A widespread thermodynamic effect, but maintenance of biological rates through space across life's major domains

Abstract

For over a century, the hypothesis of temperature compensation, the maintenance of similar biological rates in species from different thermal environments, has remained controversial. An alternative idea, that fitness is greater at higher temperatures (the thermodynamic effect), has gained increasing traction. This alternative hypothesis is also being used to understand large-scale biodiversity responses to environmental change. Yet evidence in favour of each of these contrasting hypotheses continues to emerge. In consequence, the fundamental nature of organismal thermal responses and its implications remain unresolved. Here, we investigate these ideas explicitly using a global dataset of 619 observations of four categories of organismal performance, spanning 14 phyla and 403 species. In agreement with both hypotheses, we show a positive relationship between the temperature of maximal performance rate (T_opt) and environmental temperature (T_env) for developmental rate and locomotion speed, but not growth or photosynthesis rate. Next, we demonstrate that relationships between T_env and the maximal performance rate (U_max) are rarely significant and positive, as expected if a thermodynamic effect predominates. By contrast, a positive relationship between T_opt and U_max is always present, but markedly weaker than theoretically predicted. These outcomes demonstrate that while some form of thermodynamic effect exists, ample scope is present for biochemical and physiological adaptation to thermal environments in the form of temperature compensation.

1. Introduction

All organisms are exposed to variation in ambient temperature. Such variation typically has direct effects on the physiology and population dynamics of ectotherms, ultimately exerting a marked influence on range size and dynamics [1–3]. In consequence, ectothermic animals and plants exhibit a wide range of responses to modulate the effects of ambient temperature variation [4–6]. Among their adaptive responses, temperature compensation, or the maintenance of biological rates among species from very different thermal environments, has proven especially controversial. Also known as metabolic cold adaptation [7], the Krogh effect [8], or metabolic compensation [9], temperature compensation refers to the maintenance of biological rates in the face of a temperature change [10–12]. Initially proposed on the basis of empirical evidence and the theoretical notion that rate maintenance, especially under low-temperature conditions, would result in maintenance of fitness [13–15], the idea has become controversial on both theoretical and empirical grounds. The controversy has been most prominent for metabolic rate conservation, with the theoretical counterargument being that because metabolic rate represents a cost (of maintenance) to an organism, conservation thereof, in the face of an opportunity for reduction, should not be beneficial [11]. Empirical evidence, typically from measurements of standard or resting metabolic rates across a range of biological levels, has come out both in favour of and against temperature compensation [3,5,9,15–22].

One line of evidence that has been especially effective in questioning the temperature compensation hypothesis is the discovery and description of a thermodynamic effect [23–25]. Sometimes also known as the ‘warmer is better’ hypothesis, the idea encompasses both sound theoretical reasons and evidence for a relationship between the optimum temperature of a process and the maximal rate of that process (figure 1). In other words, because rates proceed faster at higher ambient, and therefore by association for many ectotherms, higher organismal temperatures, fitness should always be higher at higher temperatures, acknowledging that upper thermal limits to performance exist for all organisms [26,27]. The strongest evidence for the thermodynamic effect comes from population growth rates in insects, with suggestions that it applies to performance traits in ectotherms generally [28–30]. Across the 65 insect species examined by Frazier et al. [28], the thermodynamic effect was found to be even stronger than predicted by theory [31], suggesting that relatively warm environments have the highest fitness benefits for organisms. In turn, these findings have also been used to explain the slow life histories of polar organisms [21].

Figure 1.

