Standardization of catch and effort data in a spatially-structured shark fishery

Fisheries Research 45 (2000) 129±145

Standardization of catch and effort data in a spatially-structured shark ®shery Andre E. Punta,*, Terence I. Walkerb, Bruce L. Taylorb, Fred Pribaca a

b

CSIRO Marine Research, GPO Box 1538, Hobart, Tasmania 7001, Australia Marine and Freshwater Research Institute, PO Box 114, Queenscliff, Vic. 3225, Australia

Received 25 February 1999; received in revised form 30 August 1999; accepted 12 September 1999

Abstract The methods used to develop catch rate based indices of relative abundance for the school shark Galeorhinus galeus resource off southern Australia are outlined. These methods are based on ®tting generalized linear models to catch and effort data for several regions in this ®shery. This is to take account of the multi-gear nature of the ®shery and the spatial structure of the trends in catch rate. The data on whether or not the catch rate is zero and the catch rate given that it is non-zero are analysed separately and then combined to provide indices of abundance. The former analysis is based on assuming the data are Bernoulli random variables. Given the uncertainty about the appropriate error-model to assume when ®tting generalized linear models to catch and effort data, four alternative error-models Ð log-normal, log-gamma, Poisson, and negative binomial Ð were explored when modelling the non-zero catch rates. # 2000 Elsevier Science B.V. All rights reserved. Keywords: Galeorhinus galeus; Shark; Catch rates; Standardization; CPUE

1. Introduction Reported landings of chondrichthyan ®shes (sharks, skates, rays and chimaeras) are about 700 000 mt annually Ð approximately 1% of the world's ®sheries production (Anon., 1996). Given that catches of these ®shes are rising and they can be generally characterized as being slow growing and late maturing and as having low fecundity, there are growing demands world-wide for improved conservation and manage-

*

Corresponding author. Tel.: ‡61-3-6232-5492; fax: ‡61-3-6232-5000. E-mail address: [email protected] (A.E. Punt).

ment for this group of ®shes. Their productivity, as measured by the fraction of the population that can be harvested sustainably, is low, and authors such as Holden (1973, 1974) have argued that they are particularly susceptible to over®shing. Underlying the overall trend of rising catch, is the pattern of increased ®shing of previously unutilized stocks while catches from established shark ®sheries are declining (Compagno, 1990; Bon®l, 1994). The histories of the ®sheries targeting basking shark (Cetorhinus maximus) off the western coast of Ireland (Fowler, 1996), school shark (Galeorhinus galeus) on the continental shelf of California (Ripley, 1946), and common thresher shark (Alopias vulpinus) off California (Bedford, 1987) are several of many examples of ®sheries exhibiting a

0165-7836/00/$ ± see front matter # 2000 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 5 - 7 8 3 6 ( 9 9 ) 0 0 1 0 6 - X

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trend of rising catch followed by rapid and substantial decline. Stock assessments for shark populations are generally based on analyses of information on catch and effort even though abundance indices based on these data have been shown to be unreliable for many species (e.g., Cooke and Beddington, 1984; Walters and Ludwig, 1994; Hutchings, 1996). The utility of indices of abundance based on catch and effort data can be improved by ``standardizing'' them to remove the impact of factors such as changes over time in the composition (and hence ef®ciency) of the ¯eet. A variety of methods are available for this purpose (e.g., Gulland, 1956; Robson, 1966; Honma, 1973; Gavaris, 1980; Kimura, 1981; Hilborn and Walters, 1992; Vignaux, 1994), all of which de®ne the ef®ciency of a vessel as its `®shing power' relative to that of a standard (hypothetical) vessel. Currently, the most popular method for standardizing CPUE is the use of generalized linear models. The ®shery for shark off southern Australia has been operating for almost 70 years. It began in the mid-1920s as a longline ®shery targeting school shark, Galeorhinus galeus Linnaeus, but during the late 1960s and early 1970s much of the longline gear was replaced by gill-nets, and gummy shark, Mustelus antarcticus GuÈnther, assumed greater importance in the catch. The ®shery also lands sizeable quantities of common saw shark, Pristiophorus cirratus (Latham), southern saw shark P. nudipinnis GuÈnther, and elephant ®sh, Callorhinchus milii (Bory de Saint Vincent). The school shark resource is currently assessed to be over exploited (Punt and Walker, 1998) while there is no evidence that the gummy shark resource is over exploited (McLoughlin et al., 1998; Walker, 1994a, b; Walker, 1998). The status of the other species is unknown. Although several tagging studies have been conducted on school and gummy shark (e.g., Olsen, 1953, 1954; Grant et al., 1979; Stanley, 1988; Walker, 1989), the main source of information on abundance comes from analyses of catch and effort data (e.g., Olsen, 1959). Analysis of catch and effort data in Australia's southern shark ®shery is, however, complicated by a variety of factors: 1. The ®shery is multi-species and its preferred target species has changed over time from school to gummy shark.

