Did over-reliance on commercial catch rate data ...

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ICES Journal of Marine Science, 62: 1139e1149 (2005) doi:10.1016/j.icesjms.2005.04.009

Did over-reliance on commercial catch rate data precipitate the collapse of northern cod? Peter A. Shelton Shelton, P. A. 2005. Did over-reliance on commercial catch rate data precipitate the collapse of northern cod? e ICES Journal of Marine Science, 62: 1139e1149. It has been suggested that a number of ‘‘lessons’’ can be learned from the collapse of the northern cod stock oﬀ Newfoundland and Labrador. However, not all purported lessons have been validated with available data. One lesson is thought to be that over-reliance on commercial catch rate data and an incorrect assumption regarding the functional relationship between catch rate and population size were major contributors to overestimating stock size, precipitating the collapse. The current study describes calibration approaches used in assessments, and evaluates alternative functional relationships between commercial catch rates and stock size. In addition, historical population size is re-estimated using only research vessel data and compared with estimates obtained based on both commercial catch rate and research vessel data. Calibration with commercial catch rate contributed to overestimating stock size in some years, but there is no evidence that the assumed functional relationship between commercial catch rate and population size was a signiﬁcant factor in the collapse. Ó 2005 International Council for the Exploration of the Sea. Published by Elsevier Ltd. All rights reserved.

Keywords: catch rate, cod, collapse, model calibration, population estimation, stock assessment. Received 3 November 2004; accepted 4 April 2005. P. A. Shelton: Department of Fisheries and Oceans, Northwest Atlantic Fisheries Centre, PO Box 5667, St John’s, Newfoundland, Canada A1C 5X1; tel: C1 709 7722341; fax: C1 709 7724105; e-mail: [email protected].

Introduction The northern cod (Gadus morhua) stock oﬀ Newfoundland and Labrador (NAFO Divisions 2J C 3KL; Figure 1) collapsed precipitously in the late 1980s and early 1990s and has not recovered. It has become the classic case study of the failures of ﬁsheries science and management to ensure sustainability of a commercially exploited ﬁsh population, despite availability of a considerable amount of scientiﬁc data. It has been suggested that many ‘‘lessons’’ can be learned from this case study (Hilborn and Walters, 1992; Hutchings and Myers, 1994; Hutchings, 1996; Walters and Maguire, 1996), but not all purported lessons have been carefully validated with available data. One lesson is thought to be that over-reliance on commercial catch rate data combined with an incorrect assumption regarding the functional relationship between commercial catch rate (CR) and population size was a major contributor to overestimating stock size, and precipitated the collapse (Hilborn and Walters, 1992; Hutchings and Myers, 1994; Hutchings, 1996; Walters and Maguire, 1996; Rose and Kulka, 1999). There is prima facie evidence that this was 1054-3139/$30.00

the case. Commercial catch rates were used extensively in the calibration of northern cod population models by DFO (Canadian Department of Fisheries and Oceans) and NAFO (Northwest Atlantic Fisheries Organization) scientists over the period from extension of jurisdiction to 200 nautical miles in 1977 up to the moratorium on directed ﬁshing in 1992 (Bishop and Shelton, 1997). It is known that assessments overestimated the size of the stock through the 1980s (Sinclair et al., 1991). It is also well known that progressive improvement in ﬁshing techniques through learning and technological advancement (Hilborn and Walters, 1992), interaction between the heterogeneity in ﬁsh distribution and searching activities of ﬁshers (Paloheimo and Dickie, 1964), and abundance-dependent expansion and contraction of range (MacCall, 1990) can all cause departures from a strictly proportional relationship of the form y Z bx between a CR index y and stock size x. In the case of northern cod, it has been claimed that the relationship between CR and stock size could best be described by a power function, y Z bxc, with c in the range 0.4e0.5 (Hutchings and Myers, 1994; Walters and Maguire, 1996). A power model with c ! 1 corresponds to CR remaining relatively high when a population declines,

Ó 2005 International Council for the Exploration of the Sea. Published by Elsevier Ltd. All rights reserved.

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P. A. Shelton

Figure 1. Boundaries of NAFO Divisions 2J, 3K, and 3L over which the northern cod stock is distributed. Division 2J is oﬀ Labrador, and 3K and 3L are oﬀ Newfoundland. Also shown are the 400-m bottom contour and the 200-nautical mile jurisdictional limit.

the so-called ‘‘hyperstability’’ phenomenon (Hilborn and Walters, 1992). The purported incorrect assumption of a strictly proportional relationship between CR and stock size by assessment scientists, instead of a power model, has been stated to be a prime factor in the overexploitation and collapse of northern cod (Hutchings and Myers, 1994; Hutchings, 1996; Walters and Maguire, 1996). The purpose of the present study is to go beyond the prima facie evidence and to look at how CR data were actually used and what eﬀect this may have had on the estimates of population size. There are three parts to this study: (i) a brief review of approaches taken in assessments to calibrate models of northern cod with CR and research vessel (RV) data; (ii) an exploration of the relationship

between CR and stock size; and (iii) retrospective analyses of estimates of population size based only on RV data, compared with the original assessments based on CR and RV data. Conclusions are then drawn regarding the actual role of CR data in assessments of northern cod.

