Comparing thermal performance curves across traits: how consistent are they?

Climate change is characterised by increasing mean temperatures and by an increase in the frequency and severity of extreme events (Easterling et al., 2000; Ummenhofer and Meehl, 2017). Surviving both rising mean temperatures and greater extremes will depend critically on the ability of organisms to maintain physiological processes by tracking their environment via phenotypic plasticity. The importance of plasticity in climate change responses will depend on several factors: whether induced changes in the phenotype are adaptive, the speed of climate change and the degree to which behavioural responses will reduce the need for plastic responses and selection on key traits (Caillon et al., 2014; Chevin et al., 2010; Huey et al., 2012; Kearney et al., 2009; Seebacher and Murray, 2007). Understanding how plasticity might impact performance in response to environmental change is central for developing a mechanistic framework for predicting species responses to climate change. A commonly used framework for doing so is the thermal performance curve (TPC) (Deutsch et al., 2008; Huey et al., 2009; Kingsolver, 2009; Overgaard et al., 2014; Vasseur et al., 2014).

The TPC describes the relationship between a trait and body temperature (T_b) (Angilletta, 2009). TPCs take on a common shape in ectotherms (Fig. S1) (Gilchrist, 1995; Huey and Stevenson, 1979) – an increasing phase reflecting biological rate processes and a declining phase describing the stressful effects of temperature on overall performance, the mechanisms of which remain uncertain (Kingsolver, 2009; Schulte et al., 2011). A number of elements/descriptors of the TPC are used to compare TPCs within and between species (Huey and Stevenson, 1979). These descriptors include maximum performance (P_max/U_max), optimum temperature (T_opt), performance breadth (T_br) and thermal limits (T_min and T_max). T_opt is the temperature of peak fitness or trait value; T_br is calculated as the temperature range where performance is above an arbitrary threshold (i.e. 80–90%) and describes thermal sensitivity; and thermal limits are the temperature at which fitness is 0 and are defined by T_min and T_max (Angilletta, 2009). The shape and position of the TPCs may change over time via evolution, or more rapidly through acclimation (Angilletta, 2009). These changes may include a horizontal shift with resultant changes in T_opt and thermal limits, a vertical shift with an increase or reduction in overall fitness (overall performance) and a width shift altering the viable thermal range, captured as performance breadth (Fig. S1) (Angilletta, 2009; Izem and Kingsolver, 2005; Sinclair et al., 2012).

TPCs are increasingly being integrated into models for understanding species responses to climate change (Deutsch et al., 2008; Hoffmann and Sgrò, 2011; Levy et al., 2015; Overgaard et al., 2014; Sinclair et al., 2016; Vasseur et al., 2014); however, such approaches make several assumptions that may contribute to uncertainty in the TPC and subsequent predictions of risk (Sinclair et al., 2016). In particular, studies that use single traits to estimate TPCs assume that traits do not vary in their thermal sensitivity, such that single-trait TPCs provide accurate predicators of thermal performance overall. Yet, work on snakes, caterpillars and Drosophila shows that different traits and even different life-stages can vary in their thermal sensitivity, producing different TPCs (David et al., 2005; Kingsolver and Woods, 1997; Stevenson et al., 1985; Woods and Harrison, 2002). An underlying assumption of TPCs is that the thermal sensitivity of the trait in question approximates the thermal sensitivity of fitness (Huey and Berrigan, 2001). However, the direct association between commonly measured traits and clearly defined fitness measurements, such as R_O and r (intrinsic rate of increase and net reproductive rate, respectively), is always assumed rather than quantified (Clusella-Trullas et al., 2010; Huey and Berrigan, 2001; Huey et al., 2012; Sinclair et al., 2016, 2012). More tractable traits are often favoured over direct estimates of fitness, because r and R_O can be labour intensive to measure and difficult to quantify across a range of temperatures (Huey et al., 2012). Although r and R_O are more representative of fitness, these different measures can also have different TPCs (Huey and Berrigan, 2001). Moreover, commonly used traits in assessments of TPCs are often taxon specific, including running speed in reptiles (Hertz et al., 1983; Miles, 2004; Phillips et al., 2014) and viability, fecundity and development time for insects (Clemson et al., 2016; Foray et al., 2011; Klepsatel et al., 2013). These traits may represent different components of fitness.