2. Many of the operators are diversi®ed and enter the ®shery only when catch rates are high or their access to other ®sheries (e.g., rock lobsters off South Australia) is denied. 3. The ®shery has historically been managed by multiple agencies (the ®sheries agencies of the States of South Australia, Victoria and Tasmania and that of the Commonwealth of Australia), which has resulted in different details relating to ®shing effort, and data at different spatial and temporal (e.g., shot, day, month) resolutions being collected by these agencies. 4. A variety of gear-types have been employed over the history of the ®shery. 5. The age-structure of the population differs among regions within the ®shery. Stock assessments for the shark populations off southern Australia are conducted by the Southern Shark Fishery Assessment Group (SharkFAG). This group consists of ®shery modellers, biologists, economists, managers, and ®shers. This paper describes the approach to constructing indices of relative abundance for school shark developed through SharkFAG. 2. Materials and methods The development of catch rate based indices of relative abundance involves ®rst selecting from amongst the available data those which are suitable for inclusion in the analyses. The next step involves constructing indices of abundance for each of the statistical cells in the ®shery (Fig. 1). These abundance indices are then combined to provide abundance indices for four of the eight regions considered when applying methods of stock assessment. The eight regions (with acronyms) are: (i) western South Australia (WSA), (ii) central South Australia (CSA), (iii) eastern South Australia combined with western Victoria (SAV), (iv) eastern Bass Strait (EBas), (v) western Bass Strait (WBas), (vi) western Tasmania (WTas), (vii) eastern Tasmania (ETas), and (viii) New South Wales (NSW). These regions were selected by SharkFAG on the basis of their physiography, the history of the ®shery, movement patterns of school sharks inferred from tag release±recapture data, and the spatial distribution of the various age-

A.E. Punt et al. / Fisheries Research 45 (2000) 129±145

131

Fig. 1. Map of southern Australia showing the eight regions and the statistical cells for reporting purposes (upper panel), and the statistical cells (some of which are combinations of the cells generally used for reporting purposes) used for analyses of this paper.

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A.E. Punt et al. / Fisheries Research 45 (2000) 129±145

classes inferred from available length-at-age and length±frequency data. The database and rules applied to select the records for inclusion in the analyses are outlined in Section 2.1. This is followed by a description of the generalized linear modelling approach used to develop catch rate indices by year and statistical cell. Finally, the method for combining these indices to develop indices by region is provided. 2.1. Selection of data used The data used in this paper were sourced from the Southern Shark Fishery Monitoring Database (SSFMDB) for the period 1976±1997. The SSFMDB provides for data validation, checking and correcting for multiple reporting from ®shers, for standardization of landed catch weights, and for reporting of data summaries for management, licensing, monitoring and research purposes. Landed catch weights of sharks are adjusted to `untrimmed carcass weight' (i.e., beheaded and gutted shark with all ®ns attached); this was necessary because the ®ns are removed from the carcasses in some regions of the ®shery. The database contains records of catches (and associated effort) for approximately 90% of the catch of school shark. Sectors not currently included in the SSFMDB include the recreational sector, the Japanese and Australian tuna ¯eets, the South East and Great Australian Bight trawl ®sheries, the shark ®shery off western Australia, and the ®sheries off New South Wales. The catch and effort data for these sectors could not be included in the analyses because the gear-types used by these sectors are not comparable with those used by the majority of the shark ¯eet. The catches by these sectors are, however, included in the stock assessment. The information provided for each shot (or group of shots recorded as daily or monthly information) recorded in the database includes: 1. 2. 3. 4.

Unique vessel identi®cation code. Year. Month. Gear-type (``unknown'', longline, 600 mesh, 6.500 mesh, 700 mesh, 800 mesh and ``unknown mesh''). 5. Region. 6. Catch.