Calibration approaches applied in assessments The approach used in annual stock assessments to derive population estimates for northern cod from CR and RV data varied from year to year, and evolved over time. The inﬂuence of these methodological changes cannot be

Commercial catch rate data and the collapse of northern cod ignored in interpreting the role of CR data in the estimation of population size. Assessment approaches between 1977 and 1993 are described in Bishop and Shelton (1997), based on details provided in annual assessment documents. Major methodological changes relevant to this study are summarized in Table 1. As methodologies improved and more data became available, assessments evolved from an ad hoc exploration of alternative values of terminal ﬁshing mortality (Ft) using virtual population analysis (VPA; Quinn and Deriso, 1999) to the use of a formal statistical framework (ADAPT; Gavaris, 1988). Starting in 1980, VPA calibration was based on regression models of standardized CR against various measures of stock size (Table 1). Standardized CR was obtained by applying a general linear model to logtransformed data (a multiplicative model), controlling for factors such as country, gear, month, and division (Gavaris, 1980). From 1980 to 1987, the regression model applied in the calibration was an intercept model, y Z a C bx, where y is the standardized CR, x a measure of stock size, a the intercept, and b deﬁnes the slope of the relationship between CR and stock size. Baird et al. (1991) reported that criteria for selecting Ft from the intercept model over this period were some combination of (i) highest r2, (ii) pattern of residuals (particularly for the most recent data points in the regression), and (iii) closeness of the intercept to the origin. These three criteria played varying roles in the decision on the appropriate Ft value, and assessment documents routinely reported that Ft was selected based on the value that ‘‘agreed best with the data’’. In practice, r2 and intercept values were often similar across a range of Ft, making the choice somewhat arbitrary. In all years, the ﬁnal model included an intercept. Ft resulting in the smallest intercept was adopted by default only when highest r2 cooccurred with the smallest intercept (e.g. 1983). Once ADAPT was introduced in 1988, a log zero-intercept model, ln(y) Z ln(bx), was routinely applied. In 1982 a major change was introduced into the assessment. Rather than treating the CR data as a single series from 1962 onwards, concerns over changes in catchability caused by changes in the ﬁshing ﬂeets after extension of jurisdiction in 1977 led to separate standardizations of CR data for the periods 1962e1979 and 1979e1982. The two series were then joined by scaling each relative to the common 1979 value. Also in 1982, preliminary RV data for part of the stock area were evaluated as an index, but the ﬁnal calibration was based only on CR data. In 1984, RV data began to inﬂuence the scientiﬁc advice from the assessment for the ﬁrst time, and Ft was chosen by averaging the values that maximized r2 from separate intercept models ﬁtted to CR and RV data. In 1985, a change in the way CR data for the two time periods were combined was introduced. Rather than scaling by 1979 values, scaling was based on both 1978 and 1979 data. A second calibration was run with data only from 1977 on, because of concerns regarding changes in catchability.

1141

Results from the second calibration only were used as the basis for scientiﬁc advice in 1985. In 1986, the use of age-aggregated population numbers rather than biomass was introduced in the calibration with RV data. Again two separate calibrations were run, the ﬁrst with CR data for 1962e1985, and the second with CR data for 1979e1985. Both calibrations were considered in providing scientiﬁc advice. From 1987 on, the CR data prior to 1978 were no longer used in the assessment because of concerns about joining the time-series spanning the periods before and after extension of jurisdiction. In 1988, the ADAPT framework was implemented, and CR and RV indices were included in a single minimization. The RV index was age-disaggregated for the ﬁrst time, and consequently received eﬀectively seven times more weight in the sums of squares minimization than the age-aggregated CR index. In 1989, separate ADAPT formulations were applied to CR and RV data, and Ft was determined as the average from the two analyses. This had the eﬀect of giving the CR and RV data equal weight in the estimation. Over the period 1990e1992, CR data were age-disaggregated and combined with age-disaggregated survey data in a single ADAPT formulation. CR data were not included in the ﬁnal model used as a basis for providing scientiﬁc advice in 1992, and were dropped completely from the assessment in 1993.

Methods Relationship between catch rate and stock size Four models of the relationship between CR and stock size were considered in the present study: y Z a C bx (intercept model), y Z bx (zero-intercept model), y Z bxc (power model), and ln(y) Z ln(bx) (log zero-intercept model). The intercept, zero-intercept, and power models are all nested within the full model y Z a C bxc. The zero-intercept model is in turn nested within both power and intercept models. The intercept model was used to calibrate the VPA from 1980 to 1987, after which the log zero-intercept model was applied within the ADAPT framework. Hutchings and Myers (1994) asserted that a power model was the more appropriate model to apply to northern cod commercial CR data. This assertion was examined for data from the 1980 to 1987 assessments by applying an F test for nested models (a Z 0.05). Zero-intercept, intercept, and power models were applied to the actual CR series from each assessment, using assessment-speciﬁc measurement units of stock size (i.e. 4C biomass, exploitable biomass, mid-year exploitable biomass, mid-year oﬀshore exploitable biomass, or beginning of year population numbers at age; Table 1), and assuming additive normal error. Stock size from the last VPA-based assessment of northern cod (Bishop et al., 1993) was used as the x-variable in the evaluation. This assessment used only RV data in the calibration of ADAPT. In the 1988e1991 assessments, a log zero-intercept model, assuming lognormal multiplicative error, was

