Some considerations of measuring temperature sensitivity in thermal ecology

Abstract

Climate change is driving a need to understand how changing temperatures affect organism physiology, including whole-organism metabolic rate. This process is sometimes quantified using Q10 values, or temperature coefficients. Although intuitive at first glance, Q10 values are limited to measuring effects at two temperatures, must be assessed with similar Q10 values across related temperature ranges to be comparable, and treat temperature effects as piecemeal. I recommend thermal ecologists adopt alternative effect sizes, for example, “percent change” as described by Heine et al. (2019) or the Arrhenius equation, to more accurately estimate effects and their associated error across more than two temperatures to understand the continuous effects of temperature. Global annual temperature is increasing by approximately 0.08°C per decade since the late 19th century (NOAA National Centers for Environmental Information 2021). This climate change is capable of having direct, adverse impacts on the physiology of organisms through shifting geographical ranges, altering behavior, restricting food availability, and influencing organism phenology, among other effects (Pörtner and Farrell 2008; Seebacher et al. 2015). Researchers, therefore, are aiming to understand both if and how organisms can respond to such increasing temperatures through integrating multiple fields of study, as well as through the development of novel research methods (Bennett et al. 2019; Hof 2021). Not only is it important which methods we use in our research but also the rationale behind our choices, provided some methods offer more accurate or useful information than others. Under Arrhenius law, the rate of chemical reactions is known to increase with temperature (Laidler 1984), including the physiological rates of organisms. Our ability to quantify the relationship between temperature and biological rates directly impacts the ability of researchers to understand how organisms can adapt to environmental change. This is due to the fact that critical physiological processes, such as oxidative phosphorylation within mitochondria (Mitchell 1961), are influenced by temperature. Therefore, if we can accurately measure how changing temperatures impact physiological rates, we can better understand—and possibly predict—how temperature influences organism maintenance, survival, and reproduction. As an alternative to the Q10 value, Heine et al. (2019) developed the “percent change” effect size and associated error estimate (Box 1). This approach utilizes the rate of change, or β1 value, obtained from the exponential and log-linear functions spanning more than two temperatures and estimates the percentage that biological rates (e.g., respiration) change per one degree change in temperature. Percent change is an improvement over Q10 values provided it incorporates more than two data points into the effect size, estimates the associated error, and does not extrapolate beyond what is measured. See Heine et al. (2019) for estimating the variance using means when replicates are measured at each temperature. Although the Q10 value adjusts the estimate across 10°C, the temperature dependence of respiration (β value) may or may not be estimated across a minimum of 10°C (see Comparisons to other Q10 values). This is not to say that we cannot estimate an average Q10 value, nor that we cannot estimate the associated error. However, doing so undermines the original pairwise Q10 estimates, each of which often provides a different rate of change across 10°C when error exists in data collection. Using pairwise Q10 values under such circumstances can be misleading, especially when data do not span 10°C and data are intentionally omitted to estimate pairwise effects (e.g., Nie et al. 2017; Lee et al. 2023). In this essay, I begin by outlining why thermal ecology has begun moving away from Q10 values (and why researchers should do so if they have not). Next, I present percent change as an alternative metric to estimate the temperature dependence of exponential rates across more than two temperatures, along with the associated error. I then present how the Boltzmann–Arrhenius principle can be used to estimate whole-animal metabolic rate under the metabolic theory of ecology. I end with brief, concluding remarks for future research. Although Q10 values extrapolate to 10°C, only considering two temperatures is less reliable, and less accurate, than accounting for more than two temperatures. A hypothetical scenario in Fig. 2 shows respiration measured at three temperatures, but the effect is quantified with Q10 values, partitioning data in a pairwise fashion. This approach raises two concerns: (1) The effect size will converge on a true rate of change as the number of measures increases and (2) different conclusions will be reached based on which temperatures are included in each pairwise measure. To say the effect