Another source of variation in TPCs is that different traits inherently capture effects of temperature at different stages of development. For instance, many studies of TPCs focus on the short-term effects of temperature exposure (minutes to hours) on adults, typically assessing responses to hardening and adult acclimation treatments on traits such as rate of locomotion and metabolism (Deere and Chown, 2006; Logan et al., 2014; Overgaard et al., 2014). In contrast, traits such as development time and growth rate, which are measured across life-stages, typically involve longer time scales of exposure (days to months) and may reflect the combined effects of developmental and adult acclimation (Kingsolver and Woods, 1997; Klepsatel et al., 2013). The timing (life-stage) and duration (hardening versus developmental acclimation) of the temperature exposure may have profound effects on trait variation and thermal sensitivity. For example, in Manduca sexta, TPCs differed depending on whether growth rates were measured in the first 24 h (short time scale) or as the duration of the larval period (long time scale) (Kingsolver and Woods, 1997). Other studies assess thermal performance by measuring acute thermal tolerance, i.e. estimates of critical thermal minimum and maximum (CT_min and CT_max) calculated from survival or righting of response assays, while T_opt can be estimated from thermal preference assays (Clusella-Trullas et al., 2011; Huey et al., 2009; Kingsolver and Buckley, 2017). Whether estimates of thermal tolerance are useful proxies for full TPCs remains unclear (Haupt et al., 2017; Huey et al., 2012; Overgaard et al., 2014), but studies in Drosophila suggest this might not be the case (Overgaard et al., 2014).

An added layer of complexity is the effect of previous thermal history on estimates of TPCs. Performance is a product not only of the current environment but also of previously experienced environments (Kellermann et al., 2017; Kingsolver et al., 2006; Kingsolver and Buckley, 2017; Tronick and Hunter, 2016). This means that TPCs from wild-caught individuals will largely be a product of their thermal history, rather than a reflection of responses to current conditions. That is, thermal performance of individuals from the field will be influenced not only by the temperatures they experience but also by the thermal regimes of their parents. Maternal and paternal effects are widely known to influence thermal performance in Drosophila (Gilchrist and Huey, 2001).

In the current study, we aimed to determine the extent to which TPCs depend on the time scale of exposure and traits measured to gain a better understanding of the uncertainty that surrounds predictions of risk when those predictions are based on TPCs. We examined whether different traits measured at different time scales of temperature exposure produce comparable TPCs. Using a single population of D. melanogaster, we estimated thermal performance over long time scales (after development at six temperatures: 16, 18, 20, 25, 28 and 30°C) and short time scales (adult test environment consisting of three temperatures: 16, 25 and 30°C) of exposure for metabolic rate and activity. To further explore how traits vary in their thermal response, we also compiled previously published estimates of thermal performance (viability and fecundity) in D. melanogaster. All traits were assessed using a common garden design, therefore controlling for the effects of thermal history on the estimated TPCs.

Thirty field inseminated Drosophila melanogaster Meigen females were collected from Melbourne, Australia (37.8136°S, 144.9631°E) in 2014, using banana baits, and were maintained in the laboratory as separate iso-female lines for two generations. A mass-bred population was then established by pooling 10 virgin females and males from each iso-female line (totalling 600 flies per population), split into two 250 ml bottles containing potato–dextrose–agar medium. For each successive generation, each mass-bred population was maintained at 25°C under a 12 h:12 h light:dark cycle at a census population size of approximately 1000 individuals across three 250 ml bottles containing potato–dextrose–agar medium. Flies were placed onto fresh food every 2 days to minimise larval crowding, with emerging adults for consecutive generations taken from parental flies that were between 3 and 7 days old. Standard metabolic rate (SMR) and activity were estimated following 7–9 generations of mass breeding.

Developmental acclimation effects on SMR and activity were examined by developing eggs to adulthood under six different constant temperature regimes: 16, 18, 20, 25, 28 and 30°C. Developmental density was controlled by picking 40 eggs into 20 vials per temperature. As developmental time varies across different thermal regimes (development time for the thermal regimes in days: 16°C: 20 days, 18°C: 16 days, 22°C: 11 days, 25°C: 9 days, 28/30°C: 8 days), egg picking was staggered so that adult flies would eclose from the different temperature regimes on the same day. Flies were collected over a 2 day period and the sexes separated using CO₂ anaesthesia 2–3 days post-eclosion. Flies were then given 2 days to recover post-CO₂ exposure (MacMillan et al., 2017), and were 5–8 days of age at the time of assessment of SMR and activity.

We compared how a short temperature exposure at the adult life stage may influence the estimation of descriptors of the TPC for SMR and activity as opposed to long temperature exposure throughout development. We assayed the SMR and activity of adult flies at two extreme and one benign test temperature (16, 25 and 30°C). These temperatures were chosen such that they overlapped with the range of temperatures used during development. Prior to estimation of SMR and activity, flies were acclimated at the respective test temperatures for 30 min to allow them to settle and to obtain a more accurate estimation of SMR (Messamah et al., 2017).

