Trend Information

Fisheries stock assessment models rely on historical time-series information to make inferences about how fishing activities have affected the stock. There are three main types of data that are commonly used in fisheries stock assessments: (1) a time series of abundance (absolute or relative abundance estimates), (2) information on mortality, and (3) compositional information on age, size, or sex ratios. It is not necessary to have all three types of data in order to proceed with estimating historical impacts, but at least one of these types is necessary.

Abundance information (relative abundance or absolute abundance) is frequently obtained from fisheries-dependent sources, and perhaps the most common statistic is the catch rate information or catch per unit effort (CPUE). The basic notion is that the rate at which fish are removed from the population is a function of the abundance and this rate is usually assumed to be directly proportional to abundance. This assumption presumes that spatial allocation of fishing operations is randomly distributed with respect to the spatial distribution of the target species, an assumption that is almost always violated. However, in many industrial fisheries around the world, this is the only information that is available to make inferences on the relative change in population abundance. Most often fisheries-dependent CPUE data are assumed to be proportional to stock size, and the underlying error structure is assumed to be log-normally distributed. This can be represented as a simple equation:

Where Bt is the biomass of the stock, q is the catchability coefficient (a scaling term) and et is the error term. Equation [1] assumes that trends in the CPUE index are proportional to trends in stock biomass. In general, there have been two strong objections to the use of commercial CPUE indices, the first being a violation of the proportionality assumption (i.e., the trends in CPUE are not directly proportional to trends in Bt). Fishery-dependent CPUE indices are most likely to be hyperstable (i.e., catch rates decline at a much slower rate than the stock size). The second major objection owes to the variability in CPUE indices among a fishing fleet. Most often, commercial CPUE indices are derived from an entire fishing fleet (e.g., CPUE = ^ Ck/^2Ek, where k is an index for individual fishing vessels, C is the catch by any individual vessel, E is the individual fishing effort, and CPUE is the mean catch rate over the entire fleet). Variability in individual catch rates or relative improvements in fishing technologies over time, or even the composition of the fishing fleet each year can change the interpretation of the CPUE index. Some people just catch more fish than others, whether it is due to better fishing gear, knowing where the fish are, or having a bigger boat. This inherent variability becomes problematic when the less apt fishermen drop out of the fishery altogether and as a result the mean CPUE increases.

When alternative abundance indices are available, such as those derived from fisheries-independent surveys, it is normally wise to severely discount or ignore indices that are derived from fisheries-dependent sources. If however, the fisheries-dependent CPUE information is the only available abundance index then standardization of the CPUE index is recommended. CPUE standardization is a fairly active research area in fisheries science, and it attempts to remove individual variability in catch rates as well as interannual variation in catch rates that are associated with changes in fishing technology, fleet composition, environmental covariates and other associated factors that could potentially affect catch rates. The standardization process is usually carried out using generalized linear models (GLMs) where the cov-ariates may be both categorical variables (e.g., individual boats, capture method, area fished) and continuous variables (e.g., water temperature, price of fish, fuel cost). Recently, this standardization process has also been integrated into the whole stock assessment framework, where the coefficients in the GLMs are jointly estimated along with all other parameters.

Fisheries-independent surveys most often employ a stratified random sampling design; therefore, trend information is much more likely to be proportional to stock size. However, fisheries-independent surveys are also capable of generating estimates of absolute abundance, primarily by using area-swept information and spatial interpolation. This approach will generate an estimate of mean density (e.g., number of fish per unit area) and multiply this density by the total area over which the stock is distributed. There are two main technologies employed to generate absolute abundance estimates over large spatial scales: (1) bottom trawls for benthic species, and (2) hydroacoustic technologies for pelagic species. Bottom trawls generate density estimates over a survey grid, and spatial statistics (e.g., bicubic splines or Kriging methods) are used to interpolate between survey points (see blue crab example in Figure 2). Hydroacoustic technologies use sound to measure the amount of backscatter in the water column, this backscatter corresponds to

Blue crab density (#/1000 m sq







Figure 2 An example of geostatistical techniques for estimating absolute abundance of blue crabs in the Chesapeake Bay based on Kriging methods for interpolation of trawl survey data. Kindly provided by Olaf P. Jensen (University of Wisconsin).

individual fish and the technology is now sufficient to estimate the size of individual targets.

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