Myers et a I.: Population growth rate of Gadus morhua 
769 
1.0 - 
15 
0.8 
19 
20 
10 
0.6 -i 
9 
12 
11 16 18 
13 
0.4 - 
„ 5 
7 8 
3 
4 1 
6 
17 14 
0.2 - 
2 
1 1 1 1 T 
Temperature (°C) 
Figure 5 
Rate of population growth (r m ) and slope at the origin ( a ) 
versus bottom temperature. Populations are represented 
by numbers (See Table 1). 
20 
15 
10 
5 
0 
15 
19 
10 
18 
7 
20 
12 
16 
9 11 8 
13 
5 
3 
1 
17 
14 
4 
2 
6 
1 1 T 
2 3 4 5 6 7 
Age of maturity (yr) 
Figure 6 
Rate of population growth (r ) and slope at the origin ( a ) 
versus age of maturity (a ). Populations are represented by 
numbers (See Table 1). 
survival (between 0.7 to 0.9) or a have a relatively 
small effect compared with age-at-maturity (Fig. 1). 
Our study has presented robust estimates (see 
Fig. 8) of r m for a variety of Atlantic cod populations, 
thus establishing recovery times for overfished popu- 
lations relieved from fishing pressure. At colder tem- 
peratures, r m is around 18% a year for all popula- 
tions, independent of how we calculate r . 
A major source of uncertainty in the SPA estimates 
of recruitment and SSB used in our analysis is that 
catches are assumed to be known without error. This 
assumption is particularly important when estimates 
of discarding and misreporting are not included in 
the catch-at-age data used in the SPA.These errors 
are clearly important for some periods of time for 
some of the cod stocks (Myers et al., 1997), and these 
errors will affect our estimates of the number of re- 
placements each spawner can produce at low popu- 
lation densities ( a ). However, we have shown that 
the estimates of r m are not very sensitive to reason- 
able changes in this parameter. 
We have carried our estimation of the model pa- 
rameters separately for each stock. An alternative 
approach is to analyze simultaneously all stocks in 
models that include separate estimation error for 
each stock and a parameter describing the variation 
among stocks. Myers et al. 1 carried out such an analy- 
sis using variance components models for the data 
analyzed in this study and found that the optimal 
estimates of the variation in a was much less than 
that estimated, e.g. the very high estimate for Irish 
Sea cod was found to be overestimated. 
The parameters estimated in this study have man- 
agement implications that go beyond the estimation 
of population growth rate. In particular, the number 
of replacements each spawner can produce at low 
population densities ( a ), is critical for determining 
1 Myers, R., G. Mertz, and N. Barrowman. 1996. Invariants 
of spawner-recruitment relationships for marine, anadromous, 
and freshwater species. ICES Council Meeting 1996 /D:ll, 17 p. 