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Table 1. Methodological changes in the calibration of the VPA in northern cod stock assessments from 1977 to 1993. Catch rate (CR) gear type comprised otter trawl and paired trawl from 1997 to 1981, but only otter trawl thereafter. Tonnage class varied somewhat, but was generally in the range 150 to O2000 grt. Ft Z terminal ﬁshing mortality. The use of research (RV) data is indicated by Y (yes) and N (no). Two calibrations were carried out in 1985 and 1986, indicate by the superscripts ‘‘a’’ and ‘‘b’’, respectively. Year

Model

CR Span

Y

RV

1977

y Z a + bx

1959e1975

Spain, Portugal

Fishing mortality

Fishing eﬀort

N

Range of Ft explored, taking into account the r2 in choice of ﬁnal Ft.

1978

y Z a + bx

1963e1973

USSR, Spain

Fishing mortality

Fishing eﬀort

Y

Range of Ft explored, taking into account the r2 in choice of ﬁnal Ft. RV not used in the ﬁnal estimates.

1979

y Z a + bx

1963e1973

USSR, Spain

Fishing mortality

Fishing eﬀort

N

Range of Ft explored, taking into account the r2 in choice of ﬁnal Ft.

1980

y Z a + bx

1962e1977, excluding 1974e1976

Spain, Portugal, Canada, USSR, UK, Iceland

4+ biomass

Standardized CR

N

Range of Ft explored, Ft with highest r2 selected.

1981

y Z a + bx

1962e1978, excluding 1974e1976

Spain, Portugal, Canada, USSR, FRG, GDR, UK

4+ biomass

Standardized CR

N

Range of Ft explored, Ft with highest r2 selected.

1982

y Z a + bx

1962e1979, excluding 1974e1976

Portugal, Canada

Exploitable biomass

Standardized CR

Y

1979e1982

Canada

1962e1979, excluding 1974e1976

Portugal, Canada, Spain

Mid-year exploitable biomass

Standardized CR

N

Separate regressions for RV index against 4+ biomass and CR against exploitable biomass. Two CR series joined by scaling by the 1979 value Ft selected that ‘‘agreed best with the data’’ based on CR data only. Range of Ft explored, Ft with highest r2 selected. Two CR series joined by scaling by the 1979 value.

1979e1982

Portugal, Canada Portugal, Canada, Spain

Mid-year oﬀshore exploitable biomass

Standardized CR

Y

Separate regressions for CR and RV data. CR series joined by scaling with the 1979 value. Ft chosen as the average of of the Ft values that maximized r2 for the two calibrations.

Mid-year oﬀshore exploitable biomass

Standardized CR

Y

Y

Separate regressions for CR and RV data. CR series joined by scaling with the 1978 and 1979 values. Two regressions with CR data e ﬁrst with 1962e1984 and second with 1977e1984. Only second used in advice. Ft that ‘‘agreed best with the data’’ selected. Separate regressions for CR and RV data. Two regressions with CR data e ﬁrst with 1962e1985 and second with 1979e1985. Both used in advice period. Ft that ‘‘agreed best with the data’’ selected.

1983

1984

y Z a + bx

y Z a + bx

1962e1979

1979e1983 1985

1986

1987

y Z a + bx

y Z a + bx

y Z a + bx

1962e1984a

CR Source

Portugal, Canada Portugal, Canada, Spain

X

1977e1984b

Portugal, Canada

1962e1985a

Portugal, Canada, Spain

Mid-year oﬀshore exploitable biomass

Standardized CR

1979e1985b

Portugal, Canada

Standardized CR

1978e1986

Portugal, Canada

Mid-year oﬀshore exploitable biomass Mid-year oﬀshore exploitable biomass

Standardized CR

Y

Calibration

Separate regressions for CR and RV data. Ft that ‘‘agreed best with the data’’ selected. (continued)

Commercial catch rate data and the collapse of northern cod

1143

Table 1 (continued) Year

Model

CR Span

CR Source

X

Y

1988

ln(y) Z ln(bx)

1978e1987

Canada, Portugal, Spain

Mid-year oﬀshore exploitable biomass

Standardized CR

Y

ADAPT applied to CR and RV data in a single formulation. RV index age-disaggregated for the ﬁrst time.

1989

ln(y) Z ln(bx)

1978e1988

Canada, Portugal, Spain

Mid-year oﬀshore exploitable biomass

Standardized CR

Y

Separate ADAPT runs carried out with CR and RV data, Ft averaged.

1990

ln(y) Z ln(bx)

1983e1989

Canada, Portugal, Spain

Beginning of year numbers at age

CR at age ages 5e8

Y

ADAPT applied to CR and RV data in a single formulation. CR data age-disaggregated.

1991

ln(y) Z ln(bx)

1983e1990

Canada, Portugal, Spain

Beginning of year numbers at age

CR at age ages 5e8

Y

ADAPT applied to CR and RV data in a single formulation. CR data age-disaggregated.

