NOTE Arrizabalaga et al : Uncertainity In slock assessments of Thunnus alalunga due to assumed stock structure 



141 



there may be some interchange be- 

 tween individuals of both stocks. An 

 earlier statistical comparison of blood 

 group frequencies in albacore found 

 in the Gulf of Guinea (lat. 0°-9°S, 

 long. 0°-8°W), northwest Atlantic 

 (lat. 23°-31°N, long. 60°-70°W) and 

 middle-north Atlantic (lat. 1-34°N, 

 long. 11°-40°W) in an earlier study 

 (Suzuki, 1962) did not show differ- 

 ences between them, again indicating 

 that the fish present in the Gulf of 

 Guinea may belong to the northern 

 population. 



Materials and methods 



Taking into account the above find- 

 ings, we assessed the uncertainty in 

 north and south Atlantic albacore 

 stock assessments by means of a sen- 

 sitivity analysis. This analysis con- 

 sisted in assessing both stocks, either 

 under alternative stock boundaries or 

 by assuming certain migration rates 

 between them. 



Stock assessment under 

 the assumption of alternative 

 boundaries between stocks 



100 w 



70 W 



40 W 



low 



20 E 



60 N 



30 N 



ON 



30 S 



60S 



60 N 



30 N 



ON 



30 S 



60S 



100 W 



70 W 



40 W 



low 



20 E 



Figure 1 



Spatial distribution of Atlantic and Mediterranean albacore {Thun- 

 nus alalunga) catches (ICCAT, 2001). The size of the circles is propor- 

 tional to the square root of the total catch at each location. 



Two alternative boundaries between 

 albacore stocks were considered: at lat. 0°N and lat. 5°S. 

 The catch-at-age within lat. 5°N-0°N and lat. 5°N-5°S 

 was removed from the southern catch-at-age matrix 

 and added to the northern one, by using available catch 

 (ICCAT'), size, and growth information (Bard, 1981; 

 Sarralde et al., 2002). For each boundary, abundance 

 and fishing mortality rates were estimated separately for 

 each stock by virtual population analysis (VPA) by using 

 the VPA-2box, vers. 3.0 program (Porch et al., 2001). 

 This program assesses the abundance and mortality of 

 one or two intermixing stocks by fitting age-structured 

 population equations to fishery data. All stock assess- 

 ment options were maintained as in the ICCAT 2001 

 report (ICCAT-) and variance of estimated parameters 

 was computed by performing 400 nonparametric boot- 

 straps of the abundance indices. 



' ICCAT (International Commission for the Conservation of 

 Atlantic Tunas). Website: http;//www.iccat.int/ (accessed 

 31 June 2005). 



2 ICCAT (International Commission for the Conservation 

 of Atlantic Tunas). 2001. Report of the ICCAT SCRS 

 albacore stock assessment session (Madrid, Spain; Octo- 

 ber 9 to 1.5, 2000). Collect. Vol, Sci. Pap. ICCAT, 52, p. 

 1283-1390. International Commission for the Conserva- 

 tion of Atlantic Tunas, Corazon de Maria 8, 28002 Madrid, 

 Spain. 



Stock assessment under the assumption 

 that there is migration between stocks 



Blood group frequency data in Arrizabalaga et al. (2004) 

 were used, with the assumption that the sample in the 

 Gulf of Guinea was within the currently accepted range 

 limit for both stocks, and therefore that it may be made 

 up of a mixture of albacore belonging to the northern 

 and southern populations. The proportion that each pop- 

 ulation would contribute to the mixture was calculated 

 according to Cavalli-Sforza and Bodmer (1981) as 



x,„ = mx^ +(l-m)xg 



(1) 



where m = the fraction of population A in the mixture; 



x,,, = the allelic frequency in the mixture; and 

 Xj^ and Xg = the allelic frequencies in populations A and 

 B, respectively. 



The variance of m is given by 



9 1 f 9 2'>/i \''2'I 



(x^-Xb) 



(2) 



where, a^,„, o^^ and aj,^ are the variances of the allelic 

 frequencies in the mixture and populations A and B, 