Conceptual figure showing expected relationships under either the temperature compensation or thermodynamic effect hypotheses. The relative performance of a given trait (a) is expected to increase with temperature until peak performance (U_max) is achieved at the optimum temperature (T_opt), after which performance declines (solid black line). In colder climates, the temperature compensation hypothesis predicts that the relationship between relative performance and temperature will shift such that U_max occurs at a lower T_opt, but remains equal to that observed in warmer climates if full compensation is achieved (solid grey line). Alternatively, the thermodynamic effect hypothesis predicts that in colder climates U_max will not only occur at a lower T_opt, but will also be lower than that observed in warmer climates (dashed grey line). Panels below show the expected relationships between (b) environmental temperature (T_env) and T_opt, (c) T_env and U_max, (d) T_opt and U_max, respectively, under the temperature compensation (solid lines) and thermodynamic effect (dashed lines) hypotheses. Both hypotheses predict a positive correlation between T_env and T_opt (b). However, the temperature compensation hypothesis predicts that U_max will be independent of T_env while a positive relationship is expected under the thermodynamic effect hypothesis (c). Likewise, U_max is expected to be independent of T_opt under temperature compensation, while the thermodynamic effect hypothesis predicts a positive relationship (d).

Despite this evidence for a thermodynamic effect, several studies continue to find empirical support for temperature compensation. For example, in plants, much evidence has been found for the maintenance of respiration rate across a broad range of temperatures [5–6,9]. In other groups, contrasting empirical outcomes continue to be published [22,32], with little indication of a developing consensus [8,21]. In consequence, despite the existence of the idea of temperature compensation for a century [13], and strong theoretical and empirical bases for the thermodynamic effect [31,33], how these contrasting ideas are related, and which might provide the strongest explanation for the evolution of biological rates in response to temperature variation across the globe remains at best unclear. Moreover, explanations also seem to differ in their support across different groups of organisms and from different environments [11], and often with little comparison among taxa (compare e.g. [17,21,34]), though with notable exceptions [9,35]. Yet at the same time, the expectations from these competing hypotheses are variously being used as the basis to understand diversity variation globally [36] and the extent to which changes in this diversity might occur as a consequence of anthropogenic warming [37,38].

Here, we seek to resolve these long-standing and important [11] contrasting ideas by examining optimum temperature and rates at those optima for a suite of biological functions across much of life's ectotherm diversity and at a global scale. Rather than treating major taxa and organisms from terrestrial and aquatic habitats separately, we use phylogenetic mixed models to investigate the extent to which both habitat and phylogenetic signal influence the relationships between optimum temperature and rates of biological functions at that temperature, and subsequently the ways in which both optimum temperature and maximum rates vary with temperature across the planet. We focus on locomotion speed as well as rates of development, growth, and photosynthesis, which are expected to be correlated with fitness [28], but we avoid investigation of metabolic rates (or respiration rate for plants, e.g. [9]). We do so because few animal ectotherm metabolic rate investigations provide measured values for maximal rates and the temperatures thereof (U_max and T_opt in the terminology of Gilchrist [39]).

Our analysis uses information from 619 observations, spanning 14 phyla, 75 orders, 300 genera, and 403 species. By contrast with previous comprehensive analyses of the slope of the relationship between rate and temperature (e.g. [35]), we are concerned here with optimum rates (U_max) and the temperatures at which they occur (T_opt). We test explicitly three predictions of the temperature compensation and thermodynamic effect hypotheses. First, if either of these hypotheses holds, a positive relationship between T_opt and a measure of environmental temperature (T_env) during the maximal activity period of the organism should be found (figure 1), assuming that some form of thermal adaptation (or coadaptation) is typical of ectotherms [40–42]. The absence of a relationship might indicate some form of performance constraint [43]. Second, the relationship between U_max and T_env should be positive in the case of the predominance of a thermodynamic effect, but absent or weak in the case of temperature compensation [42,44]. We note that in making this prediction we are assuming T_env and body temperature (T_b) are largely equivalent because the original thermodynamic effects hypotheses are explicit about body temperature, though they frequently do not actually measure it, but assume it from T_env [28,30]. We have done the same, but also seek to explore the impact of so doing. Third, U_max and T_opt should be positively related in the case of a pronounced thermodynamic effect, but weak or absent where temperature compensation predominates [28]. More specifically, when U_max is plotted against the inverse of optimum body temperature, the thermodynamic effect hypothesis suggests that the slope of the line should provide an estimate of activation energy of 0.6–0.7 eV or perhaps steeper [23,28,31].