1992

Y

ADAPT applied to RV data only.

1993

Y

ADAPT applied to RV data only.

applied using ADAPT. The ﬁt of this model was compared graphically with the ﬁt of a power model for this period. Although not used in the actual assessments, zero-intercept and power models were compared statistically for the 1988e1991 data to evaluate whether a power model provided a better ﬁt.

Retrospective analysis Retrospective analysis denotes an examination of change in successive estimates of ﬁshery variables such as population size (Sinclair et al., 1991; Mohn, 1999). In this study, annual assessments over the period 1977e1993 were replicated using terminal ﬁshing mortality estimated in the ﬁnal assessment model in each year, and resulting estimates of 4C population size were plotted to examine the retrospective pattern. This exercise was then repeated using only RV estimates for 1982 and 1984e1991 to determine terminal ﬁshing mortality (an RV index was not considered in the original 1983 assessment). This required re-estimation of Ft using RV data for those assessments for which separate calibrations were not carried out at the time of the original assessments (1988, 1990, 1991). The relative retrospective patterns from calibrations with and without CR data were then compared.

Results Relationship between catch rate and stock size Sums of squares (SS) for the ﬁt between the CR data from each assessment between 1980 and 1987 and the baseline

RV

Calibration

estimate of stock size from the 1993 assessment (most recent estimates of population trajectory) were computed for zero-intercept, intercept, and power models (Table 2). In most cases, the SS for intercept and power models were similar and provided signiﬁcantly better ﬁts to the data than the simpler zero-intercept model (P13 and P23 % 0.05). In ﬁve of the comparisons, the power model had a slightly smaller SS than the intercept model (1980, 1981, 1983, Table 2. Summary statistics for the comparison of three catch rate models for the period 1980e1987: (i) y Z a C bx; (ii) y Z bxc; (iii) y Z bx. SS1e3 corresponds to the residual sums of squares for the respective models. The probability values associated with the F ratio test for nested models are denoted by P13 for the comparison of model (i) with model (iii), and by P23 for the comparison of model (ii) with model (iii). The estimate of the exponent c for model (ii) is given in the last column. In 1985 and 1986, two separate catch rate calibrations were carried out, denoted by superscripts ‘‘a’’ and ‘‘b’’ (see Table 1). Year

SS1

SS2

SS3

P13

P23

c

1980 1981 1982 1983 1984 1985a 1985b 1986a 1986b 1987

0.250 0.793 0.223 0.868 1.335 3.041 0.279 4.868 5.985 6.094

0.230 0.756 0.223 0.826 1.370 3.100 0.273 4.828 6.000 6.103

0.502 1.782 0.454 2.060 4.560 12.926 0.323 18.964 6.080 6.326

0.003 0.003 0.001 !0.001 !0.001 !0.001 0.372 !0.001 0.790 0.621

0.002 0.001 0.001 !0.001 !0.001 !0.001 0.338 !0.001 0.807 0.629

0.718 0.642 0.593 0.562 0.411 0.283 1.305 0.227 1.233 1.216

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P. A. Shelton

Catch rate index

3.5

3.5

1980

3.0

1981

3.0

2.5

2.5

2.0

2.0

1.5

1.5

1.0

1.0

0.5

0.5 0.0

0.0 0.0

0.5

1.0

1.5

2.0

2.5

3.0

0.0

Biomass aged 4+ (millions of tonnes)

Catch rate index

3.0

3.0

1983

2.5

2.0

1.5

1.5

1.0

1.0

0.5

0.5 1.0

1.5

2.0

0.0

Catch rate index

2.0

2.5

3.0

1985b

1.5 1.0 0.5 0.0 0.1

0.2

0.3

0.4

Mid-year offshore exploitable biomass (millions of tonnes)

0.5

1.0

1.5

2.0

Mid-year offshore exploitable biomass (millions of tonnes) 3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0

2.5

0

1.5

0.0 0.5

Mid-year exploitable biomass (millions of tonnes)

2.0

1.0

1985a

2.5

2.0

0.0 0.0

0.5

Biomass aged 4+ (millions of tonnes)

1986a

0.0

0.5

1.0

1.5

2.0

Mid-year offshore exploitable biomass (millions of tonnes)

Figure 2. Comparisons of the ﬁt for the zero-intercept model (broken line), intercept model (solid line), and power model (dotted line) for those cases (1980, 1981, 1983, 1985b, and 1986a) where the power model had a slightly lower SS than the intercept model (p % 0.05). Also included is the plot for the 1985a calibration. The 1985a and 1986a calibrations resulted in the largest diﬀerence in SS between the zero-intercept model and the two more complex models. The data points are catch rate index values plotted against estimates of stock biomass obtained from the 1993 assessment.

