Temperature effects on ectotherm fitness, mediated through physiology, can generally be described by a thermal performance curve that rises, peaks, and then declines across a gradient of increasing temperature (Chown and Nicholson, 2004; Angilletta, 2009; Clissold and Simpson, 2015). The thermal performance curve reflects the range of temperatures (thermal window: Pörtner and Farrell, 2008) that organisms can tolerate and still survive and reproduce. Organisms have likely evolved to operate in thermal windows that are as narrow as possible to minimize maintenance costs (Pörtner and Farrell, 2008). Thermal performance is routinely measured in terms of metabolic rate-temperature relationships (e.g., Figure 1). But it can also be characterized in terms of other performance measures related to fitness such as locomotor behavior, growth rate, and offspring production (Kingsolver and Woods, 1997; Chown and Nicholson, 2004; Clissold and Simpson, 2015). While the exact temperature range of the thermal window will vary by species (Pörtner and Farrell, 2008), as well as the local thermal conditions faced by geographically separated populations of a species (e.g., Rosenblatt et al., 2016), the general, qualitative features of the performance curve nonetheless can help conceptualize the interplay between temperature and predation stress. We do this here by characterizing patterns of thermal performance in each of the variables used to estimate TER_C:X, using empirical insights from studies that have begun to explore the stoichiometric consequences of predation stress and temperature on ectotherm organismal performance.

A fundamental physiologic property (Chown and Nicholson, 2004) is that mass specific metabolic rate (R_C) of ectotherms will rise, peak and then decline with increasing temperature (Figure 1). Experimental research has shown that predation stress can exacerbate R_C across the temperature gradient (Culler et al., 2014; Schmitz et al., 2016). Mass specific ingestion rate may follow a similar nonlinear trend across a temperature range (Kingsolver and Woods, 1997, 1998; Chown and Nicholson, 2004), whereas assimilation efficiency A_C might be approximated as a linearly increasing function of temperature (Culler et al., 2014; Clissold and Simpson, 2015; Schmitz et al., 2016). These empirical trends can be used to begin exploring how GGE_C and TER_C:X might vary with temperature. We do this here by approximating the empirical relationships of the component variables with temperature (T), and substitute those functions into equations for GGE_C and TER_C:X. We approximate the temperature dependent functions as:

Substituting these functions into the equation for GGE_C and algebraically simplifying the coefficients gives:

Qualitatively, Equation (4) generally gives rise to a highly nonlinear function that rises, peaks and declines with rising temperature (Figure 2). It can be used to explore how perceived predation risk might influence the temperature dependent relationship by examining how the model parameters might change. It has been shown empirically that assimilation efficiency is lower when prey face perceived predation risk (Risk prey) than when facing no risk (No Risk prey), and efficiency for Risk prey rises more slowly with rising temperature than for No Risk prey (Schmitz et al., 2016). Hence, the magnitude of a_Ac and b_Ac in Equation (3c) will be lower for Risk prey than for No Risk prey. Across a temperature gradient, mass specific metabolic rate of Risk prey tends to be higher than for No Risk prey (Culler et al., 2014; Schmitz et al., 2016). Hence, as a first approximation one may assume that the magnitudes of a_Rc and b_Rc in Equation (3b) will be larger for Risk prey relative to No Risk prey. These assumptions imply further that in Equation (4), â and b^ for Risk prey will be less than for No Risk prey. Collectively, these parameter changes will lead to the same qualitative form of the temperature dependency of GGE_C (Figure 2A). However, the curve describing GGE_C for Risk prey is offset from the curve for No Risk prey.

The effects of temperature and perceived predation risk on TER_C:X can be explored by substituting the temperature dependent functional form of GGE_C into Equation (2) and then comparing trends between Risk and No Risk conditions. Doing this, however, requires making assumptions about the way assimilation efficiency of nutrient X, A_X, might vary with temperature, for which there is currently very limited general understanding (Cross et al., 2015), let alone understanding of how A_X varies between Risk and No Risk conditions. We therefore consider several possible alternatives, beginning with the assumption that A_X could remain constant, increase linearly, decrease linearly, or vary nonlinearly with rising temperature, based on some empirical insights (Culler et al., 2014; Dalton and Flecker, 2014; Lemoine and Shantz, 2016; Schmitz et al., 2016).

These assumptions give rise to at least four contingencies in which: (1) A_X is constant for both No Risk and Risk prey across the temperature gradient, but with A_X for Risk < A_X for No Risk prey (Figure 2B); (2) A_X is constant for No Risk prey and increases linearly with temperature for Risk prey (Figure 2C); A_X is constant for No Risk prey and decreases linearly with temperature for Risk prey (Figure 2D); and A_X for both No Risk and Risk prey changes nonlinearly with temperature in the same qualitative way as does R_C or I_C (Figure 1).