7. Effort (gill-net metre lifts for mesh gear and number of hook lifts for longlines). 8. Statistical cell (see Fig. 1). 9. Depth (divided into four depth-strata: 0±30, 30± 75, 75±90, 90‡ m). For the analyses in this paper, all records for the same month, vessel code, statistical cell and depth stratum are combined into a single record. One reason for combining information from different shots in this way is that some skippers total all their catches from several shots into the ®rst entry in their log-book and record ®shing effort only for subsequent entries. Another reason for combining data into monthly records is because in Bass Strait ®shermen have provided daily records (prior to June 1978) and shot-by-shot records (after and inclusive of June 1978), whereas ®shermen in South Australia have provided daily or monthly records. Therefore, when reference is made in the balance of this paper to `record', this refers to a monthly record (irrespective of the original resolution of the data). Some of the records have to be rejected because data needed for the analyses are missing (abbreviations for these reasons are given in parenthesis): (i) no information about effort is recorded (No effort), (ii) statistical cell is not speci®ed (No cell), and (iii) the gear-type is ``unknown'', or ``unknown mesh'' (Gear). Table 1 gives the number of catch±effort records and the corresponding catch of school shark for each year. The percentages of the annual catch of school shark unavailable for inclusion in the analyses for each the three reasons listed above are also given. Note that a record may be rejected for more than one reason. The column ``Percentage accepted'' in Table 1 provides the fraction of the catch of school shark not subject to any of problems (i)±(iii). The percentage of the total catch available for inclusion in the catch and effort standardization varies markedly over time (from under 23% in 1979 to over 99% in 1995). The low percentages between 1977 and 1983 are primarily a consequence of records for South Australia not containing information about the size of mesh used when ®shing with gill-nets. The increasing percentages of the catch not subject to any of the problems (i)±(iii) is a consequence of increased efforts by the State agencies to ensure that ®shers completed their log-books correctly.

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Table 1 Reported catches of school shark, total number of monthly catch±effort records, and the percentage of the reported catch of school shark rejected for use in the standardization of the catch and effort data for the three reasons listed in the text Year

1976 1977 1978 1979 1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992 1993 1994 1995 1996 1997

No. of records

4886 5361 5539 5413 6045 5355 6158 6370 6732 8015 8766 10 113 11 200 10 603 10 326 11 170 11 015 10 443 9728 11 410 16 505 18 375

Catch (t)

723.2 857.5 792.2 947.8 1256.0 1367.7 1199.2 1091.1 1550.4 1876.9 1930.2 1855.9 1594.0 1444.2 1257.9 1192.7 1024.1 1089.7 870.8 781.8 756.5 717.5

Percentage rejected

Percentage accepted

No effort

No cell

Gear

3.92 9.33 17.91 41.72 39.29 37.69 28.11 33.08 47.28 48.97 40.40 39.07 20.03 18.18 26.85 21.78 33.94 23.62 20.31 0.36 0.94 6.51

0.00 0.00 0.34 0.19 0.59 0.18 0.94 1.77 0.03 0.14 0.79 0.46 0.25 0.57 0.27 0.28 0.73 6.67 0.89 0.39 0.47 0.21

12.73 34.72 45.58 47.80 42.62 51.79 62.03 45.69 27.17 31.50 22.62 18.89 15.54 16.49 11.89 13.12 10.54 11.25 7.30 0.33 0.94 5.30

The SSFMDB contains records for over 2660 vessels for the period 1976±1997. However, the bulk of these vessels took catches of school shark infrequently and consequently over 80% of the catch was taken by only 156 vessels (Fig. 2). For 1997, 239 vessels reported catches of school shark and of the total catch 80% and 95%, respectively, was taken by 37 and 76 vessels. The model used for the standardization includes separate factors for each vessel. Including all of the vessels would have led to an unnecessarily over-parameterized model. SharkFAG decided therefore to base the catch±effort standardization on a subset of ``indicative'' vessels. It identi®ed three criteria on which to select vessels for this purpose: (i) the number of years in which the vessel recorded a catch (Yearcrit), (ii) the median annual catch of gummy and school shark combined (Catchccrit), and (iii) the median annual catch of school shark (Catchscrit). Criteria (i) and (ii) restrict the analyses to vessels that have ®shed consistently for shark over several years while the Catchscrit criterion attempts to eliminate vessels that are primarily targeting gummy shark.

87.25 65.26 47.16 22.38 26.71 26.32 25.28 42.64 52.72 50.69 57.32 60.01 76.71 74.94 71.61 70.94 60.81 67.14 78.25 99.25 98.59 89.32

The three criteria are applied to the median catch over a time period rather than to the annual catches to avoid problems caused by changes in density. In years when density (or availability) is low, even ``indicative'' shark vessels will take small amounts of school shark, and may, therefore, be eliminated from consideration for those years. Examining the median catch over several years does not eliminate this problem, but should reduce it. The vessels included in the analyses are restricted further by imposing a minimum number of records (20 for the base-case analyses) and a maximum percentage of shots in South Australia in which the catch of gummy shark equals that of school shark (25%). This last constraint was imposed to eliminate ®shers who do not attempt to divide their catch into species, noting that 50:50 splits of the catch are possible in some regions (particularly EBas and WBas).1 1

This constraint only eliminated one vessel from the base-case analysis. However, that vessel has been known to mis-report catch and effort statistics.

