Developing Indices of Abundance Using Habitat Data in a Statistical Framework

We describe the statistical application of the habitat-based standardization (statHBS) of catch-per-unit-effort (CPUE) data to derive indices of relative abundance. The framework is flexible, including multiple component models to accommodate factors such as habitat, sampling, and animal behavior. It allows the use of prior information or the completely independent estimation of model components (e.g., habitat preference). The integration with a general linear model framework allows convenient comparison with traditional methods used to standardize CPUE data. The statistical framework allows model selection and estimation of uncertainty. The statHBS model is applied to bigeye tuna in the western and central Pacific Ocean. We describe several additional improvements to the methodology. Knowledge of trends in population abundance is important for the development of appropriate management actions. Methods used to estimate trends in abundance range from population dynamics models and observational studies to surveys and experiments. Unfortunately, there are many factors that can influence our perception of results obtained from these methods, and these become more problematic as our control over the data collection process decreases. For example, opportunistic observational studies can be influenced by factors such as the time of year in which observations were recorded, which may change from year to year, resulting in bias in the estimated trends. Attempts are made to minimize bias by designing the data collection appropriately or by collecting additional variables than can be used to adjust for these factors. With such ancillary information, it is common to employ a general linear model (GLM) to model the dependent variable, which is assumed to be related to abundance (e.g., catch-per-unit-of-effort, CPUE) and to include the ancillary data as explanatory variables to remove variation that is not related to abundance (Maunder and Punt, 2004). In GLMs, time is usually modeled as a categorical variable, and is used to represent the temporal changes in relative abundance. One of the principal factors influencing observations of animal abundance is habitat. Habitat is generally defined as an abiotic factor such as temperature or a physical structure that may be abiotic (e.g., bottom type) or biotic (presence of sea grass), but could be extended to any relevant factor such as presence of other species. Habitat influences observations, either because the density of individuals varies among habitat types, or because the ability to observe the individuals varies among habitat types. Therefore, analyses of information on abundance should be adjusted for habitat type. For example, habitat type could be included as one of the explanatory variables in a GLM, but this requires that habitat type be recorded for each observation. GLMs are just one group of a multitude of methods that have been used to derive indices of abundance. They have some desirable properties, in that they can include habitat data and in that they are carried out in a statistical framework. The statistical framework allows estimation of parameters and a description of uncertainty. However, GLMs exhibit weakness in their limited ability to include scientific underBULLETIN OF MARINE SCIENCE, VOL. 79, NO. 3, 2006 546 standing about the system, particularly nonlinearities, and in some situations, they are unable to adequately model observations that sum information across multiple habitats. Hinton and Nakano (1996) derived a general framework, commonly called habitat-based standardization (HBS) that overcomes the weaknesses of the GLM models described above. The HBS method matches the sample effort data, in this case fishing effort, with distributions of the habitat and the habitat preference of the species. It does not require that the exact location of capture within the habitat be known, only that the total catch resulting from the effort (e.g., set) and a measure of the habitat for each unit of effort (e.g., hook) be known, which provides a significant advantage when designing sampling schemes for cryptic or hard-to-observe captures. The HBS method is a process model that incorporates the sampling process and scientific understanding of the system. Component models can be developed for each of the processes (e.g., habitat, sampling, and animal behavior). Hinton and Nakano (1996) illustrated their method with a simple deterministic application to Japanese longline catch and effort data for blue marlin (Makaira nigricans Lacépède, 1802) in the Pacific Ocean. The sampling effort component model was generated using the depth of hooks between the floats of a longline from a catenary curve function of the number of hooks deployed between the floats (Fig. 1). This was done because the Japanese longline fleet has increased the number of hooks between floats over time to increase the depth of the hooks so as to target bigeye tuna (Thunnus obesus, Lowe, 1839), a species that occurs at deeper depths (Nakano and Bayliff, 1992). The depths of the hooks estimated from the catenary curve model were then matched with habitat distribution from a component model based on the temperature difference from the mixed layer and the time at temperature for blue marlin relative to the mixed layer derived from acoustic telemetry data (Holland et al., 1990). The effort (number of hooks) was then converted into effective effort by weighting