The contingencies show first that rising temperature should not always lead to increased intake of C by prey stressed from perceived predation risk. In some cases (Figure 2B) C:X of Risk prey will always be lower than for No Risk prey, implying that Risk prey should always consume more N than No Risk prey. In other cases, rising temperature will cause C:X of No Risk prey and Risk prey to switch. For instance, C:X ratios of foods consumed by Risk prey may be higher than for No Risk prey up to a threshold temperature, and then switch to be lower. This means that Risk prey should consume more C with rising temperature up to a threshold, after which they are expected to consume more N than No Risk prey. The reverse may also happen (Figure 2D). Finally, the trend could be highly nonlinear across a temperature gradient leading to multiple switches where Risk prey may consume more C than No Risk prey, then more N, then again more C (Figure 2E). The contingencies depicted in Figure 2 are not an exhaustive representation of possibilities. Rather their presentation is intended to reveal the range of different nonlinearities that could emerge, depending on the temperature dependency of the component variables. This thereby reinforces earlier arguments (Cross et al., 2015) for the need to better quantify how the model variables R_C, I_C, A_C, and A_X all vary with temperature, let alone how they change with stress from perceived predation risk.

This new insight has several implications for conclusions drawn from studies testing effects of predation stress on ectotherm nutrient intake and physiological performance. First, the original argument that environmental warming should exacerbate the effects of stress from predation risk, causing prey to increase C consumption (Schmitz, 2013), is a special case of a broader range of outcomes. Second, the empirical finding that across a gradient of increasing temperature, Risk prey and No Risk prey consume equal amounts of C and N, then deviate from each other with Risk prey consuming more C, then switching where Risk prey consume equal or less C than No Risk prey (Schmitz et al., 2016) could be explained by one of the contingencies (Figure 2C). Hence, the experimental outcome could be consistent with, but a generalization of, the original idea of the effects of predation stress on organismal stoichiometry (Hawlena and Schmitz, 2010a). Third, our results may also help offer clues as to why results of studies that tested for the effects of predation stress on nutrient intake by ectothermic species were counter to original predictions (Thaler et al., 2012; Costello and Michel, 2013; Dalton and Flecker, 2014; Kaplan et al., 2014; Guariento et al., 2015; Kirschman et al., 2016; Van Dievel et al., 2016).

The higher N intake by Risk prey than by No Risk prey observed in these studies has been attributed to developmental needs that facilitate prey escape from predation. Increased N intake under perceived predation risk is needed by aquatic prey like damselflies, fish, and amphibians to increase the development rate of locomotor traits that enable prey to escape their actively hunting predators, or for terrestrial caterpillars to grow rapidly to become too large for predators to dispatch them. Our analysis shows that this could counterintuitively be achieved whenever Risk prey lower their assimilation efficiency of N, relative to No Risk prey (Figure 2B). But studies have shown that assimilation efficiency may increase (Thaler et al., 2012; Dalton and Flecker, 2014), which should, according to our analysis, lead to higher C intake by Risk prey than No Risk prey (e.g., Figure 2C). Our analysis suggests that to maintain a higher net intake of N, Risk prey that increase N assimilation efficiency would need to compensate by lowering their consumption rate of food I_C. This has indeed been observed experimentally (Thaler et al., 2012; Dalton and Flecker, 2014).

Several studies experimentally examining the interplay between temperature and predation risk have provided mixed support for the original idea that rising temperature should exacerbate predation stress causing prey to consume more C (Jansens et al., 2015; Kirschman et al., 2016; Van Dievel et al., 2016; Zhang et al., 2016). These studies used 2 × 2 factorial designs that crossed a temperature treatment with a perceived predation risk treatment. Our analysis reveals that mixed outcomes are to be expected with such experimental designs because the outcomes depend on the specific temperatures used in the experiments. A simple answer is that the experiments reared prey on both sides of a temperature threshold, in which case Risk prey on the warm side of the threshold would consume less C than individuals in cooler temperatures (e.g., Figure 2D, or Figure 2E left threshold). It could also arise if assimilation efficiency of N decreases with rising temperature (Figure 2D temperature range below the threshold) or if N assimilation increases with temperature, but the experimental temperatures put Risk prey on the descending side of the TER_C:X vs. temperature curve (Figure 2C). Essentially, the analysis shows that factorial experiments that merely cross one experimental temperature with perceived predation risk could give equivocal insight in the absence of knowing how each of the component model variables (R_C, I_C, A_C, and A_X) vary with temperature and perceived predation risk.

