Seasonality matters: a multi-season, multi-state dynamic optimization in fishery

Many biological and economic processes in fishery happen seasonally. Most of the extant literature tends to neglect this fact. This work is an initial attempt to treat seasonality in a systematic and proper way. We apply a periodic Bellman approach to obtain the optimal feedback policy of each season. Our approach has rich potentials. It could deal with seasonal patterns of uneven lengths: some may span years and some within the year. We find that, in some cases the equilibrium consists of one harvesting season followed by a moratorium period, indicating an optimal closure of the fishery that would be overlooked by a yearly model. Unlike a typical policy that enforces a moratorium to recover the stock, we find that many states first undergo harvesting all year round and later evolve into the seasonal moratorium. A rising group biomass could be the overshooting effect instead of a clear sign to increase harvest. We sometimes observe declining optimal harvest with increasing states (‘valley’), which may relate to the unit profit difference between seasons. Fishing pressure on the mature elicits even heavier harvest in the next season on the same group. A protective moratorium of the immature seems to hinder the value of the whole stock.