No universal mathematical model for thermal performance curves across traits and taxonomic groups

Angilletta, M. J. Thermal Adaptation: A Theoretical and Empirical Synthesis (Oxford University Press, 2009).Clarke, A. Principles of Thermal Ecology: Temperature, Energy, and Life (Oxford University Press, 2017).Chang, R. L. et al. Structural systems biology evaluation of metabolic thermotolerance in Escherichia coli. Science 340, 1220–1223 (2013).Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Chen, K. et al. Thermosensitivity of growth is determined by chaperone-mediated proteome reallocation. Proc. Natl. Acad. Sci. USA 114, 11548–11553 (2017).Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Li, G. et al. Bayesian genome scale modelling identifies thermal determinants of yeast metabolism. Nat. Commun. 12, 190 (2021).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Higgins, J. K., MacLean, H. J., Buckley, L. B. & Kingsolver, J. G. Growth, developmental and stress responses of larvae of the clouded sulphur butterfly Colias eriphyle to repeated exposure to high, sub-lethal temperatures. Physiol. Entomol. 40, 189–195 (2015).Article 

Google Scholar 
Laurel, B. J., Copeman, L. A., Spencer, M. & Iseri, P. Temperature-dependent growth as a function of size and age in juvenile Arctic cod (Boreogadus saida). ICES J. Mar. Sci. 74, 1614–1621 (2017).Article 

Google Scholar 
Rollinson, N. et al. A new method of estimating thermal performance of embryonic development rate yields accurate prediction of embryonic age in wild reptile nests. J. Therm. Biol. 74, 187–194 (2018).Article 
PubMed 

Google Scholar 
Kontopoulos, D.-G., Smith, T. P., Barraclough, T. G. & Pawar, S. Adaptive evolution shapes the present-day distribution of the thermal sensitivity of population growth rate. PLoS Biol. 18, e3000894 (2020).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Cruz-Loya, M. et al. Antibiotics shift the temperature response curve of Escherichia coli growth. mSystems 6, e00228–21 (2021).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Huxley, P. J., Murray, K. A., Pawar, S. & Cator, L. J. Competition and resource depletion shape the thermal response of population fitness in Aedes aegypti. Commun. Biol. 5, 66 (2022).Article 
PubMed 
PubMed Central 

Google Scholar 
Pawar, S. et al. Variation in temperature of peak trait performance constrains adaptation of arthropod populations to climatic warming. Nat. Ecol. Evol. 8, 500–510 (2024).Flanagan, P. H., Jensen, O. P., Morley, J. W. & Pinsky, M. L. Response of marine communities to local temperature changes. Ecography 42, 214–224 (2019).Article 
ADS 

Google Scholar 
Gerhard, M., Koussoroplis, A. M., Hillebrand, H. & Striebel, M. Phytoplankton community responses to temperature fluctuations under different nutrient concentrations and stoichiometry. Ecology 100, e02834 (2019).Article 
PubMed 

Google Scholar 
Wieczynski, D. J. et al. Linking species traits and demography to explain complex temperature responses across levels of organization. Proc. Natl. Acad. Sci. USA 118, e2104863118 (2021).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Yvon-Durocher, G. et al. Reconciling the temperature dependence of respiration across timescales and ecosystem types. Nature 487, 472–476 (2012).Article 
ADS 
CAS 
PubMed 

Google Scholar 
Reyes, W. M. et al. Complex terrain influences ecosystem carbon responses to temperature and precipitation. Global Biogeochem. Cycles 31, 1306–1317 (2017).Article 
ADS 
CAS 

Google Scholar 
Parain, E. C., Rohr, R. P., Gray, S. M. & Bersier, L.-F. Increased temperature disrupts the biodiversity–ecosystem functioning relationship. Am. Nat. 193, 227–239 (2019).Article 
PubMed 

Google Scholar 
Shocket, M. S. et al. Transmission of West Nile and five other temperate mosquito-borne viruses peaks at temperatures between 23 °C and 26 °C. eLife 9, e58511 (2020).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Nguyen, K. H. et al. Interventions can shift the thermal optimum for parasitic disease transmission. Proc. Natl. Acad. Sci. USA 118, e2017537118 (2021).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Kunze, C., Luijckx, P., Jackson, A. L. & Donohue, I. Alternate patterns of temperature variation bring about very different disease outcomes at different mean temperatures. eLife 11, e72861 (2022).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Dell, A. I., Pawar, S. & Savage, V. M. Temperature dependence of trophic interactions are driven by asymmetry of species responses and foraging strategy. J. Anim. Ecol. 83, 70–84 (2014).Article 
PubMed 

