the scale of models in climate and ecology have hindered impact studies that consider the complexity of both underlying systems22,23. We briefly illustrate the potential for complex interactions between climate-mediated changes in the mean, variability and auto- correlation of temperature to influence organismal performance by simulating the effects of synthetic temperature time series on the population growth rate r according to a species’ TPC (Fig. 1, see Meth- ods for modelling details). Predictably, performance under negligible temperature variation can be inferred directly from the mean of each species’ TPC (Fig. 1b,c ). However, when temporal variation in tem - perature is included in the model (that is, standard deviation; shaded region), time-averaged performance can be considerably modified9, even overturning the identity of ‘winning’ and ‘losing’ species based solely on constant temperature conditions (Fig. 1d,e). T emperature autocorrelation, which measures the temporal structure of tempera- ture fluctuations (for example, the persistence of extremes), can also play a pivotal role in determining whether a species’ performance and stability will benefit or suffer under different thermal regimes
(Fig. 1f,g). T o determine the impact of such changes over the course of the twenty-first century, we analysed the latest generation of Earth System Models from the Coupled Model Intercomparison Project
Phase 6 (CMIP6) to document spatiotemporal changes in three key aspects of air temperature: statistical distribution, variance and tem- poral autocorrelation. We then analysed the effects on population stability and extinction risk using simple mathematical models to examine the hypothesis that even under ideal conditions, popular statistical methods can yield incorrect predictions about patterns of organismal performance when dynamical and cumulative temperature effects are ignored. Regional trends in temperature distribution We examined changes in the global and regional temperature distribu- tions at each geographical location between 1850 and 2100 under the high emissions scenario, SSP5-8.524 (Fig. 2a,b). Quantile regression was used to measure temporal trends in the entire distribution of projected Nature Climate Change | Volume 12 | November 2022 | 1037–1044 1039 Article https://doi.org/10.1038/s41558-022-01490-7 These scale-dependent changes in the temporal trends of temperature fluctuations could have important ecological implications because the effect of temperature fluctuations depends on the relationship between their period and the generation time of organisms. Indeed, estimating the biological effect of temperature fluctuations by ‘nonlinear averag- ing’ of organismal performance under the relevant constant thermal regimes is much more likely to yield accurate results when the period of the temperature fluctuations is larger than the generation time of an organism because such slow variation can more easily be ‘tracked’ by a population29. We computed the spectral exponent of the temperature time series at each geographical location to quantify spatiotemporal trends, b d f c e g Mean of temperature H. pseudobrassica C. sesamiae Growth rate (r)Population density (N) Power (log) Variance of temperature Autocorrelation of temperature Temperature (°C) Time Time Time Temperature (°C) Frequency (log) /uni03B2 = –0.5 /uni03B2 = –2.0 a Cotesia sesamiae 60° N 30° N 0° 30° S 60° S 60° E 120° E 180° 120° W 60° W Hyadaphis pseudobrassicae Fig. 1 | Effects of temperature mean, variance and autocorrelation on organismal performance. a, Source locations of the 38 species whose thermal performance parameters were obtained from the Deutsch et al.5 dataset. Cotesia sesamiae is a tropical parasitoid wasp and Hyadaphis pseudobrassicae is a temperate-zone turnip aphid. b,c, Thermal performance curves and population dynamics for C. sesamiae and H. pseudobrassicae under a mean temperature (vertical line) with negligible variation. d,e, Larger temperature variation (s.d., shaded) alters mean response (dashed horizontal line) and may even overturn predictions of relative performance based on constant temperature conditions. f, The power spectrum of temperature with weak (ß = −0.5) and strong (ß = −2) temporal autocorrelation. g, Population dynamics of Hyadaphis pseudobrassicae under a greater degree of temporal autocorrelation exhibit longer-term fluctuations. Multiple aspects of temperature, such as its mean and variance,