is exponential based on two data points assumes respiration is not measured at lower temperatures where enzyme activity decreases significantly, nor at exceedingly high temperatures where proteins denature. However, select studies have updated the Arrhenius equation to account for protein denaturation and unfolding (Wu et al. 2021). This also assumes the function obtained by merely two data points is similar if more than two temperatures are measured (only accomplished through zero error in data collection). In Fig. 2, if we insist the data stem from an exponential function, the function including all three data points would have a β1 value significantly different from one that excludes any one of the three data points. Therefore, different rates of change will be calculated based on which temperature is excluded. As such, the more temperatures measured, the closer the estimated rate will converge on the true rate. We cannot measure an infinite number of rates at an infinite number of temperatures, but three measures provide far more information than two measures, especially when considering the potential for non-linearities. Temperature is a continuous variable that affects metabolism differently across periods of time (e.g., diel cycles where temperature changes incessantly, as in the subtropical copepod Pleuromamma xiphias; Tarrant et al. 2021) and does not jump across 10°C. Calculating temperature effects in a pairwise manner is ambiguous, provided (1) data are knowingly excluded from Q10 measures across more than two temperatures (e.g., Xiao et al. 2014; Lehette et al. 2016; Lee et al. 2023) and (2) it is illogical to measure multiple Q10 values within 10°C (e.g., Castellani and Altunbaş 2014; Pascal and Chong 2016; Nie et al. 2017). Although we can calculate three Q10 values in Fig. 2, temperature affects respiration at a single rate, or β1 value, across the entirety of the exponential function. However, studies often reach the conclusion that these three Q10 values have different rates of change at each of the pairwise measures, provided one of the three measures is excluded. Last, it is illogical to take this approach when multiple Q10 values are not measured across more than 10°C. We do not need multiple measures of how temperature affects respiration across 10°C when the entirety of the temperature range does not span 10°C. Q10 values are interpreted in reference to the value 1, which indicates respiration functions independently of temperature. It is difficult to determine what a given Q10 value measures without comparison to Q10 values across comparable temperatures, provided the value is an extrapolation from any two temperatures. Most biological systems operate at a Q10 between 2 and 3 (Reyes et al. 2008). However, without reference to similar temperature ranges, the value alone does not indicate the extent to which respiration depends on temperature. This is due to the fact that a Q10 calculated across 1°C does not provide us with the same range and scope of information as a Q10 across 10°C (conclusions reached using Q10 values are not always concordant; Mundim et al. 2020). Furthermore, the decision of what temperatures to include can be made after data are collected and visualized, possibly skewing our interpretation based on what we believe to be the case post hoc (see fig. 4 in Castellani and Altunbaş 2014). Therefore, Q10 values may not in and of themselves indicate meaningful effects if we compare values that may or may not span 10°C. I recommend researchers consider if there are more accurate, straightforward approaches to understanding the effects of temperature. We can convert between percent change (see below) and Q10 values; however, to calculate an overall Q10, we need to first estimate an effect for each pairwise measure, weight the measures for non-equidistant temperatures, calculate an average, then interpret what each pairwise measure means for the overall rate of change (often within 10°C). This is counterproductive and misleading, especially across many temperatures. It is possible to average Q10 values to get an overall effect (with values weighted proportional to the squared differences in temperature for non-equidistant temperatures), but this does not justify the use of pairwise Q10 values to begin with. Each pairwise Q10 assumes zero error (i.e., if we extrapolate to 10°C from two temperatures, measuring respiration at any two temperatures along the function is predicted to yield the same rate of change). One idealized scenario of measuring zero error that is rarely, if ever, accomplished in practice does not justify an estimate from merely two temperatures when additional data is available. Recent studies have presented effect sizes that serve as alternatives to the Q10 value (Heine et al. 2019; Makita et al. 2021; Oladipupo et al. 2022). These effect sizes more accurately quantify the continuous effect of temperature by incorporating data from more than two temperatures into a single