Using meta-analysis to derive a respiration model for Atlantic Salmon (Salmo salar) to assess bioenergetics requirements of juveniles in two Canadian rivers

23 Standard metabolic rates (SMR) for Atlantic Salmon have been calculated independently for 24 different life stages and populations, but the absence of a comprehensive SMR model limits its 25 application for modelling the energy use or life stage-specific growth. Atlantic Salmon 26 respiration data were compiled from a meta-analysis of 26 publications and exponential or 27 optimal relationships were fitted to the meta-data to estimate respiration equation parameters and 28 generate confidence intervals dependent on temperature and body mass. While model parameters 29 were significant for both models, mass corrected standard metabolic rates (g O ₂ ·d -1 ) increased as 30 a function of water temperature (°C) and decreased beyond ~16 °C, following an optimal 31 relationship (AIC optimal = -9185.5 vs. AIC exponential = -8948.95; ∆AIC = 236.55). Juvenile Atlantic 32 Salmon growth (cohorts 1 and 2) from bioenergetics simulations did not vary between Little 33 Southwest Miramichi and Northwest Miramichi rivers, however, variation between simulations 34 using the different respiration models (i.e., exponential vs. optimal) led to differences in the way 35 fish allocate energy throughout the year. Results from this analysis will inform conservation efforts for the species throughout its current range and predict the energetic requirements at 37 juvenile life stages.

note that only control treatments were selected in cases where SMR were measured under non-137 normal conditions (e.g., water pollution, genetically-modified organisms). Standard metabolic 138 rates for Atlantic Salmon found in figures were quantified using digitizer software (PlotDigitizer,139 http://plotdigitizer.sourceforge.net). 140 Atlantic Salmon respiration models 141 The Atlantic Salmon respiration models are based on mass-and temperature-dependent 142 respiration equations following: where R is the specific rate of respiration in g O₂·g -1 ·d -1 and is dependent on the fish 145 body mass (W) in g, water temperature (T) in °C, and activity (Act). RA and RB are the intercept 146 and slope coefficients, respectively, of the allometric mass function of oxygen consumed by a 1 147 g fish at 0 °C. We considered respiration at the resting or inactive state, therefore, the activity 148 multiplier was set to 1 (Boisclair and Legget 1989;Boisclair and Sirois 1993). The SMR values 149 sourced from literature along with associated body mass and temperature provided the input data 150 for the Atlantic Salmon respiration model (equation 1).

151
Two different temperature functions were used to account for differences in SMR where RTO (°C) is the optimum temperature for respiration (where respiration is highest) 166 and RTM (°C) is the maximum or lethal water temperature set to 30 °C (an average lethal 167 temperature for laboratory and wild conditions (Elliott 1991;Breau et al. 2011)).

168
Both nonlinear regression models were fitted to the respiration meta-data collected from 169 the literature using the "nls2" package in R (Grothendieck 2013;R core Team 2017 performs a least-squares optimization (Grothendieck 2013). Respiration models were evaluated 177 by comparing Akaike information criterion (AIC) and ∆AIC.

178
To visually compare Atlantic Salmon respiration models, mass corrected standard 179 metabolic rates (SMR corr in g O₂·d -1 , for 1 g of fish) were plotted as a function of water 180 temperature (°C). To represent both respiration models together with meta-data, we multiplied 181 SMR with body mass (W) and used 0.1272 as a power value that represents the average RB 182 (slope coefficient) from both models:

184
Atlantic Salmon respiration model evaluation using published SMR models 185 To evaluate the performance of the Atlantic Salmon respiration models explained in the 186 previous section (i.e., exponential vs. optimal relationships), we compared our predicted 187 respiration estimates with those of four previously published models, each model accounting for 188 differences in mass and temperature to predict respiration rates (  The LSWM River had higher mean daily temperatures (18.2 °C) than the NWM River 292 (14.5 °C) and greater differences in mean daily temperatures between rivers from mid-July to 293 mid-August were observed (differences ranged from 0.07 -5.32 °C, across all years).

295
-18.6 °C for the NWM River (Table 3). Bioenergetics growth simulations using LSWM river 296 summer temperature profiles and empirically-derived growth rates revealed different growth 297 trends between exponential and optimal respiration models ( Figure 4). Simulations using the 298 optimal respiration model showed a negative net energy budget at temperatures ranging between 299 11-16 ºC, while this negative net energy budget only occurred during the winter months for the 300 exponential respiration model simulation. The loss of mass during the overwintering months 301 using the exponential model can be explained by the model's propensity of overestimating the 302 energetic costs of metabolism at low temperatures ( Figure 2). Conversely, the energetic costs of 303 metabolism were low for the optimal respiration model simulation, enabling fish to gain mass 304 during overwintering months. Fish grew 12% smaller in the NWM for the optimal model 305 simulation, but grew 12% larger in the same river for the exponential model simulation (Table   306 3). Higher consumption estimates for both cohorts were generally observed for the exponential 307 model simulation over the optimal model simulation. In the absence of empirical growth data for D r a f t the NWM, growth and consumption rate simulations for Atlantic Salmon remained the best 309 available information for this river.   (1985); Maxime et al. (1989); Seddiki et al. (1996) D r a f t D r a f t Table 3. Simulation results for growth (final body mass in g) and total consumption (g) for two cohorts (1: 0+ -1+; 2: 1+ -2+ ) at the end of their second growing season, using exponential or optimal respiration, for Atlantic Salmon residing in the Little Southwest Miramichi (LSWM) and Northwest Miramichi (NWM) rivers. Growth rates for LSWM were used to estimate food consumption, for which the values were used to simulate growth for fish residing in the NWM. Observed growth rates from the LSWM were used to estimate total food consumption in both the LSWM and NWM rivers.
Growth (g) Consumption (g) Water temperature (°C) cohort 1: 0+ -1+ cohort 2: 1+ -2+ cohort 1: 0+ -1+ cohort 2: 1+ -2+ River Tmin Tmax Mean exponential optimal exponential optimal exponential optimal exponential optimal    D r a f t Figure 2. Mass corrected standard metabolic rate (g O₂·d-1) from meta-data as a function of water temperature (°C). The mass corrected metabolic rates are for a 1g fish at a given temperature. The blue line and grey area correspond to the fitted loess smoothing function ± 1 S.E.M. to the meta-data (points), while the solid and dashed black lines correspond to respiration models following the exponential and optimal relationships, respectively.
254x190mm (300 x 300 DPI) D r a f t Figure 3. Probability density plots illustrating the percent differences between predicted respiration values from the A) optimal and B) exponential models and respiration values generated from four published and independent respiration models: in pink, Berg et al. (1993); green, Fivelstad and Smith (1991); blue, Forsberg (1994); purple, Grottum and Signolt (1998).
215x279mm (300 x 300 DPI) D r a f t Figure 4. Atlantic Salmon observed (boxplots) and simulated growth in the Little Southwest Miramichi using either the exponential (solid line) or optimal (dashed line) respiration models for A) ages 0+ -1+ (first cohort), and B) ages 1+ -2+ (second cohort). Average daily temperature profile for the LSWM is shown in grey.