Thermal performance curves for aerobic scope and specific dynamic action in a sexually dimorphic piscivore: implications for a warming climate Free

Temperature and body mass are well known as the primary determinants of animal metabolism (Brown et al., 2004; Schulte, 2015). Nonetheless, the influence of these two factors on the metabolic response to feeding varies widely among studies (McCue, 2006; Secor, 2009). The postprandial rise in metabolism following the ingestion of foodstuffs is known as specific dynamic action (SDA) and includes the energetic costs of ingesting, digesting, absorbing and assimilating a meal. SDA varies widely among phylogenetic groups in magnitude and duration but is typically characterized by a sharp increase in metabolism following the ingestion of a meal, followed by a gradual decline (Secor, 2009). In ectotherms such as fish, higher temperatures cause faster digestion and higher peak SDA values (Jobling, 1981). The size and composition of a meal can also influence SDA (Fu et al., 2005a,b), as can hypoxia (Jordan and Steffensen, 2007) and activity (Blaikie and Kerr, 1996). Large, energy-dense meals typically induce a higher peak SDA, a longer SDA duration and greater energetic costs (Fu et al., 2005a,b; Wang et al., 2012).

Despite changes in the peak and duration of SDA, the total SDA cost in ectotherms is often reported to be a consistent proportion of the ingested meal energy, irrespective of temperature (Johnston and Battram, 1993; Lo et al., 2022), body mass (Boyce and Clarke, 1997) and ration size (Fu et al., 2005b), while other studies have demonstrated scaling relationships between these variables (von Herbing and White, 2002; Luo and Xie, 2008a; Norin and Clark, 2017; Tirsgaard et al., 2015). SDA comprises substantial and variable proportions of fish energy budgets, ranging from 5% to 40% of daily consumption (Secor, 2009). Proper accounting of how SDA scales with temperature, body mass and meal size is needed to make accurate predictions of metabolic needs under current and future environmental conditions.

Metabolism in fishes is commonly estimated using oxygen consumption as a proxy for aerobic cellular respiration and is typically expressed as Ṁ_O2, the rate of oxygen consumption. Feeding studies typically measure Ṁ_O2 continuously throughout feeding and the subsequent rise in metabolism. SDA is relative to the animal's resting state, or standard metabolic rate (SMR), which is defined as the resting metabolism of a post-absorbative, non-breeding, inactive organism (Chabot et al., 2016a). SDA is also often compared to the fish's maximum metabolic rate (MMR) or described as a proportion of the animal's aerobic scope (AS), which is the difference between MMR and SMR. AS constitutes the window within which fishes must operate metabolically including provisions for growth, activity, reproduction and digestion (Clark et al., 2013; Fry, 1947). As the peak Ṁ_O2 achieved following ingestion (SDA_peak) has been reported to increase exponentially with temperature (Jobling, 1981), it stands to occupy larger portions of AS at higher temperatures, which may have a constraining effect on other energetic demands (e.g. locomotion).

Given a warming climate, it can be useful to improve our understanding of how shifts in temperature and diet are poised to affect the metabolism of ectotherms. The aerobic scope protection hypothesis (hereafter, AS protection hypothesis) posits that at high temperatures, individuals will actively select smaller prey to keep SDA low, ensuring that the fish has a sufficient reserve of aerobic capability (Jutfelt et al., 2021). The implications of the AS protection hypothesis are (1) a reduction in overall consumption, leading to a reduction in growth, and (2) a potential increase in the energetic cost of acquiring and digesting multiple small meals (as opposed to one large meal), which could also lead to reductions in growth. While there is good evidence of the former (Jutfelt et al., 2021), there is mixed evidence on the latter. The total metabolic cost (SDA_cost) of digestion seems to increase with the energy content of meals (Beamish and Trippel, 1990; Jobling, 1981; Secor, 2009); this relationship is often described as a percentage, known as the SDA coefficient (SDA_coef), and represents the proportion of ingested meal energy lost to SDA. In some cases, SDA_coef has been found to be static across ration sizes (Beamish and Trippel, 1990; Jordan and Steffensen, 2007), while in others it has been shown to decrease (Boyce and Clarke, 1997; Norin and Clark, 2017; Wang et al., 2012).

A key application of quantifying SDA is in bioenergetics models. Bioenergetics models account for the energetic inputs and outputs of an animal, and have been used to estimate growth, consumption and the effects of climate warming (Chipps et al., 2022). As a result, bioenergetics models provide a first-principles approach to predicting animal responses to climate warming. Currently, bioenergetics models for fish calculate SDA as a constant proportion of the digestible energy (DE), with models for most species relying on a generalized coefficient of 15–20% of the daily energy intake (Deslauriers et al., 2017). Some models allow DE to scale with temperature and ration, as studies have shown that faecal energy is influenced by these factors (Elliott, 1976; Solomon and Brafield, 1972). Regardless, SDA can make up a substantial proportion of animal energy budgets and may have considerable impacts on model outputs (e.g. prey consumed, growth rates) if not well quantified. Bioenergetics would benefit from species-specific accounting of SDA and proper accounting of temperature, sex, body mass and ration size relationships.

