A general production model with dependence between data from multiple surveys

A fishery-independent survey for stock assessments is made sometimes more than once per year to detect a difference in relative sizes of fish populations (e.g., catch-per-unit-effort [CPUE]) in response to a seasonal change in fish spatial distributions. Many managers tended to treat such data independently instead of systematically synthesizing them. A primary objective of this study was to synthesize all survey data via a simple hierarchical structure. I used the general (Pella-Tomlinson) surplus production model for the illustration, because the purpose of this study was not a stock assessment, and the model was simpler than an age-structured model. The surplus production model has about an eight decade history (since Graham's paper in 1935) and has been prominent in fish population dynamics. The logistic (Graham-Schaefer) version was useful in the sense of simplifying the dynamics of a fish population in relation to its intrinsic growth, natural mortality, recruitment, density-dependence, and fishery catch, but it was criticized because of its unrealistic limitations. Subsequently, the general version was suggested to accommodate flexibility and be realistic. In this study, I inferred parameters in the general surplus production model, simultaneously synthesizing all available data even from different temporal ranges. I used Georges Bank yellowtail flounder (Limanda ferruginea) data for demonstration.