2. Methods

We compiled data from the published literature on optimal temperature and maximal performance (T_opt and U_max (sensu [39])) for whole organismal traits expected to be closely related to fitness including rates of photosynthesis, growth, development, and locomotion speed. Many published studies are available for these traits, making it possible for the database to cover the majority of the world and a diverse range of taxonomic groups and habitats to gain general insight. In additional to original papers, recent compilations of data and their reference lists were also searched [28,30,34,45–48]. The search ended on 1 January 2016. Performance curves where maximal performance was only estimated by models were not included [49]. We only accepted records where measured estimates of performance were undertaken beyond the measured maximal performance (i.e. T_opt and U_max). For development rates, these included high temperatures leading to no development as data points above maximal performance. We included the full taxonomy of all organisms as given by the primary publication, and adjusted for synonymy where appropriate based on online repositories (such as www.algaebase.org or www.gbif.org). The analyses were done according to the species lists as generated by the online tree of life [50]. The geographical origin of the investigated population of each species (and for each trait where the locations differed among traits) was taken from the primary literature whenever possible. When the origin of an investigated population was not available from primary literature, the origin was estimated using data from the Global Biodiversity Information Facility (GBIF). Median latitude and longitude was extracted from GBIF occurrence records using the ‘rgbif’ [51] and ‘spocc’ [52] packages in R [53] and used for that species. In cases where GBIF records were lacking the origin was estimated from other sources (described for each record in the database; [54]). For locomotion speed, we included ln-transformed body length as a covariate, and for developmental rates, we included ln-transformed dry mass as a covariate because of significant allometry of these traits (see Results). Snout–vent length (for reptiles and anurans) and body length (for fish and invertebrates) were obtained from the original literature or estimated from other sources when not available (described for each record in the database; [54]). The locomotion speed was further assigned to whether the measure represented sustained or sprint locomotion speed, and whether the measure represented aquatic (swimming) or terrestrial (running) speeds. Dry mass estimates were sourced from the original literature when given or inferred from length or fresh mass measured available using specific relationships given by Hodar [55] and Ganihar [56]. In all cases, the sources and relationships used to generate dry mass estimates are given in the database.

Data were analysed using phylogenetic mixed models [57–59], which were implemented in the ‘ASReml-R’ v. 3.0 [60] package of R v. 3.0.2 [61], with inverse relatedness matrices calculated from phylogenetic covariance matrices using the ‘MCMCglmm’ package v. 2.21 [62]. The phylogeny used for analysis was drawn from a comprehensive tree of life, accessed using the ‘rotl’ v 0.5 package of R v. 3.2.2 [50,63]. In addition to the 619 observations that were analysed, a further 319 records for 80 species were excluded from the analysis; some of these could not be matched to the online tree of life, and so were not considered further. Six extremely high maximum rates for the growth of Actinobacteria from the Luna-2 cluster [64] and one extremely high growth rate for Chlorella pyrenoidosa [65] exerted high leverage on the data and were excluded on these grounds. The remaining data were excluded because they could not be matched to climate data (see below) or because the data were presented in units that could not be reasonably converted to match the majority of the remaining data.

Environmental temperature (T_env) at the site of geographical origin (see above) for each record was calculated as the mean temperature of the warmest quarter using monthly (January 2001–December 2016) daytime data from the MODIS Land Surface Temperature dataset (MOD11C3 v6; doi:10.5067/MODIS/MOD11C3.006; 0.05° spatial resolution). Seasonality at each site was calculated as the difference between the mean temperature of the warmest quarter and the mean temperature of the coldest quarter, also calculated from the MODIS Land Surface Temperature dataset. For freshwater and coastal marine locations, monthly MODIS data were assumed to be indicative environmental temperatures of the aquatic environment. The spatial resolution of MODIS meant that most aquatic sites were covered by these data. Where aquatic sites were not directly covered by MODIS observations, the nearest valid data point within 1 km was used. Aquatic sites greater than 1 km away from a valid MODIS data point were excluded from analyses (listed as NAs for MODIS data columns in the database; [54]). These data were downloaded and analysed using the ‘MODIS’ [66], ‘raster’ [67], and ‘xts’ [68] packages in R [51].

