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Therelationshipbetweenstockandrecruitment:
Aretheassumptionsvalid?
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2402
The influence of stock structure and
environmental conditions on the recruitment
process of Baltic cod estimated using a
generalized additive model
M. Cardinale and F. Arrhenius
Abstract: The recruitment process and its underlying mechanisms are among the most studied phenomena in fisheries
ecology. Traditional models estimate fish recruitment assuming a direct relationship with spawning stock size. However,
highly variable environmental conditions, feeding conditions, and other factors can influence and complicate the results
of a simple linear regression analysis between stock and recruitment. We used generalized additive models (GAMs) to
investigate the influence of environmental conditions and stock structure on the recruitment processes of Baltic cod.
The interaction between abiotic factors and old spawners (>5+ years) and eggs produced by old spawners were the
most significant explanatory variables. Eggs produced by young spawners have a positive impact on cod recruitment
only at high levels of reproductive volume, while old spawners’ eggs have the highest positive effect at low levels of
reproductive volume. Here we show: (i) that the number of Baltic cod recruits is strictly dependent on the age structure
of the population; (ii) that interactions between biotic and abiotic factors are crucial in explaining recruitment variability; and (iii) that GAMs are a powerful technique for defining and quantifying the intricate multidimensional relationship between biotic and abiotic variables involved in recruitment processes.
Résumé : Le recrutement et ses mécanismes sous-jacents sont parmi les phénomènes les plus étudiés en écologie des
pêches. Les modèles traditionnels estiment le recrutement des poissons en supposant une relation directe avec le stock
des reproducteurs. Cependant, les conditions très variables du milieu, les conditions alimentaires et d’autres facteurs
peuvent intervenir et complexifier les résultats d’un simple analyse de régression linéaire entre le stock et le
recrutement. Nous avons utilisé des modèles additifs généralisés (GAM) pour étudier les effets des conditions
environnementales et de la structure du stock des reproducteurs sur le processus de recrutement chez la Morue franche
de la Baltique. Les relations entre les facteurs abiotiques et les recruteurs âgés (>5+ ans) et les oeufs produits par
ceux-ci se sont révélés les variables explicatives les plus significatives. Les oeufs produits par les jeunes reproducteurs
n’ont d’impact positif sur le recrutement que lorsque le volume de reproduction est élevé; en revanche, les oeufs
provenant des reproducteurs plus âgés ont une influence positive maximale lorsque le volume de reproduction est
limité. Il est donc démontré (i) que le nombre de recrues dans cette population de morues dépend de la structure en
âges de la population, (ii) que les interactions entre les facteurs biotiques et abiotiques jouent un rôle crucial dans la
variation du recrutement et (iii) que les GAM sont une technique puissante pour définir et quantifier les relations complexes et multidimensionnelles entre les variables biotiques et abiotiques impliquées dans les processus de recrutement.
[Traduit par la Rédaction]
2409
Introduction
important insights into SRR dynamics, they may not include
Cardinale and Arrhenius
An important stage in the assessment of fish resources and
their management is the relationship between stock and
recruitment (SRR). Different models have been used to describe the relationship between parental-stock size (fecundity, biomass, or abundance) and relative recruitment output
(for a review see Hilborn and Walters 1992). Although these
models (i.e., Beverton and Holt, Ricker function) provide
Received April 13, 2000. Accepted October 19, 2000. Published on the NRC Research Press web site on December 20, 2000.
J15715
M. Cardinale1 and F. Arrhenius. Institute of Marine
Research, National Board of Fisheries, P.O. Box 4,
SE-453 21 Lysekil, Sweden.
1
Corresponding author (e-mail: Massimiliano.
[email protected]).
Can. J. Fish. Aquat. Sci. 57: 2402–2409 (2000)
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key factors or account for specific situations (e.g., Fogarty
1993). Specific factors, such as age–size structure and maternal effects, may contribute significantly to explaining the
observed recruitment variability in fish stocks (Trippel et al.
