ICES Journal of Marine Science: Journal du Conseil Advance Access originally published online on January 12, 2008
ICES Journal of Marine Science: Journal du Conseil 2008 65(2):255-266; doi:10.1093/icesjms/fsm179
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Standardizing catch rates: is logbook information by itself enough?
1 20 Tooth Street, Nobby, Queensland 4360, Australia
2 CSIRO Mathematics and Information Science, PO Box 120, Cleveland, Queensland 4163, Australia
3 CSIRO Marine and Atmospheric Research, PO Box 120, Cleveland, Queensland 4163, Australia
4 Trawl Gear Services, 27 Cobble Street, The Gap, Queensland 4061, Australia
Correspondence to J. Bishop: tel: +61 746 963289; fax: +61 746 963289; e-mail: janetbishop{at}bigpond.com
Bishop, J., Venables, W. N., Dichmont, C. M., and Sterling, D. J. 2008. Standardizing catch rates: is logbook information by itself enough? – ICES Journal of Marine Science, 65: 255–266.The goal of the work was to maximize the accuracy of standardized catch per unit effort as an index of relative abundance. Linear regression models were fitted to daily logbook data from a multispecies penaeid trawl fishery in which within-vessel changes in efficiency are common. Two model-fitting strategies were compared. The predictive strategy focused on maximizing the explained variance, and the estimation strategy on finding realistic coefficients for important components of changing catchability. Realistic values could not always be obtained, because the regression factors were not orthogonal, and data on the presence of technology were sometimes unreliable or systematically incomplete. It was not possible to separate fishing power from abundance by analysing logbook data alone; it was necessary to incorporate external information within the standardization model. Therefore, the resultant estimation models incorporated external information and expert knowledge by offsets. There was no single best estimation model. Instead, a series of models provided an envelope of possible changes in relative fishing power and prawn abundance since 1970. Compared with the prediction models, the estimation models revealed different trends in relative fishing power and relative abundance.
Keywords: catchability, confounding, cpue, expert knowledge, Penaeus, Prawn Trawl Performance Model, shrimp, standardized effort
Received 24 February 2007; accepted 2 November 2007; advance access publication 12 January 2008.
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Introduction |
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Standardization is essential, in any observational dataset, to allow undistorted comparisons of rates over time or over different areas. In fisheries, commercial catch rates are often standardized for use as an index of relative abundance, particularly in fisheries where a regular resource survey has not been feasible (Hilborn and Walters, 1992; Maunder and Punt, 2004). To be useful as an index of relative abundance, raw catch per unit effort (cpue) must be standardized for changes or variations in catchability, or changes in cpue that are attributable to variable catchability may be incorrectly concluded to be due to changes in abundance. However, standardization can be problematic, and standardized results are not always proportional to abundance (Harley et al., 2001; Maunder et al., 2006). Such lack of proportionality can result when inappropriate methods are used to construct the standardized index of relative abundance; for example, methods that fail to account for spatial and temporal complexity in fishing effort (Walters, 2003; Campbell, 2004). Another cause may be inadequate standardization for variations in catchability, including changes in fleet composition and effort creep within vessels. This possibility is explored, and we describe two standardization models that fit a dataset similarly well (i.e. have similar R2), but give very different standardized results.
A commonly applied method of standardizing catch rates for varying catchability is to fit a regression model. Typically, a linear regression is fitted, with suitable choices of distributional form and treatment of effort with zero catches (for other approaches, see the review by Maunder and Punt, 2004). The dependent variable is catch, and explanatory variables represent abundance and availability, effort, vessels, and gear (Kimura, 1981; Allen and Punsly, 1984, Maunder and Punt, 2004). In a simple model, the year terms (or terms for other time-steps) correspond to the indices of relative abundance, providing that the size of areas fished, and the spatial pattern of effort, have remained constant over the years (Allen and Punsly, 1984; Hilborn and Walters, 1992; Walters, 2003; Campbell, 2004; Maunder and Punt, 2004). Alternatively, annual indices of relative fishing power may be constructed from vessel and gear variables and applied to nominal effort, to standardize effort (Kimura, 1981; Maunder and Punt, 2004).