Phylogenetic mixed models were selected over the more commonly used methods of independent contrasts [69] and phylogenetic generalized least squares [70] because the former can formally incorporate non-independence associated with phylogenetic relatedness as well as non-independence associated with multiple measurements of single species. Multiple measurements were relatively uncommon in the datasets for locomotion speed, growth, and development, where 73%, 88%, and 91% of species were represented by only one measurement, respectively, though a small number of species were represented by many measurements (up to 10 measurements per species for locomotion speed, up to 14 measurements per species for growth, and up to five measurements per species for development). Multiple measurements are more common in the data for photosynthesis, where 33% of species have one measurement, 49% of species have two measurements, and the remainder have three-to-eight measurements. Phylogenetic mixed models are an analogue of the animal model from quantitative genetics, which partitions phenotypes of related individuals into heritable (additive genetic) and non-heritable components to estimate interspecific variances and covariances between traits [59]. The significance of fixed effects was tested using Wald-type F-tests with conditional sums of squares and denominator degrees of freedom calculated according to Kenward & Roger [71]. Phylogenetic heritability, a measure of phylogenetic non-independence equivalent to Pagel's [72] λ, was estimated as the proportion of variance attributable to the random effect of phylogeny [59]. Approximate standard errors for the estimate of phylogenetic heritability were calculated using the R ‘pin’ function [73]. Seasonality was included as a fixed continuous covariate in all models because theory predicts that more seasonal environments might favour a ‘generalist’ phenotype, with a wider thermal performance breadth and lower U_max [74]; if such a specialist-generalist trade-off exists and is associated with seasonality, U_max is predicted to be inversely related to seasonality, such that seasonality might confound correlations with T_opt and T_env.

3. Results

We used phylogenetic mixed models to investigate the relationship between optimum temperature (T_opt) and environmental temperature (T_env), measured here as mean temperature of the warmest quarter (derived from the Moderate Resolution Imaging Spectroradiometer, MODIS, https://modis.gsfc.nasa.gov/) of the collection locality of the species concerned, while also accounting for temperature seasonality (see Methods). The results demonstrated a positive relationship, though with much variation, for development rate and locomotion speed, and no relationship between T_opt and T_env for growth rate and photosynthetic rate (figure 2 and electronic supplementary material, figure S1). Interaction terms (specifically between T_env and Order for development; between T_env and Phylum for growth; between T_env, Method (aquatic or terrestrial, sustained or sprint) and Phylum (and their two-way combinations) for locomotion speed; and between T_env and Class for photosynthesis) in these models were always non-significant. Thus, only models with additive combinations of main effects are presented. For all traits, a strong phylogenetic signal was detected as might be expected given the diversity of taxa and associated variation in traits among groups (Phylogenetic heritability λ = 0.82–0.98; electronic supplementary material, tables S1–S4).

Figure 2.

Relationship between mean temperature of the warmest quarter of the year (as a measure of T_env,°C) and the optimum temperature (T_opt,°C) for rates of development (d⁻¹) and growth (% d⁻¹), locomotion speed (cm s⁻¹), and rate of photosynthesis (µmol m⁻² s⁻¹), respectively. Solid lines depict significant relationships from phylogenetic mixed models testing for effects of T_env on T_opt (electronic supplementary material, tables S1–S4). Data are presented as values adjusted for the effects of random and fixed effects present in the models in electronic supplementary material, tables S1–S4; raw data are presented in electronic supplementary material, figure S1. (Online version in colour.)

In the case of the relationship between natural log-transformed maximal performance (U_max) and our measure of T_env, a significant relationship was only found for locomotion speed in models that considered no interaction terms (figure 3 and electronic supplementary material, figure S2); phylogenetic signal was strong (Phylogenetic heritability λ = 0.76–0.97; electronic supplementary material, tables S5–S8). Interaction terms were not significant for measures of development, locomotion, and photosynthesis, but there was an interaction between T_env and phylum for growth (F_8,164.5 = 4.90, p < 0.001); within the most well-represented phyla, there was a significant relationship between U_max and T_env for Chlorophyta (F_1,47.9 = 13.2, p < 0.001), but not for Arthropoda (F_1,70.3 = 2.75, p = 0.10) or Chordata (F_1,29.0 = 1.08, p = 0.31) (electronic supplementary material, figures S3 and S4).