1985b, and 1986a), but both models gave similar ﬁts to the data (Figure 2). In nearly all cases, the zero-intercept model predicted lower CR at low stock size than the intercept and power models. This would lead to larger estimates of stock sizes in the VPA when stock size was actually low. The largest diﬀerence in SS between the zero-intercept model and the two more complex models occurred in the 1985a and 1986a calibrations (Table 2). In both cases the zerointercept model ﬁtted the data poorly, under-predicting CR at low stock size, and over-predicting it at large stock size (Figure 2). Model ﬁts for the intercept and power models were similar in both cases. Graphical comparison of log zero-intercept, zero-intercept, and power models to data from the 1988 to 1991 assessments showed that ﬁts were similar (Figure 3; only age 6 model ﬁts are plotted as examples for the agedisaggregated 1990 and 1991 assessments e other ages gave similar results). The biggest diﬀerence in predicted CR overall between the two models was in 1991 for age 6. Statistical comparison of zero-intercept and power models showed that, in all cases, the reduction in SS achieved by adding the exponent was not signiﬁcant (Table 3).

Retrospective analysis The abundance of the 4C population estimated in the original assessments shows that substantial downward revisions were common (Figure 4a). A number of these revisions coincided with methodological changes in the assessment described in Table 1, but revisions also reﬂect variations in indices used to calibrate the VPA and retrospective errors from unknown sources (e.g. catch under-reporting). Both CR and RV series used in calibration went through a number of changes between 1985 and 1989, beyond merely the addition of a survey data point for each subsequent assessment (Bishop and Shelton, 1997). There were downward revisions of VPA and ADAPT estimates also when calibration was performed with RV data only, but the magnitude was less (Figure 4b). Ratios of the original assessment estimates of the 4C population to estimates based only on RV data in the calibration (Figure 4c) showed that diﬀerences were greatest in 1985, 1986, and 1989. The simplest explanation for large ratios in 1985 and 1986 is the diﬀerence in CR and RV trends over this period

Commercial catch rate data and the collapse of northern cod

Catch rate index

7

8

6

7

1988

1989

6

5

5

4

4

3

3

2

2

1

1

0 0.10

0.15

0.20

0.25

0.30

0.35

0 0.10

Offshore explolitable biomass (millions of tonnes) 30

Catch rate index

1145

0.15

0.20

0.25

0.30

0.35

Offshore exploitable biomass (millions of tonnes) 35

25

30

1990 Age 6

1991 Age 6

25

20

20

15

15

10

10

5

5

0

0 100

50

150

200

Numbers of fish aged 6 (millions)

0

50

100

150

200

Numbers of fish aged 6 (millions)

Figure 3. Comparisons of the ﬁt for the zero-intercept model (broken line), log zero-intercept model (solid line), and power model (dotted line) to data from the 1988 to 1991 assessments. Only age 6 model ﬁts are plotted for the age-disaggregated 1990 and 1991 calibrations (other ages gave similar results). The data points are catch rate index values plotted against estimates of either oﬀshore exploitable biomass or numbers of ﬁsh aged 6 from the 1993 assessment.

(Figure 5). Whereas the age-aggregated RV index had begun to decline after 1981, the CR index continued to increase until 1985. However, comparison is complicated by the fact that the RV index in the 1985e1987 assessments was based on ﬁsh aged 6C, whereas the CR index was derived from oﬀshore commercial catches, in which there were considerable quantities of ﬁsh aged 4 and 5. Table 3. Summary statistics for the comparison of two catch rate models for the period 1988e1991: (i) y Z bxc; (ii) y Z bx. SS1 and SS2 are the residual sums of squares for the respective models. P12 is the probability value associated with the F ratio test for comparing model (i) with model (ii). c is the parameter estimate for the exponent in model 1. Agg Z age aggregated. Year

Age

SS1

SS2

P12

c

1988 1989 1990

Agg Agg 5 6 7 8 5 6 7 8 9 10 11 12

9.831 19.491 19.385 20.129 31.093 17.692 88.781 45.613 67.365 64.752 12.461 2.160 0.639 0.132

9.847 19.527 20.458 25.004 35.099 19.103 122.000 79.359 72.539 66.127 14.270 2.552 0.669 0.160

0.911 0.900 0.621 0.321 0.459 0.555 0.185 0.080 0.523 0.733 0.387 0.337 0.617 0.329

1.065 0.934 0.877 0.831 1.213 1.279 0.514 0.633 0.807 0.814 0.639 0.774 0.864 1.292

1991

The 1993 assessment baseline estimates indicate that the 4C population only stopped increasing in 1985, consistent with the CR series. Although the general trends between the CR index and the 1993 assessment estimates of population size were reasonably consistent when age composition is taken into account, the magnitude of the post-1977 increase in the CR index was considerably greater than the population increase indicated by the 1993 assessment. A large 1986 RV index value resulted in a considerable upward revision in the size of the stock in the 1987 assessment (Figure 4a). When combined with the decline in CR in 1986, this resulted in a smaller ratio between estimates from the two calibrations for 1987 (Figure 4c), although in retrospect, both estimates were much too high. A sequence of major downward revisions in estimates of the size of the stock occurred in the 1988e1993 assessments (Figure 4a). The ADAPT framework was used for the ﬁrst time in 1988. Data available in this assessment showed that the RV index had dropped considerably from the high 1986 value for nearly all ages used in the calibration, and the CR index had continued to decline for a second year (Figure 5). Because the indices had both declined and the ADAPT assessment gave eﬀectively more weight to the age-disaggregated RV data, estimates of the 4C population for 1987 using only RV data and those obtained from the original 1988 assessment based on both CR and RV data were quite similar. In the 1989 assessment, the age-aggregated CR series and the age-disaggregated RV index were applied in separate ADAPT runs, and the estimates of Ft were averaged, eﬀectively giving both

