Northeast Fisheries Science Center Reference Document 02-03
An Age-Structured
Assessment Model
for Georges Bank Winter Flounder
by Jon K.T. Brodziak
National Marine Fisheries, NEFSC, 166 Water St., Woods Hole MA 02543
Print
publication date March 2002;
web version posted March 27, 2002
Citation: Brodziak, J.K.T. 2002. An age-structured assessment model for Georges Bank winter flounder. Northeast Fish. Sci.
Cent. Ref. Doc. 02-03; 54 p.
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Abstract
An age-structured assessment model for Georges Bank
winter flounder (Pseudopleuronectes americanus) stock during
1964-2000 is developed to provide an alternative to VPA-based analyses
of stock status. Age-structured population dynamics of winter flounder
are modeled using standard forward-projection methods for statistical
catch-at-age analyses.
Trends in the relative abundance of population biomass
are measured by research survey indices for Georges Bank winter flounder.
Three surveys were available: the NEFSC autumn groundfish survey
(1963-2000), the NEFSC spring groundfish survey (1968-2000), and
the Canadian spring groundfish survey (1987-2000). Two alternative
models were examined in detail: (1) a model that used all three research
survey time series (WINC, WINter flounder model including Canadian
survey) and (2) a model that used the two NEFSC research survey time
series (WIN, WINter flounder model). Both the WINC
and WIN models provided similar trends in population biomass and
fishing mortality, indicating that results were robust to the inclusion
of the Canadian research survey time series. Based on model diagnostics,
the WIN model that used the two NEFSC research survey time series
provided the best fit to the data. Conditioned on the accuracy of the model and the
assessment data, results of the best fit model indicate that: (i) Spawning
biomass exceeded 20,000 mt in 1964 but declined to less than 3,000
mt in the early-1990s. Spawning biomass in year 2000 was roughly 9,900
mt; (ii) Fishing mortality (fully-recruited, age-4 estimate) increased
steadily from less than 0.2 in the early-1960s to over 1.0 in the late-1980s
and early-1990s, but has declined since then to roughly 0.32 in 2000;
(iii) Stock-recruitment data show that the stock produced large year
classes (>15 million recruits) in the 1960s and 1970s when spawning
biomass was near or above 10,000 mt; (iv) Surplus production data show
that the stock was most productive during the 1970s and early-1980s,
with annual surplus production of roughly 3,000 mt. Since the mid-1980s
annual surplus production has decreased to roughly 2,000 mt.
Introduction
An age-structured assessment model for Georges Bank winter flounder
(Pseudopleuronectes americanus) stock during 1964-2000 is
developed to provide an alternative to VPA-based analyses of stock
status. Age-structured population dynamics of winter flounder are modeled
using standard forward-projection methods for statistical catch-at-age
analyses (Fournier and Archibald 1982, Methot 1990, Ianelli and Fournier
1998, Quinn and Deriso 1999). We describe the underlying population
dynamics model, statistical estimation approach, Southern Demersal
Working Group recommendations, model diagnostics, and model results
below.
POPULATION
DYNAMICS MODEL
The age-structured model is based on forward projection of population
numbers at age. This modeling approach is based on the principle that
population numbers through time are determined by recruitment and total
mortality at age through time. That is, if one knew the time series
of inputs and outputs to the population numbers and the initial population
size at age, then one would have complete information on the population
size, spawning biomass, and total mortality through time. In practice,
one uses available sampling data and a statistical model of how the
data were observed to estimate parameters to determine the time series
of population sizes.
Population numbers at age through time are key variables in the age-structured
model and the population numbers at age matrix N=(Ny,a)YxA contains
this information. This matrix has dimensions Y by A, where Y is the
number of years in the assessment time horizon and A is the number
of age classes modeled. The oldest age (A) comprises a plus-group consisting
of all fish age-A and older. The time horizon for winter flounder is
1964-2000 (Y=37). The choice of time horizon was determined by the
availability of landings data which are first available in 1964 and
a relative abundance index, the NEFSC autumn groundfish survey. The
number of age classes in the model is 7, representing ages 1 through
7+.