One modelling decision is the choice of explanatory variables to represent vessel, gear, and skipper characteristics, to account for changing fleet composition and effort creep caused by improvement in technology within vessels. A common approach is to force variables to represent abundance and availability into the model, then to use a stepwise procedure to select vessel and gear variables from a set of candidates, with the goal of maximizing explained variance or minimizing the Akaike Information Criterion (AIC) or the Bayesian Information Criterion (BIC; Maunder and Punt, 2004). This approach assumes that the rationale for the model is well understood, that the model is reasonably well-specified, and that the dataset is useful for estimating the effects of the variables in the model (Chatfield, 1995; Burnham and Anderson, 2002).
Gulland (1983) proposed that a designed experiment would be the ideal way to find out the impacts of changes in technology on catching power, when vessels had upgraded and increased their fishing power over time. Known impacts could become the basis of correctly standardizing catch rates. Alternatively, it is sometimes possible to look within non-experimental datasets for so-called "natural experiments" that occurred by chance: for example, when vessels with an innovation fished near other vessels without it. This approach is sometimes known as an observational study (Eberhardt and Thomas, 1991; Rosenbaum, 2002; Bishop, 2006). Rather than maximizing explained variance, or minimizing standard errors on the abundance estimates, the focus when fitting the model is to obtain realistic coefficients for the important features of the catchability process. As the emphasis is on estimating the coefficients, this approach is sometimes referred to as building an estimation model. Here, we compare two approaches for determining which vessel and gear variables should be included in the standardization. The observational study approach (which will hereafter be referred to as the estimation model approach), and the stepwise selection approach (referred to hereafter as the predictive approach) are illustrated by their application to daily logbook data from a trawl fishery for several species of penaeid—Australia’s northern prawn fishery (NPF).
The NPF is an otter trawl fishery for mixed penaeids, located along Australia’s tropical north coast, spanning 13 degrees of longitude, with almost 300 000 km2 trawlable for prawns. The fishery has been managed by input controls, with large changes in fleet composition and technology. The motivation to standardize catch and effort was to be able to provide input to the stock assessment of tiger prawns. Effort standardization has been identified for some time as a major uncertainty within the stock assessment and management decision-making process of the NPF. Stock models for tiger prawns proved highly sensitive to input values of fishing power (Wang and Die, 1996; Dichmont et al., 2003b). It became critical to obtain accurate information on fishing power, hopefully to decrease the uncertainty in stock assessments and hence to reduce the degree of precaution needed in management decisions.
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Methods |
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Models
Models were built to predict catch weight in the fishery for tiger prawns. The basic form of the model follows the catch–biomass relationship adapted by Robins et al. (1998) from that described by Kimura (1981), to allow for specific features of prawn biology to be included, i.e. continuous recruitment, spatial and temporal patterns of availability due to migration and temperature effects, and patchy aggregation of stocks and of targeting behaviour of fishers.
A log-transformation of catches and of some continuous explanatory variables was used to normalize the response variable, to linearize the relationship between the mean and the explanatory variables, to stabilize the variance, and to implement a multiplicative influence model. The fits of two other statistical distribution assumptions were also investigated: a gamma distribution with log-link function, and a Poisson quasi-likelihood with log-link. The outcomes of relative fishing power were not sensitive to the distributional form.
Concerning the explanatory variables, the variables (and interactions) that represented abundance and availability (Xq) were selected for a priori reasons of moderately fine spatio-temporal scale, and parsimony, and this selection was supported by sensitivity investigations which are described later. Two strategies were followed to select vessel, gear, and skipper variables for inclusion as described below. The resultant models are referred to hereafter as predictive models and estimation models. They are both of the form
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ijkt are iid errors; and 
0, q, βp, 
, and 
h are the model coefficients to be estimated.
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To investigate model fit, normal scores and Q–Q plots of residuals, and plots of residuals against various predictors, were inspected. Residual plots demonstrated greater uncertainty in the 1970s, as well as a handful of outliers that were not considered to be influential. Models were compared on the basis of AIC (Akaike, 1974), BIC (Schwartz, 1978), and R2. AIC and BIC give some indication of the gain in R2 attributable to a given variable relative to the increase in degrees of freedom; smaller values indicate better models.
The standardized cpue was the mean daily catch rate, in kg per standard night of 12 h trawling covering 209 ha, according to the exponent of the expected catch according to the linear predictor [Equation (1) for the predictive model and Equation (4), below, for the estimation model], with a correction for bias caused by the transformation from the log-normal to the original scale, for a hypothetical standard vessel in each region, month and year, at new moon and fixed depths:
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| (2) |
From these results for each month, region, and depth, an appropriately weighted index of relative abundance was constructed to represent the entire fishery, in each year. However, for simplicity, standardized cpue is presented, as an index relative to 1970, for only one region and depth, in May of each year, Uk = U1,k,5/U1,1970,5. The location selected for display was heavily fished throughout the history of the fishery.
