142 



Fishery Bulletin 105(1) 



respectively. When several diallelic loci 

 are analyzed, the fraction of population 

 A in the mixture can be computed as a 

 weighted average: 



m 



(3) 



Table 1 



Proportion of albacore (Thunniis alalunga). with a given blood group in the 

 North Atlantic, Gulf of Guinea, and South Atlantic determined with three 

 different lectins (Con A: Concanavaline A\ WGA: Triticum viilgare: EGA: 

 Eritrina cristagally; from Arrizabalaga et al., 2004) and estimated mixing 

 proportions in the Gulf of Guinea. OT=proportion of northern origin fish in 

 the Gulf of Guinea sample; m=weighted average proportion. Standard 

 deviation of m and m is given in parentheses. 



Lectin 



Con A 



WGA 



EGA 



North Atlantic 

 Gulf of Guinea 

 South Atlantic 



Using three lectins, for which the 

 positive lectin binding proportion in 

 the Gulf of Guinea was intermedi- 

 ate between the proportions for the 

 northern and southern populations 

 as described in Arrizabalaga et al. 

 (2004), we obtained /n values shown 

 in Table 1. The weighted mean pro- 

 portion indicated that 79% of the fish present in the 

 Gulf of Guinea would belong to the northern Atlantic 

 population, and this result was used to formulate 

 plausible migration hypotheses for the two stocks. The 

 mean historical (1975-99) catch around the equator 

 (between lat. 5°N and lat. 5°S) has been 1218 metric 

 tons (t) per year, and therefore 974 t would belong to 

 fish from the North Atlantic population and 244 t to 

 fish from the South Atlantic population. In reference 

 to the average total catch in each stock (38,960 t and 

 27,111 t in the northern and southern stocks, respec- 

 tively), these quantities would imply that about 2.5% 

 of the fish from the North Atlantic and 0.9% from the 

 South Atlantic are present in the Gulf of Guinea every 

 year. Assuming that albacore in this area are migrat- 

 ing from one stock to the other, these percentages 

 would, in broad terms, represent the yearly transfer 

 rates between stocks. 



Several scenarios were established and tested. Sce- 

 nario number 1 reflects the above situation (2.5% and 

 0.9% annual migration rates from north to south and 

 south to north, respectively). However, high variances 

 for mixing proportions were obtained because no diag- 

 nostic loci was detected, and those precision estimates 

 could, in fact, be overestimated because not all fish 

 were sampled from different schools in the study of 

 Arrizabalaga et al. (2004). This overestimation may 

 indicate that annual migration rates vary considerably 

 from those in scenario 1. Thus, a range of alterna- 

 tive migration scenarios were explored in which ad- 

 ditional biological or fishery aspects were taken into 

 account. Scenarios 2, 3, 7, and 8, reflected the situ- 

 ation in which migration occurs only in one direction 

 (5% yearly from north to south and south to north in 

 scenarios 2 and 3, respectively, and 10% from north to 

 south and south to north in scenarios 7 and 8, respec- 

 tively). Because no fishing effort targeting albacore 

 exists in the equatorial area, the real migration rate 

 may be higher than the one inferred from catches in 

 that area. Accordingly, in scenario 4, twice the migra- 

 tion rates of scenario 1 (5% from north to south and 



0.2500 

 0.2174 

 0.0357 

 0,8478(0.5553) 



0.4500 



0.3913 



0.2857 



0,6427(0,7794) 



0,7900(0.4232) 



0.0500 



0.0435 







0,8695(1,2006) 



1.8%. from south to north) were adopted. In scenario 

 5, migration was considered to be limited to the adult 

 fraction of the stock (ages 5-8-I-), as size distributions 

 in this area indicated, and finally in scenarios 6 and 9, 

 high rates of migration (5% and 10%, respectively) in 

 both directions were chosen. Although these scenarios 

 are believed to be representative of the true nature of 

 mixing between the stocks, it should be stressed that 

 they represent only some of many different possible 

 mixing scenarios. 



All scenarios were tested by assuming an overlap 

 migration model (fish return back to the area of origin 

 for spawning) and using the VPA-2box program (Porch 

 et al., 2001). No diffusive migration was considered 

 because it is not consistent with observed genetic dif- 

 ferentiation. Results for all scenarios were compared (in 

 terms of spawning stock biomass trends and the small 

 sample bias-adjusted version of the Akaike information 

 criteria ([AICc, Hurvich and Tsai, 1995]) with the base 

 case where no migration was assumed to occur between 

 stocks. 



Results 



Stock assessment under the assumption 

 of alternative boundaries between stocks 



Best fits for northern and southern stocks were 

 obtained by assuming different stock boundaries, at 

 lat. 5°S and lat. 5°N, respectively. However, estimated 

 abundance and fishing mortalities, with the assump- 

 tion of any of the alternative stock limits, showed minor 

 differences with respect to the base case (Table 2). 

 The effect of considering the limit in lat. 0°N or in 

 lat. 5°S was practically the same because most of the 

 catch in the equatorial area happens in the Northern 

 Hemisphere (between lat. 5°N and lat. 0°N). All coef- 

 ficients of variation (CV) were below 15%, except for 

 the ■F'5+**^'^® in the south Atlantic, which were between 

 15% and 30%. 



