Northeast Fisheries Science Center Reference Document 02-12
Proceedings
of the Fifth Meeting of the Transboundary Resources
Assessment Committee (TRAC), Woods Hole, Massachusetts,
February 5-8, 2002
by Robert N. O'Boyle1 and William J. Overholtz2,
TRAC co-chairmen
1Dept.
of Fisheries & Oceans, P.O. Box 1006, Dartmouth, NS B2Y 4A2
2National Marine Fisheries Serv., 166 Water St., Woods Hole, MA 02543
Print
publication date September 2002;
web version posted September
17, 2002
Citation: O'Boyle, R.N.; Overholtz, W.J., TRAC co-chairmen. 2002. Proceedings of the fifth meeting of the
Transboundary Resources Assessment Committee (TRAC), Woods Hole, Massachusetts, February 5-8, 2002.
Northeast Fish. Sci. Cent. Ref. Doc. 02-12; 56 p.
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Abstract: The fifth meeting of the Transboundary Resources Assessment Committee
(TRAC) was held during 5-8 February 2002 in Woods Hole, MA, USA to
review the assessment models for 5Z+6 cod and 5Zjm cod to be used
over the next 3-4 years. The assessment meetings will be held for
Canadian management units in mid-April 2002 and for US management
units sometime during the summer of 2002. This was the first time
that TRAC had undertaken benchmark reviews separate from the provision
of assessments and was generally considered a positive development.
The meeting also discussed issues related to yield and stock production.
Introduction
The co-chairs, R. O’Boyle and W. Overholtz, welcomed
the meeting participants (Appendix 1). It
was noted that this was the 5th TRAC meeting since 1998,
the last one being held in St. Andrew’s, N.B. in 2001.
The TRAC process was briefly summarized. It consists
of the Transboundary Assessment Working Group (TAWG) compiling the
assessment working papers, which are then peer reviewed by the TRAC.
At the 14th Canada-USA Scientific Discussions (Clark
and O’Boyle, 2001), a proposal was made to separate the review
of assessment frameworks, termed benchmarks, from application of these
frameworks to data as part of the annual management cycle. This proposal
was made not only to improve the depth of the scientific review but
also to allow each nation to provide the most timely advice to their
respective management systems. After further development, the proposal
was accepted (Appendix 2). The present meeting
was a benchmark review of the 5Z+6 and 5Zjm cod assessments.
During 2001 and 2002, negotiations between Canada and the USA on sharing
allocation formulas have been underway in the bilateral Transboundary
Management Guidance Committee (TMGC). Until the details of how the TRAC
is related to the outcome of this negotiation, the TAWG will annually
review the assessments. In 2002, the TAWG will review the Canadian management
units in mid-April while the US management units would be reviewed during
the summer of 2002.
The Terms of Reference of the meeting (Appendix
3) were briefly reviewed. The meeting sought to address various
benchmark assessment themes (Appendix 2). The
focus of the meeting was on the definition of management units and
estimation of contemporary stock status of 5Z+6 and 5Zjm cod. The
discussion on exploration of production dynamics was not as extensive
as planned. Implementation of Amendments 7 and 9 to the Northeast
Multispecies Fishery Management Plan has been legally challenged,
necessitating a review by NMFS of biological reference points the
week of 11 February 2002. Therefore, discussion at the present meeting
was undertaken to provide general observations on Georges Bank groundfish
production dynamics, which might be of use to the NMFS meeting. The
current meeting did not extensively consider procedures for projection
to evaluate TAC’s, relying instead on previous TRAC discussions.
It did however formulate assessment activities to be undertaken by
TRAC between benchmarks.
This report provides a summary of the presentations and associated
discussion and the consensus on the benchmark formulations to be used
in annual assessments.
The meeting schedule was kept flexible to allow
full discussion on the benchmarks, with day one devoted to presentations
and the remaining time to discussion, analysis and report writing.
The list of documents considered, minutes of TAWG meetings, and recommendations
made are provided in Appendices 4, 5,
and 6 respectively.
5Z+6
COD
Working Paper: |
O’Brien, L. 2002. 5Z+6 Cod Presentation: Atlantic
Cod, Simulated Data Analyzed by ASAP, retrospective Analysis
of Cod Using a Forward Approach. TRAC Working Paper 2002/01. |
L. O’Brien presented the main issues encountered
in the 2001 assessment and tabled the minutes of a TAWG meeting (Appendix
5) held in preparation for this meeting.
Diagnostic plots from the current Georges Bank cod assessment (O’Brien
and Munroe 2001) were presented that demonstrate the strong retrospective
pattern underestimating fishing mortality (F) and the domed partial
recruitment (PR) pattern since 1994. Patterns in PR prior to 1994
were flat-topped. An additional Virtual Population Analysis (VPA)
was conducted, using Extended Survivors Analysis (XSA), without F shrinkage,
that also demonstrated a similar retrospective pattern in F. In addition,
log-log plots of survey abundance indices and population numbers from
the VPA indicated that survey catchability (q) in the most recent years
(1994-2000) was generally higher than that in earlier years (1978-1993). A
shift in survey q was not expected and it was speculated that this
was perhaps due to the model formulation used in the VPA, to be investigated
at this meeting.
Definition of the Management Unit
Georges Bank cod in the US is managed and assessed using NAFO Division
5Z and Subarea 6 catch and survey index data. The assessment is conducted
on a calendar year basis although the fishing year is May-April.
Estimation of Contemporary State
Fishery
In 1994, the collection and processing of commercial catch and effort
data changed from a system of personal interviews of vessel captains
to a mandatory reporting system of logbooks and dealer reports. The
procedures for collection of biological data also changed at this time
and the numbers of samples declined for the large market category catch,
although sampling has since improved.
Since December 1994, year-round closures have been
in effect for Areas I and II (Figure 1).
Recent vessel tracking of about 40 USA
offshore vessels that account for about one third of the total groundfish
landings indicates that effort in recent years has been focused on
the northwest edge of Area II and to the west and north of Area I. Lack
of access to Closed Area II since 1994 has decreased the catch of larger
fish (Figure 2) that aggregate in this area
prior to spawning in the spring. Displaced effort may have also resulted
in the catch of smaller fish in areas nearer to shore. The shifts in
effort and the reduced availability of larger fish in the spring are
consistent with the domed PR observed in recent years.
In 1994, the regulated mesh size increased to 6" diamond. Since
August 1999, there has been a trip limit for vessels fishing for cod
on Georges Bank, however, discarding of small fish remains at historical
levels of about 5-8% (discard/kept ratio). Recreational landings of
Georges Bank cod have averaged about 7% of the total catch in recent
years (1996-2000). Sampling of these landings is minimal and insufficient
to characterize the catch-at-age. Sensitivity analyses that include
the recreational landings in the catch-at-age, apportioned to age using
commercial samples, result in an upward scaling of the biomass. This
increase in biomass results because of an overall increase in catch
in recreational numbers-at-age.
