Standardizing catch and effort data: a review of recent approaches
Introduction
Scientific advice on fisheries management is generally based on the results of the application of some form of stock assessment technique (Hilborn and Walters, 1992). Stock assessment usually involves estimating the parameters of some form of population dynamics model by fitting it to research and monitoring data and using the results of the fitting process to estimate quantities (such as the current abundance) that are of interest to the decision makers. A variety of data types can be used when fitting stock assessment models. However, the data generally must include information on at least the removals due to harvesting and an index of relative abundance. Although the index of abundance should, ideally, be based on fishery-independent data collection methods such as surveys, fishery-independent data are often extremely costly or difficult to collect, in which case it must be based on fishery-dependent data. Therefore, assessments of many stocks (e.g. sharks and tunas) are based solely on fishery-dependent data. The most common (and easily collected) source of fishery-dependent data is catch and effort information from commercial or recreational fishers, usually summarized in the form of catch-per-unit-of-effort (CPUE) or catch rate.
The use of catch rate as an index of abundance assumes that, at small spatial scales, catch is proportional to the product of fishing effort and density:where E is the fishing effort expended, N the density, and q the fraction of the abundance that is captured by one unit of effort (often referred to as the catchability coefficient).
Re-arranging Eq. (1) leads to the fundamental relationship between catch rate and density:Eq. (2) can be generalized from a small patch fished by a single fisher to the entire population fished by a large fishing fleet (in which case N is the population size rather than density) as long as q is a constant (independent of time, space, and fishing vessel). However, q may not be constant, but may change spatially and temporally due to changes in the composition of the fishing fleet, where fishing occurs, and when fishing occurs (e.g. Cooke and Beddington, 1984, Cooke, 1985, Hilborn and Walters, 1992). As an example, consider the case in which there are two fishers, and abundance is constant over time, with the result that the catch rate for each of the fishers is constant over time (Fig. 1, left panel). If the catch rate for fisher 1 is twice that for fisher 2 and the fraction the total effort expended by fisher 1 decreases from 80% of the total effort in year 1 to 20% in year 10, there is a marked decline in the ‘raw’ catch rate (total catch divided by total effort) over time (Fig. 1, right panel), even though there is actually no change in the true abundance of the resource.
The ability to use catch rate data as an index of abundance therefore depends on being able to adjust for (i.e. remove) the impact on catch rates of changes over time of factors other than abundance. This process is often referred to as ‘catch-effort standardization’. The dangers associated with basing stock assessments on ‘raw’ catch rates have been known for many years, and various methods for standardizing catch and effort data have been developed (e.g. Gulland, 1956, Beverton and Holt, 1957, Robson, 1966, Honma, 1973), all of which define the efficiency of a fishing vessel as its ‘fishing power’ relative to that of a standard (and perhaps even hypothetical) fishing vessel. The most commonly applied method prior to the use of generalized linear modeling approaches was that developed by Beverton and Holt (1957). This method involves selecting a ‘standard vessel’ and determining the relative fishing power of all other vessels bywhere RFPi is the relative fishing power for vessel i, Ci the total catch by vessel i during the period in which both the standard vessel and vessel i were in the fishery, CS the total catch by the standard vessel during the period in which both the standard vessel and vessel i were in the fishery, Ei the total days fished (or whatever measure of fishing effort is chosen) by vessel i during the period in which both the standard vessel and vessel i were in the fishery, and ES the total days fished by the standard vessel during the period in which both the standard vessel and vessel i were in the fishery.
The standardized catch rate for year t, It, is then defined aswhere Ct,i is the catch by vessel i in year t, and Et,i the number of days fished by vessel i in year t.
Although straightforward to apply, the approach of Beverton and Holt (1957) does not generalize easily to deal with multiple factors such as month and area, and when there is no fishing vessel that has been in the fishery for many years and can be used as the standard vessel. Finally, it is not straightforward to determine the precision of the standardized catch rate estimates; this information is, however, needed when applying many of the methods of stock assessment.