Walleye, Sander vitreus (Mitchill 1818), are cool water mesotherms that support some of the largest freshwater fisheries in North America, both recreationally and commercially (Barton, 2011). Walleye begin piscivory within months of hatching in the spring, and can influence ecosystems through top-down trophic cascades by foraging on the most abundant prey items (Hartman and Margraf, 1992; Sheppard et al., 2015). A bioenergetics model for walleye was first developed by Kitchell et al. (1977), and like others, estimated SDA as a fixed proportion of walleye diet based on an average value for other fishes. Currently, the model offered by Deslauriers et al. (2017) includes a temperature- and ration-dependent function for DE, from which SDA is estimated as 17.4%, and similarly relies on values borrowed from other species for body mass and temperature dependence of SMR. Walleye are also an interesting model for exploring variation in SDA because they exhibit female-biased sexual size dimorphism (SSD), in which females are consistently ∼25% larger than males (Bozek et al., 2011; Lester et al., 2000). SSD is widespread among fishes; however, the bioenergetic consequences of this phenomenon are poorly understood (i.e. it is unclear how sex differences in growth are realized in the bioenergetics equation). To date, few studies have investigated the effect of sex on SDA in fish, let alone in a sexually dimorphic species. Female-biased SSD, such as in walleye, is thought to have arisen as a result of selection for increased fecundity, given the positive correlation between body size and the number eggs that are produced (Parker, 1992). Reproductive hyperallometry is extremely common among fishes, in which reproductive output (the number and quality of eggs) increases hyperallometrically with body size, emphasizing the importance of protecting large females in sustainable fisheries (Barneche et al., 2018). Given global trends of a reduction in fish body mass (Baudron et al., 2014; Queiros et al., 2024; Vasilakopoulos et al., 2014), it is important to improve our understanding of how sex and body mass interact with bioenergetics such that we can determine how fish populations are likely to change with future warming.

The objective of our study was to investigate the effects of temperature, sex, body mass and ration size on SDA in walleye. We hypothesized that the peak and duration of SDA are constrained by the controlling effects of temperature on metabolism, but that SDA is ultimately a proportionate response to the ingested meal energy and scales isometrically with body mass. We predicted that SDA_cost would increase with ration size, but remain consistent with temperature, whereas SDA_coef would remain consistent across both temperature and ration size. Finally, we predicted that postprandial residual aerobic scope (PRAS) would be lowest at high temperatures and larger body masses, and in females. We tested these predictions by measuring Ṁ_O2 of walleye before, during and after feeding one of two ration sizes using intermittent-flow respirometry across an ecologically relevant range of water temperatures.

Fifteen walleye (8 male, 7 female) were collected via electrofishing in late October 2022 from Rice Lake, ON, Canada (44°14′23.8″N, 78°06′20.0″W, water temperature: 11°C) and an additional 12 walleye (7 male, 5 female) were collected in early April 2023 from the Bay of Quinte (by electrofishing), Lake Ontario (44°03′02.9″N, 77°03′55.5″W, water temperature: 10°C). Fish were transported to Trent University in a 660 l insulated tank supplied with oxygen and transferred to temperature-matched 900 l tanks inside the university facility. The facility is supplied with water sourced from the Otonabee River that is sand filtered, ozonated, and chilled with an industrial chiller (until river temperatures drop below ∼6°C). Each tank was supplied with constant inflow of the treated river water, a UV sterilizer (Aqua-Merik 1-M-G, Levis, QC, Canada), a multi-media cannister filter (Fluval^® FX4, Mansfield, MA, USA), temperature controllers (Inkbird ITC-308, Shenzhen, China) connected to 500 W heaters (Hygger, Shenzhen City, China), a chiller (EcoPlus 1.5 HP) and artificial vegetation. Lighting in the animal husbandry room was set to a natural photoperiod, although fish were kept in low-light conditions with tank lids.

Tanks were initially prepared with Instant Ocean^® sea salt and fish were given 5 days in a light salt bath (5 g l⁻¹) to reduce osmotic stress and the possibility of infection from any abrasions acquired during capture and transport. Partway through the salt treatment, fish were lightly anaesthetized using 150 mg l⁻¹ tricaine methanesulfonate (MS222; Syndel, Ferndale, WA, USA) buffered at a 2:1 ratio with sodium bicarbonate to be PIT tagged in the dorsal musculature, weighed to the nearest 5 g (Ohaus Defender 3000, Parsippany, NJ, USA) and sexed. Gonadal development begins in autumn and most females can be identified by the girth of the belly, although sex was confirmed via visual inspection upon euthanasia when experiments concluded. Males included in the study (n=14) had a mean (±s.d.) body mass of 1.455±0.44 kg. Females included in the study (n=9) were 70% larger on average, with a mean body mass of 2.475±0.75 kg.