Recruitment (numbers of age-1 fish) in year y (Ry) is modeled
as a lognormal deviation from an average recruitment parameter (µR),
where the Vy are independent and identically distributed
(iid) normal random variables with zero mean and constant variance.
For all years, y, from 1965-2000, Ry = Ny1 is
estimated from the recruitment deviation and average recruitment parameter.
The recruitment deviations are constrained to sum to zero over all
years.
Initial population abundance at age in 1964 is based on recruitment
deviations from average recruitment for 1959-1964 and natural mortality.
For all ages a < A, the numbers at age in the first year (ystart=1)
are estimated as a lognormal deviation from average recruitment as
reduced by natural mortality (M)
For the plus group, the initial numbers at age is the sum of numbers
at ages 7 and older based on average recruitment and recruitment deviations
for ages 7 and older in 1964 along with the natural mortality rate
Total mortality rates at age through time are also key variables in
the population dynamics model. The total instantaneous mortality at
age matrix Z=(Zy,a)YxA and the
instantaneous fishing mortality at age matrix F=(Fy,a)YxA both
have dimensions Y by A. Instantaneous natural mortality at age is assumed
to be constant with M equal to 0.2. Thus, for all years y, and age
classes a, total mortality at age is the sum of fishing and natural
mortality
To determine total mortality, fishing mortalities will be estimated.
While natural mortality might be estimable in some rare data-rich situations,
M is often highly correlated with other parameters and is not estimable
in practice (see for example, Schnute and Richards 1995).
Population numbers at age through time are computed from the initial
population numbers at age, recruitment through time, and total mortality
at age through time. For each age class, indexed by "a", that is younger
than the plus group (a < A), the number at age is sequentially determined
using a standard survival model
For the plus group, numbers at age are the sum of survivors of age
A-1 and survivors from the plus group in the preceding year
Estimation of fishing mortality at age is facilitated by making the
simplifying assumption that fishing mortality can be modeled as a separable
process. This assumption implies that Fy,a is determined
from the average selectivity pattern of age-a fish (Sa)
and fully-recruited fishing mortality in year y (Fy)
While more complicated models of time-varying selectivity may be useful,
this approximation is likely to be satisfactory if observation errors
in the catch-at-age data are substantial.
Fully-recruited fishing mortality in each year is modeled as a lognormal
deviation from average fishing mortality (µF), where
the Uy are iid normal random variables with zero mean and
constant variance
The fishing mortality deviations (Uy) are constrained to
sum to zero over all years.
Fishery selectivity at age is modeled as being time-invariant throughout
the assessment time horizon. This approach was chosen for parsimony
and because there was believed to be substantial errors in the observed
fishery age composition, especially in recent years. In particular,
winter flounder catch-at-age data to estimate fishery selectivity are
limited to 1982-2000, a period when the fishery was prosecuted primarily
by domestic trawl fishing vessels. Since 1993, fishery sampling intensity
of Georges Bank winter flounder catches has been relatively low. As
a result, temporal changes in fishery selectivity would likely be difficult
to detect given relatively high measurement errors in the fishery age
composition data.
The average fishery selectivity at age is estimated for ages 1 through
6. For ages 7 and older, fishery selectivity is assumed to be equal
to the age-6 selectivity value. This approach was chosen to reflect
the fact that age-7 fish were not likely to differ much from age-6
fish in their fishery selectivity. Two constraints are applied to the
estimated selectivity at age coefficients. First, the selectivities
are constrained to average 1 for estimated ages. This forces the scale
of each coefficient to be near unity. Second, a constraint is applied
to ensure that estimated selectivities change smoothly between adjacent
ages. Details of the implementation of both constraints are described
in the section on statistical estimation approach. Last, for each year,
the selectivity at age values are rescaled so that the maximum selectivity
at age value is unity. This rescaling ensures that estimated fully-recruited
fishing mortality rates are directly comparable to biological reference
points such as F0.1.