can interact to promote or decrease performance. Nature Climate Change | Volume 12 | November 2022 | 1037–1044 1040 Article https://doi.org/10.1038/s41558-022-01490-7 with more negative exponents indicating greater temporal autocorrela- tion over a range of lags from 2 d to 10 yr (Fig. 3a). We found increasing temporal autocorrelation (decreasing spectral exponent) at a majority of sea locations (60%) and land locations (80%), excluding Antarctica where autocorrelation is decreasing. Autocorrelation is increasing most rapidly in equatorial land areas including the Amazon and the Southeast Asian islands, with high inter-model agreement on the sign of the trend. Notable exceptions to the increasing trend in autocorrela- tion include Greenland, Western Africa, Western Europe and parts of Central Asia. Generally, agreement between models is higher at mid lati- tudes than in the polar zones or the tropics, where climate model bias and spread have historically persisted 30. Regional analysis indicates statistically significant increasing trends in temporal autocorrelation in NHEX (−1.12 × 10−3 per decade, P = 0.010), TROP (−1.14 × 10−3 per dec- ade, P = 0.001) and globally (−0.54 × 10−3 per decade1, P = 0.005), and a statistically significant decreasing trend in temporal autocorrelation in SHEX (0.53 × 10−3 per decade, P  = 0.009; Supplementary Table 1). The direction and significance of these trends are consistent across land and sea environments, although the spectral exponent is more negative for sea than land, probably due to the buffering effects of the ocean (Fig. 3b–e). In NHEX and TROP, autocorrelation is increasing at a greater rate in land locations than in sea locations, while in SHEX it is decreasing at similar rates between land and sea (Supplementary Table 2). A greater degree of temporal autocorrelation is associated with more gradual changes of state and, even without any changes in variance, results in longer durations spent under extreme conditions. A greater clustering of similar temperatures has been suggested to increase exposure to heat waves and cold snaps while decreasing the incidence of protective temporal refugia20. Regional differences in warming patterns In the northern latitudes, variance and autocorrelation exhibit oppo- site temporal trends. The decreasing variance may be attributed to a decrease in high-frequency variability and more rapid warming of the lower than the upper quantiles of the temperature distribution. Studies of reanalysis data and observations have also implicated decreasing cold-season sub-seasonal variability and rapidly warming cold days in decreasing temperature variability in mid to high north- ern latitudes20,24,29. Meanwhile, temporal autocorrelation in NHEX is increasing—a finding that has also been detected in the previous genera- tion of climate models20, weather station observations31 and monthly reanalysis data19. As a result, variation at 2 d to 10 yr periodicities is decreasing while temperature fluctuations are becoming more persis- tent, suggesting the increased probability of a series of homogeneous conditions. In contrast to the mid to high northern latitudes, variance and temporal autocorrelation show similar trends at most latitudes, that is, both variance and autocorrelation are increasing. Implications for global ectotherm populations T o better understand the independent and joint effects of these pro- jected trends in the mean, variance and autocorrelation of temperature on ecological systems, we used empirical thermal performance infor- mation from invertebrate ectotherms compiled by Deutsch et al.5. We extracted temperature time series from the eight CMIP6 climate mod- els at geographical point locations corresponding to the source sites of the 38 species (Fig. 4a). A dynamical population simulation using species-specific temperature-dependent growth rates yielded time series of population abundance for the historical period (1950–2000) and the latter half of the twenty-first century (2050–2100). We used a dynamical logistic growth model whose carrying capacity K = rt/α is determined by the temperature-dependent growth rate rt and the self-regulation parameter α . Importantly, the model captures the effects of temperatures above the critical thermal maximum and extinc- tion propensity under autocorrelated variation by allowing growth rates to become negative (see Methods for details). Using the eight climate simulations as replicates, we compared the historical and future periods to detect statistically significant temperature-driven changes in population abundance, stability (mean/standard deviation of abun- dance) and extinction probability (proportion of simulations where a species did not have a strictly positive final abundance). Under the high emissions scenario (SSP5-8.5), population abun- dance increased for the plurality of species (16 of 38) because the mean temperature grew closer to their thermal optimum and thus boosted equilibrium abundance, but it decreased for 9 species (Supplementary Table 3). Population abundance increased significantly for 3 of 5 TROP