The procedures outlined below follow the Canadian Council for Animal Care's guidelines for best practice (Trent University animal use permit #26767). Six 36 l respirometry chambers (Fig. S1; 24 cm internal diameter, 78 cm internal length; Loligo Systems, Vyborg, Denmark) were submerged in a rectangular insulated tank (121×243×60 cm deep, filled to a depth of 35 cm). A recirculating loop, consisting of a 600 l h⁻¹ aquarium pump (Eheim, Deizisau, Germany) and PVC tubing ran constantly, pushing water past an optical oxygen sensor (10 cm robust probe; Pyroscience, Aachen, Germany) connected to a four-channel Firesting oxygen reader. A second recirculating loop with a 1200 l h⁻¹ identical pump was retrofitted to the chambers to improve mixing inside the chamber. A 1200 l h⁻¹ pump (Eheim), fitted to a third opening, was set to a digital timer to re-oxygenate the chamber from the surrounding water bath when oxygen levels fell to around 80%. The water bath was supplied with two large air stones to ensure full oxygen saturation, several small aquarium pumps to ensure thermal mixing, a UV-equipped canister filter (Fluval^® 307 with in-line clarifier), a moderate inflow of treated river water to prevent waste buildup during the experiment, temperature controllers connected to three aquarium heaters (500 W, Hygger) and a small chiller (1 HP Max-Chill, AquaEuroUSA, Gardena, CA, USA). A leak test at the onset of the experiment was conducted to confirm the chambers contained no leaks. This design is consistent with standard practices for intermittent-flow respirometry, with the exception of the second recirculation loop (Clark et al., 2013).

We targeted temperature treatments of 2, 4, 10, 15 and 20°C, spanning most of the range of temperatures walleye occupy in the wild. For each temperature treatment, two trials were conducted, one each for 2% and 4% ration sizes. Trials were conducted in the following order from October 2022 to January 2023 using the fish from Rice Lake: 10, 15, 4 and 2°C. These temperatures generally coincide with the natural temperature shifts that walleye would be exposed to in the wild. Initial trials conducted at 10°C and 15°C were close in temperature to Rice Lake at the time of capture (11°C), after which walleye were gradually acclimated down to winter temperatures and tested at 4°C and 2°C from mid-December to February. The second cohort of fish, from Lake Ontario, was used for 20°C trials conducted in May 2023. Walleye are exposed to rapid increases in temperature following spawning in the spring when they move to warmer areas to forage (Peat et al., 2015). Fish were acclimated in holding tanks by adjusting the temperature no more than 1°C per day and ultimately holding at the target temperature for a minimum of 3 days, with the exception of the 20°C trial. Fish were acclimated to a maximum of 18°C to mitigate thermal stress in captivity for the final two trials at 20°C. Acclimation times varied between trials; when a cohort of fish were selected for a given trial, the remaining fish continued to be held at the target acclimation temperature. At warmer temperatures, this turnaround was quick (∼1 week), but at 2 and 4°C, trials were much longer and therefore acclimation varied substantially (∼3 weeks).

For a given trial, six fish were netted and transferred to the respirometry chambers, with the exception of the 4% ration–20°C trial, in which only five individuals were tested (one walleye died in captivity ahead of the trial). We attempted to include a mix of males and females of different sizes in each trial (see Table 1 for sex ratios). Fish were able to see each other in adjacent chambers, but opaque lids placed over the tank ensured it was dark and fish were undisturbed by other movements in the facility. Following 24 h in the chambers, fish were removed and subjected to a ‘sham’ feeding event. Sham feeding involved lightly sedating the fish in a temperature-matched solution of buffered MS222 (150 mg l⁻¹) until loss of equilibrium (typically 2–3 min), weighing the fish, and allowing a 30 s air exposure while inverted in a surgery trough before returning the fish to the chamber. The intention of this procedure was to elicit the handling effects associated with the forthcoming feeding event such that we could measure and account for the recovery time from handling in our analysis.

Twenty-four hours after the sham feeding event, fish were removed again, anaesthetized and force fed freshly euthanized (whole or partial) juvenile rainbow trout, Oncorhynchus mykiss, consisting of 2% or 4% of the individual's mass. Rainbow trout (ca. 30–50 g body mass), which were kept in tanks on site, were euthanized in 300 mg l⁻¹ MS222 the morning of the experiment. Typical meals consisted of 1–4 half or three-quarter portions of rainbow trout. Meals were gently pushed down the oesophagus using a pair of rubberized haemostats (i.e. gavage), and fish were immediately returned to the chambers. Fish remained in the chamber for 2–10 days of automated estimates of Ṁ_O2 (rate of oxygen consumption) following gavage. If a regurgitation occurred during the process of feeding all six fish, the gavage was re-attempted immediately. If the regurgitation occurred during a later inspection, it was noted, and the fish remained in the chamber to avoid disturbing the other fish. Of 59 feedings, there were four regurgitations, three of which occurred at 20°C (4% rations), and one at 10°C (2% ration). These data were removed from the dataset.

