Logistic Surplus‐Production Model with Explicit Terms for Growth, Mortality, and Recruitment

Conventional interpretations of the logistic equation and the logistic surplus‐production model appear to indicate that regulation of population size occurs as a result of competition for resources among the recruited members of a population. Compensation for fishing mortality may involve increased growth of adults and an increase in fecundity, but the major compensatory factor is increased survival of early life stages. In this study, the logistic surplus‐production model is formulated in explicit terms for growth, reproduction, and mortality, and in this new formulation the capacity of a population to increase and sustain a fishery is based on a stock‐recruitment relation that is a more realistic interpretation of fishery dynamics. All parameters can be estimated with catch and effort data. The models were applied to the American lobster Homarus americanus fishery in Maine and the spiny dogfish Squalus acanthias fishery. There is a considerable difference in the stock‐production curves between the two fisheries that can be interpreted in terms of a similar difference in the spawner‐recruit curves. Because spiny dogfish produce relatively few young, they have a lower potential for increase than American lobsters and their rate of recruitment does not increase with exploitation as greatly as that for lobsters. Received July 2, 1983 Accepted June 21, 1984