PARRISH: MARINE TROPHIC INTERACTIONS BY DYNAMIC SIMULATION 



Table 1. -Glossary of symbolic notation used in the model. [Notation defined in referenced literature, when different from that of the 



present model, is not repeated here.] 



Symbol 



Definition 



Symbol 



Definition 



8 

 8 



b 



C 



max 



Cp = Cp 



I 



t-'CICUi 



E 

 e 

 F 

 G 

 G 



9„ 



31.92 



', 



i 



k 



M 

 m 



Numerical parameter in the Beverton and Holt 



reproductive function 



Species biomass 



Biomass of the /th species 



Biomass of the food base 



Numerical parameter in the Beverton and Holt 



reproductive function 



Actual ration; actual rate of food consumption 



by an individual 



r^/laximum ration w/hen feeding to satiation 



Ration of a predator 



Consumption of the /th prey species by a predator 



Numerical predation parameter in the linear feeding 



function 



Instantaneous coefficient of natural increase of an 



"exponential grovjth" type food base 



Rate of change of population due to fishing 



mortality 



Rate of change of population due to natural 



mortality 



Rate of change of population due to predatory 



mortality 



Rate of change of population due to starvation 



mortality 



Total egg production rate of a population 



Base of natural logarithms 



Coefficient of instantaneous fishing mortality 



Actual growth rate of an individual 



Maximum growth rate; growth rate when C = C^^^^ 



Growth rate predicted by the von Bertalanffy 



growth function 



Fraction of the species population that is sexually 



mature 



Numerical parameters in the linear sexual maturity 



function for g^ 



Constant of integration for critical starvation 



mortality time 



Convenience combination of variables in Equation 



(A-2), Appendix 



Recruit body weight coefficent 



Ration assimilation coefficient; fraction of the 



ration assimilated 



Numerical parameter (theoretical maximum body 



length) in the von Bertalanffy growth function for 



length 



Coefficient of instantij--30us natural mortality 



Numerical parameter in the starvation mortality 



function 



Fish 



"1. 

 N 



w, 



N 



N'n, 



Wo 

 Wp 



n 



P 



Q 

 Q 



R 



R. 



r 



S 



i 

 u 



W 



Fish 



w, 

 w, 



a 



ffstarv 

 V 



Numerical predation parameter in the Holling 



feeding function 



Species population 



Population of a fish species 



Population of the /th species or age class 



Sexually mature species population 



Initial population 



Predator population 



Standard equilibrium value of species population 



Numerical parameter in the starvation mortality 



function 



Prey abundance 



Rate of food base biomass input to the system in a 



"constant input" model 



Rate of respiratory metabolism of an individual 



Rate of respiratory metabolism of an individual at 



maximum ration 



Rate of reproductive recruitment 



Standard equilibrium recruitment rate 



Fraction of the maximum ration actually consumed 



Fecundity: actual rate of production of reproductive 



material by an individual 



Maximum fecundity at current body weight 



Computed numerical parameter in the starvation 



mortality function 



Time 



Critical time to 100% starvation mortality 



Fecundity coefficient of an individual 



Coefficient of predator preference for the /th prey 



Body weight of an individual 



Body weight of an individual fish 



Body weight of an individual of the /th species or 



age class 



Initial body weight of an individual 



Body weight of a prey individual 



Standard equilibrium body weight of an individual 



Numerical parameter (theoretical maximum body 



weight) in the von Bertalanffy growth function 



Respiratory metabolism coefficient 



Respiratory metabolism coefficient at maximum 



ration 



Respiratory metabolism coefficient at zero ration 



Numerical parameter (weight exponent) in the 



respiratory metabolism function 



Numerical parameter in the von Bertalanffy growth 



function 



Numerical predation parameter in the Ivlev feeding 



function 



collection of data from the experimental litera- 

 ture, a level of a appropriate to an average spon- 

 taneous activity level was chosen. The instan- 

 taneous value of a is allowed to vary in response to 

 ration according to the equation 



a 



a 



starv- 



+ («r 



a 



starv 



c 



Cr 



(3) 



where Cis the actual instantaneous ration, a^j^j^. is 

 the value corresponding to minimum metabolic 

 rate at complete starvation, and a^ax corresponds 

 to the maximum metabolic rate when feeding to 

 satiation at ration C^ax- Equation (3) is a linear 

 expression that generally approximates the best 



results from the few applicable long-term fish 

 feeding and growth experiments (Davis and 

 Warren 1965, 1971; Paloheimo and Dickie 1965, 

 1966; Beamish and Dickie 1967; Warren and Davis 

 1967; Brett et al. 1969). Use of Equation (3) in 

 Equation (2) gives Q for any size fish at any feed- 

 ing level. 



Fecundity of fish must be dependent on size and, 

 at least in some limiting sense, on nutrition. A 

 number of workers have noted reduced fecundity 

 in overcrowded, undernourished fish populations 

 and have speculated on how this reduced fecundity 

 might tend to regulate the population (Woodhead 

 1960; Nikolskii 1961, 1962; Scott 1962; Bagenal 

 1967; Mackay and Mann 1969). There is good 



697 