species and for the majority (5 of 8) of SHEX species. In NHEX, outcomes were mixed, with approximately equal proportions of species experi- encing an increase in abundance, a decrease in abundance, and no significant change. NHEX population abundance followed latitudinal patterns, generally decreasing between 30° N and 45° N, and increasing above of 45° N. Under the high emissions scenario, population stability increased for the 12 out of 38 and decreased for 9 species (Fig. 4b ). Population stability increased or underwent no significant change for TROP species, while in the mid latitudes (NHEX and SHEX), changes in stability were mixed. Additional analyses showed that the trends in stability were mainly due to the emergence of two distinct dynamical regimes under climate change, with species either moving to a low-mean/low-variance mode or a high-mean/high-variance mode, 60° S 30° S 0° 30° N 60° NGLOBAL0.35 0.30 0.25 Trend (K per decade) 0.20 0.15 0.10 0.05 0 0.1 0.2 0.3 0.4 0.5 0.6 Temperature quantile 0.7 0.8 0.9 1.0 NHEX TROP SHEX 120° W 60° W 0° 60° E 120° E 0.01 0.02 0.03 0.04 0.05 /uni0394K per decade 60° S 30° S 0° 30° N 60° N 120° W 60° W 0° 60° E 120° E –0.5 –0.4 –0.3 –0.2 –0.1 0 0.1 /uni0394K2 per decade a b c Fig. 2 | Mean trends in the statistical distribution of daily air temperature between 1850 and 2100. a,b, Trends in the percentile values of air temperature (a, K per decade) and mean temperature at each geographic location (b, ΔK per decade) indicate asymmetrically warming temperature distributions in the Northern Hemisphere Extra-tropics (NHEX, 30° N to 90° N), the Tropics (TROP, 30° S to 30° N), the Southern Hemisphere Extra-tropics (SHEX, 90° S to 30° S), and the full globe (GLOBAL, 90° S to 90° N). Shaded bounds denote the 90% confidence interval based on eight CMIP6 models. c, Trends in the variance of daily air temperature (ΔK2 per decade) exhibit similarly complex regional patterns. The concurrent decrease in variability at high latitudes and increase at other latitudes suggests that temperature variation is becoming more spatially homogeneous in a warming world. Hashed contours indicate statistically significant inter-model agreement on the sign of the trend at the α = 0.05 significance level. Nature Climate Change | Volume 12 | November 2022 | 1037–1044 1041 Article https://doi.org/10.1038/s41558-022-01490-7 particularly in the extra-tropics (Extended Data Figs. 2 and 3). These results were robust to orders of magnitude changes in the growth
rate rt and self-regulation parameter α (Extended Data Figs. 4 and 5). Many SHEX and NHEX species suffered performance losses (nega- tive growth rates) during summers in their respective hemispheres, as they are generally less tolerant of hot temperatures than tropical spe- cies. For some temperate species, longer growing seasons and warmer winter temperatures offset the negative effect of the warmest part of the year, while others suffered an overall performance loss 32. This is consistent with the suggestion that increases in summer heat stress would reduce overall fitness and increase fitness variation for many mid-latitude species. Our results suggest that temperate species may be at greater risk than tropical species as a result of warm days, even when annual mean temperature remains below the thermal optimum. The results contrast with those of previous studies, which suggested on the basis of hourly temperature records and monthly temperature anomalies that warming in the tropics would be more deleterious than warming in the mid latitudes5,33. This discrepancy may be due to the fact that growth rates were allowed to become negative when temperatures exceeded the critical thermal maximum in our simulations but assumed to converge to zero (that is, were not allowed to be negative) in previous studies4. Our results are more consistent with studies that predict a greater risk of performance loss for temperate species when account- ing for negative performance values in response to climate-mediated changes in the mean and the variance of temperature15. T o tease apart the dynamical effects of climate change on popu- lation stability from its effects on mean performance as inferred by measuring average growth rate using each species’ TPC, we replicated previous efforts by comparing changes in the average growth rate under historical and future climatic conditions with vs without negative growth rates (Extended Data Fig. 6). Our results show that although allowing negative growth rates predictably leads to greater reduc - tions in performance overall, the regional patterns in performance are similar to the trends in population stability observed in the dynamical simulations, with tropical species generally enjoying performance gains and temperate species—particularly