Growth Rate Potential of Juvenile Sockeye Salmon in Warmer and Cooler Years on the Eastern Bering Sea Shelf

Table 1

Equations and parameter description of the sockeye salmon bioenergetics model. Note that subscripts i and s represent year (i = 2000 to 2006) and station, and overbars denote mean quantities within the definitions of i.

Symbol	Equation and parameter description	Value	Source
Growth: 𝐺𝑖,𝑠=𝜏⋅𝐼𝑖,𝑠−(SMR𝑖,𝑠+ACT𝑖,𝑠)
G	Growth rates (cal/s)
𝝉	Proportion of food that can be metabolized (dimensionless)	0.7	1
I	Feeding rates (cal/s)
SMR	Standard metabolic rates (cal/s)
ACT	Activity costs (cal/s)
Consumption: 𝐼=ED𝑖,𝑠⋅(𝜌⋅𝛾⋅𝑈/(1+𝜌⋅𝛾⋅ℎ⋅𝑈))
ED	Prey energy density (cal/gwet)
𝜌	Prey density (g/cm^3)
𝛾	Cross-sectional area of the reactive field (cm^2)
U	Swimming speed (cm/s)
h	Handling time (s/g)
Cross-sectional area of the reactive field: 𝛾=𝛼3⋅𝑊^𝛽3
𝛼3	Intercept (cm^2)	1	1
𝛽3	Coefficient, 𝛾 versus W	0.69	1
W	Sockeye salmon weight (g)
Handling time: ℎ=𝑊^CB−1/(CA⋅𝑓(𝑇))
CA	Intercept for maximum feeding rates (g/s)	3.51×10^−6	3
CB	Allometric exponent of maximum feeding rate	0.275	3
𝑓(𝑇)	Temperature adjustment for maximum food consumption rates
T	Sea surface temperature (^∘C; 5 m below surface)
Temperature adjustment function: 𝑓(𝑇)=𝐾𝑎⋅𝐾𝑏
	𝐾𝑎=(0.58⋅𝐿1)/(1+0.58⋅(𝐿1−1))		3
	𝐿1=exp(𝐺1⋅(𝑇−3))		3
	𝐺1=(1/(20−3))⋅ln((0.98⋅(1−0.58))/(0.58⋅0.02))		3
	𝐾𝑏=(0.5⋅𝐿2)/(1+0.5⋅(𝐿2−1))		3
	𝐿2=exp(𝐺2⋅(24−𝑇))		3
	𝐺2=(1/(24−20))⋅ln((0.98⋅(1−0.5))/(0.5⋅0.02))		3
Standard metabolic rates^∗: SMR=𝛼1⋅𝑊^𝛽⋅𝑒^𝜑⋅𝑇
𝛼1	Intercept (cal/s)	4.76×10^−5	4
𝛽	Coefficient, SMR versus W	0.87	4
𝜑	Coefficient, SMR versus 𝑇(1/^∘C)	0.064	4
Swimming costs^∗: ACT=𝛼0⋅𝑊^𝛿⋅𝑈^𝜆
𝛼0	Intercept (cal · s^-1)	1.74×10^−6	4
𝛿	Coefficient, ACT versus W	0.72	4
𝜆	Coefficient, ACT versus U	1.6	4
Swimming speed: 𝑈=𝜔⋅𝑊^𝜈⋅exp^(𝜅⋅𝑇)
𝜔	Intercept (cm/s)	11.1	4
𝜈	Coefficient, U versus W	0.097	4
𝜅	Coefficient, U versus 𝑇(1/^∘C)	0.040	4

(1) Reference [22]; (2) this study; (3) reference [27]; (4) reference [23]. ∗The oxygen consumption rates were converted from mg O₂/h to cal/s using an oxycalorific equivalent to 3.24 mg O₂/cal [30].