1997; Marshall et al. 1998; Cardinale and Arrhenius 2000).
Nevertheless, SRR is often also complicated by highly variable environmental conditions (i.e., salinity, temperature, oxygen level, and others), feeding conditions, or other factors
that can influence and mislead the results of a simpleregression analysis between stock abundance and recruitment (Sparholt 1996; Daskalov 1999). Therefore, it is considered crucial in fisheries ecology to isolate those factors
behind spawning biomass that could explain the observed
variability in the SRR and to understand the dynamics of the
interaction between biotic and abiotic factors and their effects on recruitment.
Owing to recruitment failures in recent years, the SRR relationship in Baltic cod (Gadus morhua) is currently the
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Cardinale and Arrhenius
object of much attention (Vallin et al. 1999; Vallin and
Nissling 2000). Generalized linear (Sparholt 1996) and nonlinear models (Solari et al. 1997) have been used previously
to describe the recruitment process, assuming that the
spawning biomass is proportional to the reproductive potential of the stock. However, different authors have recently
challenged this paradigm (Marshall et al. 1998;
Marteinsdottir and Thorarinsson 1998; Cardinale and
Arrhenius 2000). The recent overexploitation of marine
fish populations typically results in the loss of the large
members of the stocks (Trippel et al. 1997). Depletion of
these large individuals may not only affect the quantitative
reproductive potential of the population but, if younger fish
exhibit poorer gamete quality than older fish, the qualitative
reproductive output of the stock may also be seriously depleted (Trippel et al. 1997). Moreover, the importance of environmental factors (e.g., salinity, temperature, and oxygen) in
explaining the recruitment variability of fish stocks has recently been recognised (e.g., Daskalov 1999). Recruitment
success in Baltic cod is also affected by fluctuations in salinity, temperature, and oxygen at depths where cod eggs are
deposited (Vallin et al. 1999). These abiotic factors (temperature, salinity, and oxygen) have been included in a generalized linear model (GLM) with logarithmically transformed
data to estimate Baltic cod recruitment (Sparholt 1996). In
addition, stock structure (i.e., age–length) has recently
been shown to influence cod-stock recruitment, through a
positive relationship between female age and egg and larva
viability (e.g., Cardinale and Arrhenius 2000).
Relationships between a dependent variable and two or
more factors are often nonlinear. Generally, the response to
environmental factors is unlikely to be monotonic, linear, or
parametric (Maravelias 1997; Maravelias and Reid 1997).
Therefore, traditional linear models are often inadequate for
detecting and quantifying any environmental effects and
their complex interaction with biological factors (Maravelias
1999). Generalized additive models (GAMs) offer an attractive possibility for overcoming statistical problems linked to
the normality and linearity assumptions of GLMs (Hastie
and Tibshirani 1990; Swartzman et al. 1992). GAMs extend
the power of any conventional regression technique by fitting nonparametric functions to estimate relationships between the response and the predictors. Therefore, GAMs are
not tied to any particular functional relationship (i.e., linearity) or to any statistical distribution of the data (i.e., normality). The underlying probability distribution for the data can
be any distribution from the exponential family, including
the normal, Poisson, and binomial distributions (Swartzman
et al. 1992). In GAMs, dependent variables are assumed to
be affected by the predictors through additive unspecified
smooth functions.
In this study, we used GAMs to estimate and quantify the
effect of age structure and environmental conditions on the
recruitment processes of Baltic cod. Does the age structure
of the population constitute a key factor in explaining the recruitment variability of Baltic cod? Is the interaction between
the age structure of the population and spawning conditions
also important in explaining the variability in Baltic cod
recruitment? The aim of this study was to test these hypotheses and to discuss the results in the broader context of the
SRR.