The relative fishing power of each vessel was the exponent of expected catch rates as estimated from Equation (1) for the predictive model and Equation (4) (below) for the estimation model, relative to a hypothetical standard vessel, if all vessels were fishing under controlled availability and abundance conditions (i.e. fixed location, time of year, year, depth, and moon phase).
The mean fishing power for the fleet each year was the arithmetic mean of per-vessel fishing powers, weighted for the effort of each vessel that year:
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| (3) |
where wik is the weight for the contribution of effort of vessel i to the total annual effort of year k. cik* is the predicted catch of vessel i with its gear and skipper of year k when (hypothetically) fishing in standard abundance conditions of area 1, year 1984, month 9.
The cumulative relative fishing power each year relative to 1970, qk = Rk/R1970, and the fishing power each year relative to the previous year, qinc = Rk/Rk–1, were calculated.
Strategies for selecting vessel and gear explanatory variables
In the predictive models, effort and abundance variables [log(f) and Xq] were forced (included by default) into the model. Vessel, gear, and skipper variables were added by a forward stepwise strategy, where at each step the variable entered was that which maximized the R2 of the resultant model. The stopping rule was when no variable would increase the R2 by at least 0.5%. Candidate vessel, gear, and skipper variables are listed in Table 1. Two alternative predictive models are presented. Predictive model A resulted when vessel code (as a fixed effect) was included among the candidate variables. Predictive model B resulted when vessel code was excluded.
In the estimation models, important determinants of catchability (including components of fishing power and availability) were determined by a review of the literature and theory (Dichmont et al., 2003a). All vessel, gear, and skipper variables that had been identified as being important were included in the model, with some exceptions to minimize collinearity. In other words, if one variable was largely a surrogate for another, only one was included.
Three types of preliminary investigation were made while developing the estimation models: (i) to assess the stability of the estimates of the vessel, gear, and skipper coefficients, a series of models described by Equation (1) was fitted to a subset of years, as well as to all years; (ii) a similar set of models treated vessel code as a random effect; (iii) as confounding of technological variables with abundance was suspected, the effect of supplying tentative or hypothetical additional information on the impact of a given variable was investigated by fixing (or offsetting; McCullagh and Nelder, 1983) the coefficient for that parameter at some reasonable value, and observing the effect on all the other technology coefficient estimates.
Two final estimation models were developed, distinguished by contrasting treatments of technology variables. The so-called "low" treatment left most technology coefficients free to be estimated when fitting the model. However, it was found necessary to fix the coefficients for the three most unstable variables, to stabilize the remainder of the results. The "high" treatment fixed the coefficients for all technology variables. The values for the fixed coefficients were based on results from the restricted-years analyses, from the specific years of arrival of the new technology, provided qualitative information and expert judgement were consistent. In one case (Turtle Excluder/Bycatch Reduction Device, TED/BRD), the fixed value for the coefficient in the offset was obtained from independent experimental research (Brewer et al., 2006). The two options were referred to as the low and high offset series or schedules, because of their relatively optimistic or pessimistic impacts on the estimates of fishing power over time. The low series represents a lower bound of efficiency changes that was unequivocally detected within the available data, and the high series allows for the possibility of even greater impacts of technology that were less conclusively established.
The final estimation models had the form:
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| (4) |
a log(fijkt) is the offset for log-transformed hours trawled and its fixed coefficient a, log(Vbik) is the offset for log(swept area rate) with coefficient set to 1, c are the offsets for 1 to c of the h technology variables (Table 2), and all other terms are as described for Equation (1).
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To illustrate the contribution of changes in hours fished, skipper skill, and vessel and gear variables to the separation of relative fishing power from abundance, a nested series of models was fitted. The resultant cumulative relative fishing powers and standardized catch rates were plotted against year. The area under the cumulative relative fishing power curve was calculated at each step of the nested series of models, to illustrate the contribution of the variable added at that step.
