770 
Fishery Bulletin 95(4), 1997 
17 
2 4 6 
14 
3 5 
7 
13 18 
8 
11 {§10 
15 12 
20 
9 
1 1 
0 2 
i l l 
4 6 8 
Temperature (°C) 
1 
10 
Figure 7 
Age at maturity (a) versus bottom temperature. Popula- 
tions are represented by numbers (See Table 1). 
the limits of exploitation (Cook et al., 1997; Myers 
and Mertz, in press). A comparative approach, such 
as the one used here, should help refine our under- 
standing of the rational exploitation of fisheries. 
We have used as simple a model as possible to es- 
timate r . This has the very great advantage that 
the we can compare the crucial demographic param- 
eters (i.e. the replacements each spawner can pro- 
duce at low population densities ( a ), age-at-matu- 
rity (a), and adult survival (p s ) among populations) 
and can easily study the sensitivity of r m to errors in 
each of these parameters (Fig. 1). Furthermore, 
Hutchings and Myers (1994) found similar estimates 
of r m when they used a fully age-structured model 
for “northern” cod, i.e. cod in NAFO Division 2J3KL. 
Previous estimates of the recovery time for de- 
pleted cod stocks that have not included a detailed 
analysis of population growth rate have yielded 
widely different results. For example, it was initially 
projected that northern cod would recover close to 
historic levels of spawning biomass after a two-year 
fishing moratorium (Lear and Parsons, 1993). This 
projection has since been shown to be incorrect 
(Myers et al., 1996; Hutchings et al., 1997). Rough- 
garden and Smith (1996) estimated r m for northern 
cod to be =1 by simply taking the greatest difference 
between adjacent estimates of total population abun- 
dance from annual research vessel surveys. That is, 
they assumed that any change in the estimates rep- 
resented an increase in population abundance. 
However, this change in estimated abundance was 
almost entirely estimation error (Myers and Cadigan 
1995, a and b) and had nothing to do with an in- 
crease in abundance. At present (March 1997) there 
are six Canadian cod populations (2 to 7 in Table 1) 
that are currently protected by a fishing morato- 
rium because the populations have been greatly re- 
duced by overfishing (Myers et al., 1997). Unfortu- 
nately, our results indicate that recovery could re- 
quire a long period. Under average environmental 
conditions, our results suggest a doubling time of 
about 4 years. Given the severe depletion of these 
populations (some are less than 5% of their maxi- 
mum observed levels (Myers et al., 1996) recovery to 