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A.E. Punt et al. / Fisheries Research 45 (2000) 129±145

Fig. 2. Distribution of catches of school shark among vessels. The upper panel shows the distribution of the total catches from 1976 to 1997 and the lower panel that for the median catch over this period. The bars for total catch <10 t (2330 vessels) and median catch <2 t (2337 vessels) have been omitted to improve clarity.

The analyses in this paper are constrained further to data obtained using 600 , 6.500 and 700 mesh gill-nets only. Data for longlines and other mesh sizes are not included in the analyses because of paucity of data for these gear-types. The data for the 600 , 6.500 and 700 gears are combined because 600 mesh gill-nets have not been used much in CSA and WSA while 700 mesh gill-nets are not used much in the more eastern areas. The data for the WTas and ETas regions are ignored because they are known to be poor as there was no facility to record ®shing effort data on returns received in Tasmania during 1979±1987. No attempt is made in the present paper to develop a

catch rate index for the SAV region because, over the period considered, marked changes in targeting practices and a complex mix of gears have occurred in this region. The data are analysed separately for the South Australian zone (regions WSA and CSA) and the Bass Strait zone (regions EBas and WBas). This is because (i) few vessels ®sh in both zones, (ii) the mesh sizes used in the two zones differ, (iii) usable data are only available from 1983 for the South Australian zone, (iv) the age-structure of the population in the two zones appears to differ, and (v) targeting practices differ between the two zones.

A.E. Punt et al. / Fisheries Research 45 (2000) 129±145

2.2. Estimating year  statistical cell interactions The purpose of the catch±effort standardization is to obtain indices of relative abundance for each combination of year and statistical cell. This is achieved by ®tting a model of the form Cy;v;m;b ˆ em‡ay;b ‡


Ey;v;m;b

or Cy;v;m;b ˆ em‡ay;b ‡


Ey;v;m;b ; (1)

where Cy;v;m;b Ey;v;m;b m ay;b




catch of school shark by vessel v in statistical cell b during month m of year y effort expended by vessel v in statistical cell b during month m of year y global mean factor for statistical cell b and year y and represents other factors that influence the catch

The factors that are included in the models are chosen from: (a) year, (b) month within year, (c) vessel, (d) statistical cell, (e) depth, and (f) year  statistical cell interaction. Analyses (not shown here) con®rm that other interactions are insubstantial. Some of the interactions examined were signi®cant but led to negligible changes to the fraction of the deviance explained and had no noticeable impact on the eventual indices of abundance. A month factor is considered because some months lead to higher catch rates than others do. A year  statistical cell interaction is needed to capture the effect of catch rates in different parts of the ®shery declining at different rates over the history of the ®shery. A factor for each vessel is included in the model rather than attempting to characterize vessels by means of other variables (horsepower, tonnage, etc.) as was undertaken in several previous studies (e.g., Vignaux, 1994, 1996). This is because the ef®ciency of a vessel in this ®shery at catching school shark depends more on the ®shing master's targeting practices, skill level and annual time commitment to the ®shery than on the attributes of the vessel. It is necessary to specify the distribution of the errors in the dependent variables in models (1) and (2) in order to ®t them to the data. Several error-models were tested to determine the most appropriate one to ®t the distribution of residuals in the data for the

135

dependent variable (e.g., ICCAT, 1995; Cooke and Lankester, 1996; Dong and Restrepo, 1996): 1. Log-normal Ð this error-model has been used in most previous attempts at standardizing catch and effort data (e.g., Gavaris, 1980; Kimura, 1981; Vignaux, 1994). However, in order to use it, it is necessary to make adjustment for zero catch rates. Three alternative schemes are considered: 1.1. Ignore all records in which the catch rate is zero. 1.2. Add a constant to all catch rates. 1.3. Add a constant (g Ð arbitrarily chosen to be 1 kg Ð because the logarithm of 1 is zero!) to all catches (the option considered in this paper). 2. Poisson Ð one advantage of using this errormodel is that it allows zero catches to be included in the analyses, so there is no need to specify a value for g, to which results might be highly sensitive. The dependent variable in this case is the nearest integer to the catch. 3. Log-gamma Ð this error-model also requires that a method be speci®ed to take account of zero catches. For the purposes of this study, the dependent variable is taken to be Cy,v,m,b ‡ 1 when zero catches are included in the analysis. 4. Negative binomial Ð this error-model allows for a more general relationship between the residual variance and the expected catch. The dependent variable in this case is the nearest integer to the catch. 5. Delta-X Ð this error-model is based on the premise that it is possible to treat separately the question of whether a catch rate is zero or not, and the size of a catch rate given that it is non-zero (Vignaux, 1994). For the purposes of this investigation, the non-zero catch rates are modelled using the log-normal, Poisson, log-gamma and negative binomial error-models while whether the catch rate is zero or non-zero is modelled as a Bernoulli random variable (i.e., a binomial errormodel is assumed when ®tting to the data). Fitting to the data on whether the catch rate is zero or not, therefore, involves specifying a model of the form: g…V† ˆ m ‡ ay;b ‡


; where g is the logit link function.