To elicit MMR at the end of the trial, we conducted a standardized chase test and air exposure protocol (Norin and Clark, 2016). Fish were removed and manually chased for 90 s in a temperature-matched circular tank (340 l, 120 cm diameter), followed by a 60 s air exposure, during which body mass was measured. Next, the fish were quickly returned to the chamber and oxygen consumption was measured immediately for 10 min. Fish were then returned to a temperature-matched, or slightly cooler, salt bath (5 g l⁻¹) to recover for 3–5 days. The salt bath tank (120 cm diameter, 500 l) was slightly smaller than husbandry tanks but fitted with the same combination of cannister filter, UV sterilizer, artificial enrichment and temperature controllers. Inflow was provided to prevent ammonia build-up (which was tested for frequently) but at a reduced level to prevent rapid dilution of the salt treatment. Repeated measurements of background (microbial) respiration in the chambers were taken for 6 h following fish removal, using the same flush–measurement cycle used during the respective trial. The flush–measurement cycles for the 2, 4, 10, 15 and 20°C trials were 20:40, 15:35, 15:20 15:15 and 12:10 min, respectively. The respirometry tank was drained and scrubbed between trials and disinfected with dilute bleach every two trials to eliminate build up of microbial respiration.

Data were imported into R version 4.2.2 (http://www.R-project.org/). For each fish within each trial (referred to hereafter as individual experiments), the slopes of the measurement phases were calculated using the respR package (Harianto et al., 2019). We used a 2 min buffer on either end of the slope and conducted a linear regression on the remaining data points. We calculated the background respiration using a period of equal length from the end of the trial (once temperatures and oxygen had stabilized) and adjusted our rates by subtracting this value from each of the measured rates. Background respiration averaged 3.9±11% (mean±s.d.) of mean, whole-organism Ṁ_O2. The resulting net slopes were used to calculate mass-specific Ṁ_O2 (mg O₂ kg⁻¹ h⁻¹). Linear regressions for the raw oxygen concentration data over time had high goodness-of-fit with a mean R² of 0.96 or above across all experiments. Linear regressions following the chase protocol used a consistent 8 min period and had similar fits with a mean (±s.d.) R² of 0.99±0.01.

We visually inspected Ṁ_O2 values over time for each fish and determined that in most cases, it took 3–5 h for Ṁ_O2 to stabilize after fish were placed in the chamber, both initially and following the sham feeding event, regardless of temperature. We removed a 5 h period and used the remaining pre-feeding Ṁ_O2 values to estimate SMR. SMR was calculated using a modified script from Chabot et al. (2016a). The SMR estimation procedure applied a lower 15% quantile, a mean of the lowest 10 values, and a mean of the lowest normal distribution, and ultimately selected the best option based on the coefficient of variation for each estimate. Thirty-six experiments used a quantile and 15 used the mean of the lowest normal distribution. Two exceptions were made where Ṁ_O2 was persistently high and a 12 h acclimation period was removed prior to SMR calculations. We took MMR as the highest Ṁ_O2 value of the entire experiment, which often occurred after the fish was placed in the chamber at the beginning of the experiment, or after sham and real feedings. Only 23 of 51 MMR values were a result of the chase protocol.

We quantified the post-prandial rise in metabolism using a modified script from Chabot et al. (2016b), which combines a linear regression during the initial rise in metabolism (hours 0–5) with a non-parametric quantile regression for the remaining data. We set the ‘penalty parameter’, lambda (λ), to 36 h for most experiments, which is slightly higher than the recommended 24–30 h, as we found this was more effective in eliminating bouts of activity from the fitted curve. We adjusted λ to 24 h for the 20°C treatments to avoid underfitting, as these trials were short in duration. We set tau (τ) to the recommended τ=0.2 for most experiments, which allowed 20% of the Ṁ_O2 values to fall below the fitted line. On four occasions, we increased τ to 0.5 because the SDA response was so low at 2 and 4°C, we found it necessary to increase this parameter to avoid ending the fitted line prematurely. The SDA response was deemed to have ended when the fitted response fell to within 5% of SMR. Four experiments were omitted from the dataset due to large misalignments of the pre- and post-SDA estimates of SMR, leaving N=51. Body mass did not differ among temperature groups (P>0.05, F_4,45=0.39; two-way ANOVA for temperature and ration size), or between the 2% and 4% ration sizes (P=0.065, F_1,45=3.58). All groups contained a mix of males and females, apart from the 4% ration size at 20°C, where only two experiments were successful because of regurgitations (Table 1).

From the curve fitted to the SDA response, several metrics were calculated (Table 2). SDA duration (SDA_dur) was calculated as the time from feeding to the end of the fitted line. SDA_peak was taken as the highest Ṁ_O2 value estimated along the fitted line, and Time_peak as the associated time (hours post-feeding) of the peak response. The net SDA peak (SDA_peak,net) was calculated as SDA_peak minus SMR. The remaining capacity to elevate Ṁ_O2 above SDA_peak, the post-prandial residual aerobic scope (PRAS) was calculated as an absolute value (mg O₂ kg⁻¹ h⁻¹) by subtracting SDA_peak from MMR. The proportion of aerobic scope that SDA_peak occupied, percentage PRAS, was calculated as 100×(SDA_peak,net/AS). SDA_cost was calculated by taking the area under the curve and multiplying it by body mass and an oxycaloric coefficient to convert total oxygen consumed during SDA to kJ. We used a value of 14.06 kJ g⁻¹ O₂ as reported for ammonotelic organisms in Elliott and Davison (1975).

