Stock-recruitment models from the viewpoint of density-dependent survival and the onset of strong density-dependence when a carrying capacity limit is reached

Abstract

When viewed on a discrete time step (e.g., one year) rather than instantaneously, the Ricker and Beverton-Holt stock recruitment relationships describe a strong influence of changes in adult abundance on juvenile survival even at low biomass levels. In fact, they describe a stronger influence at lower adult abundance than at high adult abundance. This is not consistent with a simplistic interpretation of carrying capacity, where survival reduces more rapidly as the juvenile abundance approaches its carrying capacity due to resource limitation. It implies that other processes (e.g., changes in predation risk with increased abundance as described by arena theory) control density dependence. A simple habitat limitation model suggests that a similar relationship can occur if the number of juveniles produced by the adults is always more than the juvenile carrying capacity. However, the resulting stock-recruitment relationship is constant recruitment, while that of the Beverton-Holt is increasing asymptotically and the Ricker is dome shaped. Fluctuations around an average recruitment level for a wide range of adult abundance levels is common for highly fecund pelagic spawners (e.g., tuna), suggesting that the survival and recruitment relationships implied by the simple habitat limitation model might be appropriate for these species. Underpinning this argument is the concept that the adult population will saturate the juvenile carrying capacity unless the adult population is fished to extremely low levels. However, it is reasonable to expect that survival should be density independent, or possibly even decompensatory, at some low level of adult abundance. Ignoring depensation, the survival relationship would therefore be well described by a general logistic equation where the decline in survival initially accelerates as abundance increases and then deaccelerates. The resulting stock-recruitment relationship would be a hockey stick shape with the possibility of reduced recruitment at large stock sizes. The model could also be used for low fecund species (e.g., sharks) for which the juvenile carrying capacity is not saturated until the adult abundance is large (i.e., survival is density-independent for a wide range of adult population sizes). In our model, particularly for high fecund species, temporal variation in recruitment would be controlled by changes in the juvenile carrying capacity. We provide equations for the generalized logistic survival stock-recruitment model and investigate the yield consequences. We suggest that an important management consideration is the level of adult abundance at which the juvenile carrying capacity becomes saturated (i.e., when does density dependence become influential on juvenile survival).