Fishery removals from the population are accounted for through the
fishery catch numbers at age matrix C=(Cy,a)YxA and
the fishery catch biomass at age (yield) matrix Y=(Yy,a)YxA.
Both C and Y have dimensions Y by
A. Fishery catch at age in each year is computed in a standard manner
from Baranov's catch equation using population numbers, fishing mortality,
and total mortality at age
Catch biomass at age in each year (Yy,a) is approximated
by the product of catch numbers at age and the long-term mean weights
at age, where Wa is the mean weight at age computed as the
average of mean Georges Bank weights at age from fishery sampling during
1982-2000
Use of the long-term mean weights at age is likely to be a useful
approximation unless mean weights at age have varied substantially
through time. Since fishery sampling has been relatively poor in recent
years, the use of a long-term average was considered to be adequate
given the likely errors in the observed annual mean weights at age
computed from fishery samples.
Total fishery catch biomass in year y (Yy) is the sum of
yields by age class
The calculated total fishery catch biomass time series is compared
to observed values using a lognormal probability model. This model
feature was included because it was expected that observed catches
were not accurately reported in some years and that discards were not
estimated for inclusion in the catch-at-age data.
Similarly, the proportion of fishery catch at age a in year y (Py,a)
is computed from estimated catch numbers
The time series of fishery proportions at age are fitted to observed
fishery values using a multinomial probability model (see for example,
Fournier and Archibald 1982, Quinn and Deriso 1999). This model feature
accounts for the possibility that the fishery catch-at-age data are
measured with error.
Trends in the relative abundance of population biomass are measured
by research survey indices for Georges Bank winter flounder. Three
surveys were available: the NEFSC autumn groundfish survey (1963-2000),
the NEFSC spring groundfish survey (1968-2000), and the Canadian spring
groundfish survey (1987-2000). The survey biomass index in year y (Iy)
for any of the surveys is modeled as a catchability coefficient (QSURVEY)
times the population biomass that is vulnerable to the survey, where
SSURVEY,a is survey selectivity at age a and pSURVEY is
the fraction of annual total mortality that occurs prior to the survey
The survey biomass index time series are fitted to observed values
using a lognormal probability model. This model feature accounts for
the possibility that the survey relative abundance indices are measured
with error.
Survey selectivity accounts for differential vulnerability of winter
flounder age classes to the survey fishing gear and also for differential
vulnerability due to differences in the behavior and distribution of
juvenile and adult fish. For each of the three surveys, selectivity
at age is modeled using Thompson's exponential-logistic model (Thompson
1994), where 
, ß, and 
are
parameters and survey selectivity for winter flounder is assumed to
be time invariant
This model has the useful property that the maximum selectivity value
is unity. For values of >0
survey selectivity is dome-shaped, and survey selectivity is flat-topped
(i.e., constant at older ages) when =0.
Survey age composition data provide information on the relative abundance
of winter flounder age classes captured with the survey gear. Survey
catch proportion at age a in year y (PSURVEY, y, a) is computed
from survey selectivity, the fraction of mortality occurring prior
to the survey, and population numbers at age
The time series of survey proportions at age are fitted to observed
fishery values using a multinomial probability model. This model feature
accounts for the possibility that the survey age composition data are
measured with error.
STATISTICAL
ESTIMATION APPROACH
The population dynamics model is fit to observed data using an iterative
maximum likelihood estimation approach. The statistical model consists
of ten likelihood components (Lj) and two penalty terms
(Pk). The model objective function (
)
is the weighted sum of the likelihood components and penalties where
each summand is multiplied by an emphasis coefficient (
j)
that reflects the relative importance of the data.
Each likelihood component is written as a negative log-likelihood
so that the maximum likelihood estimates of model parameters are obtained
by minimizing the objective function. The Automatic Differentiation
Model Builder software is used to estimate a total of roughly 95 parameters
depending upon the model configuration. The likelihood components and
penalty terms are described below.
1. Recruitment
Recruitment strength is modeled by lognormal deviations from average
recruitment for the period 1959-2000. A total of 42 recruitment deviation
parameters (Vy) and one average recruitment parameter (µR)
are estimated based on the objective function minimization. The recruitment
likelihood component (L1) is
where
(18)
and the Vy are iid normal random variables with zero mean
and constant variance and n1 is the number of recruitment
deviations.