SDA_coef, which represents the proportion of meal energy used for its digestion (an indicator of the energetic efficiency of digestion), was calculated as SDA_cost divided by gross energy (GE) of the meal. We calculated meal GE (kJ) using an equation from Bureau (2003), who reported the GE of rainbow trout fed a standard hatchery diet across a range of sizes: GE=8.6×body mass−40.1 (where body mass is in g). From this equation, we found that a ca. 50 g rainbow trout such as ours has a whole-organism energy content of 7.8 kJ g⁻¹. We also calculated digestible energy (DE) using the egestion equation provided by Elliott (1976), in the current bioenergetics model for walleye: DE=GE−FE, where FE is faecal energy (egestion) calculated as FE=0.0158T^−0.222e^0.631×p, where T is temperature, and p is the proportion of maximum consumption (Elliott, 1976). We used p=0.5 for the 2% ration and p=1 for the 4% ration to estimate DE based on the mean trial temperature.

We fitted SMR of all fish to the temperature- and mass-scaling equation SMR=aM^be^cT, where M is body mass, T is mean trial temperature, a is the intercept, b is the mass-scaling exponent and c is the temperature-scaling exponent. We tested this model for the effect of sex, as well as a sex×temperature interaction, and a sex×mass interaction, separately using general linear models (GLMs). To facilitate comparison with future studies, we calculated the temperature scaling coefficient, Q₁₀, as Q₁₀=e^c×10 using pooled data for males and females. As mean body mass differed between sexes, we further investigated sex differences in SMR by modelling males and females separately using the above equation and adjusted SMR to a common body mass of 1800 g (rounded from the mean body mass of all individuals, which was 1855 g) using sex-specific mass-scaling exponents and the equation Rate_1800 g=Rate_observed×(1.8/M)^b (e.g. Reidy et al., 2000). We re-fitted the above equation using the mass-adjusted data where M=1.8 kg and tested for the effect of sex using a GLM. We estimated the overall difference between sexes using estimated marginal means (EMMs) and the emmeans (https://cran.r-project.org/web/packages/emmeans/index.html) package. Additionally, we tested for sex differences in SMR within temperature groups using pairwise t-tests and a significance level of α=0.01 (as per a Bonferroni correction).

As MMR retained its bell-shaped curve even after ln-transformation of temperature and MMR, we fitted the data with a second-order polynomial for temperature as the covariate, using the equation MMR=aM^be^cT+dT2, where c and d are both temperature-scaling exponents. We tested this model for an effect of sex, a sex×temperature interaction, and a sex×weight interaction using GLMs with sex as a covariate. We further investigated this by running separate models for males and females and used the sex-specific mass-scaling exponents to adjust MMR to a common body mass of 1.8 kg using the same formula as above. We re-fitted the initial MMR equation using the mass-adjusted data where M=1.8 kg and tested again for an effect of sex using a GLM.

Our study was challenged statistically by the fact that body mass varied substantially, and our meal sizes were standardized. To include both body mass and GE in our model would account for 100% of the variation in ration size, and to include both ration size and GE would account for 100% of the variation in body mass. If we evaluate body mass without considering GE, we risk misinterpreting an effect of body mass as an effect of GE, or vice versa, because of the covariance between these two terms. If we evaluate ration size without considering body mass, we risk misinterpreting an effect of ration size (relative meal size) as an effect of GE (absolute meal size). It was therefore necessary to conduct two tests for each dependent variable related to feeding: one to evaluate body mass, and one to evaluate ration size. Where we find an effect of GE in the absence of ration size, we should also find an effect of ration size in the absence of GE. We ln-transformed dependent variables SDA_dur, SDA_peak, SDA_peak,net and Time_peak to meet assumptions of homogeneity and improve fitting of parametric models. We ran GLMs against ln-transformed temperature (to improve linearity) with sex and ration size as fixed effects, and body mass as a covariate. These models were ineffective in estimating body mass effects because they account for the relative change in meal size, but it allowed us to estimate the magnitude of change between 2% and 4% rations using EMMs. We tested for sex×temperature and ration size×temperature interactions and conducted post hoc tests by running pairwise contrasts for ration size and sex when significant. A second GLM was conducted to evaluate the effect of body mass by modelling the above-mentioned dependent variables against ln-transformed temperature, with body mass and GE as a covariates and sex as a fixed effect.

We ln-transformed AS, PRAS and percentage PRAS and similarly conducted GLMs against independent variables. However, because the relationship with temperature remained curvilinear even after ln-transformation, temperature was also modelled as a second-order polynomial. Ration size/GE was of course omitted in the GLM for AS and was modelled against temperature as a covariate and sex as a factor. We conducted separate GLMs to evaluate ration size and body mass effects on PRAS and percentage PRAS, with sex as a factor in both. We did not include individual variation as a random effect in any of the above models to avoid overfitting. All model outputs are summarized in Tables S1, S2 and S3.

We modelled SDA_cost several ways. First, we ran a GLM against GE with ration size and sex as factors, and temperature as a co-variate. We excluded body mass from this model because of the strong covariance with GE (we cannot include both body mass and ration size as this accounts for 100% of the variation in GE, as mentioned above). A significant difference in slope between ration size groups would indicate that SDA_coef is inconsistent between ration sizes. We dropped the non-significant terms and conducted a second linear regression for SDA_cost against GE alone. We conducted a third linear regression using a 0,0 intercept; an intercept term is physiologically impossible in a bioenergetics context, as a 0 g meal cannot induce SDA. Lastly, we tested for the effect of body mass on SDA_cost by running a linear regression against GE with body mass as the sole covariate. We repeated these steps using DE in place of GE and compared the model fit (R²) and residuals of each model. Although the SDA_coef is best described by the slope of the SDA_cost–meal energy relationship, we compared individual estimates of SDA_coef between groups using an ANCOVA, where temperature group was the primary predictor, and sex and ration size were factors.