Given it reflects the physiological and biochemical performance underpinning key traits, SMR is one of several relevant components of thermal adaptation. SMR was estimated on female flies only. For each test temperature, two rounds of assessment were performed across 3 days. Consequently, for each test temperature, two rounds of egg picking (1 week apart) were performed to minimise age differences of the focal flies (Lane et al., 2014; Terblanche et al., 2004). On each of the 3 days, two runs were performed in the morning and the afternoon (time of experiment in analyses), always at the same time to limit the effects of circadian rhythm on estimates of SMR. We utilised a blocked experimental design with developmental acclimation equally represented across all blocks (two runs per day across 3 days). For each run, 4–5 replicate individuals from each developmental temperature were assessed with a total of 52–59 individuals assessed per developmental temperature. Because of constraints in changing the temperature, test temperature could not be randomised across the three blocks, thus each block represents a different test temperature; as such, we were unable to examine an interaction between developmental and test temperature using the current design. Throughout the estimation of SMR, the activity of flies was estimated using the Drosophila Activity Monitor (DAM2, TriKinetics, Waltham, MA, USA) system, described in detail below.

Carbon dioxide production (V̇_CO2) was measured as a proxy for resting metabolic rate. This was done using four LI-COR 7000 infrared CO₂/H₂O gas analysers (LICOR, Lincoln, NB, USA), each attached to a Sable Systems International (SSI, Las Vegas, NV, USA) multiplexer system.

Two identical set-ups were created, each accommodating two LI-COR 7000 analysers. For each set-up, compressed air was directed through Bev-A-Line tubing to three scrubber columns which scrubbed the airstream of CO₂ and water vapour, ensuring a dry, CO₂-free airflow. The airstream was then split using a PVC T-split and the flow rate set to 25 ml min⁻¹ using a Sierra 840 series mass flow valve controlled by an MFC-2 (SSI) mass flow controller, which was then directed to the LI-COR 7000, where an initial CO₂ measurement was taken. It was then directed into an MUX2 intelligent multiplexer (SSI), which housed the animals, and then back to the LI-COR 7000, where a second CO₂ reading was taken; the difference between these two measurements was taken as the V̇_CO2 reading.

Each MUX2 housed eight, 1 ml chambers (Trikinetics). Seven chambers contained a single D. melanogaster while the eighth chamber was empty and served as a baseline to account for machine drift throughout the experiment. Each of the eight chambers was placed into a DAM2 to allow for the simultaneous estimation of activity during the experiment. The MUX2 was interfaced with a computer using a UI-2 universal interface (SSI), and was programmed to sequentially measure each chamber using the software Expedata (SSI). Each chamber was measured 3 times for 5 min, with a 2 min pause period between every measurement to allow time for the CO₂ readings to stabilise. To reduce potential detrimental effects of desiccation, the chambers were flushed with a humidified air flow (above 90% relative humidity) between measurements. This was achieved using a second compressed gas flow, which was again scrubbed of CO₂ and H₂O vapour and directed to a Sierra 840 series mass flow valve controlled by an MFC-2 mass flow controller, setting the flow to 25 ml min⁻¹. This air flow was then bubbled through a weak sodium hydroxide solution and directed to the flush input of the MUX2.

The mass of each individual was recorded at the end of each trial using a Metter-Toledo XP2U microbalance (Metter Toledo, Greifensee, Switzerland). Mass was recorded in milligrams to the nearest 0.1 µg. The experiments were performed in controlled temperature rooms set at 16, 25 and 30°C and the temperature monitored via a type-K thermocouple (Omega Engineering Inc., Stamford, CT, USA) attached to a TC-2000 thermocouple meter (SSI).

Data were extracted using Expedata and baseline corrected. SMR was estimated by inserting markers over the lowest 30 s of each of the three 5 min V̇_CO2 recordings, and the values extracted using a macro. The mean of these values served as the measure of V̇_CO2 for each individual. At each marker (as above) the activity of the individuals was extracted from the DAM2 recordings and averaged. These data served as a measure of metabolic activity in further analysis.

Activity was measured in two separate experiments. Firstly, it was estimated simultaneously with SMR measurements (described above) and used to account for activity effects in estimates of SMR. In a separate experiment, activity was estimated across the same developmental and test temperatures as described for SMR but was done so in a randomised design such that all developmental and test temperatures were tested in the same runs. Activity in this second experiment was estimated on 10 female flies per developmental and assay temperature, using the DAM2 system. Each monitor can record the activity of 25 chambers (5 mm diameter×45 mm length), where activity is recorded as the number of times a fly crosses a laser beam at the centre of the chamber. We used locomotor activity as a measure of performance as it has been linked to fitness in Drosophila melanogaster but is also thought to be linked to reproductive success, dispersal and predator avoidance, and is strongly correlated with walking speed (Burnet et al., 1988; Gilchrist, 1996; Latimer et al., 2011; Long and Rice, 2007; Roberts et al., 2003). Activity was estimated across 2 days with two runs performed at 09:00 h and 13:00 h each day. At each assay temperature, for each run, five replicates per developmental temperature were assessed using two DAM2 activity monitors with replicates randomly assigned to each position within the DAM2 monitor.