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A.E. Punt et al. / Fisheries Research 45 (2000) 129±145

2.3. Estimating regional indices of abundance

the equation:

It is commonly assumed that the catch rate for a year and statistical cell is proportional to the ®sh density in that cell during that year. Hence, if it is assumed that catchability is invariant across statistical cells (within the South Australian and Bass Strait zones separately) and time, a relative abundance index can be determined using the formula: X Ab Iy;b ; (2) Iy ˆ

Vy;b ˆ

b

where relative abundance index for year y Iy relative abundance index for year y and Iy,b statistical cell b and size of the available area of statistical cell b Ab By de®nition, Ab is the area in which school shark could potentially be found. For this study, Ab is de®ned as the area of each cell shallower than 200 m. It is known that school shark are found considerably deeper than 200 m (Last and Stevens, 1994). However, the vast bulk of the catch of school shark is taken in waters shallower than 200 m. It is plausible that the size of the available area in some cells may have changed over time due to ®shing-induced habitat modi®cation but this cannot be accounted for quantitatively without a much better understanding of the habitat requirements and distribution patterns of school shark. For the non-delta-X models, the relative abundance index for year y and statistical cell b, Iy,b, is determined from Eq. (1) by setting the month, vessel, etc., terms to some reference value. There is no loss in generality by in fact setting these terms to zero and ignoring the constant term, in which case the relative abundance index is given by Iy;b ˆ e^ay;b :

(3a)

In contrast, for the delta-X models, the value for Iy,b is computed by multiplying the probability of a non-zero catch by the expected catch rate given that the catch is non-zero. This is achieved using the equation Iy;b ˆ Vy;b e^ay;b ;

(3b)

where Vy,b is the probability of a non-zero catch in statistical cell b during year y and is computed using

where f1 f2,y f3,b f4,v f5,m

ef1 ‡f2;y ‡f3;b ‡f4;v ‡f5;m ; 1 ‡ ef1 ‡f2;y ‡f3;b ‡f4;v ‡f5;m intercept of the binomial factor binomial factor binomial factor binomial factor

(4)

binomial regression for year y for statistical cell b for vessel v and for month m

The reference vessel used for the calculations is that which had the most records and the reference month m is taken to be October. Application of Eqs. (3a) and (3b) is not completely straightforward because values for ^ay;b and hence Iy,b are not available for all statistical cells and years. For those combinations of statistical cell and year for which estimates of ay,b are not available, Iy,b is obtained by applying the following algorithm:  The rule used to specify Iy,b if GLM estimates are not available for statistical cell b for any year prior to year y is: P ÿ2 highest3 Iy ;b …y ÿ y† ; (5) Iy;b ˆ P ÿ2 highest3 …y ÿ y† where Shighest 3 indicates summation over the three highest catch rates.  If GLM estimates are available for earlier and later years than year y, the value for Iy,b is set from the results of a linear regression of the GLM estimates for the two years before and after year y (one if two estimates are not available) on year. The GLM generally indicates that catch rates of school shark have been declining over the period 1976±1997. Therefore, if catch rates for the early years of the time series for a particular cell are not available and have to be selected based on those for later years, it seems most appropriate to use the years with the highest catch rates. This is achieved using Eq. (5) which is based on the three highest catch rates for statistical cell b. The (y* ÿ y)ÿ2 term in Eq. (5) is chosen to give greater weight to the data for the years closest to that for which a catch rate is needed.

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3. Results and discussion

3.2. Selection of an error-model

3.1. Selection of ``indicative'' vessels

Residuals for the log-normal error-model are shown separately for the Bass Strait and South Australian zones in Fig. 3. Results are shown for analyses that use all of the selected records (including those for which the catch of school shark is zero; g ˆ 1) and that ignore the zero catches (g ˆ 0). The residual distributions for the analyses that ignore the zero catches are notably closer to being normal than those for the analyses that use the zero catches. Similar ®gures for the other error-models (not shown here) suggest that the error distributions are closer to expected if the zero catches are ignored. These results suggest that an error-model based on the delta-X distribution is preferable. Pennington (1983) and de la Mare (1994) reached a similar conclusion for the analysis of survey data. The choice of g ˆ 1 kg is arbitrary but use of the log-normal distribution necessitates a choice for g. The most appropriate value for g for a particular case is seldom determined. An exception to this was Porch (1995) who applied the criterion of Berry (1987) to determine g for West Atlantic northern blue®n tuna. However, numerical simulations by Porch (1995) found that this criterion did not perform much more successfully than more arbitrary approaches, such as setting g to 1 kg. It is not particularly surprising that the zero catches arise from a different process than the non-zero catches for the school shark ®shery. This is primarily because of its multi-species nature. Zero catches of school shark are hardly surprising when ®shers target areas where gummy but no school sharks are found. Another reason for zero catches is that some ®shers ``round'' small catches of school shark (one or two animals) to zero. The latter factor is captured by

