Energy Balance: Ingestion

The above feeding algorithm gives the number of grams of food the crab found since it was last updated. However, the mass of food feeding on is not the same as the amount of food ingested into a crab's stomach. One reason for this distinction is if the crab is feeding on another crab it may not ingest an entire crab before it is satiated and moves on.

A crab continues to feed until either its stomach becomes full or it consumes all the mass of food feeding on. In the first case, eating status is set to not eating, mass of food feeding on is set to zero and any remaining food is returned to the estuary as part of the lower quality background prey on that triangle. In the second case, if the stomach is $<$ 95% full, eating status is changed from eating to foraging, meaning the crab can move around the estuary.

Computing the mass of food ingested requires models of a crab's stomach size and ingestion rate. The allometric relationship used between a crab's CW and mass, $G$, is (Pullen and Trent 1970; Olmi III and Bishop 1983; Cadman and Weinstein 1985; Newcombe et al. 1949):

$$G = \alpha_{\text{G}} * CW^{\beta_{\text{G}}}.$$ (A.36)

Based on these studies, is 2.7 and $\alpha_{\text{G}}$ is 0.14 g/cm $^{\beta_{\text{G}}}$. A crab's stomach volume, $V_{\text{stom}}$ (cm$^3$), is given by:

$$V_ = \alpha_{\text{stom}}CW^{\beta_{\text{stom}}}.$$ (A.37)

In small, starved crabs, the log of the mass of fresh meat consumed per gram of crab per day decreased with the log of the crab's wet weight with a slope value of $\approx$ -0.55 (Wallace 1973). If the wet weight of the crab is given by Eqn (A.36) and is 2.7, this suggests that $\beta_{\text{stom}}$ is $\approx 2$. $\alpha_{\text{stom}}$ is set at 0.0265 (cm).

The volume of food in a crab's stomach is given by $V_f = G_{\text{stom}}/\rho_f$ (cm$^3$) where the density of the food, $\rho_f=1.5$ (g/cm$^3$), is assumed constant for all food types. The rate at which food is ingested into the stomach from the mass of food feeding on depends on stomach fullness, crab size and temperature:

$$G_{\text{ingest}} = \overset{\text{Stomach Fullness}}{\overbrace{... ...ngest}}}}}\, \overset{\text{Temperature}}{\overbrace{f_{\text{ingest, temp}}}}.$$ (A.38)

The first term in Eqn (A.38) implies that the maximum rate at which food can be ingested will decrease to zero as the crab's stomach becomes full. The second term ensures that larger crabs can ingest food at a greater rate, while the last term describes how the rate of food ingestion is altered by temperature. $f_{\text{ingest, temp}} = f_{\text{Temp}}(T; Q_{\text{ingest}}=5, T_{\text{max ingest}}=33, T_{\text{opt ingest}}=25)$ is based on a model proposed for yellow perch (Kitchell and Stewart 1977):

$$f_{\text{Temp}}(T; Q_m, T_m, T_o) = \left(\frac{T_m - T}{T_m - T_o}\right)^x \, \exp\left(x - x\frac{T_m - T}{T_m - T_o}\right)$$ (A.39)

$$x = \frac{w^2 \left(1 +\sqrt{1 + 40/y}\right)^2}{400} \notag$$ (A.40)

$$w = (\log Q_m) (T_m - T_o) \notag$$ (A.41)

$$= (\log Q_m) \, (T_m - T_o - 2). \notag$$ (A.42)

$T_{\text{max ingest}}\ensuremath{^\circ\text{C }}$ is the maximum temperature at which crabs feed while $T_{\text{opt ingest}}$ is the temperature giving maximum feeding rate (Eqn A.39, Fig. A7). At $25\ensuremath{^\circ\text{C }}$, crabs with a CW of 15 cm (an empty stomach volume of $\approx 6$ cm$^3$) require approximately 15 minutes to fill their stomachs.