Equilibrium yield-curve analysis through an analytic age-structured production model: A sensitivity study for the Chilean jack mackerel fishery
Introduction
This paper deals with approaches to bridging the relationship between equilibrium surplus production and age-structured models of fisheries. It is concerned with the so called “age-structured production model” (ICES, 1997), which is a combination of yield-per-recruit and spawning biomass-per-recruit analysis with a suitable stock–recruitment (S–R) relationship, to produce total equilibrium yield curves for a fishery (Shepherd, 1982, Sissenwine and Shepherd, 1987). Usually, production modeling begins when an S–R curve is fitted to the respective stock data, i.e. when a time series of recruitment and spawning biomass data is available for the stock under analysis. However, the traditional statistical analysis of stock–recruit data pairs can be confounded by environmental variation and measurement error for several fisheries (Hilborn and Walters, 1992, Quinn and Deriso, 1999). Furthermore, time series of stock–recruit data pairs can be short and uninformative about the S–R relationship. These are real problems for many fisheries, particularly in data-limited situations.
In this paper, the S–R question is attacked from a different perspective from the traditional statistical analysis. S–R parameters are guessed from equilibrium relationships obtained by combining S–R properties with the unexploited spawning stock biomass-per-recruit. These relationships are achieved by reformulating the S–R models of Ricker, 1954, Ricker, 1975, and Beverton and Holt (1957) in terms of an unexploited spawning stock biomass (S0) and a factor, which permits the slope of the S–R relationship to be guessed (e.g. Francis, 1992, Cubillos, 1994).
We developed our analysis for the Chilean jack mackerel, Trachurus symmetricus murphyi (Nichols) fishery. This resource supports one of the largest Trachurus fisheries in the world, where catches are mainly destined for fish meal. Jack mackerel has been exploited along the Chilean coast from 1965 by industrial seiners, particularly in the northern zone (18°20′–24°S) and in the central-southern area (33–40°S). From 1978 to 1991, jack mackerel was exploited also by an international distant mid-water trawl fleet operating offshore of the 200 nautical miles off Peru and Chile (Parrish, 1989, Elizarov et al., 1993, Arancibia et al., 1995a). Total Chilean catches increased notably after 1975, from levels under 0.5 million t before 1975 to a peak of 4.4 million t in 1995. Between 1992 and 1998, the major catches occurred in the central-southern Chile, contributing with more than 90% to the national catches of jack mackerel (Fig. 1).
The objectives of this paper are to explore the equilibrium yield properties and management-related quantities for the jack mackerel fishery through an age-structured production model that uses fishery and life history parameters of jack mackerel, according to the uncertainties in both the unexploited spawning stock biomass and the functional shape of the S–R relationship.
Section snippets
Brief antecedents of the Chilean jack mackerel fishery
Jack mackerel is a middle-sized pelagic species that inhabits the southern Pacific Ocean. In the early 1970s, it was believed that the jack mackerel was found only along the coastal waters of Chile and Peru. However, the activity of Russian fleet and their research experience during the late 1970s and the 1980s, in the oceanic waters from South America to New Zealand, demonstrated that it extends all along the South Pacific Ocean over a fairly broad band (10–15° width) from Chile to New Zealand
Yield and spawning biomass-per-recruit
Yield-per-recruit (YPR) and spawning biomass-per-recruit (SPR) were computed using age-structured models. Under equilibrium, the abundance of a complete year-class of a stock is equal to the abundance of all year-classes in that stock (Beverton and Holt, 1957). In this way, the age-structured dynamics of the population at the equilibrium (per recruit) can be expressed bywhere Na is the number of fish of
Results
Spawning biomass-per-recruit (SPR) computation for jack mackerel, at the three cases of age-specific selectivity, indicates a value of 1.345 kg at . The S–R curves obtained by considering the three cases for the input parameters are shown in Fig. 3. In the S–R relationship of Ricker, there is an intersection between the curves at spawning stock biomass of about 5–8 million t (Fig. 3a). This characteristic does not occur in the case of the S–R relationship of Beverton and Holt
Discussion
This work is in the line suggested by Shepherd (1982), Sissenwine and Shepherd (1987), Cubillos (1994), Schnute and Kronlund (1996), Schnute and Richards (1998), and previously by the ‘self-regenerating model’ of Beverton and Holt (1957), the approach of Getz (1980) and that of Lawson and Hilborn (1985). In these works, except Schnute and Kronlund (1996), Schnute and Richards (1998) and Cubillos (1994), a fitted S–R model to available data is required to obtain an equilibrium yield-curve.
Acknowledgements
We thank to three anonymous reviewers for comments and suggestions of an early version of this paper.
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