1146

P. A. Shelton 1983

Millions of fish aged 4+

1980

1200

1984

1985 1986

1981

1000 800

Discussion

a

1987

1400

1988 1977

1989

1991 1992

1990

600 400

1993

200 0 1975

1980

1985

1990

1995

Year

b

Millions of fish aged 4+

1400 1200

1987

1984

1000 1985

800

1988

1982

600

1991

1992

1986

400 1993

200 0 1975

1980

1985

1990

1995

Year

Ratio Original/RV

2.0

c

1986

1.8 1.6 1985

1989

1.4 1.2

1984

1987

0.8 1970

1988 1991 1990 1992

1.0

1975

1980

1985

1990

1995

Year

Figure 4. Retrospective estimates of (a) 4C population size for the original assessments, (b) population size estimated from calibrating the VPA with research vessel (RV) data only, and (c) ratios of the population estimates from the original assessments to the RV-based estimates. Year labels refer to the assessment year.

indices equal weight. In this assessment, 1986 and 1987 CR index values were revised upwards, and with the addition of the 1988 value, this gave an increasing trend in the CR series, in contrast with the RV index, which remained low for a second year (Figure 5). The diverging indices and the approach of averaging the estimates between the separate calibrations with the RV and CR data resulted in the CR data having considerable inﬂuence in the 1989 assessment relative to the previous assessment, giving the strongest evidence of CR data being misleading over the period of the cod collapse. Although there were further major revisions in the estimates of population size over the period 1990e1993, CR data had negligible impact in the 1990 and 1991 assessments, and were not used to calibrate ADAPT in 1992 and 1993.

The widespread failure of ﬁsheries management to maintain sustainable harvests of marine ﬁsh resources is epitomized by the case of the northern cod stock oﬀ Newfoundland. Reasons for this failure are still analysed and debated, reﬂecting a desire on the part of the ﬁsheries science community to learn from mistakes. While the stock was still collapsing, it was recognized by scientists doing the assessments that population size had been overestimated, and a major downward revision was presented in the 1988 assessment (Baird et al., 1991). Three explanations were provided for the overestimation: too much weight given to misleading CR data, inﬂuence of the 1986 RV index outlier, and the use of subjective calibration methods prior to 1988. Of these three shortcomings, misleading CR data has received the most attention. Hilborn and Walters (1992) expressed an opinion that cod biologists had been misled by increasing CR values attributable to increased harvesting eﬃciency rather than increased stock abundance following extension of jurisdiction in 1977. Hutchings and Myers (1994) endorsed this view, suggesting that increased ability to locate large assemblages of ﬁsh coupled with apparent increased concentration of northern cod in the 1980s had led to a non-linearity between CR and exploitable biomass, which could best be captured by a power curve. They concluded that the assumption of a strictly proportional relationship between CR and stock size in assessments was a prime factor in the overexploitation and collapse of the northern cod stock. Based on the 1993 assessment baseline estimates, the 4C population did in fact increase from extension of jurisdiction in 1977 until 1985. However, the decline that began after 1986 was not detected until the 1988 assessment. CR data contributed somewhat to overestimation in the 1987 and 1988 assessments, but the impact was much larger in the 1989 assessment. In that assessment, the CR index suggested that the stock was beginning to increase again, whereas the RV index did not. The inﬂuence of the 1989 assessment on management decisions is considered further below. The impact of CR data on the 1990 and 1991 assessments was negligible, and from the 1992 assessments on, CR data were not used to calibrate the ADAPT. Although the impact of CR data was substantial in only a few years during the decline and collapse of northern cod, the question remains whether or not the use of a more appropriate functional form of the CR-population size relationship, such as a power model, would have reduced overestimation. Hutchings and Myers (1994) examined the appropriateness of the power model for data from two time periods: 1962e1981 and 1982e1991. Data for the ﬁrst time period correspond with the index of stock size used for calibrating the VPA in the 1982 assessment. However, the analysis by Hutchings and Myers (1994) diﬀers from that actually applied in the 1982 assessment in a number of

Commercial catch rate data and the collapse of northern cod

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Figure 5. Indices applied in the calibration of the VPA in assessments over the period 1985e1989. The CR index (C) is for mid-year oﬀshore exploitable biomass, and the RV index (O) is for the number of age 6C ﬁsh in the survey for the 1985e1987 assessments, and the sum of population numbers for ages 3e9 for the 1988e1989 assessments. Note that there were methodological changes in the computation of indices between assessments.

