occurs for two sources of dissolved nutrients through periodic depletion of 

 supplies, and only the rooted vascular plants have direct access to both 

 nutrient sources. The 7 state variables here are connected to numerous external 

 factors, both those in another subsystem and those entirely external to the 

 SAV community. 



The nature of mathematical formulations used can be illustrated with the 

 primary production term in the SAV growth equation: 



P= [C/N] [ATTEN] [LKIN] [TEMP] [NKIN] [LAI]. (1) 



Here, SAV production (P) is a multiplicative function of 6 auxilliary variables: 

 [C/N], the nitrogen-to-carbon conversion; [ATTEN], the light attenuation 

 relation; [LKIN], the photosynthesis-irradiance function; [TEMP], the temper- 

 ature kinetics; [NKIN], the nitrogen uptake relation; and [LAI], an index of leaf 

 area representing the ability to absorb photons. Light attenuation follows a 

 simple Beers-Lambert relation with various materials contributing to the effect 

 (e.g., Parsons et al., 1979): 



I z = I e~ kz (2) 



where I z and I Q are light levels at depth, z, and at water surface, respectively. 

 The attenuation coefficient k is taken as the sum of individual k's for seston, 

 epiphytic material and SAV leaves, where each k is a linear function of the amount 

 of material per m^ with the overall intercept attributable to dissolved substances 

 and the water itself. The photosynthesis-irradiance relation is approximated 

 by a rectangular hyperbola (Parsons et al., 1979): 



P " P m C K-fT ] ' (3) 



l z 



where P m is the maximum photosynthesis possible, and K^ is the light level at 

 0.5 P m . Data for all of the light relations were obtained from experiments 

 in our laboratory (Kemp et al., 1981). The temperature (T) function used is a 

 simple Arrhenius relation, 



-(K t /T) 

 TEMP = e (4) 



Values for K t were obtained from the literature for related species (Titus and Adams 

 1979, Barko and Smart 1981). A higher order equation (Johnson et al . , 1974) 

 which accounts for temperature stress via protein denaturation at elevated 

 T was used in some versions of the model. 



Little information was available concerning the appropriate algebraic ex- 

 pression for describing SAV nitrogen uptake (V) from two sources (water column 

 and sediment pore-water). We chose a formulation analogous to the Michaelis-Menten 

 relation, and assuming a single maximum uptake rate (V m = f(P m )) but differing 

 half-saturation constants 



140 