We searched the ISI Web of Science database to compare previously published estimates of TPCs in D. melanogaster with the current dataset. We used the search terms ‘thermal performance curve(s)+Drosophila’ and ‘thermal performance+Drosophila’. We only included studies where performance was estimated in more than three different acclimation treatments and where thermal history was controlled. We found eight published studies matching our criteria (Clemson et al., 2016; Cohet et al., 1980; Condon et al., 2014; Cooper et al., 2010; Klepsatel et al., 2013; Overgaard et al., 2014; Petavy et al., 2001; Schou et al., 2017). Of these, we were able to obtain the raw data for six studies (Clemson et al., 2016; Condon et al., 2014; Cooper et al., 2010; Klepsatel et al., 2013; Overgaard et al., 2014; Schou et al., 2017), while for two studies (Cohet et al., 1980; Petavy et al., 2001) data were extracted from figures with the program ImageJ. Through this program you can define the x- and y-axis of a scanned figure, which then allows the estimation of figure values. This involved scanning the image and defining the x- and y-axis. When egg-to-adult viability had been obtained as a percentage, we transformed the data into proportions using the number of eggs collected in the given study. Three studies examined TPCs in fecundity (Condon et al., 2014; Cooper et al., 2010; Klepsatel et al., 2013), another three examined TPCs in egg-to-adult viability (Cohet et al., 1980; Petavy et al., 2001; Schou et al., 2017), and two studies examined TPCs in both fecundity and egg-to-adult viability (Clemson et al., 2016; Overgaard et al., 2014). All experiments were performed on wild-caught strains that had been in the laboratory between 6 months and 4 years. Petavy et al. (2001) and Schou et al. (2017) were reared at 20°C; for all other studies, flies were reared at 25°C.

Studies examining TPCs for fecundity can examine the combined effects of developmental and adult acclimation (individuals developed and reared under the same temperatures: long time scales) or can focus on the effects of adult acclimation (individuals developed at a single temperature with fecundity estimated across a range of test temperatures: short time scales). Of the five studies that examined fecundity, two examined the effects of temperature across long time scales (Clemson et al., 2016; Klepsatel et al., 2013), while three examined effects across short time scales (Condon et al., 2014; Cooper et al., 2010; Overgaard et al., 2014). A broader thermal range (11–36°C) was investigated in the published studies, except for that of Clemson et al. (2016), who investigated the same thermal range as the current study (16–30°C). For the Condon et al. (2014) dataset, only results from the lines exposed to selection at a constant 25°C, and from flies measured after development at 25°C were examined. For the Cooper et al. (2010) dataset, only results from lines measured across all temperatures including 36°C were examined (12 of 30 lines; the remaining 18 lines were not assessed at 36°C).

We examined the role of developmental and test temperatures on metabolic rate (SMR) using general linear mixed models with the R-package (v.3.3.2) lme4 v.1.1-15 (Bates et al., 2015; https://cran.r-project.org/web/packages/lme4/index.html). Because test temperature was not randomised across blocks, separate general linear mixed models were created for each test temperature (16, 25 and 30°C). The full models included the fixed effects of developmental temperature, activity and mass and all possible interactions among the three. The effect of developmental temperature was modelled as a quadratic as it was assumed to span both sides of T_opt, and scaled (mean=0 and s.d.=1) to avoid non-independence of the temperature and temperature-squared. Activity and mass were also scaled. Effects of the time of the experiment and experimental block were accounted for by including time as a random effect in the models. The experimental set-up for activity, estimated independently from SMR, was fully randomised, allowing for the construction of a single model including all test temperatures. As activity is count data, it was modelled using a generalised linear model (GLM) with a Poisson distribution and log link. Because of over-dispersion in the model, the standard errors were corrected using a quasi-GLM (Zuur et al., 2009). The full model for activity included developmental temperature (scaled) as a quadratic fixed effect, test temperature (scaled) as a linear fixed effect, as well as the interactions between the two fixed effects.

