Budy & Luecke. Appendix I : Understanding how lake populations of Arctic char are structured and function with special consideration of the potential effects of climate change.

The modeling approach we used to estimate consumption and growth of arctic char was based on the balanced energy budget of a poikilothermic organism (Hartman and Kitchell 2008), described conceptually in greater detail in the main manuscript. We used the Wisconsin bioenergetics model (Hanson et al. 1997), scaled to arctic char to model growth and consumption.

We combined field data with the bioenergetics model to estimate average annual (365 day) consumption by an average individual in three size classes as:

C = Cmax × PropCmax × f(T)

where:,C is the specific consumption rate, g/g/day, Cmax is the maximum specific feeding rate based on allometry, g/g/day, PropCmax is the proportion of maximum consumption (0-1), f(T) is a temperature-dependent function that ranges from 0 at low or very hot temperatures to 1 near optimal temperature, and T is the water temperature. PropCmax is fit iteratively to observed growth (g/time), after accounting for losses due to respiration (active and standard), specific dynamic action, and wastes (egestion and excretion), and given the temperature effect. Please see Hanson et al.(1997)for a detailed description of each model function.

We started with the base model for lake trout (Salvelinus namaycush), substituted the model’s consumption equation number 3 for 1, and fit the maximum consumption function to match optimal temperature for consumption (CTO) for arctic char (Appendix Table 1). We used the temperature data parameters of Larsson & Berglund (2005; mean of four lakes; CTO = 15.38 °C).

Lake temperature data were taken from a long-term data set of mean seasonal temperature in each lake on 84 occasions, and used to model thermal-history (i.e., ambient water temperature) regime for char. Because temperature data were not complete for all years in either lake, we chose the warmest and coldest years of available data for Toolik Lake, where a long data series of temperature profile data is available as part of the LTER ( We then used linear regression of available temperature data for Lakes E5 and Fog2 (y) as a function of temperature data for Toolik Lake (x) in the same year, to build a complete temperature profile (by 1-m increments) for a representative ‘warm year’ and a ‘cold year’ in each of the study lakes.

Diets, as percent composition by wet weight were taken from dissected stomachs of < 300 mm and > 300 mm char; collected during the critical ice-off period of highest growth rates and consumption rates (Appendix Table 2). Growth from start to end weight was estimated from the most precise estimates available for each size class by lake using mark-recaptured fish (Appendix Table 3). Prey energy densities (joules/g wet weight) for each prey based on standard literature values (Arctic char = 5701 J/g and prey items as follows: Diptera = 2377 J/g, Trichoptera = 3342 J/g, and Mollusca = 1482 J/g; Cummins and Wuycheck 1971; Guѐnardet al.2008)) were held consistent over the entire 365-day modeling interval (20 March on day 1, ending on day 365). We did not model mass lost to spawning as we were primarily interested in relative differences.

Appendix Table 1. Arctic char bioenergetics model parameter values used to estimate growth and prey consumption.

Parameter / Value / Description
Consumption, Equation 3
CA / 0.628 / Intercept for maximum consumption(Cmax)
CB / -0.3 / Exponent for Cmax
CQ / 5.351 / Lower temperature where dependence is CK1
CTO / 15.375 / Temperature at which consumption is 98% of Cmax rate
CTM / 15.449 / Maximum temperature above which consumption ceases
CTL / 17.692 / Lethal water temperature for consumption
CK1 / 0.33 / Temperature dependence at CQ
Respiration, Equation 1
RA / 0.00463 / Intercept for maximum standard respiration
RB / -0.295 / Slope for weight dependence of standard metabolism
RQ / 0.059 / Coefficient for temperature dependence of metabolism
RTO / 0.0232 / Optimum temperature for standard respiration
RTM / 0 / Maximum temperature for standard respiration
RTL / 11 / Lethal water temperature for respiration
RK1 / 1 / Intercept for swimming speed RTL
RK4 / 0.05 / Intercept for swimming speed at all water temperatures
ACT / 11.7 / Temperature-dependent activity coefficient
BACT / 0.0405 / Coefficient for temperature dependence of swimming speed RTL
SDA / 0.172 / Proportion of assimilated energy lost to specific dynamic action
Egestion-Excretion, Equation 3
FA / 0.212 / Proportion of assimilated food egested
FB / -0.222 / Slope for temperature dependence of egestion
FG / 0.631 / Coefficient for feeding level dependence of egestion
UA / 0.0314 / Proportion of assimilated food excreted
UB / 0.58 / Slope for temperature dependence of excretion
UG / -0.299 / Coefficient for feeding level dependence of excretion

Appendix Table 2. Proportion of diet by wet weight used in the model for three size classes of arctic char from two study lakes.

Lake / Size class / Proportion of diet (by mass)
Diptera / Trichoptera / Mollusca
Lake E5 / Small / 0.79 / 0.18 / 0.03
Medium / 0.79 / 0.18 / 0.03
Large / 0.25 / 0.37 / 0.38
Lake Fog 2 / Small / 1.0 / 0 / 0
Medium / 1.0 / 0 / 0
Large / 1.0 / 0 / 0

Appendix Table 3. Arctic char weight inputs and model output for the “base” bioenergetics model under the “cold” scenario for two study lakes.

Lake / Size class / Start weight (g) / End weight (g) / Proportion of Cmax / Annual consumption (g)
Lake E5 / Small / 40.5 / 52.6 / 0.417 / 446.3
Medium / 124.5 / 153 / 0.458 / 1011.1
Large / 235.6 / 256.3 / 0.427 / 1382.1
Lake Fog 2 / Small / 37 / 48 / 0.453 / 441.0
Medium / 142.4 / 177.8 / 0.485 / 1139.4
Large / 333.3 / 437.1 / 0.549 / 2324.7

Literature cited

Cummins KW, Wuycheck JC (1971) Calorific equivalents for investigations in ecological energetic. Mitt IntVereinTheorAngLimnol18:1-158

Guѐnard GG, Boisclair D, Ugedal O, Forseth T, Jonsson B. (2008) Comparison between activity estimates obtained using bioenergetic and behavioral analyses. Can J Fish AqSci 65:1705-1720

Hanson PC, Johnson TB, Schindler DE, KitchellJF (1997) Fish bioenergetics 3.0 for Windows. Technical Report WISCU-T-97-001. University of Wisconsin Sea Grant Institute, Madison

Hartman KJ, Kitchell JF (2008)Bioenergetics modeling progress since the 1992 symposium. Trans Amer Fish Soc 137:216-223

Larsson S, Berglund, I (2005) The effect of temperature on the energetic growth efficiency of Arctic charr (Salvelinus alpinus L.) from four Swedish populations. J ThermBiol 30:29-36

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