As expected, there was a positive effect of temperature on SMR (P<0.001), characterized by a Q₁₀ of 2.9 (Fig. 1). We found no effect of sex, a sex×temperature interaction or a sex×mass interaction on SMR using pooled data (P>0.05 for all). SMR decreased with body mass; the whole-organism mass-scaling coefficient was 0.9 (R²=0.95, P=0.11 for body mass). We fitted a model using units of daily Ṁ_O2 (g O₂ day⁻¹ g⁻¹) to be consistent with bioenergetics model parameter units, yielding the equation SMR=0.000517×M^−0.095×e^0.107×T. Mass-scaling of SMR was weakly sex specific, with a coefficient of 0.73 for males (R²=0.95, P=0.061 for body mass) and 0.89 for females (R²=0.94, P=0.33 for body mass). Adjusted to a common body mass of 1.8 kg, a GLM indicated that female SMR was 7–15% higher (contrast ratio±s.e.) than male SMR (P=0.025). However, pairwise t-tests found no significant difference in SMR between sexes within a single temperature group using mass-adjusted data, nor did we find evidence of a sex×temperature or sex×body mass interaction.

We found a drastic effect of body mass on MMR, with a mass-scaling exponent of 0.55 (R²=0.82, P<0.001). We found no evidence of sex, a sex×mass or a sex×temperature interaction using pooled data (P>0.05 for all). The mass-scaling coefficient for MMR was 0.55 for males (R²=0.76, P=0.057 for body mass) and 0.72 for females (R²=0.83, P=0.043 for body mass). Sex was similarly non-significant when MMR was adjusted to a common body mass of 1.8 kg (Fig. 1).

The change in SDA with increasing temperature was characterized by a reduction in SDA_dur and an increase in SDA_peak (Fig. 2). SDA_dur ranged from 13.5 days at 2°C to 28 h at 20°C (effect of temperature, P<0.001). There was an interaction between ration size and temperature (P<0.05) such that SDA_dur was similar between ration sizes at low temperatures but differed substantially at high temperatures. Averaged across temperatures, 4% rations took 35% longer to digest than did 2% rations (Fig. 3A). Body mass had no apparent effect on SDA_dur (P>0.05).

Mean SDA_peak increased 746% from 15.4±1.6 mg O₂ kg⁻¹ h⁻¹ at 2°C to 115±18.6 mg O₂ kg⁻¹ h⁻¹ at 20°C (P<0.001; Fig. 3B). Mean SDA_peak,net increased similarly, rising 829% from 4.15±0.79 mg O₂ kg⁻¹ h⁻¹ to 34.4±9.2 mg O₂ kg⁻¹ h⁻¹ across temperatures (P<0.001; Fig. 3C). Doubling ration size from 2% to 4% led to a 6–12% increase in SDA_peak (contrast ratio±s.e., P<0.05; Fig. 3B) and a 18–29% increase in SDA_peak,net (contrast ratio±s.e., P<0.05; Fig. 3C). SDA_peak and SDA_peak,net both decreased with body mass; the mass-scaling exponent was 0.9 for SDA_peak (P=0.014) and 0.78 for SDA_peak,net (P=0.01).

Time_peak decreased substantially with temperature (P<0.001, Fig. 3D), but was statistically limited to a minimum of 5 h because of our selection of an acclimation time applied to the SDA curve; 29 of 51 experiments peaked at this time. There was an interaction with sex whereby males had shorter Time_peak at higher temperatures than did females (mean male Time_peak was 47% shorter at 14.5°C, 23% shorter at 20°C). We found no evidence that Time_peak was related to body mass (P>0.05).

AS increased from 2 to 10°C but was fairly inconsistent with additional increases in temperature (one polynomial temperature exponent was positive, the other was negative, P<0.001 for both). Mean (±s.e.m.) AS was highest at 15°C (135±10.1 mg O₂ kg⁻¹ h⁻¹), with no apparent further increase at 20°C (123±9.5 mg O₂ kg⁻¹ h⁻¹). We found weak evidence that AS was 9–24% lower in females (contrast ratio±s.e., P=0.0558). PRAS increased from 2 to 4°C but was consistent thereafter (Fig. 4A); one of the polynomial temperature coefficients for PRAS was positive, and the other was negative (P<0.001 for both). Fish had ample PRAS in all temperature groups with means (±s.e.m.) of 42±8.4, 89±7.7, 111±11.8, 104±8.4 and 88±8.7 mg O₂ kg⁻¹ h⁻¹ from 2 to 20°C, respectively. PRAS decreased by 5–25% in the 4% ration size group (contrast ratio±s.e., P=0.0355). PRAS decreased with body mass in the model with ration size (P=0.0014), but we found no effect of body mass in the second model with GE (P=0.131). Percentage PRAS decreased with temperature (both polynomial temperature coefficients were negative, P<0.001; Fig. 4B). Percentage PRAS was highest at 4°C with a mean (±s.e.m.) of 92±0.7%, and lowest at 20°C with a mean of 71±2.7% (Fig. 4B). Percentage PRAS was 4–8% higher (relatively, not absolutely) in the 2% ration size group (contrast ratio±s.e., P<0.01) and was unaffected by body mass (P>0.05, Fig. 5). Theoretically, male PRAS should be higher if male AS is higher and there are no sex-differences in SDA_peak; however, our models found no effect of sex on PRAS or percentage PRAS (P>0.05 for both).