Figure 3.

Relationship between mean temperature of the warmest quarter of the year (as a measure of T_env,°C) and the natural log-transformed maximum rate (U_max) for rates of development (d⁻¹) and growth (% d⁻¹), locomotion speed (cm s⁻¹) and rate of photosynthesis (µmol m⁻² s⁻¹). Statistical outcomes are provided in electronic supplementary material, tables S5–S8. Data are presented as values adjusted for the effects of random and fixed effects present in the models in tables S5–S8; raw data are presented in electronic supplementary material, figure S2. (Online version in colour.)

By contrast with these variable outcomes, a positive relationship between maximal performance (U_max) and optimal temperature (T_opt) was characteristic of all the traits examined. This was true in models that considered only the main effects without interaction terms: development rate, growth rate, locomotion speed, and photosynthetic rate (figure 4 and electronic supplementary material, figure S5, tables S9–S12). T_opt and Phylum showed significant interactions for growth rate (electronic supplementary material, table S13), as did T_opt and Phylum, and T_opt and Method for locomotion speed (electronic supplementary material, table S14). Data for growth rate were therefore further subdivided by Phylum (electronic supplementary material, figures S6 and S7), but there were locomotion speed data for too few species of arthropod to formally estimate model parameters for this Phylum alone. Significant positive relationships between U_max and T_opt characterized the subdivided datasets (electronic supplementary material table S15). When converted to activation energy, values ranged between 0.18 and 0.59 eV, with a mean of 0.36 ± 0.06 [s.e.] eV, which is significantly different from the value of 0.60 eV predicted from theory [28] (t₅ = −4.01, p = 0.01), and from 0.54 eV (t₅ = −3.00, p = 0.03), previously a minimum empirical value [23].

Figure 4.

The relationship between optimum temperature (T_opt,°C) and the natural log-transformed maximum rate (U_max) for rates of development (d⁻¹) and growth (% d⁻¹), locomotion speed (cm s⁻¹), and rate of photosynthesis (µmol m⁻² s⁻¹), respectively. Solid lines depict significant relationships from phylogenetic mixed models testing for significant effects of T_opt on U_max (electronic supplementary material, tables S9–S12). Data are presented as values adjusted for the effects of random and fixed effects present in the models in electronic supplementary material, tables S9–S12; raw data are presented in electronic supplementary material figure S5. (Online version in colour.)

4. Discussion

Understanding the nature of and potential limitations characterizing physiological and biochemical adaptation to temperature is a fundamental question in organismal biology [4,12,75]. Moreover, what form such adaptation might take, as reflected in the relationship between temperature and biological rates, has important implications for making general predictions about the responses of organisms to changing environments, including the influences of global climate change [6,20,37–38,42]. For example, if the thermodynamic effect predominates in the relationship between U_max and T_opt, rising temperatures would lead to an unexploited potential for increased performance because biochemical constraints are reduced. This might, in turn, prove largely beneficial for the fitness of ectotherms except perhaps in the tropics (though see [46]), assuming that ectotherms are not limited by energy availability or other costs of increased metabolism or by trade-offs with other life-history traits [76]. By contrast, if some form of compensation is more common, changing temperature regimes may have less of an effect on performance [9,11,38]. Thus, which of these major relationships between U_max and T_opt predominate is of both fundamental and applied significance.

Previous examinations of the relationship between U_max and T_opt have come out strongly in favour of the thermodynamic effect hypothesis [23,28–30], with activation energies either being within the predicted range of 0.6–0.7 eV [23], or larger, implying a stronger thermodynamic effect than theoretically predicted [28]. Based on a much larger suite of data, spanning a wide range of localities, habitats and taxa, and several key performance traits, we also find that the thermodynamic effect is generally supported for the relationship between U_max and T_opt. In contrast with previous investigations, however, we find this effect (on average an activation energy of 0.36 ± 0.06 eV) much weaker than proposed by theory or previously found empirically (i.e. 0.6–0.7 eV, or 0.54–0.97 eV) [23,28]. Thus, while a thermodynamic effect is general, it is not pronounced.