The base-case choices for the thresholds Yearcrit, Catchccrit, and Catchscrit were chosen by SharkFAG to be 5, 10 and 5 t, respectively, based on industry knowledge of shark ®shing practices. Table 2 provides statistics that summarize the vessels selected using these base-case thresholds as well as four alternative sets of choices. Statistics are also shown for analyses that increase the minimum number of records from 20 to 30 (Minrec ˆ 30). The base-case selection criteria lead to 58 vessels being selected. For South Australia, 61.9% of the school shark catch by mesh gear from 1983 to 1997 is included in the analysis as is 38.9% of the school shark catch by mesh gear in the Bass Strait zone from 1976 to 1997. The lower ®gure for the Bass Strait zone is not surprising because the ®shery in this area is targeted primarily at gummy shark so much of school shark caught in WBas and EBas is ``by-catch'' by vessels that are targeting for gummy shark. Increasing Yearcrit from 5 to 10 eliminates 11 vessels. Somewhat surprisingly, the median catch of school shark is little changed by this increase to Yearcrit, which indicates that ``long-term'' and ``short-term'' participants have roughly the same annual catches. Changing the criterion related to the total catch of gummy and school shark, increasing the minimum number of records per vessel from 20 to 30, and changing the criterion related to the total number of years in ®shery from Yearcrit ˆ 5 to Yearcrit ˆ 3 does not change the choice of ``indicative'' vessels noticeably.

Table 2 Statistics related to alternative choices for the thresholds used to select vessels for inclusion in the catch and effort standardization analyses Description

No. of records

No. of vessels

Total catch (t)

Average no. of years in the fishery

Average median catch (school shark) (kg)

(a) Base-case (b) Catchccrit ˆ 5 t (c) Catchscrit ˆ 2.5 t (d) Yearcrit ˆ 10 (e) Yearcrit ˆ 3 (f) Minrec ˆ 30

15 920 16 014 19 067 14 540 16 082 15 876

58 60 76 47 61 56

8404 8544 9072 7496 8495 8355

14.2 14.2 14.1 15.9 13.7 14.5

14 105 13 837 11 618 14 103 13 914 14 257

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A.E. Punt et al. / Fisheries Research 45 (2000) 129±145

Fig. 3. Histograms of residuals for analyses based on the log-normal error-model. The left panels are for the Bass Strait zone and the right panels are for the South Australian zone. The upper panels refer to analyses that utilize zero catches while the lower panels refer to analyses that ignore zero catches.

the ``vessel'' factor when applying the delta-X distribution. The average catch rate and the variance of that catch rate for each vessel are shown separately for the Bass Strait and South Australian zones separately in Fig. 4. A choice can be made among the Poisson, log-gamma and negative binomial error-models using the results in Fig. 4 (Dong and Restrepo, 1996). If the (overdispersed) Poisson error-model mimics the structure of the data, the variance in catch rate would fall along a straight line whereas if the log-gamma error-model ®tted the data well, the variance in catch rate would be proportional to the square of the average catch rate. The negative binomial error-model assumes that the variance of catch rate is a function of both the average catch rate and the square of the average catch rate.

Considering the results for the South Australian zone ®rst, the data are well approximated by the assumption that the variance in catch rate is proportional to the square of the catch rate, implying that the log-gamma error-model should be assumed when analysing the data for the South Australian zone. For the Bass Strait zone, the ®t of the negative binomial error-model is superior to those of the log-gamma and Poisson errormodels (P < 0.01). Given that the ®ts for the loggamma and negative binomial error-models for the South Australian zone are almost identical (Fig. 4), the base-case results of this paper are based on the negative binomial error-model. The conclusions regarding the choice of an appropriate error-model are clearly highly dependent on the data points at high catch rate. Removal of these data

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139

Fig. 4. Plots of the variance in catch rate against the average catch rate. Results are shown separately for the Bass Strait and South Australian zones. The dash±dotted line corresponds to the (over-dispersed) Poisson distribution, the dotted line to the negative binomial distribution, and the dashed line to the log-gamma distribution.