More recent methods for standardizing catch and effort data involve fitting statistical models to the catch and effort data. The first examples of these methods were by Gavaris (1980) and Kimura (1981). However, the last two decades have seen a proliferation of new methods to standardize catch and effort data, most of which extend these methods to some extent. The choice among these methods should be based on an evaluation of the underlying assumptions of the models and use of appropriate statistical tests and diagnostics. Understanding of the fishery being modeled may also provide insight into which method should be used. For example, many fishery systems are inherently nonlinear, and methods that can handle nonlinear relationships between catch rate and potential variables that capture changes over time and space in catchability may be more appropriate.
This paper reviews many (but, by no means, all) of the decisions that must be made when standardizing catch and effort data. The following sections highlight various issues related to the choice of the model on which to base the analyses and the data set to be considered, focusing, in particular, on model selection and how to deal with records for which the effort is non-zero, but the catch is zero.
Most of the catch-effort standardizations on which actual assessments are based are documented in the gray literature. We have attempted in this review, as much as possible, to restrict the examples to cases in which the basic documents are fairly readily available.
Section snippets
Generalized linear models
Generalized linear models (GLMs; Nelder and Wedderburn, 1972) are the most common method for standardizing catch and effort data. Gavaris (1980) appears to have been the first to have used a GLM approach to standardizing catch and effort data when he extended the use of multiplicative models for this purpose (Robson, 1966) by explicitly assuming log-normal errors. Gavaris (1980) applied an analysis of variance (ANOVA) model (only categorical explanatory variables) to the natural logarithm of
Dealing with zero catches
Catch and effort databases often include high proportions of records in which the catch is zero, even though effort is recorded to be non-zero (records in which effort is recorded to be zero must be either trivial if they have zero catch as well, or in error and this should be resolved in some way (e.g. discarded) prior to any analyses being conducted). This is particularly the case for less abundant species and for bycatch species. Unfortunately, these species are often those for which a
Selecting explanatory variables
The main goal in standardizing catch and effort data is to explain the variation in catch rate that is not a consequence of changes in population size by identifying explanatory variables that reduce the unexplained variability in the response variable. Both qualitative and quantitative variables can be included as explanatory variables in most methods. Qualitative variables are treated as factors while quantitative variables can be treated either as ordered values and used in functions, or
Dealing with interactions
Interactions among factors occur fairly regularly when standardizing catch and effort data. The most common interactions are among year, month/week/day and area. Discovering significant (and substantial) interaction terms can raise some interesting hypotheses. For example, discovering a year × vessel interaction implies that the relative abundance has changed differently as seen by different fishers. However, explaining interactions can be difficult, and there is often no rational explanation
Selecting data points
The bulk of the world's marine fish species are caught in fisheries that involve multiple target species. This is particularly true for species caught in trawl fisheries and those caught recreationally. Given the requirement to standardize the catch and effort data for a species that is caught in a multi-species fishery, it seems desirable to use only the effort that was directed at that species. Unfortunately, this is much easier said than done, even when fishers claim to record their target
Using indices of abundance in stock assessment models
The primary reason for standardizing catch and effort data is to develop an index of relative abundance. This can be used as the basis for management advice directly, but is typically used when fitting a stock assessment model. To use an index of relative abundance estimated from catch and effort data in a stock assessment, the index of abundance must first be extracted from the standardization analysis (see Section 2.3) and then an appropriate fitting method, usually a likelihood function,
Discussion
Standardization of catch and effort data to develop an index of the relative abundance of a fish population assumes that the explanatory variables available are sufficient to remove (or explain) most of the variation in the data that is not attributable to changes in abundance. However, even if catch and effort data are standardized to remove the impact of all known factors, there is still no guarantee that the resultant index of abundance is linearly proportional to abundance (as is assumed in
Acknowledgements
AEP was supported by NMFS grant NA07FE0473. William Bayliff, Cleridy Lennert, and Bill Venables commented on the manuscript. Paul Starr and two anonymous reviewers reviewed the manuscript. In particular, we thank Paul Starr for his thorough review and numerous suggestions for its improvement.
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