The difference between this finding and that of previous studies might owe in part to the inclusion of a specific plant performance trait, photosynthetic rate, in the current investigation. The activation energy value for this trait was one of the lowest of all of the significant values (0.23 eV); with the value for photosynthetic rate excluded, the mean activation energy increases only marginally to 0.39 ± 0.07 and is not significantly different from 0.54 (t₄ = −2.39, p = 0.08), but is significantly different from 0.60 (t₄ = −3.24, p = 0.03). This change does, however, point to a further explanation for the different outcomes between our study and others. The consideration of organisms from a wide variety of environments, which represent several life-history types and trophic groups is likely to mean much larger variation in the way U_max and T_opt are related, and how these traits are related to environmental temperature [11,35–36,42]. For example, owing to their restricted movement capability, plants may be expected to show a much greater level of thermal compensation than ectotherm animals, which can behaviourally select among a diversity of thermal microenvironments available to them in any given larger setting [4,77]. Indeed, temperature compensation of respiration rates in plants of several different groups is commonly found [5,9,20,78]. The same preponderance of compensation might be expected in aquatic versus non-aquatic groups, given the thermal inertia of aquatic environments [79]. In the one case where we were able to draw such an explicit contrast—for locomotion speed in aquatic versus non-aquatic chordates—there is a significant interaction between T_opt and Method (aquatic or terrestrial, sustained or sprint) in the full model (electronic supplementary material, table S14), and variation between groups is in the direction predicted: the relationship between U_max and T_opt for maximum locomotion speed for chordates is significant for the terrestrial data (F_1,75.7 = 13.5, p < 0.001), but not for the aquatic data (F_1,10.9 = 1.78, p = 0.21). Nonetheless, for metabolic rate variation, the reverse seems to be true, with compensation being less commonly found in aquatic marine groups than in terrestrial species [11–12].

There is a large variation in the degree of thermal compensation among organisms and traits [21]. This variation likely contributes to the variance observed in our analyses. Still, the relatively weak relationship between U_max and T_opt across traits does point to the fact that some form of thermal compensation is a general characteristic of the organisms we examined, in keeping with long-standing contentions about the importance thereof [10,13]. The typical absence of a relationship between U_max and T_env here also supports this contention, because the absence of a relationship is predicted by the hypothesis of temperature compensation [44]. For photosynthesis rate, the outcome is clearly in keeping with findings for plants, and in particular for respiration rate, where compensation is well documented [5–6,9,20]. For the other traits, and especially in animal ectotherms, the findings contrast with those from the broader thermal performance literature [4,30]. The variability around the T_env and T_opt relationship in the traits excluding photosynthesis is also perhaps surprising, although here positive relationships for development rate and for locomotion speed are in keeping with previous work [28]. Nonetheless, our results suggest that temperature compensation is more commonplace than previously estimated for animals.

Several caveats should be borne in mind, however. The thermodynamic effect hypothesis concerns the relationship between T_b and performance [28], and indeed one might interpret the compensation idea in a similar way. As is the case with previous studies [28–30], we did not measure T_b directly, but assumed it, acknowledging that for some organisms these may differ at some times [77]. Nonetheless, the typical absence of a Phylum effect or interactions with Phylum in the mixed models suggests that any effect on the outcome is likely small. Future studies should consider the likely role of behavioural thermoregulation. A trade-off between maximum population growth rate and thermal breadth (a specialist versus generalist trade-off) might also have led to a correlated decline of U_max in species from low-temperature environments [28]. This should result in a relationship between T_env and U_max, an outcome not supported by our data.

A mismatch between T_env and the peak characteristics of the performance curve—T_opt and U_max—might be also expected because such differences, especially between T_env and T_opt could be an adaptive response to environmental seasonality [42,74]. In this case, the difference between T_env and T_opt should be strongly related to a measure of environmental seasonality, with a potential difference between tropical and non-tropical organisms. We tested for such an effect of seasonality and found that the strength of the effect varied among traits and phyla, with significant relationships between seasonality and the difference between T_env and T_opt found only for locomotion speed and photosynthesis rate (electronic supplementary material, table S16 and figure S8). The latter accords well with the recent finding that terrestrial net primary production is better predicted by growing season length than by latitude or temperature [80]. Thus, some adaptive response to seasonality may be occurring in these traits and deserves further consideration.