Google Scholar 
García, F. C., Bestion, E., Warfield, R. & Yvon-Durocher, G. Changes in temperature alter the relationship between biodiversity and ecosystem functioning. Proc. Natl. Acad. Sci. USA 115, 10989–10994 (2018).Article 
ADS 
PubMed 
PubMed Central 

Google Scholar 
Amarasekare, P. Effects of climate warming on consumer-resource interactions: a latitudinal perspective. Front. Ecol. Evol. 7, 146 (2019).Article 

Google Scholar 
Wagner, T. et al. Predicting climate change impacts on poikilotherms using physiologically guided species abundance models. Proc. Natl. Acad. Sci. USA 120, e2214199120 (2023).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Janisch, E. Über die Temperaturabhängigkeit biologischer Vorgänge und ihre kurvenmäßige Analyse. Pflüger’s Arch. Physiol. 209, 414–436 (1925).Article 

Google Scholar 
Angilletta Jr, M. J. Estimating and comparing thermal performance curves. J. Therm. Biol. 31, 541–545 (2006).Article 

Google Scholar 
Woods, H. A., Kingsolver, J. G., Fey, S. B. & Vasseur, D. A. Uncertainty in geographical estimates of performance and fitness. Methods Ecol. Evol. 9, 1996–2008 (2018).Article 

Google Scholar 
Johnson, F. H. & Lewin, I. The growth rate of E. coli in relation to temperature, quinine and coenzyme. J. Cell. Comp. Physiol. 28, 47–75 (1946).Article 
CAS 
PubMed 

Google Scholar 
Ratkowsky, D. A., Olley, J. & Ross, T. Unifying temperature effects on the growth rate of bacteria and the stability of globular proteins. J. Theor. Biol. 233, 351–362 (2005).Article 
ADS 
CAS 
PubMed 

Google Scholar 
Hobbs, J. K. et al. Change in heat capacity for enzyme catalysis determines temperature dependence of enzyme catalyzed rates. ACS Chem. Biol. 8, 2388–2393 (2013).Article 
CAS 
PubMed 

Google Scholar 
DeLong, J. P. et al. The combined effects of reactant kinetics and enzyme stability explain the temperature dependence of metabolic rates. Ecol. Evol. 7, 3940–3950 (2017).Article 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Ritchie, M. E. Reaction and diffusion thermodynamics explain optimal temperatures of biochemical reactions. Sci. Rep. 8, 11105 (2018).Article 
ADS 
PubMed 
PubMed Central 

Google Scholar 
Logan, J. A., Wollkind, D. J., Hoyt, S. C. & Tanigoshi, L. K. An analytic model for description of temperature dependent rate phenomena in arthropods. Environ. Entomol. 5, 1133–1140 (1976).Article 

Google Scholar 
Lactin, D. J., Holliday, N. J., Johnson, D. L. & Craigen, R. Improved rate model of temperature-dependent development by arthropods. Environ. Entomol. 24, 68–75 (1995).Article 

Google Scholar 
Briere, J.-F., Pracros, P., Le Roux, A.-Y. & Pierre, J.-S. A novel rate model of temperature-dependent development for arthropods. Environ. Entomol. 28, 22–29 (1999).Article 

Google Scholar 
Brown, J. H., Gillooly, J. F., Allen, A. P., Savage, V. M. & West, G. B. Toward a metabolic theory of ecology. Ecology 85, 1771–1789 (2004).Article 

Google Scholar 
Pawar, S., Dell, A. I. & Savage, V. M. From metabolic constraints on individuals to the dynamics of ecosystems. In Aquatic Functional Biodiversity, 3–36 (Elsevier, 2015).Pörtner, H. O. et al. Trade-offs in thermal adaptation: the need for a molecular to ecological integration. Physiol. Biochem. Zool. 79, 295–313 (2006).Article 
PubMed 

Google Scholar 
Price, C. A. et al. Testing the metabolic theory of ecology. Ecol. Lett. 15, 1465–1474 (2012).Article 
PubMed 

Google Scholar 
Schulte, P. M. The effects of temperature on aerobic metabolism: towards a mechanistic understanding of the responses of ectotherms to a changing environment. J. Exp. Biol. 218, 1856–1866 (2015).Article 
PubMed 

