It is too early in the development of the model to state with any assurance 

 that model results apply to the real world. The model must undergo further 

 testing and evaluation before specific management recommendations can be made 

 on the basis of simulations. At this point the modeling effort suggests that 

 changes in fishing pressure can alter the balance between species in both 

 competitive and prey-predator interactions. Work with the model suggests that 

 standing stocks that are large relative to other standing stocks in the system 

 can be remarkably stable in the face of heavy fishing pressure. At the same 

 time, fishing pressure on such stocks can influence other stocks, even those 

 that are neither prey nor predator of the harvested species. The model 

 demonstrated that animals at higher trophic levels, such as marine mammals, can 

 have large impacts on lower trophic groups, such as zooplankton. Both the 

 stability and instability exhibited within the model system in the face of 

 fishing pressure were due to the complex interconnections of system structure. 



In this paper I describe the mathematical structure of the model and 

 present and discuss results of simulations. A more detailed description of the 

 north-central Gulf of Mexico near-shore marine ecosystem and the conceptual 

 basis for the model design were presented in a previous paper (Browder 1981). 



MODEL STRUCTURE 



The model is diagramed in the energy flow language of H.T. Odum (1982) in 

 figure 1. It is a food web of 12 compartments connected by flows of energy in 

 the form of organic matter and by flows of nutrients. The compartments represent 

 inorganic nitrogen; standing stocks of phytoplankton and animals in eight 

 trophic groups; and organic material of two types, high nitrogen and low 

 nitrogen. The model receives three inputs: solar radiation (as gross primary 

 productivity), inorganic nitrogen, and low-nitrogen organic material, the latter 

 two of which come from river inflow. The types of exchanges between compartments 

 of the model are nutrient uptake, phytoplankton rain to the bottom, feeding by 

 animals, release of unassimilated organic material by animals, and the release 

 of mineralized nitrogen through the decomposition of organic material and in 

 the elimination of metabolic waste products from animals. Energy leaves the 

 system as carbon dioxide (through the respiration of plants, animals, and 

 decomposers) and as harvests. 



The basic mathematical structure of the model is a set of 12 differential 

 equations : 



Ql = Jl +1% - L - P 1>2 , Qi 



Q2 = J 2 " p 2,3 -£ p 2,j " R 2. Q2 



q 3 = j 3 + p 2>3 +2fj -£p 3 ,j. Q3 



Q 4 = F 5 + (B - P 4>12 ) -£P4,j> Q4 



Q5 ^P'i.5 -£P 5 ,j " R5. Q5 



Q6 =£P*i,6 "2 p 6,j " H ~ H 6> Q6 



Q7 =2P'i,7 -£ p 7,j - R 7 , Q7 



183 



INORGANIC NITROGEN 



PHYTOPLANKTON 



LOW-NITROGEN ORGANIC 



HIGH-NITROGEN ORGANIC 



ZOOPLANKTON 



PELAGIC FISH 



BENTHOS 