The catch-at-age used in the assessment includes ages one to 10+.
Further decomposition of the plus group was not possible due to data
limitations. The number of age samples for ages 10 and older represent
only 1% of the total age samples collected during 1982-1988 and less
than 1% for all other years.
Abundance
Survey abundance indices available for calibrating the VPA include:
NEFSC spring and DFO spring survey ages 1-8 and NEFSC autumn survey
ages 0-5. Data for the DFO survey are not available for 1993-1994
because the entirety of Georges Bank was not surveyed in those years. Spawning
stock biomass weights (January 1st weights) were estimated from catch
weights (Rivard, 1982), although spawning stock biomass (SSB) might
well be better estimated using NEFSC weights-at-age from the spring
survey. There are some minor differences in the maturity-at-age between
the NEFSC and DFO surveys that need to be reconciled. The meeting recommended
that the TAWG address these data changes.
Recommendation: |
TAWG should recalculate stock weights at age, consider how to
best fill in the DFO 1993 & 94 DFO RV information, and reconcile
the differences in DFO and NMFS maturity-at-age data. |
Several differences exist between the NMFS and DFO ADAPT software
for VPA analysis. The NEFSC FACT (Fisheries Assessment Computation
Toolbox) software requires that the autumn survey indices be moved
forward a year to match beginning of the year VPA population estimates,
whereas the DFO software allows for the timing of the survey to be
implemented directly. Also, FACT uses Cohort Analysis and the DFO
software uses the catch equation.
Recommendation: |
The FACT software should be amended to allow appropriate time
matching of RV & VPA population estimates, and FACT should
be modified to use the full catch equation instead of the Pope
(1972) approximation. |
The NEFSC assessment, to be conducted in late summer 2002, will allow
for the use of the NEFSC spring survey for calibration in the VPA. This
will be a change in the formulation from previous years when the spring
survey was not available for the terminal year.
Apart from fleet distribution changes, differences in the spatial
distribution of length classes of fish may explain both the domed PR
patterns observed in recent years and the retrospective pattern in
F. Spatial patterns of Georges Bank cod in the spring and autumn
surveys were examined by 10 cm groupings to investigate differences
between length groups and to determine if cod were concentrated in
the closed areas since 1994. Young fish, less than 30 cm, tended to
occur inshore, larger sized fish were evenly dispersed in the spring,
and in the autumn inhabited deeper water on the Northern edge of the
Bank and in the Great South Channel. No changes in cod distribution
were detected after 1994, when the year-round closed areas went into
effect. No more than 10% of each length group occurred inside of Closed
Area I or II, i.e. 90% of the 51-60 cm fish occurred outside of the
closed areas during 1978-2000.
The NEFSC spring survey is conducted after the period of peak spawning
of cod on Georges Bank. Older haddock are known to preferentially inhabit
deeper water (Overholtz 1985). If this behavior is also true for Atlantic
cod, cod may move off the Bank after spawning and not be available
to the Canadian fishery because of current Canadian fishing practices
and regulations. Prior to 1993, spawning aggregations in Area II could
be fished in January, but the Northeast Peak is now closed to the Canadian
groundfish fleet from January to June. Commercial length frequency
samples were examined during 1978-1993, by quarter and area (Div. 52
and Div. 56), to determine if larger fish were landed in quarter 1
from Div. 56 compared to the remainder of the year, but no significant
difference was evident in the length of fish landed between areas or
quarters. However, the trends were hard to detect and the TRAC suggested
averaging the data across years and, examining the proportion of older
fish landed by quarter and area.
Simulation Investigations
A number of simulation exercises were conducted to determine how the
VPA results were influenced by varying data input and assumptions.
An alternate model was also examined that used forward projection instead
of the backward calculation of VPA.
VPA Simulations: Can VPA recover domed PRs from simulated data – Part
I?
An age-structured simulation model was developed to investigate the
performance of various estimation methods to detect an underlying domed
shaped PR pattern from simulated data. The purpose of this exercise
was to examine the effect of model mis-specification and changes in
model parameters. The Working Group noted that the retrospective patterns
in fishing mortality and spawning biomass in the 5Zjm and 5Z+6 cod
assessments could arise from a number of sources, and concern was expressed
that the domed PR might be an artifact of the modeling process.
Trial analyses were performed using the DFO Contouring Package (ACON)
software. The analysis was divided into two components: the first using
simulated data, and the second using actual data from the Georges Bank
cod assessment.
In the simulations, the catches were generated using a flat-topped
PR for the first 16 years and a domed PR for the last seven. This pattern
mimicked the perceived pattern in the Georges Bank cod assessment.
The simulated data were plotted as if the first year was 1978, to match
the empirical data used in the second analysis.
Although four survey time-series were available, only two were used
in the simulations because similar trends and low variability made
two of them superfluous for fitting the VPAs. All ages (1-9) were
estimated in the terminal year. VPAs were performed using two different
scenarios. The first assumed that fishing mortality on the oldest age
(F9) was equal to that at age eight. If a dome existed, this formulation
would be most appropriate. In the second scenario F on age 9 was assumed
to be the average (weighted by numbers) of F4-7. This implies that
the partial recruitment is flat-topped.
In the following figures, the upper plot shows the simulation runs
with the F on the oldest age (F9) set equal to F8. The lower plots
present the simulation results assuming F9 is equal to the average
(weighted by numbers) of ages 4-7.
Figure 3 shows the PR
patterns by year. In general, when the model is allowed to find a dome
(assumption 1), it does, whereas a mis-specified model (assumption
2) does not detect the PR very well. This also has consequences for
the retrospective pattern (Figure 4). These
patterns are also evident in the survey catchabilities derived from
a moving window analysis (Mohn 1999) (Figure 5)
where the mis-specified model shows an increase in age 7 q when the
PR is simulated as a dome.
Figure 6 shows a strong
relationship between survey catchabilities and model residuals.
Analyses using the actual Georges
Bank cod data differed from those used in the benchmark formulation
in the following ways:
- the spring survey was not separated into separate periods for
the Yankee 36 and 41 trawls;
- the survey timing was estimated to the nearest month – e.g. similar
to 5Zjm formulation; and
- the age 0 NMFS fall RV indices were not used.
As before, the upper plot of each
figure shows the VPA runs with the F on the oldest age (F9) set equal
to F8, the lower plot presents the results when F9 was set equal to
the average (weighted on numbers) of ages 4-7.
