766 
Fishery Bulletin 95(4), 1997 
Labrador / N.E. Newfoundland 
Kattegat 
Figure 3 
Recruitment versus spawning stock biomass (SSB) for the three representa- 
tive cod populations. The solid line is the maximum likelihood estimate of the 
mean for Ricker spawner-recruitment functions under the assumption that 
the probability distribution for any SSB is given by a lognormal distribution. 
The dashed line is the median slope at the origin estimated from the six points 
with the lowest SSB. The straight dotted line is the replacement line with no 
fishing mortality. 
mated parameters (Myers et al., 
1995b). Difficulties in estimating 
density-dependent model parameters 
are well known for insect and bird 
populations (Holyoak, 1993; Wolda 
and Dennis, 1993) and have been 
extensivly studied for exploited fish 
populations (Hilborn and Walters, 
1992). The most important source of 
statistical bias for exploited fish 
populations is the nonindependence 
of spawners and recruitment, i.e. 
large recruitment usually leads to 
large spawner abundance (Walters, 
1985). Bias in the parameter esti- 
mates of the spawner recruit function 
has been extensively studied with 
simulations for cod populations by 
Myers and Barrowman (1995) who 
found minimal bias in the estimates 
of the a parameter. 
The slope at the origin can be well 
estimated for cod populations, in 
spite of the large variability in re- 
cruitment, because each population 
has been reduced to very low levels 
by overexploitation (Myers et al., 
1994). Furthermore, there is no evi- 
dence that mortality increases at low 
population size, i.e. depensation or 
the Allee effect, that would invalidate 
the assumption of our spawner re- 
cruitment model (Myers et al., 1995). 
The disadvantage of using the 
Ricker model, or any other paramet- 
ric spawner recruitment model, is 
that the slope at the origin is influ- 
enced by observations far from the 
origin. We investigated an alterna- 
tive approach: we regressed recruit- 
ment versus spawner biomass with 
only six observations with the low- 
est spawner biomass, forcing the re- 
gression line through the origin. This 
simple procedure should be reason- 
able because all the populations have 
been reduced to very low levels. 
ResuSts 
The Ricker model estimates of the slope at the ori- 
gin and of the population growth rate were estimated 
for the 20 spawner recruit data sets (Table 1; Fig. 3). 
The slope at the origin, a , did not vary enormously 
among populations (Fig. 4). There is one population, 
Irish Sea, for which the a is much larger; we believe 
that this large a is an overestimate (this will be dis- 
cussed later). 
It is evident that r m strongly covaries with tem- 
perature (Fig. 5; Table 2). It is also clear that this 
behavior does not arise from any dependence of a 
on temperature, because a is not correlated with 
temperature (Fig. 5; Table 2). There is a strong de- 