2.
Fishery age composition
Fishery age composition is modeled as a multinomial distribution for
sampling catch numbers at age. The constant NE ,Fishery, y denotes
the effective sample size for the multinomial distribution for year
y and is assumed to be 200 fish per year during 1982-1993, 100 fish
per year during 1994-1997 and 2000, and 50 fish per year during 1998-1999.
These different sample sizes were chosen to reflect the relative intensity
of fishery sampling of Georges Bank winter flounder. The observed number
of fish at age in the fishery samples is computed as the effective
sample size times the observed proportion at age, denoted with a superscript "OBS" for
all variables.
The negative log-likelihood of the multinomial sampling model for
the fishery ages (L2) is
The second term in summation over ages indexed by "a" is a constant
that scales L2 to be zero if the observed and predicted
proportions were identical. Six fishery selectivity coefficients (S1 through
S6) are estimated based on the objective function minimization.
3.
NEFSC Fall survey age composition
Fall survey age composition is also modeled as a multinomial distribution
for sampling survey catch numbers at age. The constant NE ,Fall,
y denotes the effective sample size for the multinomial distribution
for year y and is assumed to be constant across time for the years
1982-2000 when winter flounder autumn survey catch-at-age data are
available. The observed number of fish at age in the survey samples
is computed as the effective sample size times the observed proportion
at age. The effective sample size was assumed to be 100 fish in each
year. The negative log-likelihood of the multinomial sampling model
for the autumn survey ages (L3) is
As with the fishery age composition, the second term in the summation
over the age index "a" is a constant that scales L3 to be
zero if the observed and predicted proportions were identical. Three
fall survey selectivity coefficients (Fall, ßFall, Fall)
are estimated based on the objective function minimization using the
survey selectivity model (Eqn. 14).
4.NEFSC Fall survey biomass
index
The fall survey biomass index is modeled by lognormal deviations of
predicted values from observed values during 1964-2000, where the log-transformed
deviations DFall, y are iid normal random variables with
zero mean and constant variance
The fall survey biomass likelihood component (L4) is
where n4 is the number of observed fall survey index values.
One fall survey catchability coefficient (QFall) is estimated
based on the objective function minimization.
5.
NEFSC Spring survey age composition
Spring survey age composition is also modeled as a multinomial distribution
for sampling survey catch numbers at age. The constant NE ,Spr,
y denotes the effective sample size for the multinomial distribution
for year y and is assumed to be constant for the years 1982-2000 when
winter flounder spring survey catch-at-age data are available. The
observed number of fish at age in the survey samples is computed as
the effective sample size times the observed proportion at age. The
effective sample size was assumed to be 100 fish in each year. The
negative log-likelihood of the multinomial sampling model for the spring
survey ages (L5) is
Three spring survey selectivity coefficients (Spr, ßSpr, Spr)
are estimated based on the objective function minimization using the
survey selectivity submodel (Eqn. 14).
6. NEFSC Spring survey biomass
index
The spring survey biomass index is modeled by lognormal deviations
of predicted values from observed values during 1968-2000, where the
log-transformed deviations DSpr, y are iid normal random
variables with zero mean and constant variance
The spring survey biomass likelihood component (L6) is
where n6 is the number of observed spring survey index
values. One spring survey catchability coefficient (QSpr)
is estimated based on the objective function minimization.
7. Canadian Spring survey
age composition
Canadian spring survey age composition is also modeled as a multinomial
distribution for sampling survey catch numbers at age. The constant
NE ,CANSpr, y denotes the effective sample size for the
multinomial distribution for year y and is assumed to be constant for
the years 1987-2000 when winter flounder Canadian spring survey catch-at-age
data are available. The observed number of fish at age in the survey
samples is computed as the effective sample size times the observed
proportion at age. The effective sample size was assumed to be 200
fish in each year. The negative log-likelihood of the multinomial sampling
model for the Canadian spring survey ages (L7) is
Three Canadian spring survey selectivity coefficients (CANSpr, ßCANSpr, CANSpr)
are estimated based on the objective function minimization using the
survey selectivity model (Eqn. 14).
