We recently published a paper in ‘Theoretical Ecology’ where we use Generalized Modeling to explore stock recruitment relationships in fisheries. Models of stock recruitment are fundamental to fish population dynamics, describing how reproduction (in terms of the biomass of new recruits) changes as a function of the density of the current stock. In many resource-limited populations, recruitment increases for lower levels of stock biomass until it levels off at higher levels of stock biomass (described by the Beverton-Holt functional response). In others, particularly when there is cannibalism or nest predation, recruitment increases, reaches a peak, and then decreases for higher levels of stock biomass (described by the Ricker functional response). In open populations, where resources are not necessarily limiting, recruitment may continue to increase with stock biomass (the Cushing functional response).
Being able to distinguish between stock recruitment relationships (SRRs) is vital for predicting the long-term dynamics of a fish population. Traditionally, SRRs are distinguished using statistical methods of best fit. In this manuscript, we present an alternative method of distinguishing between SRRs based on the response of a population to an external disturbance. The timing and degree of a population’s reaction can be used to distinguish between SRRs and is strongly resilient to observational error. The method relies on ‘generalizing’ the functional response, where we do not assume to know the specific architecture of the SRR. This approach relies on ‘Generalized Modeling’, which we review here, and is based on techniques developed by Thilo Gross et al., illustrated with respect to some really neat examples here. We extend some of these ideas by introducing generalized modeling techniques with respect to discrete-time rather than continuous time systems.
We hope that this method illustrates a different way of looking at an old problem, and think that it has particular relevance to relatively new fisheries where long-term time-series data do not exist. It offers a way to explore different aspects of fish reproduction, while remaining in a modeling framework rooted in biological mechanisms. I think the most interesting parts of these ideas are illustrated with respect to age-structured models, where the dynamics become complex.