The Effects of Increased Individual Growth Rates on Depressed Population Size

Several exploited aquatic populations have declined to low levels and remained low even after exploitation was reduced. In many of these, individual growth rate increased just prior to or during the decline and has remained at a high level. I propose herein that this increase in growth rate may contribute to the observed depressed equilibrium levels. Recruitment rate in the multiple age-class model used depends on a compensatory effect by older, larger individuals (e.g., cannibalism) and fecundity of mature individuals. The effect of density-dependent growth rate on equilibrium and stability of this population is analyzed for the case in which both the magnitude of compensatory effect and fecundity depend on individual size rather than age. The possible existence of multiple-equilibria corresponding to different individual growth rates is shown. Simulation results using life history parameters corresponding to the central California Dungeness crab demonstrate possible global behavior of this model. Fishing can increase the susceptibility of decline to a lower, stable equilibrium, or actually lead to a degenerative decline. The population remains at the lower equilibrium level even after exploitation is decreased. Characteristics of some real populations that suggest that increased individual growth rate may contribute to their depressed levels are presented. These characteristics and the results derived herein warrant investigation of increased growth rate as a possible contributor to depressed populations. The proposed new mechanism is shown to be different from those in existing population models with multiple equilibria.