PARRISH: MARINE TROPHIC INTERACTIONS BY DYNAMIC SIMULATION 



equilibrium state has been placed— in which the 

 system models are fairly stable. For these reasons, 

 it is believed that the basic form of the behavior of 

 systems demonstrated in these simulations has 

 some generality beyond the specific cases tested. 

 However, in all cases, the results shown here are 

 simply examples of interest from an infinite 

 number of possibilities. 



The simulation technique used here is amenable 

 to use in sensitivity analyses; i.e., for determina- 

 tion by a systematic program of successive trials 

 how sensitive the result is to the numerical value 

 of a parameter or an initial variable value. Such 

 analyses not only help define useful regions for 

 particular results; they also give an indication of 

 how accurately particular parameters must be 

 measured in the field or laboratory, so that effort 

 is applied where it is important to the system 

 result. 



In describing the following results, the 

 shorthand notation used to reference the trophic 

 webs has the following form: 



1 

 ,1st 



2 



2nd 



1 



3rd 





 4th 





 5th 



Trophic level 



The digit in each column indicates the number of 

 species at that trophic level. Where two species 

 appear at a common level, they compete for prey at 

 the next lower trophic level and are preyed upon 

 equally by the next higher trophic level. The 

 lowest level is always occupied by the food base 

 with biomass By. 



(A) Regulation of Body Weight and 

 Population 



The basic species model seems to have a con- 

 siderable capacity for self-regulation; i.e., it can 

 return to an equilibrium state after sizable 

 displacements of some of the variables in the sys- 

 tem. The return usually involves a series of os- 

 cillations above and below the equilibrium values, 

 with the degree of damping depending on the 

 exact structure and parameter values. 



One of the most common and interesting per- 

 turbations involves displacement of prey abun- 

 dance. Figure 3 illustrates a P 11000 trophic web 

 with a representative individual model of a species 

 A fish preying on an exponential growth type food 

 base with an Ivlev feeding function. The system 



5^ 



z 3 



< cc 

 99 



Z -J 



_ 3 

 2 O 

 O LiJ 



^Q 

 _J OC 

 =) < 



a. Q 



o 



b ^ 



CC 





a. ° 



30 40 



TIME, YEARS 



Figure 3. -Response of a single species to an initial perturbation 

 in the abundance of its prey. N = predator population; W = 

 predator body weight; B j = prey (food base) biomass. 



responded to an initial condition in which the fish 

 population was at the standard equilibrium value 

 and the prey abundance was initially about 71.4% 

 of the standard equilibrium value. The system re- 

 turned to the standard equilibrium state with 

 damped oscillations. The purely population con- 

 trols, natural mortality and reproduction (/>nat vs. 

 R), were satisfied initially, but the system was 

 unbalanced trophically because of the scarcity of 

 prey. Regulation resulted from the response of 

 body weight and resulting fecundity to food con- 

 sumption, balanced by natural mortality respond- 

 ing to the changing population level. 



Similar stable responses were demonstrated 

 with the model for cases of initial perturbation due 

 to high prey abundance, B^, high predator popula- 

 tion, A^, and high predator body weight, W. 



At suflficiently low values of prey abundance and 

 production, substantial starvation mortality can 

 occur. This is particularly true when the prey 

 abundance decreases suddenly, since the normal 

 population response of the predator through 

 reduced fecundity is delayed by the reproductive 

 time lag. Figure 4 shows such mortality for a 

 population for four age classes modeled explicitly. 

 The abundance of each year class decreased with 

 time until those which had become 4-yr-olds were 

 decimated at about 1.6 yr after the start. The. 



705 