Figure 7
Figure 8
Figure 9
Figure 10
The analysis of simulated data indicated
that VPA could produce the ‘true’ population selectivity pattern but
that it was better to use a minimally constrained estimate of F on
the oldest age in cases where partial recruitment changes over time.
This conclusion might be compromised if noise were added to the data.
The retrospective and moving window analyses behaved as expected. The
actual Georges Bank cod data also showed that the less constrained
PR fit the data better. The moving window analysis showed a discontinuity
occurring around 1994 in both scenarios, which was more pronounced for
the q's for older age groups.
VPA Simulations: Can VPA recover domed PRs from simulated data? – Part
II
A simulated population was created from average weights, initial population
sizes (N) and annual recruitment levels similar to those in the USA
Georges Bank (5Z+6) cod assessment. Fishing morality on the fully
recruited age classes varied by year but the pattern of partial recruitment
had two distinct phases. Prior to 1994, the pattern was flat-topped;
from 1994 onward, the pattern was assumed to be domed. Catches, computed
using the catch equation, were infused with a small amount of uniformly
distributed error equal to +/- 0.1% of the predicted value. Thirty
simulated abundance indices were generated as I = qN with population
sizes N and the q parameters derived from the actual Georges Bank cod
assessment. A small error term, uniformly distributed between +/- 1%
of the predicted value, was added to each simulated index. The addition
of small error terms in the catch and tuning indices was intended to
reduce convergence problems in the numerical optimization procedures. The
use of negligible error terms was also intended to isolate problems
of model configuration from problems of observational error.
Analyses of the simulated data sets using the U.S. and Canadian implementations
of ADAPT revealed that recovery of the known parameters was highly
dependent on the model formulation. In particular, the models were
sensitive to the range and number of age groups used to estimate the
average F on the oldest true age group. If the true PR pattern is domed,
then averaging Fs on younger ages (say 3-7) will result to an incorrect
estimate of the F on the oldest true age. This leads to a transient
behavior whereby the Fs are underestimated in the terminal year. Retrospective
analyses revealed a pattern of consistent underestimation of Fs on
the older age groups. When the model parameterization was modified
to restrict estimation of fishing mortality (Fold) on the
oldest age groups, then both the U.S. and Canadian formulations of
ADAPT led to nearly correct and identical estimates of F and elimination
of the severe retrospective pattern in F.
Overall, a domed PR presents particular challenges to the models and
ancillary information is required to resolve whether or not such a
pattern is present. The ancillary information could include examination
of RV trends by age and year. One would expect the RV q's to asymptote
(i.e. become flat) at a given age and not monotonically increase. Survey
mensuration research could be brought to bear on this issue (i.e. what
is the expected shape of the q – age/size relationship for survey gear?).
One would also expect that RV q by year would vary without trend (similar
to residual pattern). Further, examination of fleet and or population
spatial patterns and partial Fs by country and or fleet might provide
insight on changes in exploitation patterns. Some of these were examined
at this meeting (as described below).
If a domed PR is present, then sooner or later, the surveys should
record increases in abundance of large cod although this might take
a number of years depending on recruitment and F.
Forward Projection Model using Actual Data
A forward projection model was applied to the cod data to determine
if a different model structure could shed light on the retrospective
problem. The ASAP [age structured assessment program, Legault and Restrepo
(1999)] model uses a forward solving approach to estimate population
abundance and fishing mortality rates from catch at age and tuning
indices. The model is based on a separable approach for fishing mortality
and estimates a stock-recruitment relationship to determine the strength
of each cohort. Flexibility in the model is facilitated by allowing
selectivity to vary annually and by allowing predicted recruitments
to vary from the stock recruitment relationship. Flexibility can be
constrained by placing penalties on the parameters that determine the
amount of variance in the estimates )so that the model does not become
over-parameterized). The model is written using AD Model Builder software.
Parameters are found rapidly through automatic differentiation and
subsets of parameters can be estimated in phases, which stabilizes
the estimation procedure.
Five model formulations were used in ASAP based on the same cod data
used in the VPA analyses. All five models assumed total annual catch
in weight was known without error while the catch-at-age data were
assumed to have error rates corresponding to effective sample sizes
of 50-200 fish per year. The first two formulations had recruitment
exactly follow the stock recruitment relationship, while the remaining
three formulations allowed deviations in recruitment from the S-R curve.
Four of the models held selectivity constant in all years while the
most complex model allowed selectivity to vary from year to year, subject
to constraints.
Model |
Recruitment |
Selectivity |
1. Minimal , Flat PR |
SRR |
Flat topped all years |
2. Minimal, Dome PR |
SRR |
Dome all years |
3. Recruitment, Flat PR |
Deviations |
Flat topped all years |
4. Recruitment, Estimated curve. |
Deviations |
One curve estimated for all years |
5. Recruitment, PR estimated yearly |
Deviations |
Estimated for each year |
All models produced trends in SSB and F that were similar to the VPA, but,
different in magnitude. When selectivity was estimated, it was strongly domed,
even for an additional run when selectivity in the first year was fixed as
flat topped. All five models were examined for retrospective patterns in
SSB, recruitment and average F (ages 4-8 unweighted). Flat topped selectivity
models (1 and 3) had more pronounced retrospective patterns in SSB and F
than domed selectivity models. The simple models (1 and 2) had more pronounced
retrospective patterns in recruitment than the complex models. Use of the
asymptotic variances provided by AD Model Builder demonstrated that in general
the retrospective patterns were not “statistically significant” from one
year to the next; between when a unidirectional pattern was present, the
accumulation of change produced significantly different changes in estimates
of SSB, recruitment and average F.
The types of changes generated by the retrospective analyses of a
forward projecting model demonstrate that model formulation plays an
important role in affecting retrospective patterns. The same may be
true ofVPA, but is not generally observed due to the limited range
of formulations typically examined. One avenue for future research
is to use the results from VPA results as the starting conditions for
the ASAP model under the hypothesis that the range of solutions under
different model configurations will differ less in magnitude.
Recommendation: |
Pursue research on using VPA results as starting conditions for
the ASAP so that initial conditions for the ASAP model will be
consistent across different model runs. |
Forward Projecting Model using Simulated Data
As with VPA, a simulated data set was prepared that incorporated a flat-topped
selectivity pattern for years 1978-1993, switching to a dome during
1994-2000. The simulated data included 30 tuning indices with minor
observation error. Three model formulations were explored which each
contained recruitment deviations but differed in the treatment of the
selectivity pattern. In the first formulation, selectivity was assumed
to be flat-topped in all years. In the second formulation, a single
pattern was estimated for all years. In the final formulation, the
first year was assumed to be flat-topped, with selectivity in subsequent
years estimated under a constraint on change from one year to the next.