SDA_cost increased with GE (P<0.0001) and was unaffected by sex, temperature or ration size (R²=0.65, P>0.05 for all; Fig. 6). SDA_cost was best described by the equation SDA_cost=0.0503GE+3.1 (R²=0.65) but goodness-of-fit was negligibly lower when modelled with a 0,0 intercept (SDA_cost=0.0569GE, R²=0.64). Model fit was slightly improved using DE (P<0.0001), and indicated similar non-effects of sex, temperature and ration size (R²=0.67, P>0.05 for all). SDA_cost based on DE was best described by the equation SDA_cost=0.0617DE+2.69 (R²=0.66) but model fit was near-identical using a 0,0 intercept (SDA=0.0685DE, R²=0.65; Fig. 6). We found no effect of body mass on SDA_cost (P>0.05), nor were there noticeable differences between any of the above model residuals. An ANCOVA for SDA_coef found a positive effect of GE (P<0.01) but no relationship with temperature, sex or ration size (P>0.05 for all).

We found support for our hypothesis that temperature dictates the shape of the SDA response in walleye, but that SDA is ultimately a consistent proportion of the ingested meal energy. Sex played a minimal role in shaping SDA in our experiments. We present the finding that males reached Time_peak more quickly with caution because the fitted SDA curve is susceptible to misidentifying random bouts of activity/high Ṁ_O2 as Time_peak. While many fish reached Time_peak at the minimum possible time of 5 h, regardless of temperature, there were more instances of female Time_peak that were longer than this minimum threshold. Alternatively, we found substantial effects of body mass on walleye metabolism and SDA. Body mass had a negative effect on PRAS, which is the sum of a constraining effect of body mass on MMR and a relieving effect of body mass on SDA_peak. In the context of the AS protection hypothesis, our findings suggest that large walleye, most of which are females because of size dimorphism, may be more susceptible to constraints on AS at high temperatures as a result of the strong, negative influence of body mass on MMR. The fact that SDA_peak decreased with body mass suggests that aerobic scope may be intrinsically ‘protected’ as fish grow and their AS declines.

Our results do not suggest that walleye need to avoid larger meals to protect AS within habitual temperatures (cf. Norin and Clark, 2017); increasing ration size only led to a small increase in SDA_peak, leaving fish with ample PRAS. The primary response to an increase in ration size was to prolong the digestive response, rather than increasing SDA_peak. However, our study was limited to a maximum experimental temperature of 20°C, and walleye are known to inhabit temperatures up to 24°C during the summer (Peat et al., 2015). Should our findings be extrapolated to supra-optimal temperatures, we may find that constraints arise. As female walleye are naturally larger at a given adult age (Bozek et al., 2011), we posit that large (old) females would be most susceptible to the potential consequences of AS protection, such as a reduction in growth and reproductive output.

We found no evidence that SDA_coef changed with ration size; instead it was a consistent ∼6–7% of DE. From an evolutionary standpoint, it is sensible that SDA_coef is unaffected by modest variation in meal size. Natural selection favours efficiency, so digestive systems have likely evolved to handle meals with the proportionate response. The mechanical component of SDA (chewing, swallowing, peristalsis) and the catabolic component (digestion, absorption) are relatively small in comparison to the biochemical components of protein synthesis and growth (Tandler and Beamish, 1979; Wieser, 1994), which are substrate limited. Here, we omitted a portion of the mechanical process by force-feeding walleye. Tandler and Beamish (1979) have shown that the mechanical component has an asymptotic relationship with ingested energy, i.e. there is very little difference in mechanical cost between small and large meals. Although this is only a small component of SDA, in theory this would contribute to changes in SDA_coef with ration size.

Evidence of an effect of ration size on SDA_coef among fishes is almost entirely limited to juvenile life stages. Boyce and Clarke (1997) found that SDA_coef decreased with increasing ration size in juvenile Antarctic plunderfish (Harpagifer antarcticus) and attributed this difference to the mechanical component of feeding. There were mixed relationships in juvenile Chinese catfish (Silurius asotus), where SDA_coef increased between 0.5% to 2% rations but decreased from 2% to 4% rations (Fu et al., 2006). Juvenile snakehead (Channa argus) exhibited a negative correlation between ration size and SDA_coef (Wang et al., 2012). Norin and Clark (2017) reported that SDA_coef decreased exponentially with meal size in juvenile barramundi (Lates calcarifer), concluding that fish must ‘eat big’ for growth efficiency; however, they also present a linear relationship between SDA_cost and meal size with an intercept. We suspect that this intercept term is responsible for the reported changes in SDA_coef and possibly a reflection of the fixed contributions of the mechanical portion of SDA as we mention above. In contrast, no evidence of ration size effects on SDA_coef was found in southern catfish (Silurius meridionalis; Fu et al., 2005b) or in Atlantic cod (Gadus murhua; Jordan and Steffensen, 2007).

