FISHERY BULLETIN: VOL. 73. NO. 4 



Figure 4. -Effects of starvation mortality on the 4 age classes of 

 a species population and on the total population. A new class of 

 recruits entered one year after the start of the simulation. 

 Arrows indicate when starvation mortality began for each year 



class. ( actual population of an age class; population 



of an age class in the absence of starvation mortality; 



N/Ng, where N = total species population, Ng = standard 

 equilibrium value of total species population.) 



dashed lines indicate the course of natural mor- 

 tality. As interesting as the fate of individual year 

 classes is the substantial effect on the total 

 population (shown by the upper broken line in 

 Figure 4). 



Theoretically, starvation mortality should be 

 capable of regulating the population. However, 

 based on a considerable range of simulation runs, 

 it appears that with the usual sets of reasonable 

 parameter values for the species considered here, 

 body weight and fecundity normally respond to 

 produce regulation so that a starvation condition 

 is not reached. With longlived, slowly growing 

 species, starvation would tend to become a more 

 important factor. In some of the cases simulated, 

 where trophic conditions were sufficiently extreme 

 to produce heavy starvation mortality, total ex- 

 tinction occurred. Figure 4 represents such a case, 

 in which the food base biomass, B^, was initially 

 20% of the standard equilibrium value and c^ was 

 10%. Extinction occurred during the initial 2-yr 

 reproductive time lag before fecundity changes 

 could be reflected in recruitment. Some simula- 



tions were run in which fecundity was made 

 unresponsive to actual body weight so that the 

 effects of starvation could be better observed. 

 With the nutritional control on fecundity thus 

 removed, starvation occurred for some systems 

 and started with B^ at 50% of standard equilibrium 

 and c■^ at 90%. With normal nutritional control on 

 fecundity, these systems had survived. 



Experience with the model indicates that for the 

 types of species used, where extreme trophic con- 

 ditions exist, disruption of the system is more 

 likely to result from excessive stunting of growth 

 and resultant failure of spawning than from star- 

 vation mortality. In age class models, the stunting 

 can be observed directly in the failure of in- 

 dividuals of a year class to grow normally while in 

 the recruited population. Where food supply is ex- 

 tremely low, actual weight loss by an individual 

 can also be observed. In representative individual 

 models, these separate effects are combined in the 

 single continuous variable, W. A smaller-than- 

 standard W represents a population that, on the 

 whole, is undersize. If the population as a whole 

 becomes sufficiently stunted, at some point, egg 

 production will be reduced to zero. This corres- 

 ponds to a population unable to reach sexual ma- 

 turity. If the entire population fails to spawn for 

 enough successive years, extinction of the local 

 species population must result. It is difficult to see 

 how a species could persist if it failed to spawn for 

 a continuous period as long as its lifespan. 



In most of the results shown here, no effort has 

 been made to impose a sexual maturity limit on 

 fecundity; i.e.. Equations (4) and (13) with N^^^ = N 

 determine the egg production, E, at any body 

 weight. 



E = N,„uW 



Nu W. 



(22) 



For exploring the limits of stability of systems 

 against perturbations, it seems useful to represent 

 the attainment of sexual maturity in the model. A 

 "knife-edge" representation— one in which fecun- 

 dity has a substantial positive value or functional 

 form above some age, length or weight, and zero 

 below it— has been used for simplicity in much 

 fishery work. This may be a justifiable 

 approximation of nature for some species, 

 especially those with short lives, fast growth, and 

 infrequent spawning. However, a smoother and 

 more realistic representation seems desirable. For 

 some species, data exist on the fraction of all in- 



706 