The forward projection modeling results failed to recover the true
population size but the trends were consistent with the VPA. One reason
for the lack of agreement was the dependency of the forward simulation
on the estimated stock-recruitment function. Since the simulated data
were not generated from a specific S-R function, the forward projection
method estimates the S-R parameters. If the underlying simulated data
do not support a particular model formulation, then the lack of a good
S-R fit will induce population size errors that are not considered
in VPA-based approaches. Under these circumstances, a better test
of the forward projection model approach would be to initiate the simulated
population with the VPA results and generate the recruits (and therefore,
subsequent population estimates) with a known underlying S-R function.
When selectivity was estimated, a strong dome resulted, and when selectivity
changes over time, a stronger dome is estimated in the most recent
years. In contrast with the VPA, however, was absent. This may be due
to the small amount of observation error allowing the ASAP model to
fit the data consistently while the larger amount of noise in the real
data allow for a retrospective pattern to be expressed in the VPA output.
One possible explanation for the strong dome estimated by ASAP is
that there was no tuning information for the plus group. To examine
this possibility, an additional run was performed which linked the
selectivity at ages 8 through 10+. A dome selectivity pattern was still
obtained, with selectivity at ages 8 to 10+ approximately the midpoint
of the individual estimates from the full model.
Patterns in Relative Fishing Mortalities
Patterns in the partial recruitment and relative fishing mortality
were evaluated using relative indices obtained from the ratio of catch-at-age
divided by the catch rate-at-age from each of the RV surveys. This
type of analysis is useful in examining changes in exploitation when
there are uncertainties in VPA results. However, trends from this
analysis will be affected by changes in the rate of catch reporting
and/or changes in survey catchability.
The analysis was conducted with the 5Z+6 cod data. The ratio of catch-at-age
to the RV catch rate at age was calculated for the US spring survey
and the Canadian winter surveys for ages 1 to 8. To examine partial
recruitment over time, this ratio was normalized by year (highest value
set equal to 1) and averaged over the time period. Averages were
then calculated over three periods (1978-1985, 1986-1992 and 1995-2000).
The resulting trends from each of the survey indices
indicate that the partial recruitment pattern is somewhat domed over
the entire period (Figure 11). However, this
could be due to an increasing pattern of survey catchability up to
an asymptotic age. Because fish of younger ages are likely not fully
recruited to the survey, the peak of the dome is shifted to younger
ages and not representative of the PR in absolute terms. However, the
relative change in PR should be representative of temporal changes
that have occurred either in survey catchability or in the fishery. The
dome in the partial recruitment is more pronounced (steeper descending
limb) in the post-1994 period.
The trend in relative F was further examined by normalizing by age the
catch-at-age to survey indices ratios over the entire time period. The
resulting values were averaged for ages 4 to 6, the age groups considered
fully recruited to the fishery.
The results (Figure 12) indicate
an increasing trend in fishing mortality in the late 1980s and early 1990s,
followed by a sharp decline in 1995 an low F afterward. This is consistent
with the decline in fishing effort that occurred in these years.
Given the variability in the survey indices, the results are relatively
consistent with the VPA. The VPA suggested a flat-top PR in the early time-series
and a shift to a dome since 1994. The relative F’s also suggest a decline
in PR at older ages in recent years. It would thus appear that the dome
PR in recent times is not an artifact of the VPA calibration.
Estimation
Virtual Population Analysis
Catch-at-age for Georges Bank 5Z+6 cod includes ages 1-9 with a 10+ age
group from 1978-2000. Further decomposition of the 10+ age group is not
possible due to lack of sufficient age data prior to 1982 and after 1988.
All survey indices (NEFSC spring and DFO ages 1-8, NEFSC autumn ages 0-5)
are used in the calibration of the VPA. Although the 5Zjm benchmark assessment
excluded the DFO age 1 and 8 indices and the NEFSC autumn 0 indices (see
below), this was not necessary in the 5Z+6 assessment. Examination of the
indices shows no lack of fit between the survey values and the VPA estimates
that was observed in the 5Zjm assessment. This is perhaps due to the difference
in the number of strata used in the estimation of abundance indices for 5Z
vs. 5Zjm.
Stock sizes were estimated for ages 1-8 in the terminal year plus one and
in the corresponding unweighted F estimates for ages 1-7 in the terminal
year. Full recruitment was assumed at age 4 and F on ages 8 and 9 in the
terminal year was an unweighted average of ages 4-8. The F on age 9 for
all years prior to the terminal year was derived from a weighted average
(by numbers) of ages 4-8. Age 10+ F was set equivalent to age 9 F in all
years.
The model is sensitive to the choice of age groups used
in estimating F on the oldest age (9). Different combinations of age groups
to estimate F on age 9 were applied to determine if the choice of ages influenced
the retrospective pattern. The retrospective pattern in F still persists
regardless of the F assigned to the oldest age (9), although the magnitude
shifts slightly in some cases (Figure 13).
Exploratory analyses were conducted to determine if
weighting of cohorts in the catch at age (CAA) would influence the retrospective
pattern, based on the assumption that since less information is known about
the incomplete cohorts then less weight should be given to their contribution
in the analysis. A weighting factor was derived for each year and age of
the cohort based on the number of years of catch data available to derive
the estimate. In the terminal year, all cohorts were assigned a value of
1, in terminal year -1, each cohort was assigned a value of 2, etc. All complete
cohorts were assigned a weight of 10. All weights were then divided by the
maximum weight in that age group across all years and multiplied by 10. The
retrospective pattern in F still persisted using either an average F on ages
4-8 or an average F on ages 6-8. The magnitude of F shifts depending on
the F assigned to the oldest age 9 (Figures 14 and 15)
and these shifts are slightly more than that observed in the unweighted CAA
analysis (Figure 13).
The ADAPT formulation for 5Z+6 cod differed from the benchmark ADAPT formulation
for 5Zjm. The 5Zjm benchmark calculated F10 as a weighted F of ages 7-8
for 1978-1996 and population sizes were estimated for 1997-2001 (see below).
This could not be done using FACT for 5Z+6 due to required changes to NMFS
software (FACT).
Recommendation: |
Modify FACT to allow more flexibility in estimating F on older ages
in the terminal year and most recent years. |
The TRAC recommended that the 5Z+6 cod be assessed using the same model
formulation as used for 5Zjm cod to eliminate confusion and produce comparable
results. The 5Z+6 formulation was then run using the DFO software (ADAPT).
The age 10+ calculations were not performed but were generated outside the
final analysis.
