[[alternative]]The study of optimal harvesting strategy in an artificial reef ecosystem

[[abstract]] 我國四面環海，原本漁業資源充裕，但由於漁民過度捕撈，且近岸和沿海地區生態環境受污染的負面影響之下，漁業資源已逐漸出現枯竭現象。而由過去研究及實務經驗得知，人工魚礁之投放為一良好之水域漁產資源復育方式，它可以非常有效的吸引並聚集大量魚群，可藉改變水流為魚類提供理想的覓食機會。因此，人工魚礁區之建置對漁業資源枯竭問題當有顯著性改善。然而，我國在過去已投放許多人工魚礁，雖然對漁業資源的永續發展有部分改善，但由於人工魚礁在投放過後，並未有進行有效積極管理，因而人工魚礁的壽命比先進國家短少許多，殊為可惜。 而現行應用漁業管理於人工魚礁之方式之一即為將原本屬於公共財之人工魚礁轉成私有財的方式來經營，因此本研究擬就當魚礁為私有財之情況討論廠商之最適撈捕模式(Artificial Reef Harvesting Model，簡稱ARH模式)，以獲得最大之經濟效益。由於魚礁區之生態系統有其特性存在，其具有一定長度時間之生命週期，之後則會因為發生沉陷而消失；此外，若當魚礁區之使用方式為私有財之情況，則其又因具可滲透性之邊界而產生一非封閉性之生態系統。因此本文所提出之ARH模式嘗試加入Buechner (1987)及 Stamps et al. (1987)所提出之魚群動態遷徙模式以修正傳統漁業管理所討論之獨立且封閉之開放撈補(Open access)系統，也因此本文所提出之ARH模式更能符合魚礁區之特性。在求解方面，本研究利用最適控制理論推得控制函數之特殊形式，進而將原屬於動態最佳化的問題簡化為普通的函數極值問題。最後並針對參數之敏感性加以分析以提出在不同之參數條件中所應相應之撈捕對策。 研究結果顯示，在利率較高、或人工魚礁之保護區面積較大、或人工魚礁之保護區週長較小 (即形狀較偏方正或圓形)、或目標物種移動速度較慢(如龍蝦相對於魚來說)、或單位魚價較高、或單位撈捕漁船之操作成本較低之情況下，應派遣更多之漁船進入人工魚礁撈捕，始可獲得較大之利潤；至於撈捕之時機則是愈早越好。唯前述撈捕策略之擬定尚應滿足利潤率大於未受限之邊界所造成之生物族群損失率與實質成長率之比值(即 )之前提，否則不能直接斷言參數與變數(即派遣之漁船數量 及派遣漁船出海之時機 )間之關係。[[abstract]] The over-harvesting of fishery resources has leaded to exhaustion of fishery stock around the island. Moreover, the environmental pollution along the coastal line also aggravated the environmental deterioration and consequent resource depletion. Past empirical studies by experimental researches and practical programs find that the artificial reefs (ARs) as a fishery habitat that can change the water flow to improve the environment for fishery. In this case, the construction of ARs in the sea is an effective way to restore the fishery stocks and improve fishermen’s income. As most constructed ARs in Taiwan were not taken care duly, the service life was much shorter then that in developed countries. In this paper, if fishery resources are seen as a private ownership, we attempt to analyze the cost benefit of an ARs construction through the proposed artificial reefs harvesting model to accomplish the optimal harvesting strategies. Since an ARs ecosystem has its characteristic existence, it will be buried and scoured later due to its finite service life; and when the ARs is deemed to the private goods, it would be a non-closed ecosystem because of its permeable boundary. For this reason, this study incorporates with the population dispersal dynamics (Buechner, 1987; Stamps et al., 1987) into the conventional open access fishery management model to conform to the characteristic of practical application in ARs. An optimal number of fishing boats and the timing to dispatch the boats (i.e., control variables U and τ) at steady state are obtained by using optimal control theory with the Most Rapid Approach Paths (MRAP). Then we transform the optimal control problem into static optimization problem. Sensitivity analyses on the effects of environmental parameters on optimal harvesting strategies are analyzed. The results reveal that the fishery firm will dispatch more fishing boats as early as possible to achieve the maximization of profit in case of the following situations: discount rate is increased, area of ARs is expanded, target species move less mobile, the price per unit catch increases, and operation cost is decreased. This harvesting strategy is also constrained by the rule that the profit rate (i.e.,1-b ) must be greater than the ratio of population loss rate to intrinsic growth rate (i.e., λ/r0 ). In brief, the effect of permeable boundary in ARs ecosystem has been considered and incorporated in our model presented in this paper. The major contribution of this paper is our focus on open populations of mobile, long-lived species, boundary type and geometrical configuration of an ARs ecosystem that plays an increasingly crucial role in determining the potential equilibrium population size