Estimation of Age-Specific Migration in an Age-Structured Model

The standard Eastern Bering Sea (EBS) walleye pollock (Theragra chalcogramma) age-structured stock assessment model has no spatial dimension. To better understand its dynamics on finer spatial and temporal scales, an age-specific movement (ASM) model was developed. The ASM model stratifies the assessment data into two regions (northwest [NW] and southeast [SE] EBS), includes movement, and allows population parameters to be region-specific. The ASM model was used to evaluate hypotheses on age-specific movement between the NW and SE and covered years 1977 to 2005 and ages-3 to 10+. Estimates of biomass and population parameters from the ASM model were similar to those of the standard stock assessment model. The ASM model fitted the yearly observed catch numbers and yield, and catch-age composition data well, but some population parameters were highly uncertain or highly correlated. More in-depth information on finer spatial and temporal scales is needed from spatially explicit studies of EBS walleye pollock. Having additional information from a mark-recapture study would help to stabilize the ASM model and allow some assumptions to be relaxed. 162 Miller et al.—Age-Specific Migration Introduction Fish are mobile creatures so it seems natural to include movement and spatial structure in a model that estimates abundance and affects fisheries management policies. Yet, movement and spatial structure of fish populations are infrequently incorporated into stock assessment (Quinn and Deriso 1999, Chapter 10). Ignoring spatial structure can lead to misinterpretations of basic population-dynamic processes (Härkönen and Harding 2001), and ignoring movement can lead to errors in detecting potential stock declines (Nielsen 2004, Chapter 1). Walleye pollock (Theragra chalcogramma) is the dominant species in the commercial groundfish catch off Alaska. In 2003, the eastern Bering Sea (EBS)–Aleutian Islands walleye pollock fishery accounted for 76% of the groundfish catch (1.49 million metric tons [t]) and 63% of the total ex-vessel value ($302 million dollars) (Hiatt et al. 2004). Of this catch, 0.36 million t were caught in the northwest (NW) EBS, and 1.13 million t were caught in the southeast (SE) EBS (Ianelli et al. 2004) (Fig. 1). The modern fishery (since the early 1990s) has had two seasonal components: a winter roe fishery on spawning aggregations (“A-season”) with an opening on January 20, and a summer/fall “B-season” opening in mid-late June (prior to 2000 the opening was later). Beginning in 2002, the A-season was allocated 40% of the catch and the B-season, 60%. Both seasons’ lengths depend on the catch rates (Ianelli et al. 2005). Juvenile Figure 1. Fishery management areas and the hydroacoustic (EIT) survey are divided between the NW and SE Eastern Bering Sea by 170oW. Area 518 is the Bogoslof district and areas 541-543 encompass the Aleutian Islands region. 163 Resiliency of Gadid Stocks to Fishing and Climate Change walleye pollock reach sexual maturity and recruit to the fishery at about age-4 at lengths of 40 to 45 cm (Wespestad 1993). The stock structure of walleye pollock in the EBS is poorly understood (Ianelli 2005). Walleye pollock exhibit movements throughout their life history and during the year. During the spring and summer EBS walleye pollock migrate to feeding areas, and during the winter they migrate to spawning areas. Most walleye pollock populations spawn during the late winter and early spring (Mulligan et al. 1989, Bailey et al. 1999). Interannual variations in walleye pollock recruitment are important because they drive the annual population size that affects higher and lower trophic levels and the harvest levels of the fishery. Walleye pollock recruitment is determined by both biological (egg production, cannibalism, predators, food sources, spawning biomass, larval mortality, year-class strength), and environmental-oceanographic (temperature, storms, ice cover and retreat, currents, cold-pool) factors (Wespestad et al. 2000, Mueter et al. 2006). Studies have shown that there are differences in the biological and behavioral aspects of walleye pollock in the NW and SE EBS (Fig. 1). Walleye pollock in the NW EBS are slightly smaller and have lower average growth rates than walleye pollock in the SE EBS (Lynde et al. 1986, Ianelli et al. 2004). Differences in cannibalism rates, spawn timing, feeding rate, and reproductive output may also occur between the SE and NW EBS. Some of these observations can be explained by the hypothesis that as walleye pollock get older (ages 3+), there is a general ontogenetic movement from the NW to SE EBS (Bailey et al. 1999, Buckley et al. 2001). The standard EBS walleye pollock stock assessment model is an age-structured population dynamics model (Quinn and Deriso 1999, Chapter 8; Ianelli et al. 2004). The main structure of the model is represented by “true” but unobservable population numbers-at-age that are based on an array of parameters for fishing and natural mortality, and recruitment, some of which are estimated within the model. Fishing mortality is parameterized to be semi-separable with both year and age (selectivity) components. Parameters such as mean weights-at-age and -year, maturity-at-age, and natural mortality are estimated independently of the model. Currently there are no estimates of EBS walleye pollock movement rates. We determined if age-specific movement could be estimated from the current disaggregated assessment survey and fishery data. We tested the two following hypotheses: (1) The age-specific movement (ASM) model can estimate migration without movement (tagging) data, but with a great deal of uncertainty; and (2) The ASM model performs better than a non-movement version of the spatial, two-season ASM model. 164 Miller et al.—Age-Specific Migration Methods Data sources Thirteen data sources were used to fit the model (Table 1). Stock assessment data from the bottom trawl survey (BTS), the echo-integration trawl (EIT) survey, and the fishery were stratified into two regions, the northwest (NW) and southeast (SE) EBS (scientist personnel, Alaska Fisheries Science Center, 2006). The fishery data were further stratified into two seasons (“A” and “B”). The fishery management areas and the EIT survey are divided into NW and SE by 170oW (Fig. 1). The bottom trawl survey data are defined by a slight angle from the 170oW dividing line. The division differences are a function of the sampling design. The Bogoslof district (area 518) fishery data could not be disaggregated from the EBS data when the data were split between the NW and SE and the A and B harvest seasons. The only significant catch from the Bogoslof district came from 1984 to 1991 (Ianelli et al. 2005) (Fig. 1). Age-specific movement model A discrete-time region specific age-structured model was specified as an operational population dynamics model (e.g., Fournier and Archibald 1982, Hilborn and Walters 1992, Schnute and Richards 1995) that was a simplified version of the 2005 stock assessment (Ianelli et al. 2005). This age-specific movement (ASM) model was divided into components throughout the year as follows: spawning and recruitment (starting at time A in the winter), the A fishing season (A to A), walleye pollock movement after spawning to summer feeding areas along with half of the natural mortality (A to B), the B fishing season (B to B), and finally walleye pollock movement before spawning along with half of the natural mortality (B to A) (Fig. 2). There were 185 total parameters estimated in the ASM model. Table 1. Thirteen disaggregated data sources showing available data years in parentheses and unavailable data years labeled missing. BTS stands for bottomtrawl survey and EIT stands for echo-integration trawl survey.