Energy Balance: Respiration and Excretion

The costs of respiration (g/hr) depend on a crab's size and the temperature of its environment while excretion costs are modeled as a fixed fraction of respiration costs:

$$\begin{aligned}G_{\text{(resp + excrete)}} = (1.0 + \gamma_{\te... ...min met}} \, G^{\beta_{\text{met}}}\, f_\text{Temp} \end{aligned}$$

where $\gamma_$excretion is set at 0.05  (Guerin and Stickle 1992, Tables 2 and 3), $\alpha_$min met$= 0.00166$ (g $^{1-\beta_{\text{met}}}$/hr)  (Houlihan et al. 1985; Booth and McMahon 1992), and $\beta_{\text{met}} = 2/3$ (Houlihan et al. 1985; Laird and Haefner 1976) governs how the rate of energy expenditure increases with increasing crab mass, $G$ (g). Metabolic rate has been shown to increase four-fold between $\approx$ 10 and 33 $\ensuremath{^\circ\text{C }}$ (McGaw and Reiber 2000). The function $f_$Temp$= f_{\text{Temp}}(T; Q_{\text{met}}=2.5, T_{\text{max met}}=35, T_{\text{opt met}}=26)$ is given by Eqn (A.39). Between 13 and 28 $\ensuremath{^\circ\text{C }}$, different sized crabs utilize their mass at $\approx 6.6\times 10^{-5}$ to $\approx 1.26\times 10^{-3}$ (g wet wt)/(g wet wt hr) (Crisp 1984; Booth and McMahon 1992; Laird and Haefner 1976; Leffler 1972). See Fig. A9 for plots of the costs of respiration and excretion per g of crab mass as a function of mass and temperature.