Clam Growth Dynamics

Adult clams are generally less than 2.5 cm wide (McErlean 1964), although a few may reach 3.0 cm  (Bachelet 1980). In northern climates, clams can live as long as 35 years (Bachelet 1980), while 6-10 years is common in more southern climates (Gilbert 1973). Clam growth is most rapid between April and June (1.9-3.7 mm/month) (Holland et al. 1987), slows in July and August and continues to decrease throughout the fall/winter. The variability in clam growth rates depends on temperature and possibly salinity resulting in southern clams growing faster than those further north. For Rand Harbor, Massachusetts, clams grew $\approx$ 1.0 and $0.7$ cm in the first two years, respectively, before growth slowed considerably (Gilbert 1973). A similar growth pattern has been observed in other locations (Commito 1982; Bachelet 1980). At temperate latitudes, the mass of bivalve molluscs generally declines during winter, declining more during warmer than colder winters (Honkoop and Beukema 1997). Females reproduce when they are greater than 1 cm, or approximately 2.9 yrs for clams in northern climates like Maine (Commito 1982) and at a younger age in warmer climates.

Our clam growth model closely follows the bivalve model proposed by  Solidoro et al. (2000). We assume that clams on each triangle grow according to the same model with differences in growth rate occurring between triangles due to spatial differences in temperature and dissolved oxygen. Possible salinity effects are ignored (Holland et al. 1987). Because anthropogenic loading should increase algae, the primary food of clams (Hummel 1985b), we assume that clam growth is not limited by food availability (Holland et al. 1980). Clam wet weight, $w_$c,w (g), is related to shell length, $L_$c (cm), by the allometric model

$$w_ = \alpha_ ^{\beta_\text{c}},$$ (A.16)

where $\alpha_{\text{c}} = 0.1$ g.cm $^{-\beta_\text{c}}$ and $\beta_$c$= 3.0$ (Bachelet 1980; Gilbert 1973, Table 2). The maximum size of clams in the Neuse is $\approx$ 2.5 cm (Bachelet 1980, Table 7).

Clam growth rate is proportional to the difference in the grams of energy available for feeding and the energy used for respiration (Solidoro et al. 2000, Eqn 1):

$$\frac{\Delta w_\text{c,w}}{\Delta t} = g(DO)\left( G_{\text{c,max... ...G} \, w_\text{c,w}^{2/3} - r_{\text{c,max}}\, f_{c, r} \, w_\text{c,w} \right).$$ (A.17)

The temperature and DO values used are constant over $\Delta t$ and the values used are those from the start of the time interval. $f_{c, G} = f_{\text{c}}(T; \beta_{\text{c,grow}}=0.2, T_{\text{c,max grow}}=31, T_{\text{c,opt grow}}=22)$ and $f_{c, r} = f_{\text{c}}(T; \beta_{\text{c,resp}}=0.17, T_{\text{c,max resp}}=33, T_{\text{c,opt resp}}=20)$ are given by Eqn (A.18) and $g(DO)$ by Eqn (A.19). $f_{\text{c}}(T; \cdot)$ is maximum at the optimal temperature and alters clam intake and respiration with bottom water temperature. The rate of clam growth at a given temperature and mass is shown in Fig. A4. $f_{\text{c}}$ is given by:

$$\begin{aligned}f_{\text{c}}(T; \beta, T_\text{max}, T_\text{opt... ...opt})} \exp\left({\beta}(T - T_{\text{max}})\right) \end{aligned}$$

which is taken from Solidoro et al. (2000) and is similar in shape to that found by McMahon and Wilson (1981, Fig. 2).

Bivalves either conform to or regulate their rate of oxygen consumption independent of oxygen concentrations (Wang and Widdows 1993). In Macoma, oxygen consumption decreased with decreasing DO concentration (McMahon and Wilson 1981, Fig 5) and based on these results, we assume that this decrease in oxygen consumption represents an overall decrease in growth rate in Eqn (A.17) according to:

$$g(DO) = \begin{cases}1 & \text{ if DO $>$\ 4 mg/l} \\ DO/4 & \text{ 0 $\leq$\ DO $\leq$\ 4. } \end{cases}$$ (A.19)

Thus, $g(DO)$ decreases linearly with DO for DO $\leq$ 4 mg/L.

The wet weight of the clams in each of the 8 year classes for spring and fall recruitment on each triangle in the estuary are updated according to Eqn (A.17) every 24 hours. The maximum rate of respiration, $r_{\text{c,max}}$=0.00034 (1/hour), is based on  McMahon and Wilson (1981) and Hummel (1985a, Table 1). In Eqn (A.17), as a clam's mass increases its respiratory demands increase faster than its rate of food intake making it impossible for a clam to grow beyond a given mass. This fact was used to establish $G_{\text{c,max}}$ at 0.00034 (g$^{1/3}$/hr).