259 KOBE II STRATEGY MATRIX FOR THE BIGEYE AND YELLOWFIN TUNA STOCKS OF THE EASTERN PACIFIC OCEAN IN 2012 Carolina V. Minte-Vera, Mark N. Maunder and Alexandre Aires-da-Silva 1. INTRODUCTION The second joint meeting of the tuna regional fisheries management organizations (tRFMOs) recommended the computation of a “strategy matrix” in order to improve further the standardization of the presentation of stock assessment results for fishery managers. The Kobe II strategy matrix “would present the specific management measures that would achieve the intended management target” (Report of the second joint meeting of the tuna RFMOs). Following this recommendation, the IATTC staff computed the following Kobe II strategy matrices and decision matrices for yellowfin tuna and bigeye tuna in the eastern Pacific Ocean (EPO) in 2012. For this exercise, the reference points cited in Maunder and Deriso (2013) and that will be recommended by the staff to the Commission for adoption as an interim measure were used (IATTC 2013): Stock Target reference point Limit reference point Bigeye tuna S MSY ; F MSY 50% of S MSY ; 30% above F MSY Yellowfin tuna S MSY ; F MSY 40% of S MSY ; 40% above F MSY S MSY : Spawning stock biomass corresponding to the maximum sustainable yield (MSY); F MSY : fishing mortality rate corresponding to the maximum sustainable yield The Kobe II strategy matrix was computed with F MSY , because the IATTC staff recommendations have treated F MSY as a target reference point, and the informal harvest rule used to management tunas in the EPO has been based on reducing fishing mortality to F MSY if it exceeds F MSY. The Kobe II strategy matrix is substantially more demanding computationally for calculating biomass reference points than for calculating fishing mortality reference points. Therefore, biomass reference points are presented only as a traditional decision table. 2. METHODS 2.1. Kobe matrix For the Kobe II strategy matrix, the fraction δ of the current fishing mortality (F cur ) that is required to ensure a given probability P that it will be at or below fishing mortality target reference point (e.g. F MSY ) was computed: (  <   )=P The normal approximation method was used, due to the excessively long computational time that is required for the use of either the Bayesian or the bootstrap methods with the current bigeye and yellowfin stock assessment model (Maunder et al. 2012) implemented in Stock Synthesis 3 (SS3; Methot and Wetzel 2013). The standard deviation of F mult 1 = F MSY /F cur was estimated using the stock assessment models for yellowfin (Minte-Vera et al. 2013) and bigeye (Aires-da-Silva and Maunder 2013). It follows that: (  <   )= �     <1� = �     >1� =1 −�     <1� =1 −�    <1� Assuming that F mult ~N(μ Fmult, ,σ 2 Fmult ), it follows that    ~ (    ,   2  2 ) 1 F multiplier (F mult ): the number of times the effort would have to be effectively increased relative to the average fishing mortality during 2010-2012 to achieve MSY.