利用貝氏統計估計太平洋黑鮪族群動態並考慮其不確定性

Abstract

本研究在利用貝氏統計分析估計太平洋黑鮪族群動態，將可量化的不確定性整合至生物量的估計中。可量化的不確定性可能來自於我們建構的生產量模式，包含發生於豐度指標的觀察值誤差和由模式衍生的過程誤差。在套適六個時序列豐度指標於模式時，藉由貝氏統計分析可同時估計未知參數的數值、這些參數的變異和不確定性。並利用投射分析和風險分析來描述未來可能會發生的不確定性。由於應用貝氏統計分析於非線性生產量模式時，牽涉高維度的積分運算，因此所有參數經過100,000次Markov chain Monte Carlo (MCMC)模擬後，丟棄前5,000筆不穩定的數值，然後再保留每第10筆數值以除去相臨數值的高相關性。透過標準的測試值如Geweke、Heidelberger and Welch和the Rftery and Lewis檢測模擬序列是否達收斂。結果顯示，因Pella-Tomlinson模式所估計的參數和管理上有用的參數，較Schaefer模式所估計的參數更不確定，導致兩種模式有不同的風險程度。然而，兩種模式的族群生物量和漁獲死亡率，顯示相近的趨勢。自1970年代起，族群生物量低於最大生產量時的生物量( )且漁獲死亡率超過最大生產量時的漁獲死亡( )，族群開始呈現過漁狀態且被多漁具所過度捕撈。如果維持未來的年漁獲量於20,000公噸，也就是低於所估計的最大生產量，雖然資源呈現過漁狀態的風險還是很高，但資源會崩潰的風險很低。然而，如果未來的年漁獲量增加至40,000公噸，也就是高於所估計的最大生產量，族群生物量會持續下降，族群最候會崩潰的風險非常高。因為漁獲量在沒有管理下是變動的，因此有必要定期監控黑鮪族群。為了避免資源遭致崩潰的風險，建議控制漁獲量在20,000公噸，不要超過40,000公噸。

This study integrates quantifiable uncertainties into estimation of population dynamics for Pacific bluefin tuna. Uncertainties arise from the state equation (process error) and data link equation (observation error) were constructed within the production models. The values of unknown parameters and variables and their variability were simultaneously estimated by using Bayesian approach, when fitting the models to time series of abundance indices. Uncertainty in risk assessment of projection associated with different functional forms of production models was addressed. As a result, the Pella-Tomlinson models were more uncertain than the Schaefer models in terms of parameter estimation and management measures resulting in different risk levels. However, the population biomass and fishing mortality rates yielded similar trends between them. Since the stock biomass declined below the 97.5% quantiles of biomass at the level that yields the maximum production and the fishing pressure started to increase above the 2.5% quantiles of fishing mortality rate that produces the maximum production in 1970, the stock has been overfished. The future stock biomass was projected from the current year (2005) into the future if the current catch level is taken. The stock maintains its biomass for next 10 years but would still be in the overfished state. If the annul catch maintains at the 20,000 tons level which is lower than maximum production, the risk of collapse is low in the 5-10 years and the risk of being overfished is decreasing as time increases. However, if the annul catch increased to 40,000 tons, the biomass would drop down and the stock eventually collapsed. Because catch is fluctuated without regulation, the routine monitoring of Pacific bluefin tuna is necessary. To avoid this stock incurring the risk of collapse, my suggestion is to control annual catches around 20,000 tons and annual catches should not over than 40,000 tons.