There is growing interest in examining the interactive effects of climate and other environmental stressors on organismal stoichiometry (Cross et al., 2015; Rosenblatt and Schmitz, 2016). Such examinations of the interactive effects of temperature and perceived predation risk on prey performance is in line with the growing need to understand how environmental warming will influence trophic interactions in communities. The current, small body of research examining effects on prey of interactions between temperature and perceived predation stress means that our current understanding is rather piecemeal, with limited ability to make empirical generalizations at this time.

Nevertheless, the field is also at an opportune juncture to improve how future studies are undertaken. Specifically, the existing research has revealed that prey responses to temperature and perceived predation risk are highly context dependent. It currently remains unclear whether or not the nature of nutrient intake in the presence and absence of perceived predation risk by different species is a unique attribute of each species or if they are temperature-specific manifestations of a more general temperature dependent response to predation stress (Schmitz et al., 2016). Our analysis presented here suggests the general TER framework of ecological stoichiometry can help to reconcile these different outcomes and suggests that they are part of a more general temperature dependent response to predation stress. However, our general framework also shows that outcomes will be contingent on how each of the component variables of the TER framework vary with temperature and predation stress. This highlights that experiments that simply manipulate temperature and perceived predation risk and measure prey consumption of C and nutrients (e.g., N or P) could provide equivocal results if the treatment effects of the key underlying physiological variables R_C, I_C, A_C, and A_X are not measured. Moreover, given the potential for threshold effects of increasing temperature identified in our qualitative analysis (Figure 2), we suggest that studies examine the interplay between temperature and perceived predation risk across temperature gradients.

Such studies need to be predicated on knowing the thermal tolerance range of the focal species (i.e., the range between the minimum and maximum thermal limits). Experimentation would then systematically increment temperature within this range as well as the presence and absence of perceived predation risk (e.g., Culler et al., 2014). The key physiological variables would then be measured at the different temperatures. Given the potential for nonlinear responses of prey to temperature and predation stress, we suggest measuring physiological variables across a gradient of at least four temperatures, although more will allow clearer characterization of the degree of nonlinearity (e.g., Culler et al., 2014). Such studies can provide insight into the nature of organismal performance curves (e.g., Culler et al., 2014; Schmitz et al., 2016) that can help inform which of the potential contingencies (Figures 2B–E) can be expected for a particular study organism.

There is also a need to explore the connection between TER_C:X and the biochemical compounds that make up nutrients. This is because animals do not metabolize elements, but instead metabolize biochemicals (Anderson et al., 2004; Wilder and Jeyasingh, 2016). TER_C:X is a first approximation that implicitly equates energy and nutrient selection with the total content of elemental C and X (e.g., N or P) in food resources. Because elements are bound up in biochemicals such as carbohydrates, fats, and proteins, this assumes that C, N, and P are constant fractions of those biochemicals. But this assumption may not always hold, especially in terrestrial plants where elements contained in the digestible fraction of food may be uncorrelated with the fraction of total available elements (Anderson et al., 2004; Wilder and Jeyasingh, 2016). And, these digestible fractions can shift with changing environmental temperature (Zvereva and Kozlov, 2006; Rosenblatt and Schmitz, 2016; Wilder and Jeyasingh, 2016; Zhang et al., 2016). The conceptual theory also assumes that animals derive their energy-C from carbohydrates. But stressed prey may either consume more protein-N for energy or metabolize stored body protein to release energy via gluconeogenesis (Hawlena and Schmitz, 2010b) especially when other energy sources are at low concentrations. The effect of increased N intake for energy is not accounted for in estimation of TER_C:X, which could then lead to incorrect predictions about dietary elemental intake of C and N under stress. Thus, a future avenue of research might consider how to revise TER_C:X theory to accommodate the need to consider diet selection for elements contained within biochemicals. In addition, exploration of how organisms select and utilize different biochemicals as a means to balance competing demands of allocating nutrients to cope with the stressors and allocating for growth and development would help inform such revisions (Schmitz et al., 2016).

In conclusion, the realization that non-consumptive effects of perceived predation can be important drivers of food web, community, and ecosystem dynamics was a crucial step forward in our understanding of ecological processes. However, rapid environmental shifts brought about by climate change and other global change drivers demand that we integrate the study of predation risk with our understanding of the ecological effects of other stressors. As part of this effort, we suggest that a fruitful avenue to pursue would be to build on existing linkages between ecological stoichiometry, nutrition, and phenotypic responses of prey to consider multiple environmental stressors (Rosenblatt and Schmitz, 2014, 2016). By expanding our understanding of the effects of predation risk on prey nutritional ecology across a range of potential future climates, our ability to accurately predict how future food webs and ecosystems may change will become more robust and reliable (Rosenblatt and Schmitz, 2016).

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.