For 5Z+6 cod, population sizes were estimated for
ages 1-9 in the terminal year and for age 9 in 1997-2000 for 1978-1996, fishing
mortality at age 9 was set equal to a weighted F of ages 7-8. Results showed
the PR was flat-topped from 1978–94 and was domed after 1994, consistent
with FACT runs (Figure 16). Population size for
ages 1-9 were estimated reasonably well and the correlation matrix was acceptable. The
survey q's were asymptotic at age 5+ (Figure 17)
and average F at ages 4-6 showed no persistent retrospective patterns (Figure
18). This formulation of ADAPT largely addressed the retrospective pattern
seen in the FACT runs.
TRAC agreed that this formulation should be used for the 5Z+6 benchmark.
Alternate Explanations for Dome-Shaped Partial Recruitment
While partial recruitment (PR) in the Georges Bank cod fisheries was flat-topped
prior to 1995, since then a dome-shaped PR appears to be more consistent
with catch-at-age data (CAA) and with research survey indices of abundance. Changes
in fishing practices due to management regulations, instituted about 1994,
appear to be the primary causal factor. If this is indeed the case, changes
in CAA patterns relative to survey indices (for older fish) should emerge
clearly within the next 5 years or so. However at this point in time, it
is difficult to know with certainty that a change in PR has occurred.
Scenarios other than a change in PR that may be also be consistent with
the CAA and survey indices. These involve influences on the catch and on
the population, (i.e., affecting the numerator and denominator of the fishing
mortality equation respectively). Alternative explanations were discussed
briefly , but were not considered to be really viable options by the TRAC. Some
of the hypothetical scenarios discussed include:
[Alternative 1] Migration out of Area 5Z:
PR in 5Z has not changed (i.e. PR remains flat-topped) but significant
movement of older cod out of 5Z and into the Gulf of Maine (GOM) has been
occurring. This movement occurs seasonally after the time of the spring
survey but before the height of the fishery occurs. High fishing mortality
rates (F) in the GOM results in the capture of nearly all of these cod
within a year or two of their out migration. While such a scenario may
be consistent with the observed data from Area 5Z, there is not much evidence
of movement into the GOM (from tagging data). Further although large cod
are thought to move into deeper water, this deeper habitat is still part
of Area 5Z.
[Alternative 2] Spatial misreporting of the catch
PR in 5Z has not changed (i.e. PR remains flat-topped) but a significant
spatial misreporting of older cod has occurred since 1994. A major restructuring
of the USA sampling program occurred in 1994. Proper area allocation of
the catch to stock area is thought to be less reliable as a result of this
change. However, if the catch of older 5Z cod has been misreported to other
stock areas (such as the GOM), it is not apparent in the statistics from
these other areas. In addition, similar evidence for a change in PR can
be seen in the Canadian data even though no change has occurred in the
Canadian sampling program.
[Alternative 3] Discarding older cod
PR in 5Z has not changed (i.e. PR remains flat-topped) but a significant
increase in discarding of older cod has occurred since 1994. Since discards
are not routinely reported, such a scenario may be consistent with the
observed data from Area 5Z. However, there does not appear to be any economic
(or other) incentive for fishermen to discard older (larger) cod.
[Alternative 4] Change in natural mortality
PR in 5Z has not changed (i.e. PR remains flat-topped) but natural mortality
(M) on older cod has increased since 1995. An increase in M on older cod
would affect the observed 5Z CAA data in a fashion similar to the out migration
described in Alternative 1, above. However, the survey indices should
also be likewise affected, and this does not appear to be the case in either
the NMFS spring or fall surveys.
Although these alternative explanations are mentioned and were discussed,
they are not considered to be useful explanations for the change in PR since
1994. The benchmark assumes that fishing effort changes have resulted in
a change in PR (flat-topped to domed) beginning about 1994. This appears
to be the scenario that is most consistent with the observed data and general
knowledge of the cod fisheries. However, a more complete understanding of
the the spatial and temporal effort patterns in cod fisheries is important
in refining this understanding.
5Zjm
COD
Working Paper: |
Hunt, J. and B. Hatte. 2002. Eastern Georges Bank Cod in 5Zejm Assessment
Evaluation. TRAC Working Paper 2002/02. |
J. Hunt presented issues from the 2001 TRAC and noted interim changes from
the last benchmark formulation, including expansion of the catch at age to
age 10 and using ages 7-9 (rather than ages 4-9) to estimate fishing mortality
on the oldest ages. Issues and concerns identified in the 2001 TRAC included
calculation of F on oldest age method, lack of improved recruits with increasing
SSB, utility of an industry longline survey, ability of the survey to sample
ages zero and one, and a relatively strong retrospective pattern.
Two TAWG meetings at Saint Andrews Biological Station were conducted and
minutes of discussions were tabled (Appendix 5).
Definition of the Management Unit
The operational management unit for this resource consists of unit areas
5Zj and 5Zm. Several ongoing projects are presently considering transboundary
management issues. A major cod tagging program is underway including releases
by Canada, NMFS and State agencies in the Inner Gulf of Maine, Bay of Fundy, Scotian
Shelf and Georges Bank. Results will be available after 2004 and have implications
for timing of the next benchmark.
Estimation of Contemporary State
Fishery
Input data available for the ADAPT formulation included combined 1978-2000
Canada and USA catch at age for ages 1-10 without a plus group.
Abundance
RV abundance indices consisted of ages 1-8 spring (NMFS 1978-1981, NMFS
1982-2000 and DFO 1986-2001), 0-5 fall (NMFS 1978-2000) and ages 2-8 for
a 1996-2000 Canadian industry longline survey. The longline survey was considered
a new index and an evaluation was made after development of a formulation
with the previously used indices.
Estimation
The updated catch at age (ages 1-10) incorporating revised landings statistics,
assignment of decimal year to RV indices and a numbers-weighted average F
on ages 7-9 for F on the oldest age groups were used in the TRAC
2001 ADAPT formulation as a baseline model. Comparison of results from this
formulation with those from the last assessment revealed no significant differences
in population estimates or exploitation rate.
Examination of the relationship between RV indices and
population estimates (Figure 19) identified three
potential candidate indices for exclusion. The DFO RV age 1 index vs. VPA
age 1 seems to have a power relationship rather than proportional, with RV
q increasing with N.
This effect was not apparent in the NMFS RV spring age 1 index and use of
a smaller/lighter footrope on the 36 trawl for the NMFS survey might be the
reason. Given the lack of a proportional relationship and poor precision
for parameter estimates of a power relationship, it was decided that the
best option was to exclude the DFO age 1 index. A similar lack of fit for
the DFO age 8 index was accepted as the basis for its exclusion.
