Clam Recruitment

Clams are iteroparous broadcast spawners, with males and females releasing gametes synchronously, typically between May to June although fall recruitment can also occur depending on how far south the clams are located (Harvey and Vincent 1989; Gilbert 1978). Release of sperm and eggs is likely triggered by temperature cues (7 to 14 $\ensuremath{^\circ\text{C }}$), spring tides and/or quantity of food available (Harvey and Vincent 1989; Gilbert 1978). After a few weeks of pelagic life, the larvae ( $\approx 300$ $\mu$m) settle from the water column to the sediment (Bouma et al. 2001). Juvenile clams are capable of migration (Beukema and de Vlas 1989), but this is unlikely to be an important factor in spatially structuring clam distribution.

Using a mesh size of 0.5 mm, Hines and Comtois (1985) reported 34,000 clams per m$^2$ (119 g/m$^2$ dry weight, 780 g/m$^2$ wet weight) in mud and 22,000 clams per m$^2$ (177 g/m$^2$ dry weight, 1150 g/m$^2$ wet weight) in sand at the mouth of the Rhode River, Maryland - similar to the biomass and larval densities reported for sites in Europe (Bouma et al. 2001; Rosenberg et al. 1992). In the Dutch Wadden Sea, recruit to egg ratio for clams varied between 0.0001 to 0.001 (Honkoop et al. 1998). Although 37% of year-to-year variation in recruit densities could be explained by inter-annual variation in winter temperature, only 7% was explained by variation in egg density. Thus, the number of adults and total spawned eggs are poor predictors of subsequent recruit abundance (Honkoop et al. 1998).

The model uses two discrete spawning events which occur on March 31 and August 31. At these times, female clams (assumed to be half of the population) with a shell length greater than 1 cm reproduce (Commito 1982; Honkoop et al. 1998). The number of eggs produced per female is:

$$= 10,000(L_ )^3 L_c >$$ (A.22)

A mature female with a size of 1.5 cm (0.34 g wet wt) will produce approximately 34,000 eggs - within the range reported by Honkoop et al. (1998). The initial wet weight of recruited clams in the model is assumed to be 0.001 g (2.2 mm, Eqn A.16). Recruitment for the entire estuary is the sum of the fecundities for each female. The potential recruitment egg density, $\rho_{ce}$ (#/m$^2$), is the total number of eggs divided by the area of the estuary and multiplied by a random estuary recruitment factor which is generated uniformly over the range 0.0001 to 0.001 (Honkoop et al. 1998). How the potential recruitment egg density is altered on each triangle by depth, current clam biomass and density is described below.

It is necessary to control the density of clam egg recruitment on each triangle because our model does not include all of the different predators and causes of mortality present in the actual estuary. In summary, fewer spat are assumed to settle on shallower ($<$ 1.5 m deep) than deeper areas and recruitment is limited both by a triangle's current clam biomass density (Eqn A.23) and clam density (Eqn A.24).

Let $\gamma_{cD} = 1- \exp{(-D^2)}$ be the depth factor limiting clam recruitment on shallow triangles and let $\rho_{cB}$ (g/m$^2$) be the grams of clam biomass on the triangle and $\gamma_{cB}$ the factor limiting clam recruitment on triangles with high clam biomass:

$$\gamma_{cB} = \begin{cases}1 - \exp{\left(-5 \left(\frac{\rho_{cB... ...f $\rho_{cB} < \rho_{cB,\text{recruit}}$} \\ 0 & \text{ otherwise } \end{cases}$$ (A.23)

which places an upper bound on the clam biomass density on each triangle: $\rho_{cB, \text{recruit}} = 850$ g/m$^2$ (Hines and Comtois 1985).

Finally, let the density of clams already present on each triangle be given by $\rho_{\text{c,tri}}$ (#/m$^2$) and let $\rho_{cu} = 1300$ (#/m$^2$) (Holland et al. 1980) be an upper bound on clam density. Accounting for depth, current clam biomass and clam density, the number of clams recruited to a triangle as a function of $\rho_{ce}$, (or potential recruitment egg density), is:

$$^2 ) = \begin{cases}\left((\rho_{c u} - \rho_\text{c,tri})+\rho_{cu}... ...ght)^2\right]} & \text{ if } \rho_{\text{c,tri}} \geq \rho_{c u} \\ \end{cases}$$ (A.24)

The first condition governs recruitment when clam density on the triangle, $\rho_{c, tri}$, is less than both the upper bound on clam density, $\rho_{c u}$, and the potential recruitment egg density, $\rho_{ce}$. The second condition applies when the potential egg density is less than the upper bound for clam density on a triangle. The last condition applies when the clam density already present on the triangle is greater than the upper bound for clam density on a triangle. In this last case, the density of clams recruited goes to zero rapidly as $\rho_{ce}$ gets larger.