A continuous time delay-difference type model (CTDDM) applied to stock assessment of the southern Atlantic albacore Thunnus alalunga

Abstract

A continuous time delay-diff erence model (CTDDM) has been established that considers continuous time delays of biological processes. The southern Atlantic albacore (Thunnus alalunga) stock is the one of the commercially important tuna population in the marine world. The age structured production model (ASPM) and the surplus production model (SPM) have already been used to assess the albacore stock. However, the ASPM requires detailed biological information and the SPM lacks the biological realism. In this study, we focus on applying a CTDDM to the southern Atlantic albacore (T. alalunga) species, which provides an alternative method to assess this fishery. It is the first time that CTDDM has been provided for assessing the Atlantic albacore (T. alalunga) fishery. CTDDM obtained the 80% confidence interval of MSY (maximum sustainable yield) of (21 510 t, 23 118t). The catch in 2011 (24 100 t) is higher than the MSY values and the relative fishing mortality ratio (F2011/FMSY) is higher than 1.0. The results of CTDDM were analyzed to verify the proposed methodology and provide reference information for the sustainable management of the southern Atlantic albacore stock. The CTDDM treats the recruitment, the growth, and the mortality rates as all varying continuously over time and fills gaps between ASPM and SPM in this stock assessment.