We also calculated T_env as the mean temperature of the warmest quarter from the collection locality of the population investigated (see Methods). This may not fully represent the thermal environment typical of the organisms collected, though it is likely a better estimate of the temperature where most organisms are actively growing and developing than mean annual temperature [81]. Moreover, the estimate of environmental temperature used can have an effect on the form of the relationship between a trait and temperature [82]. The estimates of relationships between T_env and performance-related traits provided here differ, however, from those made for activation energy of traits in other studies (e.g. [35,36]). In those studies, the temperature dependence of the traits is estimated not from comparisons of T_opt or U_max across species from different environments, but rather from trait values at a given range of experimental temperatures leading up to and moving away from T_opt within a given species. Third, the current analysis does not adequately represent the polar regions. Whereas data on the relationship between U_max and T_opt for the traits we investigated are sparse for these regions, the question of compensation has been investigated using data on realized performance rates (e.g. field growth rates in marine invertebrates and swimming speeds in marine fish; reviewed by Peck et al. [21,83]). These studies suggest that performance is strongly constrained by temperature for most, but not all traits, at very low temperatures (around 0°C) [21]. While those studies are not directly comparable with the analyses presented here (which rely on U_max and T_opt rather than environmental temperature and performance at that temperature), we acknowledge that thermodynamic constraint might be elevated at low temperatures. Certainly, more comprehensive data from these regions, which stand out not only owing to low mean environmental temperatures, but also because some are extremely stable (especially Antarctic marine habitats) or variable (Arctic terrestrial habitats), are needed to promote better understanding of the way in which thermal adaptation takes place in these regions. Indeed, previous work focusing largely on temperature compensation in metabolic rate has drawn attention to the need not only to contrast these differing thermal habitats (e.g. [11,17]), but also to understand what the fitness costs and consequences might be of different strategies [11,21].

In conclusion, given these outcomes, it is clear that while some form of thermodynamic effect exists, ample scope is present for biochemical and physiological adaptation in the form of temperature compensation. Indeed, the overriding influence seems to be one of biochemical and physiological adaptation, at least for the traits examined here, so vindicating earlier views on the significance of such adaptation [10,13,75,84]. Much variation exists, however, within and among traits, and among taxa and environments. This variation stems likely both from biological variation among organisms and traits and from the difficulties inherent in the use of compiled data from studies that adopt a variety of experimental and analytical approaches [49,85]. Such variation would have to be considered when using these general relationships to forecast the broader implications of environmental change, as has become clear from related studies of the thermal dependence of performance-related traits [35,36]. To some extent, the variation seen may also explain the many contrary findings in the literature to date. In the case of assessments based on metabolic rate of animal ectotherms, which have often dominated the animal literature, much of the debate on the existence of compensation [5,11,15–19,21–22] might, however, be overcome by trait assessments which include the full performance curve providing empirical estimates of T_opt and U_max, as is done for plants (e.g. [9]), rather than just on the increasing side of the curve.

Data accessibility

The database used for the analyses presented here are available from the Dryad Digital Repository: doi:10.5061/dryad.56s5d84 [54].

Authors' contributions

J.G.S. and S.L.C. designed the study and collected the data from the literature. G.A.D. provided input to the design of the study, and prepared environmental data and the conceptual figure. C.R.W. performed the analyses and associated figures. J.G.S. and S.L.C. prepared the first draft of the manuscript, and all authors contributed to the final version.

Competing interests

The authors declare no competing interests.

Funding

Research funding for this project was provided by a Sapere Aude DFF-Starting grant from The Danish Council for Independent Research | Natural Sciences and a sabbatical grant from the Aarhus University Research Foundation (AUFF) to J.G.S. and by the Australian Research Council through ARC DP170101046 to S.L.C. and FT130101493 to C.R.W.