Computational experiments were devised to investigate the sensitivity of model outputs to modelling decisions (Morris, 1991; Saltelli et al., 1998). Each experiment investigated 12 decisions. A series of 32 models was specified where, for a given model, the outcome or direction of each decision was determined by a fractional factorial experimental design (Robinson, 2000). The resultant model outputs were pooled and investigated by ANOVA. This process revealed which of the modelling decisions were influential and merited further investigation (Dichmont et al., 2003a).
Application: Australia’s northern prawn fishery
The analysis used commercial fishery logbook records collected from trawler skippers, from five main stock regions where tiger prawns dominate the catch, and days when tiger prawns were deemed to have been the target according to their dominance in the catch record. At different times of the year, different species predominate: in May the catch of tiger prawns is predominantly Penaeus esculentus, the brown tiger prawn, and in September it is P. semisulcatus, the grooved tiger prawn (according to data from scientific observers; Somers, 1994; Venables and Dichmont, 2004). The two species of tiger prawn are not distinguished in the logbook records. All species caught in the tiger prawn fishery were assumed to have similar catchability (Eayrs, 2003).
The logbooks have been deemed reliable according to annual reconciliations of logbooks with independent landed weights (Perdrau and Garvey, 2005), and because there has been no incentive to misreport.
Catch and effort information from the daily logbook records was linked to annual information on vessel and skipper characteristics and technology onboard, which had been collated from a variety of sources (Bishop and Sterling, 1999; Dichmont et al., 2003a). The final dataset for analyses comprised more than 530 000 daily catch records from 570 vessels that targeted tiger prawns, from March to November of the period 1970–2002. Each record represented the daily catch weights (in kg), with attributes of location (depth, stock region) and time (month, year, percentage of lunar cycle), the total hours trawled each day, and vessel and skipper characteristics for that year.
A deterministic, engineering model (the Prawn Trawl Performance Model, PTPM; Sterling, 2005) transformed engine, propulsion, and trawl system specifications into a single index of swept area performance for each trawler, which became an explanatory variable for the models. The average error in the predicted swept area performance was <1 m2 s–1, according to validation against independent at-sea observations (
2%; Sterling, 2005). The uncertainty around estimated swept area performance will be much greater in the current application than in the sea trials, because of uncertainty (especially for the 1970s) as to the historical vessel and gear characteristics input to the PTPM. The PTPM became a means of injecting some engineering information into the standardization model, reducing problems of collinearity and varying relationships among vessel specifications as input regulations changed, and made the standardization model more parsimonious.
To illustrate annual relative fishing power (but not for estimating model coefficients nor standardized cpue), missing vessel and gear information was imputed to build a so-called reconstructed fleet dataset. The missing values were filled by interpolation within vessels from adjacent years, imputation by physical relationships dictated by laws of hydrodynamics, allocation of mean values from sister ships or vessels of similar class that fished at the same period (determined by a least squares cluster analysis), and random allocation of technology status in proportions expected according to historical fleet surveys (Dichmont et al., 2003a).
The scientific literature on catchability of the target species was reviewed (Dichmont et al., 2003a), and expert knowledge of trawl fishing and the fishery was sought (i) to decide what data items to acquire, (ii) to inform the modelling decisions, (iii) to build the reconstructed fleet dataset with features faithful to the known history of the fishery, and (iv) to define model coefficients for variables treated as offsets. The expert judgement of fishers was provided by (i) the fishing engineer on our team, (ii) fishers’ ratings of their view of the relative impacts of various technology items, obtained in a formal written survey (Bishop and Sterling, 1999) and in a less formal workshop setting (Northern Prawn Fishery Management Advisory Committee, pers. comm.), (iii) review by fishers and fleet managers in meetings of the NPF Assessment Group, and (iv) reference to published descriptions of fishing technology in the NPF (described by Dichmont et al., 2003a).
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Results |
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The period of discovery and exploration of the tiger prawn fishery during the 1970s was characterized by variable catch rates. Nominal catch rates in both May (predominantly P. esculentus; Figure 1) and September (mainly P. semisulcatus, not shown) declined from the late 1970s to the mid 1980s, then subsequently recovered.
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AIC, BIC, and R2 for the selected abundance and availability variables and interactions are given in Table 3 (model #04). Results for some alternative models are also given (models #02, #03, #11). The AIC, BIC, and R2 criteria all select the most complex model including all potential explanatory variables (model #11), even though this model, which includes the three-way interaction of year, area, and month, involves a large number of parameters.