The NMFS RV fall age 0 index has seven zero values in the last 10 years
and substitution of proxy values based on a relationship between 5Zj,m and
5Z was examined. Inclusion of proxy values resulted in only marginal improvement
in precision and it was concluded that this index for 5Zj,m did not contain
sufficient information to justify inclusion in the formulation.
The Canadian longline survey has been conducted in late
August since 1996 using five commercial vessels. Problems in adhering to
the design have been noted but consistency with the RV indices for ages 2-8
has been observed. Inclusion of the index in the formulation gave similar
parameter estimates and some improvement in parameter precision. However,
it was noted that this index was a short time series, with coverage restricted
to Canadian side. The time series is too short to discern shifts in distribution
and, if distribution changes, this series could be misleading. Trends in
the proportion of the total 5Zj,m biomass within the Canadian zone show about
80% in recent years and about 50% in the early time period (Figure
20).
Therefore, it was concluded the index is not useful as an index within the
ADAPT formulation but it could be of use as an independent index after assessment
to corroborate trends.
The effect of intrinsic (inverse of internally calculated mean squared residual)
and extrinsic (RV proportions at age) weighting on RV indices was examined
and, based on examination of mean square residuals (MSR) for each index and
age, homogeneous blocks were identified. Results showed slightly more even
distribution and balance of residuals with intrinsic weighting having the
most influence. It was noted that as years are added to the analysis, the
perception of variability of RV indices might change, necessitating a change
in the groupings by block; this is primarily a problem with short data sets.
The influence of year effects was discussed and an example using the 1982
NMFS spring survey showed that inappropriate weight might be given to an
index if a strong residual pattern existed in the series. In this specific
case the MSR between the three RV indices was comparable when the 1982 values
were excluded, negating the potential benefit of weighting. It was therefore
concluded that weighting in this formulation would not be an improvement.
However, it was recognized that the merit of weighting should be considered
on a case by case basis in developing model formulations.
Three options for estimating fishing mortality or population size at the
oldest age were considered.
- F10 = weighted mean of F 8-9 for 1978-1999; all ages estimated in 2000
- Imposed Flat-topped PR (4-10) in 2000; 4-6 estimated and 7-10 calculated
- Estimation of N10 in 1997-2001 with F10 = weighted mean F 8-9 for 1978-1996
Partial recruitment patterns and trends in RV q were
used to evaluate each option. The first option produced a dome PR for 1999
and 2000 but an unrealistic pattern for 1995-1999 and Rv q’s that increased
monotonically. The second option also had an unrealistic PR for 1999 and
1994-1998 to an even more pronounced monotonic increase in RV q’s. The third
option gave results that seemed more consistent with fishery trends (Figure
21) and an asymptotic pattern in RV q’s (Figure 22).
Correlation among variables of the matrix was examined as an influencing
effect but was considered not to be a problem.
The apparent dome-shaped partial recruitment from option 3 required explanation.
Cod distribution in relation to Canadian and USA fleet distributions could
have induced a reduction in exploitation of large cod. Prior to 1994, about
50% of the annual landings of age 7+ was caught during the winter (Jan-Mar)
fishery. The fishery harvests large spawners and after spawning, cod move
into deeper water. Since 1994, the Canadian fishery has been closed between
January 1 and June 1, which is consistent with reduced exploitation of large
cod. Since December 1994, the USA has closed these areas on Georges Bank
year round including Closed Area II on the Northeast Peak. Also, the Canadian
fishery avoids areas of cod abundance to avoid overruns of limiting cod allocations
while directing for haddock,. Both fishery and survey observations suggest
that large cod are not in commercial aggregations after spawning, making
it uneconomic to direct for them.
Under option 3 of the ADAPT assessment formulation the
retrospective pattern showed significantly less effect (Figure
23), and there was also less of a trend to underestimate recruitment.
Overall, it is considered that estimation of age 10 stock size during 1997-2001
with F10 = weighted mean F 8-9 for 1978-1996 gave results that were consistent
with fishery trends, and thus should be used for the 5Zjm benchmark.
Partial Fishing Mortality by Country
Partial F's by age and year were calculated for the 5Z and 5Zjm areas to
examine patterns during 1978-2000. These analyses were accomplished by dividing
the catch at age by country by the total catch at age for the assessment
area.
The pattern in the US fishery indicated that partial F's
were relatively flat for ages 4-9 during 1978-1988 (Figure
24a). This pattern began to change in the early 1990s and partial F for
the oldest ages (7-9) started to decline. During the 1990s, the pattern was
variable but generally indicated lower partial F on the older age groups
(Figure 24d).
Analyses for the 5Zjm assessment area indicated similar
trends by year. Partial F for the Canadian portion of the catch at age showed
a flat trend during 1978-1987, a relatively increasing trend during 1988-1994,
and a dome shaped trend during 1995-2000 (Figure 25a). The
pattern in the US fishery in 5Zjm was similar to the 5Z trends with a relatively
flat trend during 1978-1987, a slight dome in 1988-1994, and a more pronounced
dome during 1995-2000 (Figure 25b).
Discussion centered on potential reasons for a dome in
1995-2000 in the US fishery. Several ideas were discussed including a change
in fleet distribution and composition, a decline in the proportion of otter
trawl landings (was 80%, now 60%), and various seasonal effects. No single
factor is likely responsible, so the TRAC concluded that further investigation
was necessary to better define the mechanism for the dome in the recent US
fishery.
CHARACTERIZATION
OF PRODUCTIVITY TO DETERMINE HARVEST STRATEGY
Fisheries management harvest strategies are typically operationalized
through reference points. Reference points may be used as signposts against
which forecasted outcomes for specified management actions are compared or
they may underpin the specification of harvest control rules. Reference points
serve as a gauge of resource productivity, therefore their derivation is
implicitly based on an understanding of the production dynamics. Fisheries
production dynamics can be summarized by mortality, by growth and fishery
selectivity processes which are captured by yield per recruit analyses, and
by the recruitment process which is described by a stock recruitment relationship.
Yield per recruit analysis can be combined with a stock recruitment relationship
to characterize the response of yield to fishing mortality and the associated
biomass implications. However, concern was expressed about using the yield
response to identify reference points associated with maximum sustainable
yield (or suitable proxies).
Various parametric forms of stock recruit relationships have
been proposed and it is generally not possible to convincingly demonstrate
a better fit to one form than another (particularly for chronically overfished
stocks). Reference point estimates can be sensitive to the choice of parametric
form. Stock recruit forms of the Ricker type have been criticized because
the mechanisms that can cause over-compensation are not thought to be common
in the marine environment. Stock recruit forms of the Beverton-Holt type
have been criticized because they typically imply very high biomass for the
unfished state compared to the maximum sustainable yield biomass. Non-parametric
scatterplot smoothers can be used to summarize the stock recruit relationship
without having to specify a model form. Estimates of reference points can
be sensitive to subtle differences in the shape of a smoothed relationship
that may be caused by the choice of the smoothing criteria or by peculiarities
of the observed data.