important respects. They used CR values from a preliminary analysis carried out by the NAFO Scientiﬁc Council in June 1982, rather than data from the ﬁnal assessment, which took place in September 1982. Concerns were expressed at the June 1982 meeting that high CR values in 1980 and 1981 may have resulted from increased availability and not from increased abundance, and concerns were also expressed that catchability may have changed through increased eﬃciency after 1973 (Bishop and Shelton, 1997). For those reasons, data for the periods 1962e1979 and 1979e1982 were standardized separately (Bishop and Shelton, 1997). The two standardized series were then joined by scaling with the common 1979 value. This had the eﬀect of decreasing the 1979e1981 CR values compared with the data analysed by Hutchings and Myers (1994). Further, in the calibration of the VPA in the assessment, data points for 1974e1976 were eliminated as outliers, whereas those data were included in the analysis by Hutchings and Myers (1994). In their analysis Hutchings and Myers compared a zerointercept and a power model ﬁt, and concluded that a power model provided a signiﬁcantly better ﬁt. In the actual

assessment, an intercept model was ﬁtted. In the present analysis, both the intercept and power models provided signiﬁcantly better ﬁts to the data than the zero-intercept model (a Z 0.05), but the SS for intercept and power model ﬁts were nearly identical and there were negligible diﬀerences between predicted values from the two models. The present study therefore concludes that the assessment would have been no diﬀerent had a power model been used in the calibration rather than an intercept model. This conclusion also holds for other assessments over the period 1980e1987, corresponding to the period when ad hoc VPA calibration methods were used. Catch rate data from the second time period analysed by Hutchings and Myers (1994), 1982e1991, do not correspond to any CR data series used in an actual stock assessment. The closest match is from the 1991 assessment, the last in which CR data were used in the calibration of the VPA. In that assessment, age-disaggregated CR data for ages 5e12 for the period 1983e1990 were applied in an ADAPT formulation. Hutchings and Myers (1994) used an age-aggregated index of CR and compared zero-intercept

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and power models. The actual model used in the assessment was a log zero-intercept model [ln(y) Z ln(bx)]. In the present analysis, the zero-intercept and power models were compared on an age-by-age basis for the 1991 assessment data, and for none of the ages were the reduction in SS achieved by the power model signiﬁcant. Graphical comparison of the log zero-intercept model and power model for CR data from the 1988 to 1991 assessments suggested little diﬀerence in predicted CR. It is therefore concluded that the assessment outcome would not have been diﬀerent had a power model been used over the period 1988e1991. Walters and Maguire (1996) endorsed the view that an erroneous assumption that CR data accurately reﬂected changes in abundance led to gross overestimation of the size of the northern cod stock and was partly to blame for the collapse. They concluded that assessors were ‘‘badly wrong’’ in assuming a ‘‘strictly proportional relationship (y Z bx)’’ to abundance, citing the ﬁndings of Hutchings and Myers (1994) that a power relationship with an exponent in the range 0.4e0.5 was applicable. Walters and Maguire (1996) were unaware that an intercept model was used in the assessments and that a power model would have given almost identical estimates to the intercept model. MacCall (1999) also overlooked the details of the approach actually taken in the assessments in forming an opinion that the northern cod collapse provided a ‘‘notorious recent example’’ of the problem of non-linear catch per unit eﬀort relationship, citing the ﬁndings of Hutchings (1996) related to hyperstability in the CR index, which were based on Hutchings and Myers (1994). The role of CR data in the collapse of northern cod has therefore been widely misinterpreted. Although the intercept model used in the assessments over the period of ad hoc tuning does not have a mechanistic justiﬁcation, it nevertheless provided a reasonable approximation to the functional relationship between CR and stock size within the range of the data, and did not lead to overestimation of population size through model mis-speciﬁcation, as suggested by Hutchings and Myers (1994). This does not mean that a power model of the relationship between CR and stock size is not more appropriate in most cases. There is evidence from this stock and others that a power relationship with an exponent !1 is commonly applicable to modelling CR data. For most of the northern cod annual assessment data sets between 1980 and 1987 examined in this study, the exponent was signiﬁcantly less than 1.0. These analyses were carried out under the assumption that the independent variable (1993 assessment estimates of stock size) was known precisely, and that the error in CR was normally distributed, to be consistent with the approach taken in the stock assessments and by Hutchings and Myers (1994). Recently Harley et al. (2001) carried out a meta-analysis of 297 CR data sets and, based on observation error and random eﬀects models, found strong evidence of hyperstability (exponent ! 1). In contrast with