8. Canadian Spring survey
biomass index
The Canadian spring survey biomass index is modeled by lognormal deviations
of predicted values from observed values during 1987-2000, where the
log-transformed deviations DCANSpr, y are iid normal random
variables with zero mean and constant variance
The Canadian spring survey biomass likelihood component (L8)
is
where n8 is the number of observed Canadian spring survey
index values. One Canadian spring survey catchability coefficient (QCANSpr)
is estimated based on the objective function minimization.
9. Catch biomass
Catch biomass is modeled by lognormal deviations of predicted values
from observed values during 1934-1999, where T y are iid
normal random variables with zero mean and constant variance
The catch biomass likelihood component (L9) is
where n9 is the number of observed catch biomass values.
10.
Fishing mortality
Annual values of fully-recruited fishing mortality are modeled as
lognormal deviations from average fishing mortality during the period
1934-2000. A total of 37 fishing mortality deviation parameters (Uy)
and one average fishing mortality parameter (µF) are
estimated based on the objective function minimization. The fishing
mortality likelihood component (L10) is
where
and n10 is the number of observed catch values.
11. Fishery selectivity
Two constraints on fishery selectivity are included in a penalty function.
The fishery selectivity penalty function (P1) is
The first term constrains the fishery selectivity coefficients to
scale to an average of 1. The second term constrains the fishery selectivity
coefficient of age a+1 to be near to the linear prediction of this
value interpolated from age a and age a+2 selectivities over the range
of estimated selectivity coefficients.
12. Fishing mortality penalty
One constraint on fishing mortality is imposed to ensure that during
the early phases of the iterative estimation process the observed catch
could not be generated by an extremely small F on an extremely large
population size. The fishing mortality penalty function (P2)
is
The constraint is weighted with a value of 10 for the initial estimation
phases and is weighted with a value of 0.001 for all later estimation
phases. The value of 0.1 was used because this value is sufficient
to ensure that the estimated mean F will be on the order of the value
of natural mortality for Georges Bank winter flounder.
Initial values are input for all parameters before the estimation
phases are conducted. A total of nine estimation phases were used for
the iterative minimization of the objective function. Any parameters
first estimated in a given phase, say N, are estimated in all subsequent
phases, N+1, N+2, etc. The first phase estimates average recruitment.
The second phase estimates average fishing mortality and fishing mortality
deviations. The third phase estimates recruitment deviations. The fourth
phase estimates fishery and NEFSC spring survey selectivity coefficients.
The fifth phase estimates the spring survey catchability coefficient.
The sixth phase estimates the NEFSC fall survey selectivity coefficients.
The seventh phase estimates the fall survey catchability coefficient.
The eighth phase estimates the Canadian spring survey selectivity coefficients.
The ninth phase estimates the Canadian spring survey catchability coefficient.
The twelve emphasis values (s)
used for the baseline model were:
- Recruitment 1=10
- Fishery age composition 2=1
- NEFSC Fall survey age composition 3=1
- NEFSC Fall survey biomass index 4=10
- NEFSC Spring survey age composition 5=1
- NEFSC Spring survey biomass index 6=10
- Canadian Spring survey age composition 7=1
- Canadian Spring survey biomass index 8=10
- Catch biomass 9=100
- Fishing mortality 10=1
- Fishery selectivity penalty 11=10
- Fishing mortality penalty 12=1
SOUTHERN
DEMERSAL WORKING GROUP RECOMMENDATIONS
After making some adjustments to the initial model configuration to
better reflect the timing of the surveys and the emphasis factors for
the fishery and survey age composition likelihood components, the Southern
Demersal Working Group recommended that two final models be examined:
(1) a model that used all three research survey time series (WINC, WINter
flounder model including Canadian survey) and (2) a model
that used the two NEFSC research survey time series (WIN, WINter
flounder model). Both the WINC and WIN models provided similar trends
in population biomass and fishing mortality, indicating that results
were robust to the inclusion of the Canadian research survey time series.
