An Improved Sibling Model for Forecasting Chum Salmon and Sockeye Salmon Abundance

—The sibling model is often one of the best methods for calculating preseason forecasts of adult return abundance (recruits) for populations of Pacific salmon Oncorhynchus spp. This model forecasts abundance of a given age-class for a given year based on the abundance of the previous age-class in the previous year. When sibling relations fit historical data well, the sibling model generally performs better than other forecasting methods, such as stock– recruitment models. However, when sibling relations are weak, better forecasts are obtained by other models, such as naı̈ve models that simply use an historical average. We evaluated the performance of a hybrid model that used quantitative criteria for switching between a sibling model and a naı̈ve model when generating forecasts for 21 stocks of chum salmon O. keta and 37 stocks of sockeye salmon O. nerka in the northeastern Pacific Ocean. Compared with the standard sibling model, the hybrid model reduced the root mean square error (RMSE) of forecasts by an average of 27% for chum salmon stocks and 28% for sockeye salmon stocks. Compared with a naı̈ve model, the hybrid model reduced the RMSE of forecasts by an average of 16% for chum salmon stocks and 15% for sockeye salmon stocks. Our results suggest that hybrid models can improve preseason forecasts and management of these two species. Fishery management agencies often generate preseason forecasts of returns of Pacific salmon Oncorhynchus spp. for initial guidance on the fishing regulations that may be needed to achieve spawner abundance (escapement) or harvest-rate goals. The fishing industry has also used these forecasts to regionally allocate harvesting and processing equipment and personnel. However, the predictive performance of preseason forecasts is often poor (Adkison and Peterman 2000; Haeseker et al. 2005), due in part to high interannual variation in survival and recruitment rates (Peterman 1987; Bradford 1995). As a result of forecasting error, management agencies may have difficulty achieving escapement goals or harvest-rate targets, and the fishing industry may experience economic losses (Bocking and Peterman 1988; Eggers 1993). The standard sibling model (Peterman 1982) has often demonstrated relatively good forecasting ability for sockeye salmon O. nerka and chum salmon O. keta (Bocking and Peterman 1988;Wood et al. 1997). Adults of both species return to their natal streams and rivers across two or more ages (e.g., as 4–5-year-olds), but the proportion at each age is not constant across years, thereby creating a challenge for forecasting total abundances. Furthermore, juvenile sockeye salmon rear in lakes for 1 or 2 years before migrating to the ocean; thus, the number of years spent in freshwater (i.e., before ocean entry) varies. Ages of sockeye salmon and chum salmon are designated as x.y, where x is the number of winters spent in freshwater and y is the number of winters spent in the ocean. The chum salmon stocks evaluated in this analysis mainly consisted of ages 0.2, 0.3, and 0.4 (Table 1), while the sockeye salmon stocks mainly consisted of ages 1.1, 1.2, 1.3, 2.1, 2.2, and 2.3 (Table 2). The sibling model forecasts the abundance of adult recruits of a given age returning in year t from the abundance of the previous adult age-class that returned in year t! 1. By using data on such siblings from the same brood year that also spend the same number of winters in freshwater (but one less winter in salt water), the sibling model takes advantage of the covariation in response to critical environmental influences that these age-groups of fish share during their early life stages (Peterman et al. 1998; Pyper et al. 2002, 2005). Nevertheless, there are examples of naı̈ve time series models outperforming sibling models (Noakes et al. 1990; Wood et al. 1997). In this context, naı̈ve models are those that do not require statistical parameter estimation but rather simply summarize past observations to make forecasts. For example, naı̈ve models could be based on average recruitment over the previous 5 years or the prior year’s recruits. Recently, some biologists have adopted hybrid approaches that use both sibling and naı̈ve models for forecasting the age-specific components of salmon returns (Eggers 2003). However, there is little guidance on when to use a sibling model, a naı̈ve model, or a hybrid approach. * Corresponding author: [email protected] 1 Present address: U.S. Fish and Wildlife Service, Columbia River Fishery Program Office, 1211 Southeast Cardinal Court, Suite 100, Vancouver, Washington 98683, USA 2 Present address: Institute for Fisheries Research, 1109 North University Avenue, 212 Museums Annex Building, Ann Arbor, Michigan 48109-1084, USA Received March 24, 2006; accepted September 20, 2006 Published online April 26, 2007 634 North American Journal of Fisheries Management 27:634–642, 2007 ! Copyright by the American Fisheries Society 2007 DOI: 10.1577/M06-094.1 [Management Brief]