Livingston et al.: Estimating the annual proportion of nonspawning adult Macruronus novaezelandiae 
109 
Table 5 
Estimation of total proportion spawning ( p ) of age-7 + hoki based on (p + 
and on the number of hoki in the plus group on the Southern Plateau in 
of hoki x 10 3 , SE = standard error; M = natural mortality). 
the proportion of prespawners on the Southern Plateau 
December 1991, 1992, and May 1992, 1993. ( n = number 
M = 0 
M = 0.25 
M = 0.3 
Year 
n (SE) 
n (SE) 
n (SE) 
1992 
Observed, December 1991 
17, 945 (1,700) 
17, 945 (1,700) 
17, 945 (1,700) 
Observed, May 1992 
15, 682 (1,400) 
15, 682 (1,400) 
15, 682 (1,400) 
Expected, May 1992 
17, 945 (1,700) 
16, 170 (1,500) 
15, 837 (1,500) 
Missing, May 1992 
2, 263 (2,200) 
488 (2,100) 
155 (2,100) 
Migration ratio 
0.14 (0.16) 
0.03 (0.14) 
0.01 (0.14) 
Proportion spawning 
0.70(0.05) 
0.67 (0.05) 
0.66 (0.05) 
1993 
Observed, December 1992 
23, 250 (1,800) 
23, 250 (1,800) 
23, 250 (1,800) 
Observed, May 1993 
10, 902 (1,700) 
10, 902 (1,700) 
10, 902(1,700) 
Expected, May 1993 
23, 250(1,800) 
20, 950(1,600) 
20, 518 (1,600) 
Missing, May 1993 
12, 348 (2,400) 
10, 048 (2,300) 
9, 616 (2,300) 
Migration ratio 
1.13 (0.43) 
0.92 (0.39) 
0.88 (0.38) 
Proportion spawning 
0.84(0.03) 
0.82 (0.03) 
0.81 (0.04) 
Age 
Figure 6 
Proportion of prespawners at age from 1992 and 1993 surveys. The error bars 
indicate two standard errors. 
Table 5 shows the estimates of the total propor- 
tion of adult fish that will spawn (i.e. including those 
fish that have already left the area) calculated as 
above. The calculations were done with three esti- 
mates of natural mortality M, including the best es- 
timate M = 0.25, and two bounding values M - 0 and 
M = 0.3 (Sullivan et al. 2 ). Table 5 shows that this 
makes little difference to the estimate of p. Stan- 
dard errors of the estimates were calculated by us- 
ing the resampling technique. 
The best estimate of the total proportion of adult 
fish that would have spawned in the 1992 winter sea- 
son was 0.67 (SE 0.05, with M - 0.25). If M is as high 
as 0.3 or as low as 0, the estimate of p decreases to 
0.66 or increases to 0.70 respectively. The best esti- 
mate of the total proportion of adult fish that will 
spawn in the 1993 winter season was 0.82 (SE 0.03). 
If M is as high as 0.3 or as low as 0, the estimate of p 
is 0.81 or 0.84 respectively. 
Figure 7 shows the effect of the estimate of x on 
the estimate of p for 1992 and 1993. In each plot 
there are three curves for p as a function of x. The 
solid curve is the function given the estimated value 
of p + (0.66 in 1992 and 0.65 in 1993). The two dot- 