MODEL
DIAGNOSTICS
Model diagnostics showed that the WIN model provided a better fit
to the observed catch biomass series (RMSE=0.137) than the WINC model
(RMSE=0.149). The WIN model also provided a better fit to the NEFSC
fall biomass series (RMSE=0.356) than the WINC model (RMSE=0.373).
The fits to the NEFSC spring biomass series were nearly identical for
the two models (WIN, RMSE=0.472 vs WINC, RMSE=0.473). In addition,
the trend in the observed Canadian spring biomass series was lower
than the WINC model predictions during 1998-2000, suggesting that the
Canadian survey was not tracking relative abundance in recent years.
Overall, the WIN model that used the two NEFSC research survey time
series provided the best fit to the catch biomass and NEFSC survey
biomass series while the WINC model provided a poor fit to the Canadian
survey biomass series in recent years (see Figure 4 below). The condition
numbers of the hessian matrices of the two models were also different
with the WINC model having a much higher condition number (
=6.83•1012)
than the WIN model ( =2.83•107).
This indicated that the numercial solution of the WINC model was not
well-determined relative to the WIN model. Based on model diagnostics,
the WIN model that used the two NEFSC research survey time series was
considered to be the best model among the statistical catch-at-age
models examined for winter flounder. Computer code to fit the WIN model,
the input data file, and the standard deviation parameter file are
listed in the Appendix.
Plots
of diagnostics for the two models include the discrepancies between
observed data and predicted values for the catch biomass series (Figure
1), the fall survey biomass series (Figure
2), the spring survey biomass series (Figure
3), and the Canadian spring survey biomass series (Figure
4, shown for the WINC model only). For the best fit WIN model,
diagnostic plots include the fishery age composition series (Figure
5), the fall survey age composition series (Figure
6), and the spring survey age composition series (Figure
7). For the WINC model, a diagnostic plot of the Canadian spring
survey age composition series is also shown (Figure
8).
MODEL
RESULTS
Model
estimates of spawning biomass, fishing mortality, recruitment, and
population biomass for the WIN model during the period 1963-2000 are
listed in Table 1. Fishery
and survey selectivity estimates at age are shown in Figure
9. Recruitment estimates are shown in Figure
10 (see also Table 1). Population biomass estimates
are shown in Figure 11 (see also Table
1). Spawning biomass estimates (at start of the spawning season)
are shown in Figure 12 (see also Table
1). Fishing mortality estimates are shown in Figure 13 (see also
Table 1). Stock-recruitment data are shown in Figure 14. Surplus production
implied by the age-structured estimates of exploitable biomass and
observed catches are shown in Figure 15.
Other model outputs included
depletion ratios for year 2000, relative to 1964, for spawning biomass
(46%) and population biomass (53%). Similarly, depletion ratios for
year 2000, relative to 1982, were computed for spawning biomass (88%)
and population biomass (81%). Long-term average recruitment was estimated
to be 5.550 million age-1 fish during 1959-1999.
Sensitivity to the assumed
value of M was investigated by systematically varying this parameter
using the likelihood profile feature of the AD Model Builder software.
This analysis showed that the model was not stable for moderate departures
from M=0.2. In particular, running the baseline model under alternative
assumptions about M showed that the model did not converge in its
final configuration for M=0.195, 0.196, 0.2005, 0.201, 0.2015, 0.2025,
0.203, while it did converge for M=0.197 (-lnL=3445.2), M=0.198 (-lnL=3444.8),
M=0.199 (-lnL=3444.2), and M=0.202 (-lnL=3443.0). The objective function
value for the assumed value of M=0.2 was -lnL=3443.8. This suggested
that the objective function surface was a complicated function of
natural mortality and that the model was sensitive to the assumed
value.
