Energy Balance: Foraging and Finding Clams or Background Prey

Blue crabs are highly omnivorous, feeding on molluscs (both bivalves and gastropods), fish, small benthic infauna, algae, vascular plants and conspecifics - depending on prey availability  (Eggleston 1990; Laughlin 1982). A summary of previous diet studies done on the genus Callinectes noted that molluscs (primarily soft shelled clams) and crustaceans account for between 41% and 71% of a crab's diet, with molluscs accounting for between 21% and 45% (Mantelatto and Christofoletti 2001). Macoma balthica and Macoma mitchelli - the dominant bivalves in the Neuse estuary - thus form the dominant component of a crab's diet (Sullivan and Gaskill 1998). Crabs, clams and the background prey have different caloric contents: crabs 1000 cal/g wet  (Cummins and Wuycheck 1971), clams 500 cal/g wet (Szaniawska et al. 1986; Cummins and Wuycheck 1971), background prey assumed to be 350 cal/g wet.

Model crabs feed on clams, background prey or killed crabs (Appendix A.5.3). The average caloric content of the food a crab fed on between updates is found using a feeding algorithm. The crab's eating status is determined based on gut fullness, and is set to foraging (meaning the crab can move) if it previously was not eating, its stomach is $<$ 10% full and it is not molting. If a crab killed another crab (Appendix A.5.3), it becomes food for the attacking crab. If this is insufficient to satiate the attacking crab, it attempts to find clams and if insufficient clams are found then low caloric content background prey are fed on. The average caloric content of all food fed on, $q_{\text{feed}}$, is computed as a mass-weighted average. The algorithm for feeding on clams involves the following steps that are discussed in greater detail below: determining the number of clam searches, determining the average probability of finding clams on each search, determining whether an individual crab actually fed, and if so which clams it fed on given the environmental variables and clam size distribution on the triangle.

The number of searches that a crab could undertake over the interval $\delta t$ since its last update is generated randomly according to a Poisson distribution with mean $6 \delta t$. Thus, over a one hour period a foraging crab would on average search for clams six times. Each fine-level triangle stores clams according to increasing size which enables a binary search to be conducted to find the range of clam sizes small enough for the crab to eat. The criteria used is that the shell length of the clam divided by the crab's CW must be less than 1/3. Once the range of forageable clam sizes is known, the probability that a crab finds suitable clams is calculated based on the density of forageable clams $\rho_{\text{c$[,]$}}$ (#/m$^2$) according to:

$$= 1 - \exp{\left(-\left(\rho_\text{c$[,]$}\,\, \gamma_{\text{c,encounter}} \right)^3\right)}.$$ (A.31)

$\gamma_{\text{c,encounter}} = 1/75$ (m$^2$/#) governs how the probability of finding a clam decreases as $\rho_$c$[,]$ decreases. Using the third power means that unless the density of clams is less than $1/\gamma_{\text{c,encounter}}$ (#/m$^2$), crab's will likely find clams.

An individual crab feeds if a realization from a uniform random variable, $u$, is less than the probability given by Eqn (A.31). This is used to reflect the reality that as clam density decreases, the probability of an individual crab being successful in finding clams decreases. The purpose of this is to afford clams a low density refuge while distributing found clams to individual crabs. Thus, if a crab feeds the number of clams consumed is just the expected value or the number of times it searched multiplied by the probability of finding clams. This is rounded to the largest integer value and is given by:

$$= \lceil ( )( )\rceil.$$ (A.32)

The number of clams found are selected from the clam age classes on the triangle. The number of clams actually taken will either be the number of clams to be found (Eqn A.32) or less than this number if the mass of food feeding on is sufficient to fill the crab's stomach.

Bigger clams are buried deeper in the sediments than smaller clams. Thus, clams from each forageable age class, $i$, on the triangle are selected randomly using weighting factors which account for the mass, $w_{{(c,w)}_i}$; number of clams, $\eta_i$, in that age class; and DO on the triangle. The weighting factor, $\phi_i$, for forageable age class $i$ is given by

$$\phi_i = \eta_i\exp\left(-\gamma_\text{clam}w_{{(c,w)}_i}\right)$$ (A.33)

The weighting factors are constructed so that if the number of clams is the same across all age classes, clams of smaller mass will have larger $\phi_i$ values than larger clams. With $\gamma_{\text{clam}} > 0$ which occurs when DO $\geq 1$ mg/L (Eqn A.34), the larger the mass of the clam the smaller will be its weighting factor and likelihood of being preyed upon.

Short low oxygen durations that are not severe enough to produce mortality can cause clams to extend their siphons farther to reach higher oxygen concentrations (Tallqvist 2001; Taylor and Eggleston 2000) in principle increasing the possibility of crab predation. This is accounted for using:

$$\gamma_ = \begin{cases}0 & \text{ if DO $< 1$\ } \\ \gamma_\text{clam, def}(1 - \exp(-(DO - 1)) & \text{ if DO $\geq 1$} \end{cases}$$ (A.34)

where $\gamma_$clam, def is the default factor for a clam's depth refuge. It should be noted that the actual effect of $\gamma_$clam was subsequently found to be rather small due to crab avoidance of water with DO $< 3$ mg/L, and thus the actual rate of clam predation was no higher under hypoxic than normoxic conditions, agreeing with empirical findings (Seitz et al. 2003a).

If at the end of the above clam feeding algorithm a crab cannot find sufficient clams to fill its stomach more than 50% full and if the mass of food feeding on is less than 50% of the potential grams of food it could feed on over the time interval if food were widely abundant (Eqn A.38), the crab then attempts to feed on background prey.

$$= 1 - \exp{\left(-\left( \gamma_{\text{b,encounter}}\, \frac{N}{A}\right)^{2.5}\right)}$$ (A.35)

where $\gamma_{\text{b,encounter}}$ = 1/100 (m$^2$/#) governs how the probability of finding background prey increases with the density of background prey, $N/A$ (Eqn A.25). If a realization from a uniform random variable, $u$, is less than the probability it finds background prey, the crab feeds on the background provided the number of grams of background to be consumed is actually present on the triangle.

The mass of background prey a crab finds is exactly the difference between the mass required to fill its stomach 50% full and the mass of food feeding on found in the previous part of the feeding algorithm. Thus, if a crab is forced to feed on background prey, its stomach will never be more than 50% full.