PARRISH: MARINE TROPHIC INTERACTIONS BY DYNAMIC SIMULATION 



dividuals mature as a function of age, length, or 

 weight. In some cases (e.g., Bagenal 1957) the 

 weight function appears reasonably linear. This 

 means that in Equations (13) and (22) the mature 

 spawning population, A^,„, can be expressed as 



and 



^,n = 9,,/^, 



9m ^ 9l+ 9-2^^ 



(23) 



(24) 



where g^^ and g^g ^re numerical parameters, for all 

 values of IF between that which gives g^^ = and 

 that which gives ,9„, = 1.0. At lower and higher 

 values of W,g,,, is and 1.0 respectively. 



For species A and C, information from Bigelow 

 and Schroeder (1953) permitted a rough fitting of 

 this function. The length corresponding to the 

 body weight at which all were mature agreed 

 reasonably well with the ratio: length at maturi- 

 ty/theoretical maximum length (Lqq) of Beverton 

 and Holt (1959) for both species. The same sort of 

 weight limits for the function were assumed for 

 species D, in the absence of better data. The stan- 

 dard equilibrium weight and the 100% sexual ma- 

 turity weight were made to coincide in each 

 species. This means that in this particular modified 

 model, any reduction below standard equilibrium 

 weight decreases the number of mature spawners. 

 The effect of the linear sexual maturity of Equa- 

 tion (24) on the total population egg production is 

 shown in Figure 5. 



Figure 6 illustrates the response of a single 

 PllOOO trophic web with sexual maturity of 

 species A modeled in this way. For the first 4 yr of 

 the simulation run, input production at the food 

 base level was about 20% of the standard 

 equilibrium value; subsequently it was always at 

 the standard equilibrium value. The reduced food 

 supply resulted in stunting the population so much 

 that from year 6 through 9 there was no recruit- 

 ment. The subsequent reduced total food con- 

 sumption by the greatly reduced population tend- 

 ed to bring the system into balance. If it survived, 

 it would eventually return to standard equilibrium 

 conditions. However, for this species with a life- 

 span of 6 yr or less, an interruption of recruitment 

 for 4 yr is very dangerous. This, combined with a 

 minimum population of about 1.4% of the standard 

 at one point in the simulation, suggests that the 

 condition reached here was very near a critical one 

 for survival of the local species population. This 



E 



en 

 CO 



> 





< 



Q 

 > 



5 10 15 20 



INDIVIDUAL BODY WEIGHT, gm. 



Figure 5.— Relationship between inaiviaual fecundity, S, and 

 body weight and between total population egg production, E, and 

 body weight. Sexual maturity is a linear function of body weight. 





(3a: 



LU 



30 



Q. 



era: 

 o . 



<2 



_ LU 



170 - 



150 - 



100 



30 40 50 



TIME, YEARS 



70 



Figure 6.-Response of a single species, with sexual maturity a 

 linear function of weight, to an initial 4-yr perturbation of low 

 production by its prey. (Pj = 20% of standard equilibrium value 

 for the first four years.) Reproduction ceased between years 6 

 and9. N = predator population; W = predator body weight; R = 

 predator recruitment. 



707 