in NHEX—suffering perfor- mance losses (Extended Data Fig. 6). Our simulations indicated mean warming as the dominant driver of ecological impacts. Changes in temporal autocorrelation alone (mean temperature and variance held at historical levels) had no significant effects on population abundance and a significant desta- bilizing effect on just 1 NHEX species. Changes in temporal autocor- relation and variance (mean temperature held at historical levels) led to an increase in population abundance in 2 NHEX species and a decrease in population stability in 2 NHEX species. These results sug- gest that NHEX species are more susceptible to changes in temperature variability than TROP or SHEX species. Finally, changes in mean and temporal autocorrelation (variance held at historical levels) led to increased population abundance in 18 global species and increased stability in 14 global species, versus 16 and 12 under the high emissions scenario-projected changes in all three aspects of temperature. Thus, projected changes in temperature variability have a weak moderating effect on the positive effects of mean warming on population abun- dance and stability. T o determine how these complex changes in population abun- dance and stability translate to persistence, we quantified extinction risk as the proportion of the 8 CMIP6 models for which population abundance declined below an arbitrarily small threshold of 1 × 10−9 at any point during the 50 yr simulation (Fig. 4c). In our simulations under the high emissions scenario, extinction risk increased significantly under future climate conditions relative to historical baselines for 18 species, increased (but not significantly) for 6 species, decreased for 1 species, and did not change for 13 species. We found statisti - cally significant increases in extinction risk globally (Mann–Whitney U = 423, n 1 = n2 = 38, P = 8 × 10−4) and in NHEX (Mann–Whitney U = 166, n1 = n2 = 25, P = 3 × 10 −3). These findings suggest that temperature changes promote extinction risk, despite having a largely positive or neutral effect on population abundance and idiosyncratic impacts on stability. Hence, although variability among climate models produces a wide range of changes in stability across species and geographical locations, uncertainty at the climate level yields consistent biological impacts in the form of systematically higher extinction risks (Extended Data Fig. 7). Conclusion By forcing simple strategic and dynamical models of population growth with fine temporal scale temperature projections from the latest gen- eration of Earth System Models, we demonstrated increased extinc - tion risk under climate change across globally distributed ectotherm populations. Unfortunately, using more complex tactical dynamical 60° S 30° S 0° 30° N 60° N 120° W 60° W 0° 60° E 120° E –1.0 –0.5 0 0.5 Change in spectral exponent per decade a b d c e –1.24 GLOBAL NHEX TROP SHEX –1.26 –1.28 Spectral exponet –1.30 –1.32 –1.34 Land Sea 1850 1900 1950 2000 2050 2100 1850 1900 1950 2000 2050 2100 1850 1900 1950 2000 2050 2100 1850 1900 1950 2000 2050 2100 Land Sea Land Sea Land Sea –1.24 –1.26 –1.28 Spectral exponet –1.30 –1.32 –1.34 –1.36 –1.38 –1.40 Spectral exponet –1.42 –1.44 –1.46 –1.12 –1.14 –1.16 –1.18 –1.20 –1.22 –1.24 Spectral exponet Fig. 3 | Increasing temporal autocorrelation in daily air temperature between 1850 and 2100. a, Spatiotemporal trends in temporal autocorrelation suggest changes in the chronological sequence of temperature conditions, with increasing temporal autocorrelation (decreasing spectral exponent) at 80.04% of global land locations, excluding Antarctica. Hashed contours indicate statistically significant inter-model agreement on the sign of the trend at the α = 0.05 significance level. b–e, Regional analysis indicates statistically significant increasing trends in temporal autocorrelation in NHEX and TROP, and a statistically significant decreasing trend in temporal autocorrelation in SHEX. While sea environments generally exhibit a greater degree of temporal autocorrelation than land, in NHEX autocorrelation is increasing at a greater rate on land locations as to overturn this relationship by the end of the twenty-first century. Nature Climate Change | Volume 12 | November 2022 | 1037–1044 1042 Article https://doi.org/10.1038/s41558-022-01490-7 models would require extensive species-, age- and life-stage-specific information about the effects of temperature fluctuations on popu - lation growth rates that is simply not available at the relevant scales. Tactical models would also need to consider thermoregulation 34, the effects of microclimates 35, acclimatization or adaptation 36, par- titioning of activity periods 37 and synecological processes such as predator-prey interactions