the 1980e1987 calibrations, there was little statistical evidence in the present study of hyperstability in the northern cod CR data used in the ADAPT calibrations over the period 1988e1991. This result is somewhat unexpected given that the ﬁshing ﬂeet was able to target remaining oﬀshore aggregations of northern cod until just before the moratorium (Rose and Kulka, 1999; Shelton and Lilly, 2000). It may reﬂect management measures to spread ﬁshing eﬀort, noise in the data, and the short CR time-series used in the 1990 and 1991 assessments. Although there is no evidence to support the contention of Hutchings and Myers (1994) that the assumption of an inappropriate functional relationship between CR and stock size was a prime factor in the overexploitation and collapse of the northern cod stock, it is nevertheless true that recovery of the stock following extension of jurisdiction was overestimated, detection of decline lagged actual decline, and the extent of the decline was underestimated. Use of CR data contributed to these errors. Overestimation in the 1989 assessment stands out, because much smaller estimates of stock size would have been obtained had CR data not been used in the calibration. One can speculate as to whether or not a lower estimate of stock size in 1989 would have had an impact on the management decisions taken then. Fishing mortality levels, although above the F0.1 target and increasing through the early to mid-1980s, were not out of control, and simulations suggest that, had the F0.1 control rule been followed, the stock would not have collapsed, despite the retrospective problem (Shelton, 1998). However, the F0.1 control rule was discarded by ﬁshery managers in 1989 in favour of Fstatus quo, which resulted in a fully recruited F O 1.0. Subsequent stepwise reductions in TAC were ineﬀective in preventing F rising to O3.0 in 1992, when the moratorium was declared. While a more pessimistic assessment in 1989 might have had some eﬀect, there was a strong reluctance at the time to reduce the TAC to the extent indicated by the scientiﬁc assessments. The apparent disappearance of the 1986 and 1987 year classes (Shelton and Lilly, 2000) led to major retrospective errors in the assessment over this period, which were independent of CR data, but by that time, management decisions were not based on scientiﬁc assessments and ﬁshing mortality was out of control.

References Baird, J. W., Bishop, C. A., and Murphy, E. F. 1991. Sudden change in the perception of stock size and reference catch levels for cod in northeastern Newfoundland shelves. Northwest Atlantic Fisheries Organization Scientiﬁc Council Studies, 16: 111e119. Bishop, C. A., Murphy, E. F., Davis, M. B., Baird, J. W., and Rose, G. A. 1993. An assessment of the cod stock in NAFO Divisions 2J C 3K, NAFO SCR Document, 93/86. Bishop, C. A., and Shelton, P. A. 1997. A narrative of NAFO Divs. 2J3KL cod assessments from extension of jurisdiction to moratorium. Canadian Technical Report of Fisheries and Aquatic Sciences, 2199: 66 pp.

Commercial catch rate data and the collapse of northern cod Gavaris, S. 1980. Use of a multiplicative model to estimate catch rate and eﬀort from commercial data. Canadian Journal of Fisheries and Aquatic Sciences, 37: 2272e2275. Gavaris, S. 1988. An adaptive framework for the estimation of population size. Canadian Atlantic Fisheries Scientiﬁc Advisory Committee Research Document, 88/29. Harley, S. J., Myers, R. A., and Dunn, A. 2001. Is catch-per-uniteﬀort proportional to abundance? Canadian Journal of Fisheries and Aquatic Sciences, 587: 1760e1772. Hilborn, R., and Walters, C. 1992. Quantitative Fisheries Stock Assessment and Management: Choice, Dynamics and Uncertainty. Chapman & Hall, New York. 604 pp. Hutchings, J. A. 1996. Spatial and temporal variation in the density of northern cod and a review of hypotheses for the stock’s collapse. Canadian Journal of Fisheries and Aquatic Sciences, 53: 943e962. Hutchings, J. A., and Myers, R. A. 1994. What can be learned from the collapse of a renewable resource? Atlantic cod, Gadus morhua, of Newfoundland and Labrador. Canadian Journal of Fisheries and Aquatic Sciences, 51: 2126e2146. MacCall, A. D. 1990. Dynamic Geography of Marine Fish Populations. University of Washington Press, Seattle. 153 pp. MacCall, A. D. 1999. Use of decision tables to develop a precautionary approach to problems in behaviour, life history and recruitment variability. Proceedings of the 5th NMFS NSAW. NOAA Technical Memorandum, NMFS-F/SPO-40: 43e64.

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Mohn, R. 1999. The retrospective problem in sequential population analysis: an investigation using cod ﬁshery and simulated data. ICES Journal of Marine Science, 56: 473e488. Paloheimo, J. E., and Dickie, L. M. 1964. Abundance and ﬁshing success. Rapports et Proce`s-verbaux des Re´unions du Conseil Permanent International pour l’Exploration du la Mer, 155: 152e163. Quinn, T. J., and Deriso, R. B. 1999. Quantitative Fish Dynamics. Oxford University Press. 542 pp. Rose, G. A., and Kulka, D. W. 1999. Hyperaggregation of ﬁsh and ﬁsheries: how catch-per-unit-eﬀort increased as the northern cod (Gadus morhua) declined. Canadian Journal of Fisheries and Aquatic Sciences, 56: 118e127. Shelton, P. A. 1998. A comparison between a ﬁxed and a variable ﬁshing mortality control rule used to manage the cod stock oﬀ southern Labrador and the east coast of Newfoundland. Fisheries Research, 37: 275e286. Shelton, P. A., and Lilly, G. R. 2000. Interpreting the collapse of the northern cod stock from survey and catch data. Canadian Journal of Fisheries and Aquatic Sciences, 57: 2230e2239. Sinclair, A., Gascon, D., O’Boyle, R., Rivard, D., and Gavaris, S. 1991. Consistency of some Northwest Altantic groundﬁsh stock assessments. NAFO Scientiﬁc Council Studies, 16: 59e77. Walters, C., and Maguire, J-J. 1996. Lessons for stock assessment from the northern cod collapse. Reviews in Fish Biology and Fisheries, 6: 125e137.