Van Eeckhaute et al.; Movements o\ Melanogrammus aeglefinus determined from a population model 



667 



timing. The 5Zj,m population numbers at the begin- 

 ning of quarters 2 and 4 as obtained from the quar- 

 terly VPA were used. Numbers of haddock dying from 

 natural mortality and from fishing were summed for 

 quarters 2 and 3 to give 1 April numbers and for 

 quarters 4 and 1 to give 1 October numbers. The pro- 

 portions of haddock at ages 1 to 8 on the Canadian 

 side of the ICJ line were averaged for the two spring 

 surveys for 1987 to 1993. These were then combined 

 with the 1985 and 1986 proportions from the NMFS 

 spring survey and, along with the NMFS fall pro- 

 portions, were applied to the 5Zj,m population abun- 

 dance at the beginning of quarters 2 and 4 to obtain 

 population abundance on the Canadian side: 



^Can.y.a = ^ y,a^Can.y.a ' 



where R^^,, ^.^ - the proportion occurring on the Ca- 

 nadian side. 



By convention, ^,,„ and E^,^^ is positive when the 

 net direction of migration is towards the U.S. side 

 and negative when it is towards the Canadian side. 



Results 



Ratios of relative abundance 



Although the ICJ line was not established until Oc- 

 tober 1984, to provide a historical perspective of had- 

 dock relative abundance with respect to the line, we 

 make reference to Canadian and U.S. sides of east- 

 ern Georges Bank for all surveys conducted since 

 1963. Because relative abundances of older haddock, 

 greater than age 8, are difficult to interpret because 

 of the small numbers caught, an aggregated age 

 grouping of 9-(- was used. 



The number of fish dying from natural mortality 

 on the Canadian side of the ICJ line was assumed 

 proportional to the fraction of the population occupy- 

 ing the Canadian side on average during the period: 



M^Can.x.a 



M 



Ny.a Ncan.y.a 



^^Can.y.a + -^C/SA.v.o ' 



where -^fg,,,,, and N ^^jg^ ,^ = the average population 



abundances on the 

 Canadian and USA 

 sides, respectively, 

 during the period. 



The net number of fish migrating from the Cana- 

 dian side to the U.S. side of the ICJ line was obtained 

 by subtracting the number offish caught by the Cana- 

 dian fishery at age, F^can. v. «> and the number of fish 

 dying fi-om natural mortality on the Canadian side fi'om 

 the difference between population abundance on the 

 Canadian side at the beginning of the two sLx month 

 periods: 



\T - \T _ AT _ 



£-'*v.a "-"Can.v.o '^ Can.y+t .a+t 



N - N 



Instantaneous rates of migration were calculated in 

 relation to the average abundance in 5Zj,m as follows: 



N..Al-e-'^- 



where the total mortality 



N 

 Z^,„=-ln^^^^:i^^ 



Fall season The multiplicative model accounted for 

 about half of the total variation in catch per tow ( mul- 

 tiple R~=0.47 ). The stratum influence with an F-value 

 of 7.245 andP<0.001 accounted for most of the varia- 

 tion, but the year effect also accounted for some with 

 an F-value of 3.247 and P<0.001. The frequency dis- 

 tribution of residuals approximated a normal distri- 

 bution. The strata coefficients from the multiplica- 

 tive model give an indication of the relative abun- 

 dances between strata sections, i.e. the higher the 

 value, the higher the abundance. For those strata 

 sections that were used in the model, the shading in 

 Figure 3 was scaled to the magnitude of the strata 

 coefficients. All Canadian sections of strata had 

 higher coefficients than the corresponding U.S. sec- 

 tions. The four sections on the U.S. side that were 

 not used in the model were dominated by zero catch 

 per tow. Canadian strata sections having depth zones 

 of 56 to 183 m exhibited the highest coefficients. The 

 model results indicate that the strata on the Cana- 

 dian side had higher abundance than those on the 

 U.S. side. 



For each stratum the abundances by stratum or 

 stratum section are contained in Table 1. The domi- 

 nant strata were 16c, 16u, and 17c. Abundance in 

 19u and 20u used to be quite high but in recent times 

 almost no haddock have been caught there. In con- 

 trast, 17c has shown an increase in its relative abun- 

 dance in recent years in comparison to early catches, 

 although that abundance since the 1960s has dropped 

 substantially. Total fall abundance showed that more 

 haddock were caught on the U.S. side during the 

 1960s and early 1970s, after which haddock became 

 more abundant on the Canadian side. Numbers es- 

 timated by the multiplicative model accounted for a 

 significant amount of the abundance on the U.S. side 