2403
Materials and methods
Time series
We analysed fishery-dependent and independent data from the
Baltic cod (Gadus morhua) stock (Fig. 1) from the ICES (International Council on the Exploration of the Sea) annual stock assessment database calculated with a virtual population analysis (VPA)
(Anonymous 1998). Catch-at-age data from commercial landings
were tuned with a survey index of abundance estimated from trawl
surveys. Natural mortality was set at 0.2 for all age-classes. For
more details on the mathematical calculations of a VPA-type model,
see Hilborn and Walters (1992). Numbers of cod are given for each
age-class using the VPA (Anonymous 1998). Cod recruitment is
considered to be the number of 2-year cod at the beginning of the
year (Anonymous 1998).
To assess the contribution to Baltic cod recruitment of different
age-classes, we calculated the potential egg production for each
age-class. The total egg production was based on stock numbers,
proportion of mature individuals, sex ratios, and weight at age in
the stock (Anonymous 1998). For proportion of mature individuals
and sex ratios, the ICES Working Group assumed that the values
estimated during 1980–1984 were applicable to all previous years,
and thus these values were used in this study (Anonymous 1998).
Relative fecundity estimates (number of eggs × weight of fish (g))
were available from Kraus et al. (2000). The value used in this
study (630 eggs·g–1) was the mean of the different yearly estimations relative to the period between 1978 and 1996.
The time series of reproductive volume (RV) are from MacKenzie et al. (2000). RV is the volume of water suitable for the successful development of the early life stages of Baltic cod. It is
defined by threshold levels in temperature (>1.5°C), salinity (>11‰),
and oxygen (>2 mL·L–1). Below these thresholds, development of
cod eggs ceases before hatch (Nissling and Westin 1991). The hydrographic data set consists of measurements from 36 different
standard stations. The survey data were used to calculate the thickness of the Baltic cod spawning layer, i.e., the vertical extension of
the water body considered suitable for successful egg and larval
development (as defined below). Horizontal fields of the thickness
of the reproductive layer were constructed by objective analysis,
which was based on a standard statistical approach, the Gauss–
Markov theorem, that gives an expression for the last square error
linear estimate of the variables. Thus, at every single point, an estimate can be given that depends, linearly, on the total number of
measurements, i.e., a weighted sum of all observations. Therefore,
the reproductive volume is calculated by a simple integration between two horizontal planes, whereby the upper plane is usually
given by the 11‰ isohaline and the lower one by the bottom of the
layer below which the oxygen content declines to 2 mL·L–1. Data
are available for February, March, April, May, August, and October for each of the deep basins in the Baltic Sea, except the central
Gotland Basin, for which estimates are available as the mean for
the periods February–May, May, and August (MacKenzie et al.
2000). As a delay in cod peak spawning time was observed in the
Bornholm Basin during recent years, RV was adjusted to account
for these changes. Therefore, mean values for April–June (1967–
1989), May–July (1990–1992), and June–August (1993–1998) were
used. RV is the adjusted reproductive volume in cubic kilometres
calculated for the entire Baltic Sea. For further details on RV calculation, see MacKenzie et al. (2000). The data series used are presented in Table 1.
Data analysis
A nonparametric GAM was used to examine the effect of different
variables on Baltic cod recruitment. In GAMs, scatterplot smooths
replace least squares fits used in regression analysis (Hastie and
Tibshirani 1990). In this study, we used the gamma distribution, in
which the data variance is proportional to the square of the mean.
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Can. J. Fish. Aquat. Sci. Vol. 57, 2000
Fig. 1. Map showing the sampling stations (䊉) for cod (Gadus morhua) in the Baltic Sea.
The gamma distribution was chosen, because when testing different distributions, we found that the gamma distribution gave a
better fit with the data with the minimum residual deviance in the
models. Kolmogorov–Smirnov and χ2 tests (with degrees of freedom adjusted) were used to test for different distributions of cod
recruitment showing that the gamma distribution was appropriate
(Kolmogorov–Smirnov test: dmax = 0.078, p > 0.05; χ2 = 3, p >
0.05; Fig. 2).