Google Scholar 
Michaletz, S. T. Evaluating the kinetic basis of plant growth from organs to ecosystems. New Phytol. 219, 37–44 (2018).Article 
PubMed 

Google Scholar 
Pawar, S., Dell, A. I., Savage, V. M. & Knies, J. L. Real versus artificial variation in the thermal sensitivity of biological traits. Am. Nat. 187, E41–E52 (2016).Article 
PubMed 

Google Scholar 
Schoolfield, R. M., Sharpe, P. J. H. & Magnuson, C. E. Non-linear regression of biological temperature-dependent rate models based on absolute reaction-rate theory. J. Theor. Biol. 88, 719–731 (1981).Article 
ADS 
CAS 
PubMed 

Google Scholar 
Molnár, P. K., Sckrabulis, J. P., Altman, K. A. & Raffel, T. R. Thermal performance curves and the metabolic theory of ecology—a practical guide to models and experiments for parasitologists. J. Parasitol. 103, 423–439 (2017).Article 
PubMed 

Google Scholar 
Dell, A. I., Pawar, S. & Savage, V. M. Systematic variation in the temperature dependence of physiological and ecological traits. Proc. Natl. Acad. Sci. USA 108, 10591–10596 (2011).Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Shi, P. & Ge, F. A comparison of different thermal performance functions describing temperature-dependent development rates. J. Therm. Biol. 35, 225–231 (2010).Article 

Google Scholar 
Krenek, S., Berendonk, T. U. & Petzoldt, T. Thermal performance curves of Paramecium caudatum: a model selection approach. Eur. J. Protistol. 47, 124–137 (2011).Article 
PubMed 

Google Scholar 
Shi, P.-J., Reddy, G. V. P., Chen, L. & Ge, F. Comparison of thermal performance equations in describing temperature-dependent developmental rates of insects: (I) empirical models. Ann. Entomol. Soc. Am. 109, 211–215 (2016).Article 

Google Scholar 
Shi, P.-J., Reddy, G. V. P., Chen, L. & Ge, F. Comparison of thermal performance equations in describing temperature-dependent developmental rates of insects: (II) two thermodynamic models. Ann. Entomol. Soc. Am. 110, 113–120 (2017).Article 

Google Scholar 
Low-Décarie, E. et al. Predictions of response to temperature are contingent on model choice and data quality. Ecol. Evol. 7, 10467–10481 (2017).Article 
PubMed 
PubMed Central 

Google Scholar 
Quinn, B. K. Performance of the SSI development function compared with 33 other functions applied to 79 arthropod species’ datasets. J. Therm. Biol. 102, 103112 (2021).Article 
PubMed 

Google Scholar 
Corkrey, R., Olley, J., Ratkowsky, D., McMeekin, T. & Ross, T. Universality of thermodynamic constants governing biological growth rates. PLoS ONE 7, e32003 (2012).Article 
ADS 
CAS 
PubMed 
PubMed Central 

Google Scholar 
Kontopoulos, D.-G. et al. Data from: No universal mathematical model for thermal performance curves across traits and taxonomic groups. Figshare https://doi.org/10.6084/m9.figshare.24106161.v3 (2024).Ruggiero, M. A. et al. A higher level classification of all living organisms. PLoS ONE 10, e0119248 (2015).Article 
PubMed 
PubMed Central 

Google Scholar 
Kingsolver, J. G., Higgins, J. K. & Augustine, K. E. Fluctuating temperatures and ectotherm growth: distinguishing non-linear and time-dependent effects. J. Exp. Biol. 218, 2218–2225 (2015).PubMed 

Google Scholar 
Rohr, J. R. et al. The complex drivers of thermal acclimation and breadth in ectotherms. Ecol. Lett. 21, 1425–1439 (2018).Article 
PubMed 

Google Scholar 
Sugiura, N. Further analysis of the data by Akaike’s information criterion and the finite corrections. Commun. Stat. Theory Methods 7, 13–26 (1978).Article 

Google Scholar 
Hothorn, T., Hornik, K. & Zeileis, A. Unbiased recursive partitioning: A conditional inference framework. J. Comput. Graph. Stat. 15, 651–674 (2006).Article 
MathSciNet 

Google Scholar 
Hothorn, T. & Zeileis, A. partykit: A modular toolkit for recursive partytioning in R. J. Mach. Learn. Res. 16, 3905–3909 (2015).MathSciNet 

