706 



Fishery Bulletin 93(4), 1995 



0) 



o 



o 



area 1 , season 1 



area 1 , season 2 



area 2, season 1 



50 100 150 200 250 300 



area 2, season 2 



50 100 150 200 250 300 



Sample size 

 Figure 6 



Coefficients of error of the estimates for the parameters of the discrete model under strong 

 diffusivity. The three curves in each graph correspond to zone B recovery probabilities of 0.0 

 (squares), 0.1 (triangles), and 1.0 (crosses). 



based estimates of movement and of certain other pa- 

 rameters, such as fishing mortality, are highly corre- 

 lated (Hampton, 1991; Porch et al. in press; Aldenberg 1 ). 

 A number of competing hypotheses may return simi- 



p= 1 o 



r~~i 



P=0.1 

 P=0.0 



200 

 150 



O 1 °° 



CD 



c 50- 



CO 



o 



CO 

 Q_ 0- 



-50 



-100 



a1,s1 a1,s2 a2.s1 a2,s2 



Area and season 

 Figure 7 



Percent error of the estimates for the parameters of 

 the discrete model under strong diffusivity. The legend 

 refers to the probability (P) of recovering a tag in zone B. 



larly low values of the objective function. Trajectory- 

 based methods may prove very useful in this regard by 

 supplying independent estimates of the velocity field 

 that can be fixed in the abundance-based model. This 

 would both reduce the dimensions of the search and 

 eliminate some of the correlation problems. Another 

 possibility might be to combine the abundance and tra- 

 jectory-based approaches by including both formula- 

 tions in the objective function. 



The most important limitation of trajectory-based 

 estimators is that there is no guarantee that they 

 are unbiased unless either the diffusive displace- 

 ments are negligible relative to the advective dis- 

 placements or the recovery rates are fairly homoge- 

 neous. Fortunately, the validity of the first assump- 

 tion can be inferred rather easily from the output of 

 the model itself. Estimates of the mean-square dis- 

 persion, which reflects the level of velocity variance, 

 can be obtained by using Equation 17. If the square- 

 root of the estimated mean-square dispersion is neg- 

 ligible compared with the actual displacement of the 



1 Aldenberg, T. 1975. Virtual population analysis and migra- 

 tion: a theoretical treatment. ICES Working Document (Counc. 

 mtng.) 1975/F, 32 p. 