points would eliminate most of the ability to distinguish among alternative error-models. Furthermore, the results will show that catch rates have been declining over time so the variance in catch rate will be in¯ated because it includes the impact of the declining trend in abundance over time. Given these uncertainties, the sensitivity of the results to varying the base-case error-model is examined. 3.3. Construction of abundance indices The model ®tted to the data on whether the catch of school shark is zero or not includes only the main effects (year, month, vessel and statistical cell). This model explains 13% of the deviance for the Bass Strait zone and 21% for the South Australian zone. Fig. 5 plots the observed versus expected fraction of records

with non-zero catches (constructed by sorting all of the observed and predicted values on the predicted value, grouping the data into bins based on the predicted value, and computing the average observed values). This ®gure suggests that the model ®ts the data for WBas and EBas fairly well. This is, however, somewhat misleading because there is substantial variation about the ®t (the model explains only a relatively small fraction of the overall deviation). The situation for CSA ‡ WSA is less clear but it should be noted that the sample size for the South Australian zone is smaller than for the Bass Strait zone and the number of zero catches is much less for South Australia than for Bass Strait. The most important of the factors in the model for the South Australian zone was vessel while for the Bass Strait zone statistical cell, vessel, and month all had a large impact on the

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Fig. 5. Observed fraction of records with non-zero catches of school shark versus model predicted values. Results are shown separately for the Bass Strait and South Australian zones. Results based on less than 20 data points have been omitted from this figure.

probability of achieving a non-zero catch of school shark. The importance of vessel is hardly surprising because this re¯ects inter alia much greater targeting of school shark off South Australia than in Bass Strait, and differences in reporting practices (e.g., temporal resolution of the CPUE data). Fig. 6 shows trends in standardized catch rate for the WSA, CSA, WBas and EBas regions as well as for South Australia (WSA and CSA combined) and Bass Strait (WBas and EBas combined). The results in Fig. 6 are based on assuming that the errors are distributed according to the negative binomial model, as discussed above. For South Australia, rule (b) was applied seven times and rule (a) four times (i.e., catch rates are available for 94% of the cell±year combinations for the CSA and WSA regions). For the Bass Strait zone, rule (b) was applied once and rule (a) ®ve

times (i.e., catch rates are available for 98% of the cell±year combinations for the WBas and EBas regions). The ®ve applications of rule (a) in the Bass Strait zone relate to cell 33 (Fig. 1), which does not have any usable data for the years 1976±1979. The standardized catch rate series for the two South Australian regions decline by over 50% from 1983 to 1997 (Fig. 6). The trend in catch rate in the Bass Strait zone is also downward though not nearly as markedly so as in the South Australian zone. The trend in standardized catch rate for the EBas region is notably steeper than that for the WBas region. A variety of sensitivity tests to the results in Fig. 6 were conducted, and the results for some of these are reported in Figs. 7 and 8. There is no noticeable difference between the results when the log-gamma or Poisson error-models rather than the negative bino-

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Fig. 6. Annual catch rate indices for school shark in the Bass Strait and South Australian zones based on the negative binomial error-model.

mial error-model is assumed (Fig. 7). Quantile±quantile plots based on the residuals about the ®ts for the different error-models con®rm, however, that the negative binomial is the most satisfactory. Changing rules (a) and (b), including the extreme option of replacing rule (a) by one which sets the catch rate to the maximum over the time series (curve ``Replace by maximum'' in Fig. 8) has little impact on the trends in catch rate. Similarly, changing the speci®cations for ``indicative vessels'' has little impact on the trends (curves ``Catchscrit ˆ 2.5 t'' and ``Yearcrit ˆ 10 t'' in Fig. 8). Other sensitivity tests (not shown here) had even less impact. 3.4. General remarks The results of this study highlight the importance of considering different error-models when conducting

catch±effort standardizations. In particular, the results con®rm the importance of examining assumptions regarding the treatment of zero catch rates (Fig. 3). The use of the delta-X distribution provides a useful way to deal with zero catch rates. However, using this distribution complicates the construction of an overall index of abundance because Eq. (4) depends on choices for standard vessels and months. The results of sensitivity tests (not shown in Fig. 8) indicate that the results are not particular sensitive to the choices made in this regard. It is unclear, however, whether this is a particularly general result. The abundance indices for the four regions exhibit different trends and variability (Fig. 6). Although the indices for all four regions decline over the period 1976±1997, those for the WSA and CSA regions decline at a substantially greater rate over the years 1983±1989. The indices for these two regions vary less

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Fig. 7. Annual catch rate indices for school shark in the Bass Strait and South Australian zones. Results are shown for three choices for the error-model used when analysing the non-zero catch rates.