Baltic cod recruitment (dependent variable) was expressed as a
sum of the smooth functions of the predictors. The hypothesised
predictors were number of eggs produced by age-classes 2, 3, and
4 (young spawners (YS)), number of eggs produced by age-class
5+ (old spawners (OS)), RV, and their first-order interactions. These
classification categories were based strictly on age, as in Cardinale
and Arrhenius (2000). Individuals of Baltic cod older than 5 years
are usually assumed to have spawned at least for a second time
(Vallin and Nissling 2000). We used cubic B splines (s) to estimate
the smoother (Hastie and Tibshirani 1990). The following two-step
procedure was applied in analysing the data. First, the functional
relationship between the response was explored using nonparametric
GAM. In this way, the form of the function was found empirically,
according to data without prior assumptions. The backward stepwise elimination was used to select significant predictors in the
analysis. Second, model fit and parsimony were evaluated through
analysis of deviance, using Akaike information criteria (AIC;
Chambers and Hastie 1992). The AIC statistic accounts simultaneously for the degrees of freedom used and the goodness of the
fit, whereas more parsimonious models have a lower AIC statistic.
Confidence intervals and significance levels for the predictors were
estimated using permutation tests and bootstrap resampling (1000
samples; percentile method) (the techniques are described in detail
in Swartzman et al. 1992). Residuals were analysed to test for departure from the model assumptions or other anomalies in the data
or in the model fit, using both analytical (Kitanidis 1997) and
graphical (Cleveland 1993) methods. The Q1 statistic was used to
verify the general unbiased conditions of the model. Q1 is defined
as:
n
Q1 =
1
∑ εk
n −1
where ε k is the orthonormal residual and n is the number of observations. The null hypothesis is that Q1 is normally distributed with
mean 0 and variance 1/(n – 1). Therefore, we reject the model, if
Q1 >
2
n −1
Further, we tested whether the residuals were normally distributed
using the Shapiro–Wilk test and that the residuals were not autocorrelated using the Durbin–Watson test. Residuals were also plotted against the predicted values, to test for their homogeneity.
Statistical analyses were performed with the S-PLUS software
(version 2000; 1999 Statistical Sciences, Seattle, Wash.). The level
of significance was set at 95% for the statistical tests used in this
study.
Results
Results of the significance values of all the predictors initially included in the model are presented in Table 2. The final GAM included the following variables:
recruitment = s(RV) + s(OS) + s(YS⋅RV)
+ s(OS⋅RV)
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Table 1. Data series used in this study.
Year
Recruitment
(106 individuals)
Reproductive
volume (km3)
Young spawners
(1012 eggs)
Old spawners
(1012 eggs)
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
320
272
217
242
292
401
473
281
283
465
788
570
403
654
651
433
280
228
244
330
203
118
116
79
130
176
129
151
154
440
85
525
325
260
100
540
580
280
125
400
61
82
230
162
170
100
99
100
80
90
180
158
235
440
116
154
200
250
22.26
28.82
23.55
22.99
18.48
15.51
17.94
21.08
30.03
35.14
20.70
22.73
38.10
58.95
40.85
31.69
50.60
55.33
35.60
23.45
18.16
21.95
31.23
19.60
13.01
10.93
10.33
15.42
18.63
37.42
52.18
60.69
57.93
56.24
55.06
55.26
55.72
63.63
88.00
115.60
104.71
102.93
159.17
233.68
219.75
197.61
188.99
201.56
182.39
149.24
77.90
94.01
95.74
67.24
44.66
28.41
32.21
45.57
Fig. 2. Frequency distribution of the variable recruitment. The
line indicates the expected gamma distribution.
Table 2. Significance values (p levels) for the generalized additive model predictors.
Predictor
p
Young spawners (YS)
Old spawners (OS)
Reproductive volume (RV)
YS–RV interaction
OS–RV interaction
YS–OS interaction
>0.05
0.01
0.04
0.03
0.01
>0.05
Variance
explained (%)
29
12
19
40
Note: The level of significance was set at 0.05.
