Fishery resources management

We consider management of the fish species Plecoglossus altivelis altivelis, a major inland fishery resource in Japan playing important roles from economic, cultural, and recreational viewpoints. We firstly summarize the collected body weight data of the fish in the Hii River, Japan since 2016. The two kinds of data are available in each year with few exceptions: the historical data during summer and autumn collected with the help of an angular and the annual distribution data at the Toami (casting net) competition where we could obtain the data from many anglers during two hours in one day. We fit deterministic and uncertain logistic growth models to the data in each year and discuss their performance. The fitted uncertain logistic growth model is applied to an optimal harvesting problem of the fish subject to a sustainability concern and model distortion. Several numerical schemes for solving the problem are examined and compared both theoretically and numerically.