For both activity and metabolic rate, the full models (see above) were validated by a model comparison against the null model, containing only the random effects. As the full models were significant for both activity and metabolic rate, we proceeded to identify the minimal adequate model (Crawley, 2013). P-values were obtained by comparing the full model with a reduced model in which the highest order interaction term had been omitted. If a term was non-significant, it was omitted from the full model, which was then further reduced to evaluate the significance of another term and so forth. Model comparisons for activity were done using F-tests because of the use of a quasi-GLM, whereas for metabolism we used likelihood ratio tests. Visual inspection of model diagnostic plots showed that the assumptions of parametric analyses were fulfilled in all models.

To make the analyses for the published datasets comparable to the above analysis, we used the same analytical framework. For all studies, we initially modelled temperature (scaled) as a quadratic effect, but visual inspection revealed a poor fit of the model for the fecundity data, except for those of Overgaard et al. (2014), and we therefore used a cubic smoothing spline (Wood, 2004). These models were then used to infer descriptors of the TPCs (see below). For model fits, see Fig. S2.

For each published study, slightly different analytical methods were used that best fitted each dataset. Fecundity data from Overgaard et al. (2014), Cooper et al. (2010), Klepsatel et al. (2013) and Clemson et al. (2016) were modelled with a generalised additive model (gam) using a cubic smoothing spline to model the effect of temperature. The Condon et al. (2014) fecundity dataset was modelled using a gam with a negative binomial distribution and cubic smoothing spline to model the effect of temperature. For Condon et al. (2014), Cooper et al. (2010) and Klepsatel et al. (2013), the variation across temperature between different replicate lines was modelled as random intercepts and slopes. All models including a smoothing spline were constructed using the R-package ‘MGVC’ v.1.8-23 (Wood, 2004), and with the number of knots set to the number of assessed temperatures and smoothing optimisation by REML.

Egg-to-adult viability (Clemson et al., 2016) was modelled using a logistic regression with developmental temperature as a quadratic effect, a typically observed shape for viability (Cohet and David, 1978). No over-dispersion was detected in the model. However, in the egg-to-adult viability data from Schou et al. (2017), Cohet et al. (1980), Overgaard et al. (2014) and Petavy et al. (2001), over-dispersion was detected when modelled with a logistic regression, with developmental temperature as a quadratic effect; consequently, we added an observation level random effect. The Cohet et al. (1980) egg-to-adult viability data contained different populations and we therefore included random slopes and intercepts for the replicate populations to account for any population-level differences in trait responses.

Optimum temperature (T_opt), thermal tolerance (T_min and T_max) and thermal breadth (T_br) were extracted from the models described above. Because we compared TPCs across studies that used very different methods, we did not attempt to compare maximal performance (P_max/U_max), which is likely to be highly confounded by experimental protocol and rearing conditions. T_br was calculated as the temperature range where performance was above an 80% threshold (Huey et al., 2012; Huey and Stevenson, 1979). T_br has classically been used as a measure of specialisation, i.e. a narrow T_br is indicative of a specialist phenotype while a broad T_br suggests a generalist phenotype (Angilletta, 2009), and as such T_br can be used as a measure of the flatness of the TPC. As activity and viability represent count data, the correct model choice (see above) results in the model fit approaching zero via an asymptote. This gives an estimation of T_min and T_max at zero a limited biological meaning; consequently, we calculated T_min and T_max as the temperatures at which performance was 5% of maximum performance (see Fig. S1); to make it comparable across traits, we did this for all traits. To estimate confidence in the TPC descriptors and to be able to compare the descriptors across traits and studies, we generated 95% confidence intervals (CIs) via non-parametric/parametric bootstrapping, essentially generating 10,000 curves and estimating the descriptors from each curve. Because several types of models were implemented (described above), it was necessary to use different bootstrapping approaches. For datasets where cubic spline models and quasi-Poisson models were the most appropriate models, we used non-parametric bootstrap (n=10,000) to estimate 95% CI. When multiple independent populations/lines were present in the model, a descriptor was estimated for each population/line and then averaged across populations/line in every sampling round of the non-parametric bootstrap; 95% CIs were then estimated from these averages. For datasets utilising linear models, parametric bootstraps (n=10,000) of the minimal adequate models using the function boot in the R-package boot v.1.3-20 were employed (https://cran.r-project.org/package=boot). For datasets modelled with linear mixed models, we estimated the 95% CI by parametric bootstraps (n=10,000) of the minimal adequate models using the function bootMer in lme4 (Bates et al., 2015). The random effects were also bootstrapped (use.u=FALSE). As the effect of developmental temperature on SMR was dependent on mass and activity, we report descriptor estimates and CIs at the median mass and activity.

Because the developmental thermal regimes investigated did not encompass the entire performance curve for some traits (SMR in the current study and two published studies of viability: Clemson et al., 2016; Schou et al., 2017), we were unable to estimate with confidence T_min and T_max for these traits; therefore, we refrained from including these in our comparisons.