Google Scholar 
Padfield, D., O’Sullivan, H. & Pawar, S. rTPC and nls.multstart: A new pipeline to fit thermal performance curves in R. Methods Ecol. Evol. 12, 1138–1143 (2021).Article 

Google Scholar 
Yin, X. No need to switch the modified Arrhenius function back to the old form. New Phytol. 231, 2113–2116 (2021).Article 
PubMed 
PubMed Central 

Google Scholar 
Kontopoulos, D.-G., García-Carreras, B., Sal, S., Smith, T. P. & Pawar, S. Use and misuse of temperature normalisation in meta-analyses of thermal responses of biological traits. PeerJ 6, e4363 (2018).Article 
PubMed 
PubMed Central 

Google Scholar 
López-Urrutia, Á., San Martin, E., Harris, R. P. & Irigoien, X. Scaling the metabolic balance of the oceans. Proc. Natl. Acad. Sci. USA 103, 8739–8744 (2006).Article 
ADS 
PubMed 
PubMed Central 

Google Scholar 
García-Carreras, B. et al. Role of carbon allocation efficiency in the temperature dependence of autotroph growth rates. Proc. Natl. Acad. Sci. USA 115, E7361–E7368 (2018).Article 
PubMed 
PubMed Central 

Google Scholar 
Smith, T. P. et al. Community-level respiration of prokaryotic microbes may rise with global warming. Nat. Commun. 10, 5124 (2019).Article 
ADS 
PubMed 
PubMed Central 

Google Scholar 
Kontopoulos, D.-G. et al. Phytoplankton thermal responses adapt in the absence of hard thermodynamic constraints. Evolution 74, 775–790 (2020).Article 
PubMed 

Google Scholar 
Ikeda, T. Marine zooplankton metabolic data ver. 2. http://hdl.handle.net/2115/76282 (2019).Acuña, J. L., López-Urrutia, Á. & Colin, S. Faking giants: the evolution of high prey clearance rates in jellyfishes. Science 333, 1627–1629 (2011).Article 
ADS 
PubMed 

Google Scholar 
DeLong, J. et al. Habitat, latitude and body mass influence the temperature dependence of metabolic rate. Biol. Lett. 14, 20180442 (2018).Article 
PubMed 
PubMed Central 

Google Scholar 
Nilsson-Örtman, V., Stoks, R., De Block, M., Johansson, H. & Johansson, F. Latitudinally structured variation in the temperature dependence of damselfly growth rates. Ecol. Lett. 16, 64–71 (2013).Article 
PubMed 

Google Scholar 
Phillips, J. A. et al. The effects of phylogeny, habitat and host characteristics on the thermal sensitivity of helminth development. Proc. R. Soc. B Biol. Sci. 289, 20211878 (2022).Article 

Google Scholar 
Lear, K. O. et al. Thermal performance responses in free-ranging elasmobranchs depend on habitat use and body size. Oecologia 191, 829–842 (2019).Article 
ADS 
PubMed 

Google Scholar 
Dell, A. I., Pawar, S. & Savage, V. M. The thermal dependence of biological traits. Ecology 94, 1205–1206 (2013).Article 

Google Scholar 
Padfield, D. & Matheson, G. nls.multstart: Robust Non-Linear Regression using AIC Scores. https://CRAN.R-project.org/package=nls.multstart. R package version 1.2.0. (2020).Kontopoulos, D.-G. et al. No universal mathematical model for thermal performance curves across traits and taxonomic groups. dgkontopoulos/Kontopoulos_et_al_83_TPC_models_2024. Zenodo https://doi.org/10.5281/zenodo.12608191 (2024).Quarteroni, A., Sacco, R. & Saleri, F. Numerical Mathematics (Springer, 2010).Sokal, R. R. & Michener, C. D. A statistical method for evaluating systematic relationships. Univ. Kans. Sci. Bull. 38, 1409–1438 (1958).
Google Scholar 
Regehr, D. L. & Bazzaz, F. A. Low temperature photosynthesis in successional winter annuals. Ecology 57, 1297–1303 (1976).Article 
CAS 

Google Scholar 
Yu, G., Smith, D. K., Zhu, H., Guan, Y. & Lam, T. T.-Y. ggtree: an R package for visualization and annotation of phylogenetic trees with their covariates and other associated data. Methods Ecol. Evol. 8, 28–36 (2017).Article 

Google Scholar 
Gu, Z. Complex heatmap visualization. iMeta 1, e43 (2022).Article 
PubMed 
PubMed Central 

Google Scholar 

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