that could affect ectotherm population dynamics. Additionally, due to their 1° spatial resolution, the climate projections used in this study are much coarser than the microclimates experienced by individual organisms and may thus lead to underes - timates of organismal performance due to the presence of thermal refugia in the real world23,34. Hence, our results should be viewed as a qualitative baseline prediction of how the spatiotemporal distribution of extinction risk is likely to shift due to climate change rather than a a b c 60° N 37 38 27 12 11 10 7 15 25 26 22 23 13 34 21 32 3130 2829 17 1819 16 33 36 35 2420 14 9 6 5 8 4 3 2 1 30° N 0° 30° S 60° S 300 100 50 0 –50 100 50 0 –50 100 50 0 –50 100 50 0 –50 Mean, variance and autocorrelation Mean and autocorrelation Variance and autocorrelation Autocorrelation Mean, variance and autocorrelation Mean and autocorrelation Variance and autocorrelation Autocorrelation 200 100 0 –100 Percent change in population stability Change in extinction probability 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20 Species 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 1 2 3 4 5 6 7 8 9 10 1112 13 14 15 16 17 18 19 20 Species 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 –100 300 200 100 0 –100 300 200 100 0 –100 300 200 100 0 60° E 120° E 180° 120° W 60° W NHEX TROP SHEX NHEX TROP SHEX Fig. 4 | T emperature has idiosyncratic effects on stability but increases extinction risk globally. a, Source locations of the terrestrial ectothermic invertebrate species, numbered 1 (southernmost latitude) to 38 (northernmost latitude). Species are colour-coded according to latitudinal region (orange, SHEX; green, TROP; red, NHEX). b, Percent changes in population stability (mean ÷ s.d.) between a historical reference period (1950–2000) and a future period (2050–2100) under multiple aspects of temperature change indicate greater risk to temperate than to tropical species. Under a high emissions scenario, stability shows a statistically significant increase for 12 of 38 species and a statistically significant decrease for 9 species. Points in the violin plots represent the 8 climate model outputs. c, Extinction probability shows a quasi-universal increase globally between the historical period (1950–2000) and a future period (2050–2100) under high emissions scenario changes in temperature. Nature Climate Change | Volume 12 | November 2022 | 1037–1044 1043 Article https://doi.org/10.1038/s41558-022-01490-7 quantitative forecast of when each species is likely to be extirpated from each geographical location. Despite the limitations of TPCs in accounting for temporal car- ryover and dynamical effects, the lack of obvious alternatives calls for strategies to make these approaches more robust to real-world condi- tions38, such as by integrating more realistic, fine-scaled temperature variation into our predictive models than previous studies. Although bioclimate envelope approaches have been criticized for not account- ing for important ecological factors, such as species interactions and dispersal, when attempting to predict the ecological effects of climate change39–42, we have shown that even under ideal conditions when the influence of such factors can be assumed to be negligible, statistical frameworks that ignore the dynamical consequences of temperature variation are likely to yield inaccurate forecasts of the impact of climate change on organisms. Our results show that accounting for shifts in the entire statistical distribution of temperature over time via dynamical models can better capture the cumulative effects of climate-mediated changes in thermal stress on extinction risk. By bringing together climate data and a minimal dynamical model from ecology, we demonstrated a strong and systematic amplifica- tion of extinction risk in ectotherms due to projected changes in fine-grained temperature variability. Furthermore, our finding of greater risk to sub-tropical than tropical species highlights the impor- tance of accounting for the dynamical effects of projected changes in the mean as well as the variance of temperature over the course of the twenty-first century to accurately predict the response of ecological systems around the globe. Online content Any methods, additional references, Nature Research reporting sum- maries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contri- butions and competing interests; and statements of data and code avail- ability are available at https://doi.org/10.1038/s41558-022-01490-7. References 1. The Global Risks Report 2021 Insight Report 16th edn (World Economic Forum, 2021). 2. Bellard, C., Bertelsmeier, C., Leadley, P., Thuiller, W. & Courchamp, F. Impacts of climate change on the future of biodiversity. Ecol. Lett. 15, 365–377 (2012). 3. Parmesan, C. Ecological and evolutionary responses to