The effect of the significant predictors and their interactions on recruitment is shown on the y-axis for different values of the predictor (x-axis) (Figs. 3 and 5). The 0 line
indicates mean recruitment estimated by the model, while
the y-axis is a relative scale where the effect of different values of the predictors on the response variable (i.e., recruitment) is shown. Thus, negative values on the y-axis indicate
that, at the levels of the predictor (x-axis), the model esti-
mates recruitment that is lower than the mean, while the opposite holds for positive values on the y-axis. The interaction
between OS and RV and OS are the most significant explanatory variables (Figs. 3 and 4), explaining 40 and 29% of the
variance, respectively. The effect of YS and of the interaction between YS and OS on recruitment (106 individuals) is
not significant (Table 2) and, therefore, was excluded from
the final model. Importantly, when the reproductive contribution from OS is at the lowest level, recruitment is strongly
depleted, while recruitment was greatest at the highest OS
levels (Fig. 4). Concerning the interaction between OS and
RV, the greatest effect occurs for low values of RV
(<100 km3) for OS. At larger abundances of both OS and
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Can. J. Fish. Aquat. Sci. Vol. 57, 2000
Fig. 3. Generalized additive model derived effects of the interaction term between the number of potential eggs produced by old
spawners (OS) and reproductive volume (RV) on the recruitment
(106 individuals) of Baltic cod.
Fig. 5. Generalized additive model derived effects of the interaction between the number of potential eggs produced by young
spawners (YS) and the reproductive volume (RV) on the recruitment (106 individuals) of Baltic cod.
Fig. 4. Generalized additive model derived effects of the number
of potential eggs produced by old spawners (OS) on the recruitment (106 individuals) of Baltic cod. The broken line and open
circles denote mean values; the solid lines denote the 95% confidence intervals.
Fig. 6. Generalized additive model derived effects of the reproductive volume (RV) on the recruitment (106 individuals) of Baltic cod. The broken line and open circles denote mean values;
the solid lines denote the 95% confidence intervals.
RV, the effect on recruitment is also positive but to a lesser
extent. The contributions from the interaction between YS
and RV and from RV are also important to Baltic cod recruitment, explaining 19 and 12% of the explained model
variance, respectively, (Figs. 5 and 6). In contrast, with regard to the interaction between YS and RV, the effect on recruitment is positive only at values of RV larger than
300 km3, irrespective of YS values (Fig. 5). An increase in
the variation at larger values of both OS (Fig. 4) and RV
(Fig. 6) was probably due to sparse data.
The final model showed good accuracy in predicting recruitment of Baltic cod (Fig. 7), and the successive analysis
of the residuals confirmed the validity of the model. Q1 values were not significantly different from 0 (Q1 = 0.00035;
n = 30; p < 0.001). The Shapiro–Wilk (n = 30; p = 0.21) and
Durbin–Watson (n = 30; p = 0.34) tests were not significant.
The residuals plot did not show evidence of strong violation
of the model assumptions (Fig. 8).
Discussion
Recent studies have shown strong evidence of a maternal
effect on the quality of offspring in fish (e.g., Kjesbu et al.
1996; Marshall et al. 1998; Marteinsdottir and Thorarinsson
1998). The age of a parental fish not only influences the size
of eggs and larvae, but also has important effects on the
chemical composition of ovaries and eggs, egg metabolism
and fertilisation, and embryonic, larval, and juvenile survival (for a review see Kamler 1992). That larvae derived
from larger eggs are larger than larvae derived from smaller
eggs is a well-known phenomenon (Kamler 1992) and many
recent studies have supported this theory (e.g., Kjesbu et al.
1996; Trippel 1998). Predation, which is recognised as one
of the major causes of larval mortality in fish (Mills 1982),
operates in a size-dependent way, with smaller larvae suffering higher levels of mortality than larger larvae (Miller et al.