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Vessel and gear explanatory variables
For the predictive models, the forward stepwise strategy entered vessel code as the first explanatory variable (factor) (Predictive model A; R2= 47.6%; Table 1), and the vessel–year interaction at the second step (Predictive model A2; R2 = 53.4%). No other explanatory variable then made as much as a 0.5% improvement in R2. For comparison (to investigate the consequence if vessel code was not available in the dataset, as is often the case), an alternative and more parsimonious predictive model was also fitted. A categorical variable representing net size/type of rig was selected at the first step (Predictive model B; R2 = 44.1%) and the log-transformed measure of swept area performance at the second step (R2 = 44.7%). Log of engine power and others were similar to the log of swept area performance in their contribution to R2 at the second step. No other factor then made as much as a 0.5% improvement in R2 at the third step of Predictive model B.
For the estimation model, the variables for inclusion were selected by prior consideration, as described earlier. The focus of estimation modelling was to estimate realistic coefficients, particularly for the vessel and gear variables. The low treatment for the vessel and gear variables was to estimate most coefficients from the data, when fitting the model. The high treatment was to fix the values of most vessel and gear coefficients. Between them, the low and high treatments enclose a range of realistic values of coefficients that can be supported by the data and additional information (Table 2; columns on the right side).
Below we give some illustration of the coefficient values in the high treatment, taking two examples, global positioning systems (GPS) and trygear. Trygear is a small net that is deployed frequently—say every 10–30 min. The catch in the trygear informs a skipper’s decision-making: whether or not to turn and retrawl the same ground.
Many of the technology variables were binary, corresponding to the presence or absence of a particular innovation. The coefficient estimated for a factor has a direct meaning for the contribution of that factor to the catch. The estimated coefficients for the technology variables could be compared with skippers’ reports of the contribution of the innovation to the catch rate. For example, the estimated impact of GPS was exp(0.064) = 1.066. On a night where a vessel without GPS caught 300 kg, a vessel with GPS would be expected to catch 320 kg. This is consistent in direction with skippers’ ratings of the importance of GPS, but underestimates the magnitude of the impact of GPS on catch rates, according to skippers.
The estimated coefficients for many of the binary technology variables varied across years in the single-year analyses, and across the fixed or random effects models in the preliminary analyses (Table 2; columns on the left side). For some innovations, this can be explained by the history of the technology, and its introduction and spread throughout the fleet. Some innovations, such as GPS, spread rapidly. It took only 3 years from the first appearance of GPS to almost universal adoption. During the specific years of arrival of the new technology, the dataset had optimal contrast for a given item. The estimated impact of rapidly appearing technology was attenuated when years of no contrast were included in the dataset. For example, during the 3 years of uptake 1989–1991, the estimates for the impact of GPS and plotter systems on catch (compared with satellite navigation systems) were 0.04, 0.11, and 0.13; whereas in the all-years model, the comparable estimate was 0.064. These observations suggest that the estimate of the impact of GPS was confounded with the year effect when all years were included in the analysis. Skippers reported that GPS had a high impact on catch rates, and that the impact of GPS increased each year, in the first years, as skippers developed their plotter information base. In the high estimation model, the coefficient for GPS was fixed at the equivalent of 0.13 relative to satellite navigation (obtained from the restricted years analyses), and given a small precautionary increment to allow for improvements in plotter information over time, then rescaled to the all-years baseline of no radar.
Other innovations such as trygear and sonar spread gradually. It took >15 years from the first appearance of trygear to almost universal adoption. In the restricted years models, there was considerable scatter in the results for trygear. However, there seemed to be a negative trend in the coefficients with time: at the beginning of trygear adoption, the model coefficient was 0.2, and this declined to 0 when trygear was almost fully adopted. A plausible operational scenario that could explain this trend is that vessels without trygear benefited by following those with trygear. To reflect this scenario, the trygear coefficient for the high model was fixed at 0.2 in the first year of trygear in the fishery, and the coefficient value declined each year during the period of adoption.
For three items (radar, autopilot, and the first echosounders), there was only 1 year of reliable data on their presence or absence onboard. Coefficients were fixed at the values obtained by a model restricted to that year. Doing so stabilized the rest of the results.