For maximum sustainable yield reference points, the zone of interest for
the stock recruitment relationship is at moderate to high biomass, and often
outside the range of observation. In these instances, reference points derived
using either parametric or non-parametric approaches are highly dependent
on behavior in the extrapolated zone.
In the absence of an objective statistical estimation procedure, fishery
and population dynamic principles and meta-analyses may be employed to constrain
the domain of possibilities. However, it is important to clearly identify
the limitations of the data and the reliance on expert subjective judgment.
Bounding the range of plausible subjective choices and characterizing the
consequences of selecting the wrong hypothesis could further enhance the
decision process. The implications for conservation, economic opportunity
and the potential to learn more about the productive capacity of the resource
should be examined for alternative hypotheses. It is not obvious that meaningful
quantification of uncertainty can be carried out when results are highly
conditioned by subjective judgment. All of these results are also conditioned
on the assumption that these production dynamic processes are stationary
and not subject to regime shifts.
A presentation was made which demonstrated the use of
multiple models to compare measurement, process and model uncertainty. Measurement
and process error were estimated in the usual way, with conditioned bootstrapping.
Within the Sissenwine-Shepherd (S-S) framework, fitting a Ricker stock-recruitment
curve was considered to be process error, which is subsequently re-expressed
as error in MSY estimation. MSY as a process was also estimated directly
from production data in a Schaefer model and bootstrapped to estimated confidence
regions. The direct and the Sissenwine-Shepherd process errors were of similar
magnitude and both were much greater than the errors in estimation for a
population via VPA. The model uncertainty, that is the difference between
the S-S and Schaefer MSY-BMSY estimates (Figure 26),
was about the same magnitude as the process errors. This approach seemed
promising and it was recommended that it be applied to ther stocks.
These presentations and the ensuing discussion highlighted the prudence, for
medium term projections, of sampling from stock/recruitment data, rather
than using parametric forms, to derive estimates of recruitment and this
prevents extrapolating recruitment outside the range of observations. How
the sampling is conducted is very important and should be carefully considered.
Conceptually, the approach can be used to derive biological reference points.
Where the uncertainty of stock productivity processes is high, it is probably
worthwhile to establish biomass and fishing mortality reference points based
on direct examination of the data rather than using derived parametric models.
There was a discussion on the use of flat top and dome PRs in short, medium
and long-term projections. For short and medium-term projections, it was
agreed that the dome PR should be used as this is most reflective of current
conditions. Further, it was agreed to use the modal ages to calculate fishing
mortality for both indicator and reference points.
However, it is not obvious what PR to use for long-term forcasts, potentially
causing inconsistency in approach to these projections. If the fleet behavior
reacting to management measures is causing the dome PR, then depending on
management activities, a flat top PR might return. It was therefore considered
prudent to examine the consequences of using both flat top and dome PRs in
long-term projections.
GUIDANCE ON
ACTIVITIES
The TRAC discussed procedures for undertaking assessments on an annual or
as needed basis. The application of the benchmark, as outlined in the next
section, to the latest information constitutes an assessment update. The
sensitivity of the assessment to any suggested modifications to the assessment
framework needs to be examined. The TAWG can undertake these modifications
if they are judged to be straightforward. Otherwise, the TAWG should discuss
with TRAC the need for a benchmark review.
Participants also discussed additional that might require a benchmark review.
If it becomes evident that the assessment model is performing poorly e.g.
increasing retrospective pattern, a benchmark review would be warranted.
Consideration of new data or research results would not automatically require
a benchmark, unless deemed necessary after consultation between the TAWG
and TRAC.
The meeting also considered that, notwithstanding the above, a benchmark
review of the 5Z+6 and 5Zjm cod assessment frameworks should be held in February
2006 (e.g. at 5 year intervals).
CONSENSUS
BENCHMARK FORMULATIONS
5Z+6 Cod
Definition of the Management Unit
The management units employed for cod in the USA is primarily based on the
findings of Wise (1963) who concluded that four distinct stocks could be
recognized within the New England area, Georges Bank, Gulf of Maine, Southern
New England and the South Channel, and the New Jersey coastal cod. Operationally,
the Georges Bank management unit is defined as comprising cod in NAFO Division
5Z and Subarea 6 (Serchuk and Wigley 1992).
Estimation of Contemporary State
Characteristics of the fishery, including commercial landings and discards,
recreational catch, and sampling for length and age are summarized in O'Brien
and Munroe (2001). Sampling prior to 1978 is not considered sufficient to
derive a catch at age. Concern had been expressed about low sampling intensity
of the USA fisheries during the late 1990s. Although sampling intensity increased
to satisfactory levels in 2000, the market category, spatial and temporal
pattern of sampling needs some attention to ensure adequate coverage of all
components. The age composition is derived by the application of age length
keys to length frequencies, stratified by quarter and market category (USA
fishery) or gear (Canadian fishery).
While catch rates from the commercial fishery are examined, only the NMFS
fall, NMFS spring and DFO bottom trawl surveys are employed as indices of
abundance (O'Brien and Munroe 2001). The NMFS spring survey used a Yankee
41 net during 1978 to 1981 and a Yankee 36 net since 1982 and is treated
as two distinct series. All three surveys are conducted according to stratified
random designs and the indices are calculated using standard design based
estimators.
Estimates of population abundance in numbers at the beginning of the year
following the terminal year (the last year for which catch at age is available)
are obtained by calibrating a simple Virtual Population Analysis with the
three bottom trawl surveys. VPA models assume that errors in the observed
catch at age are negligible compared to errors in the abundance indices.
Such an assumption allows a deterministic application of the catch equation
recursively to derive the abundance of a year-class at any time given the
observed catch at age and an estimate of abundance for that year-class at
one point in time. The following formulation produced results that were most
consistent with observations and expected biological and fishery processes
(a indexes age and y indexes year):
Observations
Ca,y = catch at age for a = 1 to 9 and 10+ and y
= 1978 to terminal year
I1,a,y = NMFS fall survey for a = 0 to 5 and y
= 1977 to terminal year
I2,a,y = NMFS spring survey for a = 1 to 8
and y = 1978 to 1981
I3,a,y = NMFS spring survey for a = 1 to 8
and y = 1982 to terminal year +1
I4,a,y = DFO survey for a = 1 to 8 and y
= 1986 to terminal year +1
Spring survey abundance is related to the beginning of year VPA abundance
while the fall survey abundance is related to the subsequent year’s VPA abundance.