1988). In addition, the adaptive significance of larval size in
Atlantic cod is also related to the broader feeding spectra of
larger larvae compared with smaller individuals (e.g.,
Knutsen and Tilseth 1985). It has also been argued that, in
general, larger fish larvae may survive better than small larvae, owing to their higher growth rates (Moodie et al. 1989)
and larger energy reserves (Blaxter and Hempel 1963). In
contrast, many authors found no effect of egg size on viability of the progeny of different fish species (Kamler 1992).
Egg size was not found to be related to female body size in
North Sea cod (Oosthuizen and Daan 1974), but an effect of
body size on egg size can often result from parental age
(Kamler 1992). However, recently, in Baltic cod, it was
shown that egg size does not affect hatching success (Nissling
et al. 1999) but that larval viability and egg size are positively
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Fig. 7. The observed against the predicted numbers of recruits of
Baltic cod, estimated by the final generalized additive model: recruitment = s(reproductive volume) + s(old spawners) + s(young
spawners × reproductive volume) + s(old spawners × reproductive volume).
related to female size and (or) age (Vallin and Nissling
2000). These results are in agreement with experimental studies of Kjesbu et al. (1996) and Trippel (1998) showing that,
in Atlantic cod, there is a positive correlation between egg
size and female size and that viability of eggs and larvae is
greater for repeat than for recruit spawners. First-time spawners perform poorly compared with second-time spawners.
They breed for a shorter period, produce fewer egg batches,
and exhibit lower fecundity (Trippel 1998).
Nevertheless, the maternal effect on recruitment and its
interaction with environmental conditions are probably multidimensional and nonlinear. Therefore, results derived from
experimental studies on egg and larval survival or viability
are not necessarily applicable to the complex dynamics of
recruitment. However, results from our study have shown the
importance of stock structure for the recruitment of Baltic
cod, stressing the presence of maternal effect on recruitment
(e.g., Marshall et al. 1998; Scott et al. 1999; Cardinale et al.
2000). Moreover, the survival probability of cod eggs in the
Baltic is dependent on (among other factors such as predation, food, etc.) the buoyancy of eggs (Nissling and Vallin
1996). Egg buoyancy is affected by salinity levels and is regarded as a major limiting factor in the successful spawning
of Baltic cod, since maintenance of low specific gravity is
crucial in avoiding stressful oxygen conditions in the deep
layers (Nissling and Vallin 1996). Vallin and Nissling (2000)
have recently shown that egg buoyancy is directly related to
female age and (or) size. Data from our study strongly support this hypothesis. We found that eggs from OS have a
strong positive effect at very low levels of RV (<100 km3).
Levels of RV lower than 100 km3 correspond to a year of extremely low inflow from the North Sea (MacKenzie et al.
2000). In the absence of such inflow, oxygen concentrations
below the halocline progressively decrease to <2 mL·L–1,
concentrations at which no Baltic cod eggs will develop and
hatch successfully (Nissling and Vallin 1996). Data from this
study suggest that, under such unfavourable environmental
conditions, highly buoyant eggs from older individuals, having lower mortality rates than eggs from younger individu-
2407
Fig. 8. Residual deviance of the generalized additive model plotted against the predicted recruitment.
als, make the largest contribution to recruitment. In contrast,
when levels of salinity, temperature, and oxygen are adequate in most of the reproductive areas of the Baltic, differences in survival are probably minor, and larger numbers of
eggs derived from YS are most likely to survive. As a consequence, low values of RV had a negative effect on cod recruitment, while, when RV increased and conditions were
favourable for the survival of cod eggs and larvae, the effect
was positive, although the effect does not increase at RV
values larger than 300 km3.
Another important point emerging from this study is the
usefulness of GAMs for analysing complex interactions
between environmental factors and biological variables
(Swartzman et al. 1995; Daskalov 1999; Maravelias et al.