For activity, measured independently from SMR, there was no interaction between test temperature and developmental temperature and thus different test temperatures produced comparable developmental temperature TPCs; as such, tests temperatures were combined to give one value for T_opt, T_min, T_max and T_br.

The effect of developmental temperature on metabolic rate was fairly consistent and significant across the three test temperatures; metabolic rate was reduced at the cooler and hotter developmental temperatures (Table 1, Fig. 1). Increasing test temperature (16, 25, 30°C) increased metabolic rate, with test temperature having larger effects on metabolic rate than developmental temperature (Fig. 1). T_opt and T_br were higher at a test temperature of 25°C than at test temperatures of 16 and 30°C, but significantly so only for T_opt (see 95% CI in Table S1). The experimental design did not allow examination of the interaction between test and developmental temperature because test temperature was not randomised across all blocks.

For all three test temperatures, body mass had a significant effect on SMR (Table 1), such that larger flies tended to have a higher SMR. The effect of activity on SMR was significant for the 16°C test temperature, with more active flies showing a higher SMR. Activity did not have a significant effect on SMR at the test temperature of 25°C, but at 30°C there was a negative effect of activity on SMR via a significant interaction with body mass. Body mass tended to be larger at the cooler developmental temperatures and decreased with increasing developmental temperature, while activity was lower at the coldest and hottest temperatures. A significant body mass×temperature interaction was also detected when metabolic rate was measured at test temperatures of 25 and 30°C. Because estimates of wet mass were calculated after estimation of metabolic rate was completed, flies at the test temperature of 30°C were likely to have lost more water (and therefore have reduced wet mass) than flies at other test temperatures, and this is likely to have driven the size×temperature interaction observed at this temperature.

Developmental temperature had a significant effect on activity, assessed independently from SMR, with activity displaying a classic TPC shape: increasing activity with increasing temperature at low temperatures and declining activity at hotter temperatures (Table 2, Fig. 1). Developmental temperature tended to have a larger effect on activity than test temperature, with absolute differences in activity across the developmental temperatures ranging from 29.55 to 55.15 (activity measured as the number of times a fly crosses a laser beam at the centre of the chamber, averaged over 3 h). While activity significantly increased with test temperature, we found no significant interaction between test temperature and developmental temperature. Thus, while activity increased with test temperature, reflected in a vertical shift in the TPC, the width (i.e. breadth) and horizontal position of the curve did not change. Because the shape of the developmental temperature TPC did not change across test temperatures, further dissection of the activity TPC descriptors was performed on a single curve, combining test temperatures.

Across all traits and studies, thermal optima (T_opt) differed by up to 6.7°C, ranging from 21.47 to 28.21°C (Fig. 2; Table S1). Within viability and fecundity, irrespective of the timing of the temperature exposure (short versus long time scales), T_opt varied between 1.1 and 2.4°C across studies. In contrast, T_opt for SMR varied by up to 4°C across test temperatures (short time scale). The highest values of T_opt were found for fecundity (28.21°C), which was significantly higher than T_opt for egg-to-adult viability (Table S1: 95% CIs did not overlap). Developmental TPCs for SMR estimated at test temperatures 16 and 30°C produced qualitatively similar estimates of T_opt, while significantly higher estimates of T_opt were found for TPCs tested at 25°C (95% CIs did not overlap) (Table S1).

Across the different traits and studies, excluding traits with broad 95% CIs, thermal tolerance varied between 6.13 and 6.84°C for T_min and T_max, respectively (Table S1). Estimates of T_min and T_max were similar across studies for viability and for fecundity but only when looking within the same timing of the temperature exposure treatments (short versus long time scales). Fecundity produced higher estimates of T_min than did viability and activity but the 95% CIs overlapped when comparing trait groups (fecundity, activity and viability); having said that, 95% CIs did not overlap for some studies (Table S1). No significant differences in T_max were found between fecundity, activity and viability. However, the time scale at which fecundity was estimated produced qualitatively different estimates of T_max (Fig. 2; Table S1). Measurements of the TPC based on flies developed and acclimated at the same temperature (Clemson et al., 2016; Klepsatel et al., 2013) produced significantly lower estimates of T_max than measurements of fecundity based on adult acclimation alone (Condon et al., 2014; Cooper et al., 2010; Overgaard et al., 2014) (Table S1).

Across traits and studies, the average T_br was ∼12°C ranging from 5.60°C (fecundity) to 20.70°C (viability). Similar to the other descriptors, estimates of T_br were more consistent within traits across studies than between traits (Table S1; Fig. 2). In general, TPCs for fecundity were narrower than other traits, with the 95% CI for T_br not overlapping any other trait except activity. Viability showed the widest T_br and hence the flattest TPCs of all the traits, indicating that viability does not vary much across temperature.