Based on the Southern Demersal
Working Group's recommendations, a sensitivity analysis was conducted
on the value of the effective sample size time series for the fishery
age composition likelihood. This was done to see how the model results
might change if different effective sample sizes were used. The SDWG
suggested multiplying the effective sample size time series by ½ and
2. The use of multipliers of less than 0.8 did not lead to model
convergence, presumably because there was insufficient information
assigned to the fishery age composition in these cases. Nonetheless,
estimated spawning biomass, a key model output, was insensitive to
using effective sample sizes that were 80% and 200% of the baseline
values, which ranged from 50 to 200 fish (Figure 16). Overall, this
suggested that the model solution would not be well-determined if
effective sample sizes for the fishery age composition were below
40 fish per year, but, for values above this, the results appeared
to be robust.
CONCLUSIONS
Conditioned on the accuracy
of the model and the assessment data, results of the best fit model
indicate that:
- The Georges Bank winter
flounder stock appears to have a dome-shaped fishery selectivity
pattern with age-4 fish being fully-recruited (Figure 9).
- The NEFSC fall bottom
trawl survey appears to have a dome-shaped selectivity pattern
and provides an index of the relative number of age-5 fish (Figure 9).
- The NEFSC spring bottom
trawl survey appears to have an asymptotic selectivity pattern
and provides an index of the relative number of age-3 and older
fish (Figure 9).
- Recruitment appears
to have been relatively strong during the early-1970 to early-1980s
with the 1974 year class being the largest observed during 1964-2000
(Figure 10).
- Population biomass was
over 20,000 mt in the early-1960s, declined to less than 5,000
mt in the early-1990s, and has subsequently increased to roughly
10,000 mt in year 2000 (Figure 11).
- Spawning biomass exceeded
20,000 mt in 1964 but declined to less than 3,000 mt in the early-1990s
(Figure 12). Spawning biomass in year 2000 was roughly 9,900 mt.
- Fishing mortality (fully-recruited,
age-4 estimate) increased steadily from less than 0.2 in the early-1960s
to over 1.0 in the late-1980s and early-1990s (Figure 13), but
has declined since then to roughly 0.32 in 2000.
- Stock-recruitment data
show that the stock produced large year classes (>15 million
recruits) in the 1960s and 1970s when spawning biomass was near
or above 10,000 mt (Figure 14).
- Surplus production data
show that the stock was most productive during the 1970s and early-1980s
(Figure 15), with annual surplus production of roughly 3,000 mt.
Since the mid-1980s annual surplus production has decreased to
roughly 2,000 mt.
- The results of the age-structured
model appear to be sensitive to the assumed value of natural mortality
of 0.2.
- The results of the age-structured
model do not appear to be sensitive to the effective sample size
for the fishery age composition data provided that effective sample
sizes of 50-200 fish are collected each year.
ACKNOWLEDGMENTS
I thank the members of
the Southern Demersal Working Group for their helpful comments and
suggestions. I also thank the members of the 34th Northeast
Regional Stock Assessment Review Committee for their helpful comments
and thoughtful review.
LITERATURE
CITED
Fournier, D. A., and C.
P. Archibald. 1982. A general theory for analyzing catch at age data.
Can. J. Fish. Aquat. Sci. 39:1195-1207.
Ianelli, J. N., and D.
A. Fournier. 1998. Alternative age-structured analyses of NRC simulated
stock assessment data. NOAA Tech. Memo. NMFS-F/SPO-30. pp. 81-96.
Methot, R. D. 1990. Synthesis
model: an adaptive framework for analysis of diverse stock assessment
data. Int. North Pac. Fish. Comm. Bull. 50:259-277.
Quinn, T. P., II, and R.
B. Deriso.1999. Quantitative fish dynamics. Oxford University Press,
New York, 542 pp.
Schnute, J. T., and L.
J. Richards. 1995. The influence of error on population estimates
from catch-age models. Can. J. Fish. Aquat. Sci. 52:2063-2077.
Thompson, G. G. 1994. Confounding
of gear selectivity and the natural mortality rate in cases where
the former is a nonmonotone function of age. Can. J. Fish. Aquat.
Sci. 51:2654-2664.
Table 1. Baseline model
results for Georges Bank winter flounder.