each hook by the appropriate habitat preference and summing over all hooks on the entire longline. Much controversy has surrounded the applications of the Hinton and Nakano (1996) HBS method (Goodyear et al., 2003; Ward and Myers, 2005; Prince and Goodyear, 2006). Much of this is related to the details of the specific illustration of HBS using blue marlin data as presented by Hinton and Nakano (1996), which they stated was intended “To illustrate the method ...” (p. 176). However, the HBS method is a general framework, and many of the criticisms are unfounded or have been addressed in later works (e.g., Bigelow et al., 2002). For example, a criticism that the method does not consider when individuals are feeding is not a deficiency of the method, but a deficiency in the component process model and data used to determine the habitat, and if “differences are found, then ... [HBS] may be structured to account for [them]” (Hinton and Nakano, 1996, p. 178). In limited simulation studies, Hinton (1996) illustrated that the method could perform well in the presence of environmental variability. Several tests have been used to determine the appropriateness of the HBS-derived indices of abundance. Comparison of total likelihoods from stock assessment models, including indices of abundance based on nominal effort and those based on HBS (e.g., Hinton, 2001; Hinton and Bayliff, 2002), have been used to determine if the HBS effort was more consistent with the assumed population dynamics and other data (e.g., total catch) compared to nominal effort (Hinton and Maunder, 2004a). MAUNDER ET AL.: STATISTICAL HABITAT-BASED STANDARDIZATION 547 In another indirect test, population dynamics model (MULTIFAN-CL) results with nominal effort were unreasonable, but results obtained from effort obtained from HBS allowed model fits with reasonable estimates of ancillary parameters, such a growth and mortality (Kleiber et al., 2003). The controversies continued over the appropriateness of the results obtained from applications of the HBS method, which inspired further testing of estimation and modeling using the method. A more traditional testing approach using several testing criteria (Akaike Information Criterion [AIC], Bayesian Information Criterion [BIC], Bayes factors) was applied by Maunder et al. (2002). This method compared observed and predicted catch using nominal and HBS effort for yellowfin (Thunnus albacares Bonnaterre, 1788) and bigeye tuna in the Pacific Ocean. They found that the HBS effort was substantially better than nominal effort. However, these and other results indicated that certain habitat preference models developed from archival tag information may not always be the best or appropriate models to use in a given habitat-based standardization. More discussion about the inappropriateness of the archival tag data is presented later. The method of testing the HBS method used by Maunder et al. (2002) led to a logical process of estimating the parameters of the HBS method in a statistical framework (statHBS). In statHBS, the estimation of the habitat preference parameters (or parameters for other components of the model) can be allowed to improve the fit of the model to the observed catch data. This allows for more direct model testing and calculation of confidence intervals than would be possible in a non-statistical framework. There have since been a number of applications of statHBS (e.g., Bigelow et al., 2003; Hinton and Maunder, 2004b; Langley et al., 2005). However, the statHBS model has yet to be described in the primary literature. Applications of HBS and statHBS are not limited to situations involving longline catch and effort data. The method is more general and can be applied in many other situations. First we describe why GLM and related approaches may not be suitable for application when observations sum information across multiple types of habitat. Next we describe the basic concepts of statHBS. Then we apply statHBS to the Japanese longline catch of bigeye tuna and effort data in the western and central Pacific and compare it to two alternative approaches, a “deterministic” application of the HBS method (detHBS), which is similar to the Hinton and Nakano (1996) illustration shown with blue marlin and nominal effort. Finally, we describe potential modifications of the statHBS. Figure 1. Vertical distribution of hooks based on catenary geometry from a typical longline set in the Japanese longline fishery that deployed 15 hooks between floats. BULLETIN OF MARINE SCIENCE, VOL. 79, NO. 3, 2006 548 Summing Data Across Multiple Habitats There are many possible scenarios for which observed data can be summed across multiple habitat types. The longline catch and effort application of Hinton and Nakano (1996) is a common example in fisheries. Other marine examples include plankton tows with continuous or periodic oceanographic (e.g., temperature) recorders, and trawl surveys with continuous or periodic depth recorders. To model this type of data, an equation is needed to predict the observations. The equation must sum the predicted catches for each of the units of effort with reference to the habitat type and compare that sum to the total observed catch. For a simple example, let Ci,j represent the predicted catch for component j for observation i, and Ti,j represent the temperature as a continuous variable for component j of observation i. If a linear relationship is assumed between catch and temperature C T , , i j i j = + a b C C T J T , , , i i j