recent climate change. Annu. Rev. Ecol. Evol. Syst. 37,
637–669 (2006). 4. Pearson, R. G. & Dawson, T. P. Predicting the impacts of climate change on the distribution of species: are bioclimate envelope models useful? Glob. Ecol. Biogeogr. 12, 361–371 (2003). 5. Deutsch, C. A. et al. Impacts of climate warming on terrestrial ectotherms across latitude. Proc. Natl Acad. Sci. USA 105, 6668–6672 (2008). 6. Cheung, W. W. L. et al. Projecting global marine biodiversity impacts under climate change scenarios. Fish Fish. 10, 235–251 (2009). 7. Thuiller, W. et al. Consequences of climate change on the tree of life in Europe. Nature 470, 531–534 (2011). 8. Angilletta, M. J. Thermal Adaptation: A Theoretical and Empirical Synthesis. Thermal Adaptation (Oxford Univ. Press, 2009). 9. Ruel, J. J. & Ayres, M. P. Jensen’s inequality predicts effects of environmental variation. Trends Ecol. Evol. 14, 361–366 (1999). 10. Lawson, C. R., Vindenes, Y., Bailey, L. & Pol, Mvande Environmental variation and population responses to global change. Ecol. Lett. 18, 724–736 (2015). 11. Denny, M. The fallacy of the average: on the ubiquity, utility and continuing novelty of Jensen’s inequality. J. Exp. Biol. 220, 139–146 (2017). 12. Denny, M. Performance in a variable world: using Jensen’s inequality to scale up from individuals to populations. Conserv. Physiol. 7, coz053 (2019). 13. García-Carreras, B. & Reuman, D. C. Are changes in the mean or variability of climate signals more important for long-term stochastic growth rate? PLoS ONE 8, e63974 (2013). 14. Benedetti-Cecchi, L., Bertocci, I., Vaselli, S. & Maggi, E. Temporal variance reverses the impact of high mean intensity of stress in climate change experiments. Ecology 87, 2489–2499 (2006). 15. Vasseur, D. A. et al. Increased temperature variation poses a greater risk to species than climate warming. Proc. R. Soc. B 281, 20132612 (2014). 16. Schwager, M., Johst, K. & Jeltsch, F. Does red noise increase or decrease extinction risk? Single extreme events versus series of unfavorable conditions. Am. Nat. 167, 879–888 (2006). 17. Kingsolver, J. G., Diamond, S. E. & Buckley, L. B. Heat stress and the fitness consequences of climate change for terrestrial ectotherms. Funct. Ecol. 27, 1415–1423 (2013). 18. Meehl, G. A. More Intense, more frequent, and longer
lasting heat waves in the 21st century. Science 305,
994–997 (2004). 19. Lenton, T. M., Dakos, V., Bathiany, S. & Scheffer, M. Observed trends in the magnitude and persistence of monthly temperature variability. Sci. Rep. 7, 5940 (2017). 20. Di Cecco, G. J. & Gouhier, T. C. Increased spatial and temporal autocorrelation of temperature under climate change. Sci. Rep. 8, 14850 (2018). 21. Li, J. & Thompson, D. W. J. Widespread changes in surface temperature persistence under climate change. Nature 599, 425–430 (2021). 22. Lembrechts, J. J. et al. Comparing temperature data sources for use in species distribution models: from in-situ logging to remote sensing. Glob. Ecol. Biogeogr. 28, 1578–1596 (2019). 23. Potter, K. A., Arthur Woods, H. & Pincebourde, S. Microclimatic challenges in global change biology. Glob. Change Biol. 19, 2932–2939 (2013). 24. O’Neill, B. C. et al. The Scenario Model Intercomparison
Project (ScenarioMIP) for CMIP6. Geosci. Model Dev. 9,
3461–3482 (2016). 25. Hansen, J., Sato, M. & Ruedy, R. Perception of climate change. Proc. Natl Acad. Sci. USA 109, E2415–E2423 (2012). 26. Bathiany, S., Dakos, V., Scheffer, M. & Lenton, T. M. Climate models predict increasing temperature variability in poor countries. Sci. Adv. 4, eaar5809 (2018). 27. Screen, J. A. Arctic amplification decreases temperature variance in northern mid- to high-latitudes. Nat. Clim. Change 4, 577–582 (2014). 28. Stouffer, R. J. & Wetherald, R. T. Changes of variability in response to increasing greenhouse gases. Part I: temperature. J. Clim. 20, 5455–5467 (2007). 29. Gouhier, T. C. & Pillai, P. Commentary: nonlinear averaging of thermal experience predicts population growth rates in a thermally variable environment. Front. Ecol. Evol. 7, 236 (2019). 30. Tian, B. & Dong, X. The double-ITCZ bias in CMIP3, CMIP5, and CMIP6 models based on annual mean precipitation. Geophys. Res. Lett. 47, e2020GL087232 (2020). 31. Dillon, M. E. et al. Life in the frequency domain: the biological impacts of changes in climate variability at multiple time scales. Integr. Comp. Biol. 56, 14–30 (2016). 32. Adamo, S. A., Baker, J. L., Lovett, M. M. E. & Wilson, G. Climate change and temperate zone insects: the tyranny of thermodynamics meets the world of limited resources. Environ. Entomol. 41, 1644–1652 (2012). 33. Dillon, M. E., Wang, G. & Huey, R. B. Global metabolic impacts of recent climate warming. Nature 467, 704–706 (2010).