TPCs are increasingly being used to bring a mechanistic approach to understanding species responses to climate change (Deutsch et al., 2008; Huey et al., 2009, 2012; Levy et al., 2015; Overgaard et al., 2014; Vasseur et al., 2014). The strength of the predictions from this approach will depend on the accuracy of the TPC descriptors used to parametrise the models. However, the relationship between performance and temperature may depend on the trait measured and the time scale at which measurements occur (minutes/hours versus days/months) (Kingsolver et al., 2015). Many traits are estimated at fewer than four temperatures and the degree to which reliable estimates of T_opt, T_br and thermal limits (T_max/T_min) can be made when obtained over so few temperatures is also unclear (Kingsolver et al., 2013; Murren et al., 2014). Using D. melanogaster, we examined TPCs for metabolic rate and activity, and collated previously published data on TPCs for fitness-related traits: fecundity and egg-to-adult viability. We show that variation in the descriptors of the TPC (T_opt, T_min, T_max and T_br) tend to be more consistent for the same trait across studies than between traits. We also show that the time scale at which traits are measured (short versus long time scales of exposure) can have large effects on estimates of T_max and T_br, descriptors often used in models of climate change responses.

TPCs varied across the traits examined and the time scales at which the traits were measured. Across all traits, the descriptors of the TPC varied considerably, with a tendency for fecundity to produce higher estimates of T_opt than the other traits. Within traits, measured at the same time scale, all descriptors varied less, suggesting a high level of repeatability of the TPC within traits across studies. Variation in the descriptors and shape of the TPCs could be suggestive of different types of selection acting on the different traits to produce narrow and wider TPCs. Of the traits examined, viability and metabolic rate produced broad TPCs suggestive of stabilising selection reducing trait variation to produce stable phenotypes across environments (Falconer and Mackay, 1997; Stearns et al., 1995). But differences in the shape and width of TPCs could also occur for mechanistic reasons. For example, wider TPCs for metabolic rate could represent differences in the cost of maintaining biological functions across different temperatures (Clarke, 1993). Yet, the similarity between the descriptors and the shape of the TPC for metabolic rate with other traits may also suggest that metabolic rate is under selection. Variation in TPCs across traits and time scales, particularly for fecundity, is suggestive of labile TPCs, although low within-trait variation could also be indicative of constraints.

Consistent with the idea that the time scale at which traits are measured will impact the shape of the TPC (Kingsolver and Buckley, 2017; Kingsolver and Woods, 2016), we found fecundity measured at longer time scales (developmental acclimation) produced broader curves and significantly lower estimates of T_max than fecundity measured at shorter time scales (adult acclimation). In addition, the TPC of metabolic rate measured at 25°C (short time scale) produced a significantly higher estimate of T_opt than the TPC of metabolic rate estimated at a test temperature 16 or 30°C. Not all traits were as sensitive to changes in test temperature as metabolic rate; while increasing test temperature (short-time scale) increased activity, there was no effect of test temperature on the actual shape and descriptors of the TPC for this trait. Differences in trait sensitivity to temperature changes are likely to reflect the underlying mechanisms and the speed at which a plastic response is induced (Schulte et al., 2011; Sgrò et al., 2016); in Drosophila, the induction of the heat shock response occurs within a matter of minutes (Telonis-Scott et al., 2013), while cold acclimation can take weeks and is highly dependent on temperature and the number of exposures (Marshall and Sinclair, 2012; Rako and Hoffmann, 2006; Slotsbo et al., 2016). Different traits also capture the effects of temperature exposure at different stages of development. Intrinsic rate of increase, for example, captures the effects of temperature across all life-stages, while traits such as viability, fecundity or running speed capture different aspects of developmental and adult responses to temperature. Thus, the trait-dependent nature of the effects of exposure will affect the TPCs and the conclusions that can be drawn.

The relevance of the descriptors of the TPCs, as predictors of climate change responses, measured at short- or long-time scales (adult versus developmental acclimation) may depend on how the effects of changes in the mean temperature and variation in climate will shape species fitness. Rapid responses, reflected in the ability of the TPC to change in response to short time scales of exposure, may be more important for coping with rapid temperature fluctuations. However, the relative importance of a rapid response may also depend on the frequency and duration of climate fluctuations (Hochachka and Somero, 2004). If fluctuations are relatively rare, then rapid responses may not be under strong selection, particularly if these responses are costly (Gabriel, 2006). Climatic fluctuations will vary across environments (Kingsolver and Buckely, 2017), meaning that rapid responses may be more important for species that experience regular climate fluctuations, such as species occupying mid-latitudes. For these species, rapid responses and TPCs measured over short time scales of exposure (hardening/adult acclimation) may capture the critical responses for responding to climate change. However, for low-latitude species that experience relatively stable environments, TPCs measured over long time scales of exposure (developmental acclimation) may be more important. It is also likely that responses to climate change will be dictated by a combination of responding to short and long time scales of exposure (hardening, adult and developmental acclimation) and the relative importance of these different components of plasticity will depend on the daily average temperatures and the frequency and duration of climatic fluctuations (Dillon et al., 2016; Marshall and Sinclair, 2012).

