METHODS 



This initial nitrogen flux model AR0SAN1 is constructed as a set of non- 

 linear, discontinuous differential equations representing the fluxes. For all 

 fluxes into a biotic compartment, (e.g., ingestion) feedback control is effected 

 by means of functions which provide for representing 1) a maximum rate of 

 ingestion of N, 2) a refuge of available N, 3) an upper satiation level for 

 available N, 4) a maximum density or carrying capacity for the feeding compart- 

 ment (this is based solely on space, assuming available N levels are optimal), 

 and 5) a lower response threshold which specifies that density at which negative 

 effects of crowding are first manifested. 



In linear fluxes (such as excretion, detritus production, nonpredatory 

 mortality plus egestion, and fluxes between abiotic state variables) simple 

 donor-dependent equations have been used. In the case of the fluxes representing 

 exploitation by man, we have assumed, that the fishing effort (and the harvest) 

 is directly proportional to the density of a resource. Thus a linear donor- 

 dependent equation is reasonable. At least this is so in mussel and oyster 

 fisheries although it is arguable in fishes and crustaceans. 



Input of inorganic nitrogen by upwelling is represented by a rate of 

 intrusion and is given a different value for each of the four seasons. Thus, 

 upwelling is averaged over seasonal (3-mo) periods and is not simulated as 

 separate events. This is a serious constraint in this initial model although 

 in general its effect is to exaggerate the potential shellfish production and 

 thus reinforce the conclusions about the potential effect of additional rafts. 



The resource feedback terms included in all nonlinear fluxes are, in most 

 cases, of the linear form given in Wiegert (1974). Only for microbial action on 

 the three particulate organic nitrogen state variables did we employ the resource 

 feedback based on the ratio of microbial biomass to substrate, given by Christian 

 and Wetzel (1978). Crowding feedback functions are linear in all cases. 



The Program AR0SAN1 . The FORTRAN program AR0SAN1 simulates the dynamics 

 of this system through time. Numerical integration is done with a simple 

 Euler routine and the iteration interval is 0.1 day. By means of an arithmetic 

 IF statement, in one out of 37 iteration loops, the standing stocks of the 22 

 state variables are stored in a data array. At the end of the simulation, 

 this data array is transferred to an external data file to be plotted. This 

 array then contains the variation of standing stocks and fluxes by means of 99 

 values through the year of simulation. 



THE MODEL 



Twenty-two state variables, five abiotic and 17 biotic, were defined (table 

 1) based on their position in the trophic web of the ecosystem. In some cases, 

 the state variables represent taxonomic units rather than trophic ones. This 

 is so in epibenthic fauna (Echinoderms , Crustaceans, Fishes), where trophic 

 differentiation is quite troublesome, for most important groups are omnivorous 

 and, in some cases, the data were available only for taxonomic units. Two 

 species cultured on rafts (mussel and oyster) are represented as separate 

 state variables, due to their high biomass, their importance in the trophic 

 web, and our interest in simulating the variations of their yields, and the effects 



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