MARINE TROPHIC INTERACTIONS BY DYNAMIC SIMULATION 



OF FISH SPECIES 



James D. Parrish' 

 ABSTRACT 



A mathematical model was developed for performing dynamic simulations of groups of interacting 

 animal species. The energy balance of the individual animal was modeled so that growth and 

 reproduction respond to food consumption after metabolic expenses are met. Populations change in 

 response to recruitment (based on parental spawning) and mortality from natural causes, predation, 

 starvation, and (where applicable) human exploitation. The forms of the various component mathema- 

 tical functions were derived from the available ecological sources. Functions and parameters are 

 especially applicable to marine fish species. Trophic webs of any size or form can be constructed using 

 this basic species model. Computer solution of the essentially continuous differential model gives a time 

 history of trophic and population variables for all species in the web. 



Models of trophic webs of 2, 3, and 4 levels were constructed and exercised. These were used to 

 examine effects of age class structure, reproductive time lag, and population regulation by starvation 

 mortality and fecundity control. Competition between species and the effects of a top predator on 

 competitors, with and without human exploitation, were studied. 



Thus far in the history of trophic ecology there has 

 been little effort to bring together the important 

 results of the diverse studies which provide the 

 components of the total trophic system into a con- 

 struct that will permit analyzing the effects of 

 metabolism, food consumption, reproductive ef- 

 fort, and the structure of the trophic web upon the 

 weight, population, and biomass of the various 

 species involved. Perhaps the most complete and 

 useful approaches in the literature are those of 

 Menshutkin and Kislyakov (1967, 1968), 

 Menshutkin (1968), Menshutkin and Prikhodko 

 (1968, 1969, 1970), Karpov et al. (1969), Krogius et 

 al. (1969), Menshutkin and Umnov (1970), Lassiter 

 and Hayne (1971). The present work is an attempt 

 to create a complete model for fish in the natural 

 environment and to employ it for the stated type 

 of total trophic analysis. 



The mathematical "trophic anatomy" of the 

 generalized species modeled contains certain 

 functions which represent trophic interactions 

 with other species. The trophic web consists of an 

 arbitrary number of such interacting species, 

 coupled in this way into any arbitrary design; e.g., 

 with any number of trophic "levels" (or coupled 

 across levels), any number of species at each level, 

 any number of predator species on a single prey 

 species, etc. The trophic properties of the 



'Present address: Massachusetts Cooperative Fishery Unit, 

 U.S. Fish and Wildlife Service, 204 Holdsworth Hall, University 

 of Massachusetts, Amherst, MA 01002. 



Manuscript accepted February 1975. 

 FISHERY BULLETIN: VOL. 73, NO. 4, 1975. 



generalized, modular species are established by 

 specifying a set of equations which define its 

 various ecological functions, such as respiratory 

 metabolism, feeding, natural mortality, and 

 reproduction. The composite nature of the model 

 species' trophic anatomy permits considerable 

 structural flexibility in model development. A 

 particular ecological function, such as feeding rate 

 as a function of prey abundance, may be expressed 

 differently in different simulation runs by 

 changing a single component equation. The 

 separate identity of each species is determined 

 primarily by the numerical values of the 

 parameters in its component functions, but the 

 form of functions may be different in different 

 species where the data dictate. 



The model approach used allows a number of 

 different levels of approximation. In the simula- 

 tions performed here, no differentiation is made 

 between sexes in the populations. The sexes could 

 easily be represented separately at the cost of 

 more computing time and a larger data base. A 

 common and convenient simplification that is used 

 in most of the present simulations is construction 

 of an entire species population of identical in- 

 dividuals. Thus, the individual must be given a set 

 of characteristics and parameter values that are in 

 some sense representative of the entire life his- 

 tory after recruitment. A population with 

 separate age classes has also been created 

 explicitly with the present model. 



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