Clam Mortality

Clams experience mortality due to temperature extremes, other causes not directly modeled, hypoxia, and crab predation. This section focuses on the first three while crab predation is discussed in Appendix A.5.6. Mortality due to the first three causes is updated every 24 hours (along with all the environmental variables) while the effects of crab predation on the number of clams in each age class are applied as the crabs forage. The cumulative proportion of clams dieing from the first three causes over $\Delta t$ is the sum of the probabilities resulting from Eqns (A.20) and  (A.21).

Mortality caused by temperature extremes and other causes (which in the parameterization below includes predation by fishes and other non-crab estuarine organisms) are modeled according to an exponential probability distribution (van der Meer et al. 2001) with hazard rate:

$$\lambda(T) = \begin{cases}8\lambda_{\text{Base}} & \text{ if clam... ...sp}}$= 33 $\ensuremath{^\circ\text{C }}$} \\ 0 & \text{ otherwise.} \end{cases}$$ (A.20)

$\lambda_$Base$= 1.2\times 10^{-5}$ corresponding to 90% annual survivorship after the first year. Commito (1982) found a 75% annual survivorship under predation. Under no predation, 50% reductions in year 0+ clam densities have been reported (Holland et al. 1980) over 2 months. During winter, we would expect mortality to decrease. The high mortality during this early life stage is reflected in Eqn (A.20) with $8 \lambda_{\text{Base}}$ corresponding to 43% annual survivorship.

The thermal tolerance of clams can be as low -5 $\ensuremath{^\circ\text{C }}$  (Bourget 1983) and as high as $\approx$ 35 $\ensuremath{^\circ\text{C }}$  (Wilson 1981). Kennedy and Mihursky (1971) found LC50 values of $\approx 33 \ensuremath{^\circ\text{C }}$ and that an increase of 1 $\ensuremath{^\circ\text{C }}$ could mean the difference between 0% and 100% mortality. In the above hazard rate, if the temperature is less than $T_{\text{c,min resp}}= -5^\circ$ C clams, survive on average for 2 hours and if temperature is greater than $T_{\text{c,max resp}}=33$ they survive on average for 4 days.

Hypoxic exposure can also cause clam mortality. In the Calvert Cliffs region of Chesapeake Bay, hypoxia is severe enough that near total faunal depletion (molluscs, annelids, crustacea) occurs during the summer months due to low dissolved oxygen (Holland et al. 1977; Holland et al. 1987).  Buzzelli et al. (2002) estimated that in the Neuse the clams Macoma balthica and M. mitchelli, which are the biomass dominants in the benthic assemblage, declined by 90-100% over 38% of the estuary in 1997. To model clam mortality due to hypoxic exposure, we use the logistic cumulative probability distribution function of times-to-death for a given fixed DO exposure  (Borsuk et al. 2002):

$$F(t\vert DO) = \left(1 + \exp\left(-\frac{(t - (\lambda_a + \lambda_b\,DO))}{\lambda_c}\right)\right)^{-1}.$$ (A.21)

The most likely values of the parameters were $\lambda_a = 32.16$ (hr), $\lambda_b = 27.36$ (L.hr.mg$^{-1}$) and $\lambda_c = 9.6$ (hr), where $t$ is the duration of hypoxia in hours. We are not aware of any studies examining how survival probabilities are altered by temperature or exposure to periodic hypoxic conditions. We assume that no clams will die at DO $>$ 3 mg/L. To compute the number of clams dying under fluctuating DO, each triangle keeps track of the time at which its DO became $\leq 3$ mg/L and the continuous contribution to the cumulative hazard is computed according to  Borsuk et al. (2002, Eqns 7-13).