Standardized catch rates and relative fishing power
According to Predictive model B, in the region and depth selected for illustration of the cpue trends, standardized catch rates declined during the early 1980s, and recently there has been a slight recovery in May (predominantly P. esculentus; Figure 1a) and a substantial recovery in September (predominantly P. semisulcatus). According to the estimation models, standardized catch rates declined during the early 1980s, and there was no recovery for the following decade. Since 1996, there has been a further slight decline in May and a slight recovery in September.
The fishing power series obtained with the different models display strong similarity in some key aspects. Except Predictive model A, the series generate higher and lower values at about the same time points (Figure 1b). The major variations coincide with known events in the history of technology in the fishery.
Over the whole time period, the mean annual increment in relative fishing power from the low estimation model (where most coefficients for technology variables were estimated) was qinc = 1.049, and for the high estimation model (with most coefficients fixed) it was qinc = 1.060 (Tables 3 and 4). The average increment in annual relative fishing power (average qinc) for Predictive models A and B were both 1.02, lower than for any of the nested steps of the estimation model.
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Illustrating model outputs
To illustrate the impact of abundance, vessel, gear, and skipper explanatory variables of the estimation models, each variable was fitted incrementally. The values of AIC, BIC, and R2 at each step are listed in Table 3. Models #01 to #10 are models with variables added sequentially, without any variables with fixed coefficients, and "low" and "high" are the two final models with the fixed coefficients. Neither the low nor the high form of the estimation model would be selected by the R2, nor by the AIC or BIC criteria, if they were applied to select among this subset of models. The R2 criterion would select simply abundance with log swept area performance (#05) as the preferred model. Both the AIC and the BIC criteria would select the most complex or full model (#10) from among the series of #01 to #10. AIC and BIC decreased at each step, as variables were added to the model, only increasing when the variables with fixed coefficients were added to the model. The p-value of the F-statistic was <0.0001 at every step.
Increments in estimated standardized catch rates corresponded consistently (inversely) to the increments in relative fishing power when vessel and gear variables were successively added to the models (Figure 1; Table 3). In other words, standardized estimates of catch rate were lower for the estimation models than for any of the predictive models, whereas cumulative relative fishing power estimates were correspondingly steeper and higher. Therefore, the apparent separation of relative fishing power from standardized catch rates was greater for both low and high forms of the estimation model than for the models identified by the predictive modelling strategy.
Searching technology, including trygear, navigation, communication, and information storage, together accounted for 50% of the area under the high series cumulative fishing power curve (Figure 2). Another 29% was accounted for by harvesting power (i.e. swept area performance and TED/BRDs, both treated as offset). Increases in hours fished per day accounted for 4% of the change in relative fishing power. An additional 2% of changes in fishing power was attributable to skippers’ years of experience in the fishery. Finally, the high series of offsets relative to the low series of offsets accounted for 15% of the area under the high series curve.
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Relative fishing power outputs from the computational experiments were smoothed over years for different levels of the trialled factors, to provide a summary of the main features (Figure 3). Figures 3a–c illustrate the impact of decisions about the abundance and availability variables, and effort, whereas Figures 3d–f depict the main features of models with and without various vessel and skipper variables. The figures reveal the range of fishing power outcomes that can result when some important variables are either included or omitted. Diagrams of log(qinc) against year (Figure 4) demonstrate the differences in variability of outcomes arising from the different models. Models with highly variable outcomes were less able than the preferred final model to provide separate trends in fishing power and natural variability in abundance.
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Discussion |
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TopIntroductionMethodsResultsDiscussionReferences |
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The goal of standardization was to maximize the accuracy of an index of relative abundance that was adjusted for changes in fishing power, including technology changes within vessels and changes in fleet composition. Methods to maximize the accuracy of standardizations are particularly relevant to fisheries where there has been no regular resource survey, and where commercial logbook data are the only available source for input to stock assessments.
The standardization problem for this fishery, with its complex spatio-temporal history, input controls, and technology change within vessels, proved to be a difficult one to solve. A semi-automated model-selection strategy that aimed to maximize variance explained (the predictive strategy) did not achieve an adequate standardization, in part because of the large number of data points, but also because the usual criteria for model selection were not relevant. The large sample size led to meaningless F-statistics, and with this sort of sample size (>500 000 data points), AIC and R2 are essentially equivalent. In any case, criteria to enter based on R2 or F are only appropriate when the goal is to predict catch within the sample space of the commercial dataset. In this analysis, the goal was standardization, and the focus was to estimate coefficients of abundance and fishing power to predict the catch for a hypothetical standard vessel, somewhat outside the sample space (Harrell, 2001; Bishop, 2006).