about the overall trend than the indices for the two Bass Strait regions. These inter-region differences highlight the importance of careful consideration of the spatial structure of the ®shery when analysing catch and effort data. In this case, it is perhaps not too unexpected that the trends in standardized catch rate in different areas differ because it is known that that the ®shery for school shark off South Australia started well after that in Bass Strait, the age-structure of the catch off South Australia is different from that in Bass Strait, and the main gear-types differ between these two areas. Early analyses of catch and effort data for school shark attempted to pool data across zones and achieved a result that did not represent the trend in either zone adequately. Spatial structure needs to be accounted for when standardizing the catch and effort data for this shark ®shery owing to the factors listed above implying that

trends in catch rate differ across the ®shery. However, accounting for spatial structure increases the complexity of the analysis markedly for several reasons. These include: (a) the model requires a much greater number of parameters, (b) ``rules'' are needed to deal with any missing values and these will be arbitrary to some extent, and (c) the area within each cell in which school shark could potentially be found has to be de®ned. Similar procedures have been adopted to standardize the catch and effort data for southern blue®n tuna, Thunnus maccoyii (Campbell, 1998). Furthermore, the inability to construct indices of abundance for regions other than WSA, CSA, WBas and EBas and the lack of comparability between the indices for the South Australian and Bass Strait zones necessitates that account be taken of the spatial structure of the ®shery in the models used for stock assessment.

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Fig. 8. Annual catch rate indices for school shark in the Bass Strait and South Australian zones based on the negative binomial error-model. The results in this figure explore the sensitivity of the results to varying some of the specifications of the base-case analysis.

The models considered in this paper have a very large number of parameters. It is therefore of some concern that it is possible to explain only a relatively small fraction of the overall deviance. However, the inability to explain a substantial fraction of the variability in the data when conducting catch±effort standardizations is not particularly unusual (e.g., Vignaux, 1994, 1996). Whether, in this case, this is due simply to environmental impacts on catch rates or is also a consequence of the inability to identify and include all of the key variables that determine catch rates is unclear. For example, changes in skippers on some of the vessels, and the introduction over time of navigational aids such as colour echo sounders and the Global Position-®xing System undoubtedly in¯uences catch rates. However, information about the use of these aids is not readily available.

The analyses involve pooling the data obtained from three gill-net mesh sizes (600 , 6.500 and 700 ). For the Bass Strait zone, this is not a major concern because over 98% of the catch used in the catch±effort standardization was taken using 600 mesh gear. In South Australia, however, the fraction of the catch used in the analyses taken using the most important gear-type (700 mesh) is only 75%. This ®gure is also misleading to some extent because it re¯ects a gradual reduction in mesh size over the period considered in the analyses. For example, 82% of the catch was taken using 700 mesh from 1983 to 1989, but this percentage is only 63% for 1996. In 1997, a new maximum mesh size of 6.500 was introduced into the ®shery. This meant that only a very small fraction of the catch in South Australia was taken using 700 mesh during that year. This change in mesh size must introduce some

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bias into the trends in abundance because it is known (e.g., Kirkwood and Walker, 1986) that the various mesh sizes select somewhat different components of the population. Whether this leads to a positive bias in that the ®shery can now target younger/smaller ®sh (whose abundance is probably higher) or a negative bias because the range of ages is reduced, is unclear. This can be dealt with to some extent in the stock assessment model by allowing the component of the population to which catch rate relates to change over time to re¯ect changes in mesh size. Finally, it should be noted that there are many situations in which the assumption that catch rate is proportional to abundance is violated even though the data have been standardized to remove the impact of known factors (e.g., Cooke and Beddington, 1984; Hilborn and Walters, 1992; Walters and Ludwig, 1994). It is, therefore, unreasonable to assume that the indices of relative abundance from the analyses of this paper are completely free from the effects of changes in ef®ciency. This is because information about skippers, ``learning'' behaviour, advances in ®shing technology, and the effects of the introduction of management regulations are not incorporated in the analyses, as data quantifying these effects are unavailable. Acknowledgements The remaining members of SharkFAG are thanked for their input on the options selected. Rob Campbell, Tony Smith (CSIRO Marine Research) and two anonymous reviewers are thanked for their comments on an earlier draft of this paper. Yongshun Xiao (South Australian Research and Development Institute, Adelaide) is thanked for useful discussions. References Anon., 1996. Fishstat PC. Fishery Information, Data and Statistics Unit, FAO Fisheries Department, Food and Agriculture Organisation of the United Nations, Rome. Bedford, D., 1987. Shark management: a case history Ð the California pelagic shark and swordfish fishery. In: Cook, S. (Ed.), Sharks: An Inquiry into Biology, Behaviour, Fisheries, and Use. Oregon State University Extension Service, Corvallis, pp. 161±171.

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