A family of general production curves for exploited populations

A form for the growth term in the differential equation for biomass change with time is proposed, which is based on a versatile new family of stock-recruitment curves. The resultant yield curves of a general production model are investigated. The form of the curves is more variable than is usual in such models, but depends systematically on the values adopted for biologically well-defined parameters such as natural mortality and natural rate of increase. The consequences for management are explored by examining the magnitude of the maximum sustainable yield (MSY) and suitable values for the yield?biomass ratio.It is concluded that the MSY is of the order of but usually somewhat less than 0.5 MB₀, although variation by a factor of three either way is possible. MSY is usually attained at a yield?biomass ratio no more than a few times M (the natural mortality), and at biomasses less than half the pristine biomass (B₀). However, exploitation of stocks having domed stock-recruitment curves at MSY is dangerous, because the ability of the population to recover from perturbations is impaired. This is associated with an increase in the return time for the population.