Rock-lobsters, mussels and man: A mathematical model

Abstract

The palinurid rock-lobster Jasus lalandii (H. Milne-Edwards), which forms the basis of an important South African fishery, feeds mainly on the mussel Aulacomya ater (Molina). Natural populations of A. ater exhibit a bimodal size frequency distribution, believed to be caused by intense predation pressure upon medium-sized mussels. This may lead to situations in which rock-lobster productivity is severely restricted by food availability even in the presence of a large standing crop of prey. The present rock-lobster harvesting strategy is based on a minimum size limit; however, by not catching small rock-lobsters, an imbalance may be created in the lobster size distribution, resulting in an overabundance of small rock-lobsters which have insufficient food to grow fast. The need to predict an economically and biologically optimal harvesting strategy provided motivation for the present model, in which an alternative harvesting strategy, involving decrease of the minimim size limit, was compared with the present strategy. It appears that the mussel biomass could be increased by 87% and the rock-lobster yield by 19%. Simultaneously, the rock-lobster density and egg production are seen to decrease by 24 and 35%, respectively. The model assumes that rock-lobster populations have constant recruitment; therefore, the effect of the decline in fecundity cannot be predicted. Therefore, any major policy change should be delayed until the larval biology of J. lalandii has been researched more fully.