effect size and estimating the associated error. Each of these studies utilizes the rate of change obtained from the exponential and log-linear functions spanning more than two temperatures (Box 1). We have previously used meta-analysis across 32 studies to analyze the effect of temperature on copepod respiration (Heine et al. 2019). For every one degree increase in temperature, copepod respiration increases by ~ 7% across calanoid, cyclopoid, and harpacticoid copepods. We refer to this effect size as “percent change”, provided it measures the percentage respiration changes per one unit change in temperature. This effect size is considered to be an improvement over Q10 values as it accounts for more than two temperatures, does not extrapolate beyond what is measured, and estimates the associated error. Similarly, Oladipupo et al. (2022) used percent change to quantify the effect of temperature on respiration across nine orders of insects. The study found that respiration increases by ~ 8% per °C increase in temperature, concluding that overall, the respiration rates of insects and copepods (both poikilothermic arthropods) respond similarly to increasing temperatures. Under the percent change effect size, if temperature x leads to respiration y, then temperature x + 1 gives us respiration y × 1.08. Q10 values do not require data to span 10°C, however, all data obtained using percent change span a temperature range of at least 1°C, and the effect size is expressed as such, along with the associated error (see also Makita et al. 2021). Whether researchers should seek alternative effect sizes depends on whether the study measures data beyond two temperatures or if the data stem from a non-exponential function (e.g., a logistic function). For example, if we take the hypothetical scenario in Fig. 3, the data appear more sigmoidal than exponential, provided respiration approaches a maximum value at higher temperatures and does not continue to increase exponentially (e.g., in the copepod Temora longicornis; Castellani and Altunbaş 2014). Here, partitioning data in a pairwise manner is problematic because multiple Q10 values are estimated within 10°C, and which two temperatures are used to calculate the values will determine which data are excluded when estimating the rate of change. To further complicate estimates, some studies calculate multiple Q10 values that overlap within 10°C (e.g., Lehette et al. 2016; Pascal and Chong 2016). Here, determining an overall respiration model may be the best approach (e.g., Macnaughton et al. 2019). The metabolic theory of ecology is a unified theory that represents the relationship between temperature, body mass, and metabolic rate, allowing researchers to understand constraints on ecological processes governed by temperature from the organismal level (e.g., life history) through ecological processes (e.g., population growth). In this respect, use of the Boltzmann–Arrhenius factor provides a more accurate representation of temperature effects than pairwise measures. What metric researchers use will depend on the aims of the study, provided percent change—as it currently stands—is geared toward understanding the incremental change in rates per °C and their associated error. The use of Q10 values has been shown to limit the ability of researchers to extrapolate findings and reach accurate conclusions in thermal ecology. Few studies are very rarely, if ever, truly limited to measuring two temperatures; and temperature does not affect physiology in a pairwise fashion. Therefore, thermal ecology has begun to develop alternative effect sizes, such as percent change, to more accurately estimate temperature effects (e.g., Heine et al. 2019). Use of the Arrhenius equation has also emerged as a crucial means to understanding the temperature dependence of reaction rates in thermal ecology, however, it is not universal. Aside from developing alternative effects sizes, our assumption that the relationship between respiration and temperature obeys exponential laws may need adjustment altogether, as power laws may be more appropriate (Mundim et al. 2020). In measuring the temperature dependence of biological rates, researchers should: (1) Measure more than two temperatures, (2) not exclude data points, (3) estimate error, and (4) watch for non-exponential trends. Our decision to develop more comprehensive, accurate methods to understanding the effects of temperature directly impacts our ability to mitigate the influences of climate change throughout thermal ecology research. None declared. I thank Ash Abebe, Nick Justyn, Alan Wilson, Wendy Hood, the Hill and Hood labs, and two anonymous reviewers for comments on earlier versions of the manuscript. Acknowledgment of the aforementioned individuals does not indicate their support for, nor disagreement with, the ideas herein. This work was funded by an Ocean Sciences Postdoctoral Research Fellowship (2126224) awarded to K.B. Heine by the National Science Foundation.