2000). The use of GAMs is a relatively new approach in
fisheries (e.g., Swartzman et al. 1995; Daskalov 1999;
Cardinale and Arrhenius 2000)—an approach that can identify functional relationships suggested by the data alone in
cases where linear techniques have previously failed (Daskalov
1999). However, the price of the greater flexibility is the
restricted possibility of statistical inference typical for
nonparametric techniques and the large number of degrees
of freedom used by smoothing terms (Daskalov 1999).
Vallin and Nissling (2000) have also recently indicated the
positive effect of abundance of OS on Baltic cod recruitment.
They showed a positive relationship between the amount of
eggs produced by females age 5+ and recruitment that explained between 28 and 48% of the variance of Baltic cod
recruitment (Vallin and Nissling 2000). However, one of the
major problems in the analyses was that the relationship was
modelled using linear estimations, therefore neglecting the
importance of nonlinear interactions between biotic and
abiotic factors. In contrast, the use of a GAM allowed identification of the quantitative effect of both biotic and abiotic
factors and their nonlinear interactions on the intensity of
Baltic cod recruitment. The results of this study indicates
that the impact of stock structure on Baltic cod recruitment
is even larger under certain unfavourable environmental conditions. These abiotic factors and, mostly, their interaction
with biotic variables should be carefully considered in future
estimations of Baltic cod recruitment and its management.
However, the results of this study also have a general importance in understanding the recruitment variability of fish
populations and, therefore, for fisheries management. As
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stated below, a crucial assumption in fisheries science is that
spawning biomass is proportional to the reproductive potential of the stock, implying that the survival rates of offspring
do not substantially change with the age or size of the spawners (Trippel et al. 1997). However, the commercial extinction of many marine fisheries worldwide (Myers et al. 1997)
has raised concerns about the management of renewable resources (Pitcher et al. 1998), and even the proportionality assumption has been challenged (Gilbert 1997). In our study,
we showed that the influence of parental age on Baltic cod
recruitment is highly substantial. Our results confirm what
has been hypothesised by different authors (Kjesbu et al.
1996; Trippel 1998; Marshall et al. 1998) and recently
shown for different cod stocks (Scott et al. 1999; Cardinale
and Arrhenius 2000). The presence in the spawning population of a rich variety of age-classes increases the probability
of successful recruitment (e.g., Marshall et al. 1998;
Marteinsdottir and Thorarinsson 1998). The positive effect
of older and larger individuals on cod recruitment is likely
due to the production of larger larvae with higher rates of
survival, in combination with more batches being produced
over a longer spawning period (Kjesbu et al. 1996; Trippel
1998). Nevertheless, abiotic factors may also influence recruitment (Daskalov 1999). Temperature, oxygen, and salinity (as it affects egg buoyancy and survival), or food
availability, contribute significantly to recruitment variability in Baltic cod stocks (Vallin and Nissling 2000; this
study). The implications for stock assessment and management are important. Conventional approaches overestimate
the reproductive potential of the age-truncated populations,
assuming proportionality between spawning biomass and recruitment (Trippel 1998). Therefore, current stock assessment increases the risk of commercial extinction, when
populations are truncated by fishing mortality and the number
of high-quality OS is below a certain limit (Trippel et al.
1997; Cardinale and Arrhenius 2000; this study). A certain
minimum number of repeat spawners must, therefore, be
present in the population, to ensure a large number of surviving offspring. In the case of the present data set, the impact of OS on recruitment was even larger where
environmental conditions strongly affected the survival of
eggs and larvae. This important effect of population structure (Marshall et al. 1998; Trippel 1998; Cardinale and
Arrhenius 2000), as well as the influence of environmental
conditions on recruitment (Sparholt 1996; Daskalov 1999;
this study), should be taken carefully into account in the
management of exploited fish populations in the future.
Acknowledgements
We are deeply indebted to Christos Maravelias for his
support and for suggestions about the use of GAM models.
We are grateful to two anonymous reviewers for their useful
suggestions.
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