Parameters
a,y = ln abundance
for a = 1 to 9 in y = terminal year +1, and for a = 9
in y = 1997 to terminal year.
1,a = ln NMFS
fall survey catchability for a = 0 to 5.
2,a = ln NMFS
spring survey catchability for a = 1 to 8.
3,a = ln NMFS
spring survey catchability for a = 1 to 8.
4,a = ln DFO
survey catchability for a = 1 to 8.
Structural Conditioning
Natural mortality was assumed to be 0.2 for all ages and years.
Fishing mortality on age 9 for 1978 to 1996 was assumed to be equal to the
population number weighted average fishing mortality on ages 7 and 8.
Age 10+ was calculated using the catch equation and the fishing mortality
on age 9.
Error Conditioning
Catch at age error was assumed negligible compared to the index error.
Error on the ln index observations was assumed to be independent and
identically distributed.
Estimation
Parameters were obtained by minimizing the objective function
Characterization of Productivity to Determine Harvest Strategy
Yield per recruit analysis has been used to derive fishing mortality reference
points. Analyses using age aggregated surplus production models have also
been used to derive MSY reference points. Concerns were expressed about the
comparability of reference points derived from age aggregated models to the
estimates of current stock status derived from VPA. Age disaggregated analyses
of productivity and associated reference points are currently being investigated.
Procedure for Projections
Implementation of the bias corrected percentile method in the NMFS FACT
software and the use of survey weights to calculate population biomass would
make DFO and NMFS analyses more compatible and allow assessment results to
be more easily compared.
For short term projections, catch and stock weights at age, maturity ogives
and partial recruitment to the fishery should be averaged over a recent period
of stable patterns if there are no trends over time. If trends are detected,
suitable measures to reflect the most recent patterns should be applied.
For short-term projections, recruitment should be based on observations from
the most recent years with similar SSB or from the entire time period if
an SSB threshold is not evident.
Medium to long term projections were considered most useful for for evaluating
the relative performance of alternative harvest strategies. The utility of
long term projections for establishing explicit annual measures to achieve
rebuilding is considered less certain. Probability statements about medium
term forecasts should be considered conditional and not be taken as representing
the actual probabilities of eventual outcomes.
5Zjm Cod
Definition of the Management Unit
A review of tagging results and geographic distribution of survey catch
and commercial fishery catch indicated that some discontinuity between the
cod aggregations on eastern Georges Bank and those in the Great South Channel
and Cape Cod area. Operationally, the management unit was defined to be unit
areas 5Zj and 5Zm (Hunt 1990).
Estimation of Contemporary State
Characteristics of the fishery, including commercial landings and discards,
and sampling for length and age are summarized in Hunt and Hatte (2001).
Sampling prior to 1978 is not considered sufficient to derive a catch at
age. Concern has been expressed about low sampling intensity of the USA fisheries
during the late 1990s. Although sampling intensity increased to satisfactory
levels in 2000, the market category, spatial and temporal pattern of sampling
needs some attention to ensure adequate coverage of all components. The age
composition is derived by the application of age length keys to length frequencies,
stratified by quarter and market category (USA fishery) or gear (Canadian
fishery).
While catch rates from the commercial fishery and a longline industry survey
have been examined, only the NMFS fall, NMFS spring and DFO bottom trawl
surveys are employed as indices of abundance (Hunt and Hatte 2001). The NMFS
spring survey used a Yankee 41 net during 1978 to 1981 and a Yankee 36 net
since 1982 and is treated as two distinct series. All three surveys are conducted
according to stratified random designs and the indices are calculated using
standard design based estimators.
Estimates of population abundance in numbers at the beginning of the year
following the terminal year (the last year for which catch at age data are
available) were obtained by calibrating a simple Virtual Population Analysis
with the three bottom trawl surveys. VPA models assume that errors in the
observed catch at age are negligible compared to the errors in the abundance
indices. Such an assumption allows a deterministic application of the catch
equation recursively to derive the abundance of a year-class at any time
given the observed catch at age and an estimate of abundance for that year-class
at one point in time. The following formulation produced results that were
most consistent with observations and expected biological and fishery processes
(a indexes age and y indexes year):
Observations
Ca,y = catch at age for a = 1 to 10 and y = 1978
to terminal year.
I1,a,y = NMFS fall survey for a = 1 to 5 and y = 1978
to terminal year, occurring about 0.69 into each year.
I2,a,y = NMFS spring survey for a = 1 to 8
and y = 1978 to 1981, occurring about 0.29 into each year.
I3,a,y = NMFS spring survey for a = 1 to 8
and y = 1982 to terminal year, occurring about 0.29 into each
year.
I4,a,y = DFO survey for a = 2 to 7 and y
= 1986 to terminal year +1, occurring about 0.16 into each year.
Since projections for entire calendar years are required, the index
in terminal year + 1 was taken as occurring at the beginning of the
year.
This is a departure from the previous assessments in that DFO age 1 and
8 and NMFS fall age 0 are not used as indices.
Parameters
a,y = ln abundance
for a = 2 to 10 in y = terminal year +1, and for a = 10
in y = 1997 to terminal year.
1,a = ln NMFS
fall survey catchability for a = 1 to 5.
2,a = ln NMFS
spring survey catchability for a = 1 to 8.
3,a = ln NMFS
spring survey catchability for a = 1 to 8.
4,a = ln DFO
survey catchability for a = 2 to 7.
Structural Conditioning
Natural mortality was assumed to be 0.2 for all ages and years.
Fishing mortality on age 10 for 1978 to 1996 was assumed to be equal to the
population number weighted average fishing mortality on ages 8 and 9.
Age 10+ was calculated using the catch equation and fishing mortality on
age 9.
Error Conditioning
Catch at age error was assumed negligible compared to the index error.
Error on the ln index observations was assumed to be independent and
identically distributed.
Estimation
Parameters were obtained by minimizing the objective function
Characterization of Productivity to Determine Harvest Strategy
Yield per recruit analysis has been used to derive fishing mortality reference
points for the cod in management unit 5Zjm. Historically, the chance of good
recruitment (more than 5 million fish at age 1) has been higher when the
adult biomass is greater than a 25,000 t threshold. The objective of management
has been to rebuild the resource to be above this threshold.
Procedure for Projection to Evaluate Tactics
For short term projections, catch and stock weights at age, maturity ogives
and partial recruitment to the fishery should be averaged over a recent period
of stable patterns if there are no trends over time. If trends are detected,
suitable measures to reflect the most recent patterns should be applied.
Alternative TAC tactics are evaluated through risk analysis.