Criteria based on AIC or BIC require that the dataset contains meaningful information on the effects of all factors in the model (Chatfield, 1995; Burnham and Anderson, 2002), whereas in this case the effects of some factors could not be estimated reliably owing to limitations in the dataset. This was made obvious by very unstable coefficients when candidate vessel and gear variables were fitted within various subsets of data. Although a very large number of records and many variables were available for analysis, there turned out to be a paucity of information on certain topics.
Information is used here in the sense of information that can be summarized by a model, i.e. the structure of relationships between variables, estimates of parameters, and components of variance (Burnham and Anderson, 2002). In the current example, information on some of the important factors appeared to be satisfactory according to all criteria that we could observe, but some other required information was either completely absent or deficient in some way, so that it was not possible to find stable estimates of some effects. The observational data turned out to be not sufficiently informative to estimate all the important effects of the catchability process well enough to unlock the confounding and to separate the components of abundance and fishing power.
The most serious issue in this investigation was the highly unbalanced and non-orthogonal design for factors in the regression model, which was unavoidable owing to non-random (very targeted) commercial fishing strategies. Other unavoidable complications were attributable to correlations between vessel and gear variables, varying relationships among gear variables as a consequence of input control history, technical change within vessels caused by innovations and changing regulations, the target species with short lifespan recruitment coinciding with vessel upgrades, and possible confounding of technical upgrades with spatial patterns of fishing. Missing information, variable quality of information, and unmeasured items caused some problems, demonstrating the great advantage of regular collection of detailed vessel and gear specifications in fisheries where effort creep is an issue.
We argue that the most likely outcome of these problems is distortion of relative indices of abundance and fishing power, caused by a failure to unlock the confounding between the two and to separate these components of catch rates. Trends in both standardized cpue and relative fishing power would therefore appear to be artificially stable and inadequate as relative indices.
When input to stock assessments, the types of difference in trends reported from the two modelling approaches in this study are significant enough to alter conclusions about the status of stocks, and to trigger different management decisions (Wang and Die, 1996; Dichmont et al., 2003b). On the basis of the evidence described here (comparison of all years with within-year values for coefficients, and fixed effects with random effects; sensitivity analyses; review of catchability in this fishery; judgement of fishers; degree of separation of relative abundance from relative fishing power; comparison of trends with those expected from known history of the fishery), we felt that the estimation models achieved better standardization.
Obtaining an adequate result required external information about the impact of technology on catch rates. The external information came from (i) an independent study, (ii) ancillary analyses of subsets of data, and (iii) substantive knowledge and expert judgement. The information was incorporated into linear regression models by fixed values for coefficients of some vessel and gear explanatory variables. Doing so makes use of the linear model’s facility for integrating all available information. The linear model estimates year and area coefficients, adjusted for all explanatory variables. This offers some protection against distorted relative abundance indices by ensuring that the indices have been adjusted for the variables with coefficients fixed to values determined externally, as well as for the variables with coefficients estimated by the model. This is a straightforward extension of the usual linear modelling approach, akin to adopting Bayesian priors.
A single conclusive result could not be obtained. A range of possible offset variables and fixed values for their coefficients was investigated, and summarized as an envelope of possible relative fishing power curves over time. This is sufficient representation of uncertainty for management purposes. In addition, we acknowledge that there is an obligation to continue to review the plausibility of results in the light of all available evidence. The low series represents a lower bound of fishing changes that is unequivocally detected within the available data, and the high series incorporates some element of precaution. Therefore, this study achieved a bounding envelope of possibilities that was an improvement on the previous state of knowledge for the fishery, and consequently removed some of the risk and uncertainty from its management.
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Acknowledgements |
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We acknowledge David Die for establishing the direction for the work, the fishers of the northern prawn fishery and the Australian Fisheries Management Authority (AFMA) logbook programme for continuing to provide valuable logbook information, and reviewers Malcolm Haddon, Marinelle Basson, Iain Cartwright, Ben Stewart-Koster, and four anonymous referees, for their valued critical comments. The work was funded by the AFMA Research Fund, and the Australian Government Department for Agriculture, Fisheries and Forestry Research Fund. Much of the analytical work was carried out while the first author was employed by CSIRO Marine and Atmospheric Research.
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References |
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