In the context of AS protection, the implication of a consistent SDA_coef is that animals consuming multiple small meals instead of one large meal would not have consequences for growth. However, it seems unlikely that physically acquiring (foraging) multiple small meals is equally efficient given the activity component of foraging. Small fish are slower, and possibly easier to acquire, but the overall cost of multiple predation events may be greater. The relative meal size of walleye decreases with predator length (Gaeta et al., 2018), likely as a result of an abundance of small fishes (Knight et al., 1984), and the energetic consequences of this (if they exist) may already occur naturally. Research has shown that walleye growth rates are positively correlated with the presence of cisco (Coregonus artedi), a large-bodied prey species (Kaufman et al., 2009), which adds support to the idea that larger prey items are more efficient forage overall.

Although we are the first to use intermittent-flow respirometry to estimate SDA in adult walleye, others have investigated feeding efficiency in juvenile conspecifics. Beamish and MacMahon (1988) reported an SDA coefficient of 12–19% for juvenile walleye and found a negative correlation with meal size in a study using flow-through group respirometry. Kelso (1972) investigated food conversion efficiency in juvenile walleye using whole-organism energy density measured via calorimetry and determined that conversion rates of yellow perch and emerald shiner as prey items were highly efficient at 96.9% and 97.9%, respectively. Kelso (1972) found no effect of ration size, but did find an effect of body mass, where larger individuals had lower conversion efficiencies. Tarby (1981) estimated SDA of two juvenile and one small adult walleye fed a variety of rations and reported a mean SDA_coef of 10% with very little variation (8.8–10.9%). There is little agreement between these studies, ours included, on the magnitude and mass scaling of walleye SDA, which may simply be due to different techniques being used, or differences between juvenile and adult SDA.

Our estimate of SDA_coef (∼6%) differs substantially from the current number being used in bioenergetics, which is 17.5% (Deslauriers et al., 2017). It is possible that our estimate of GE was inaccurate as we did not conduct bomb calorimetry ourselves to determine rainbow trout energy density. Our estimate of rainbow trout GE (7.8 kJ g⁻¹) is substantially higher than estimates of GE for common prey items such as Notropis sp. (5 kJ g⁻¹; Kelso, 1972) and yellow perch (5.7 kJ g⁻¹; Hurley et al., 1986), but similar to another estimate for rainbow trout (7.3 kJ g⁻¹; Bennett and Hart, 1993). Regardless, even a large reduction of GE in our calculations would leave our SDA coefficient well below the 17.5% being used currently, so we conclude that walleye have much lower SDA_coef than previously thought. The small improvement in model fit using Elliot's (1976) egestion equation to calculate DE (which was derived from studies on brown trout, Salmo trutta) supports its inclusion in the walleye bioenergetics model.

Our study is limited in its ability to estimate the effect of body mass on SDA because we standardized meal sizes. After accounting for meal mass, there are essentially only two ‘relative’ body masses in our study, 50×meal mass and 25×meal mass. Some studies have shown that SDA scales allometrically with body mass using the model SDA=aM^bP^c, where M is body mass, P is meal energy or mass, a is an intercept term, b is a mass-scaling coefficient and c is a meal mass coefficient (Beaupre, 2005). Studies have found inconsistent results on the effects of body mass on SDA in fish, reporting positive, neutral or negative relationships (von Herbing and White, 2002; Luo and Xie, 2008b; Tandler and Beamish, 1981). We suggest future research projects use a minimum of three ration sizes to improve the statistical power in estimating allometric relationships with body mass.

In conclusion, our findings on SDA in adult walleye differ from the small body of literature on juvenile walleye regarding the effects of ration size and meal energy on SDA. As a result, our data will provide a useful update to the fish bioenergetics model for walleye, presumably improving its accuracy for forecasting effects of climate warming and invasive species (Gartshore and Rennie, 2023; Madenjian et al., 2018; Quist et al., 2002). We found notable effects of temperature and body mass on aspects of walleye metabolism, leading us to believe that large females may be more susceptible to aerobic constraints in a warmer future. However, we found no evidence that sex differences in SDA are proximate mechanisms that contribute to female-biased size dimorphism in this species. We suspect that bioenergetics models are currently overestimating the daily costs of SDA in adult walleye, and we propose future research projects re-examine these models and the effect on growth when SDA is reduced.

We would like to thank Kurt Smith and Paul Bzonek from the Great Lakes Laboratory for Fisheries and Aquatic Sciences for leading fish collection from Rice Lake. Erin Ritchie also assisted with fish collection and transport. Thanks to Steve McNevin, Erin Brown, Sonya Kranzl and Colin Lake (MNRF Lake Ontario Management Unit) for collection of Bay of Quinte fish. We would also like to thank the Trent University Animal Care Committee staff for facilities support.