Energy Balance: Egestion

There are two components to egestion: egestion from a crab's stomach and egestion from the crab itself. The stomach is emptied due to egestion at a rate which depends on a crab's size and the temperature of its environment:

$$= 1_{[V_f/V_\text{stom} > 0]}\,\rho_f \,\alpha_\text{egest} CW^{\beta_\text{egest}}\, f_\text{ingest, temp}.$$ (A.43)

The indicator function $1_{[V_f/V_\text{stom} > 0]}$ ensures that egestion can only occur if the stomach contains food. $\alpha_$egest and $\beta_$egest are set at 0.004 ( cm$^{3-\beta_\text{egest}}.{\text{hr}}^{-1}$) and 2.0, respectively, based roughly on gut evacuation times (McGaw and Reiber 2000). By specifying the temperature dependence with $f_$ingest,temp, we assume that temperature alters ingestion (Fig. A8) and egestion similarly.

The rate a crab egests mass, $G_$egest, (g/hr) is a fraction of the rate at which food is egested from the crab's stomach:

$$= (1 - \gamma_{\text{absorption}}\, q_\text{stom})\,G_\text{egest stom}$$ (A.44)

where $q_{\text{stom}}$ is the average food quality of the food in the crab's stomach (Eqn A.43), $\gamma_{\text{absorption}}$ is the absorption coefficient, set to 0.6  (Guerin and Stickle 1992).

The mass of food in the stomach, $G_{\text{stom}}$ (g), following ingestion and egestion is computed as:

$$G_{\text{stom new}}= \begin{cases}G_{\text{stom old}} + (G_{\text... ...xt{ingest}} - G_\text{egest stom})\delta t > \rho_f V_{\text{stom}} \end{cases}$$ (A.45)

where $\delta t$ is the size of the time step since the crab was last updated.

If $G_{\text{stom new}} > 0$, the new stomach food quality, $q_$stom which is dimensionless and always between 0 and 1, is given by:

$$q_{\text{stom new}} = \frac{q_{\text{stom old}} G_{\text{stom old... ...tom}}\delta t + q_{\text{feed}} G_{\text{ingest}}\delta t}{G_{\text{stom new}}}$$ (A.46)

where $q_$feed is the food quality of the food the crab is ingesting. If $G_{\text{stom new}} = 0$ then $q_$stom$= 0$. $q_$stom$=1$ if the crab is feeding on crabs. Since the caloric content of clams is 1/2 that of crabs (Appendix A.5.6) the food quality of clams is set at 0.5 and background at 0.35.