The ability to accurately estimate TPC descriptors will in part depend on the number and breadth of temperatures examined. Despite the use of six temperatures in the current study to examine TPCs, they did not span the full viable temperature range of Drosophila and resulted in large CIs for estimates of T_min and T_max for SMR, although our confidence in T_opt was high. This highlights the difficulty with obtaining accurate descriptors of TPCs, where the number and choice of temperature range will often trade-off with confidence in different descriptors of the TPC (Huey et al., 2012). In addition, a common problem with the estimation of TPCs is that model choice can have a large impact on estimation of the descriptors (Angilletta, 2006). In the current study, we chose to re-analyse all the data without consideration of how previous studies had analysed their data or the models they had used. Despite likely differences in these methods, we found that our estimates of T_opt (the most common descriptor) did not differ significantly from those reported (Clemson et al., 2016; Cohet et al., 1980; Klepsatel et al., 2013). Note that most of the studies did not explicitly measure the descriptors of the TPC, despite their discussions often centring on the TPC framework (Condon et al., 2014; Cooper et al., 2010; Overgaard et al., 2014; Petavy et al., 2001; Schou et al., 2017).

Here, we have attempted to capture some of the sources of uncertainty in TPCs within a species. There are, however, other factors that will contribute to variation in the TPC that are seldom captured. In particular, TPCs are mostly measured under constant temperature conditions, yet populations and species rarely experience stable temperatures in nature, and fluctuating temperatures have the potential to change many aspects of the TPC (Colinet et al., 2015; Kingsolver et al., 2004; Niehaus et al., 2012). Whether fluctuating temperatures will have a large impact on the shape or position of the TPC is not that clear. Klepsatel et al. (2013) produced similar estimates for fecundity T_opt to those of the current study using ecologically realistic fluctuating thermal regimes. Plasticity for heat resistance (measured as acute dynamic T_max, not T_max from a TPC) also did not differ when measured on flies developed under fluctuating versus constant environments (van Heerwaarden et al., 2016). However, constant-temperature TPCs were poor predictors of fitness in marsh frogs, suggesting the need to incorporate fluctuating temperatures into estimates of the TPC (Niehaus et al., 2012). Previous thermal history (the environments experienced by individuals which may be unknown if individuals are collected from the field prior to assessments) may also drive variation in the TPC. Specifically, developmental temperatures can affect all aspects of fitness and thermal tolerance (Chown and Terblanche, 2007; Kingsolver et al., 2015; van Heerwaarden et al., 2016) and their effects are unlikely to be reversed by extended periods of laboratory acclimation (Kellermann et al., 2017). The extent to which TPCs vary across populations also remains poorly understood, although Klepsatel et al. (2013) found little variation in T_opt across broadly distributed Drosophila populations, suggesting there may be little inter-population variation in TPCs. Finally, biotic interactions, such as predation and competition, will also contribute to variation in the TPC (Davis et al., 1998; Luhring and DeLong, 2016). However, the degree to which biotic interactions will alter thermal preferences in nature remains poorly understood.

TPCs have their advantages but also their disadvantages (Kingsolver and Buckley, 2017; Sinclair et al., 2016); their ease of use and interpretation means they have been employed in many streams of ecology and evolution and we can draw from historical datasets to examine variation in the TPC across species and environments (Deutsch et al., 2008). Other estimates of performance, such as acute thermal tolerance, may have the potential to provide better descriptors for thermal adaptation and species response to climate change (Overgaard et al., 2014). However, they are also unlikely to be a practical solution for many species where lethal assays of thermal limits are not feasible. Future studies should focus on the explicit consideration of the time scale of exposure, how different traits inherently reflect different time scales of exposure, i.e. viability versus activity, and how different traits will generate different TPCs. These sources of variation in the TPC will ultimately influence any predictions of species responses to climate change based on TPCs. Consideration of which traits are likely to be most important with respect to the time scale of environmental change itself, i.e. average temperatures versus extreme events, may be necessary for producing relevant predictors of species responses to climate change.

We are grateful to Fiona Beasley for technical assistance, and to the reviewers for their comments, which improved the manuscript.