Elsevier

Fisheries Research

Volume 54, Issue 3, February 2002, Pages 395-407
Fisheries Research

Equilibrium yield-curve analysis through an analytic age-structured production model: A sensitivity study for the Chilean jack mackerel fishery

https://doi.org/10.1016/S0165-7836(01)00273-9Get rights and content

Abstract

An analytical age-structured production model is used to explore the equilibrium yield-curve properties, and management-related quantities, for the Chilean jack mackerel (Trachurus symmetricus murphyi) fishery. The objective is to summarize management-related quantities for the jack mackerel fishery according to uncertainties in both the unexploited spawning stock biomass (S0) and the functional shape of the stock–recruitment relationship. The age-structured model includes age-specific weights, selectivity, maturity, and natural mortality rate, which permit yield-per-recruit (YPR) and spawning biomass-per-recruit (SPR) to be determined as a function of the fishing mortality rate (F). Equilibrium yield (Ye) curves were obtained by combining YPR, SPR and the stock–recruitment (S–R) relationships of Ricker, and Beverton and Holt. The parameters of the S–R models are reparameterized in terms of the unexploited spawning stock biomass (S0) and a factor that permits the slope of the S–R models to be guessed as a function of the unexploited spawning biomass-per-recruit, i.e. SPR at F=0(SPRF=0). The Ye curves derived using the Ricker S–R model were slightly symmetric as functions of F and S, while asymmetric equilibrium yield curves were derived using the S–R model of Beverton and Holt. The maximum sustainable yield (MSY), the spawning biomass at MSY (SMSY), the fishing mortality at MSY (FMSY), and the fishing mortality at collapse (Fcrash) were the management-related quantities, which were analyzed in relative terms (e.g. MSY/S0). In the case of the Ricker S–R model, it was found that MSY fluctuated between 10.9 and 24.4% of S0, while FMSY ranged between 0.8 and 1.6 times the natural mortality rate (M=0.3 yr−1). In the Beverton and Holt S–R model, MSY ranged between 6.2 and 11.5% of S0, and FMSY fluctuated between 0.44 and 1.74 times M. The quantity Fcrash was about 2.3–2.4 times FMSY by considering the S–R model of Ricker, but in the case of Beverton and Holt recruitment model Fcrash ranged between 2.7 and 9.4 times FMSY due to the asymmetric yield-curve. The values for FMSY and Fcrash were independent of S0 for each S–R model, but these mortalities were dependent of the slope at the origin of the S–R relationship. It is now necessary to clarify the shape of the S–R relationship for Chilean jack mackerel because the results were very sensitive to this uncertainty.

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 byNa=R=1,a=ar,Na=Na−1exp(−(va−1F+M)),a=ar+1,…,am−1,Na=Na−1exp(−(va−1F+M))1−exp(−(vaF+M)),a=amwhere 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 F=0(SPRF=0=1.345kg). 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.

References (57)

  • D.P. Andrianov

    Study on the reproduction of Peruvian scad, Trachurus murphyi (Carangidae), of the Peruvian shelf

    Voprosy Ikhtiol.

    (1985)
  • Aracena, O., Alarcón, R., Collado, S., Lépez, I., Arraigada, D., 1998. Aspectos reproductivos del jurel (Trachurus...
  • H. Arancibia et al.

    The fishery of horse mackerel (Trachurus symmetricus murphyi) in the south Pacific Ocean, with notes on the fishery off central-southern Chile

    Sci. Mar.

    (1995)
  • H. Arancibia et al.

    A landing forecast for horse mackerel, Trachurus symmetricus murphyi (Nichols, 1920) off Central Chile

    Sci. Mar.

    (1995)
  • Arcos, D.F. (Ed.), 1998. Biologı́a y Ecologı́a del Jurel en Aguas Chilenas. Instituto de Investigación Pesquera,...
  • Arcos, D.F., Grechina, A.S. (Eds.), 1994. Biologı́a y Pesca Comercial del Jurel en el Pacı́fico Sur. Editorial Anı́bal...
  • Arcos, D., Cubillos, L., Sepúlveda, A., Grechina, A.S., Peña, H., Alarcón, R., Hernández, A., Miranda, L., Vilugrón,...
  • K. Bailey

    Description and surface distribution of juvenile Peruvian jack mackerel, Trachurus murphyi, Nichols from the subtropical convergence zone of central south Pacific

    Fish. Bull. US

    (1989)
  • Bakun, A., 1996. Patterns in the ocean: ocean processes and marine population dynamics. University of California Sea...
  • Beamish, R.J. (Ed.), 1995. Climate Change and Northern Fish Populations. Canadian Special Publication on Fish. Aquatic...
  • Bernal, P., 1990. La oceanografı́a del sistema de corrientes de Chile–Perú en relación a las pesquerı́as pelágicas: una...
  • R.J.H. Beverton et al.

    On the dynamics of exploited fish population

    Fish. Invest. Ser.

    (1957)
  • Böhm, G., Caballero, L., Muñoz, H., Bocic, V., Hidalgo, H., Serra, R., Nilo, M., 1994. Diagnóstico de las principales...
  • J.F. Caddy et al.

    Targets or limit for management of fisheries

    North Am. J. Fish. Mgmt.

    (1996)
  • W.G. Clark

    Groundfish exploitation rates based on life history parameters

    Can. J. Fish. Aquat. Sci.

    (1991)
  • Clark, W.G., 1993. The effect of recruitment variability on the choice of a target level of spawning biomass per...
  • L. Cubillos

    Estimating the parameters of the stock–recruitment model of Ricker from a yield-per-recruit model in data-limited situations

    Fish. Res.

    (1994)
  • Cubillos, L., Sepúlveda, A., Arcos, D., 1998. Evaluación del stock de jurel con modelos edad-estructurados separables:...
  • A.A. Elizarov et al.

    Peruvian jack mackerel, Trachurus symmetricus murphyi, in the open waters of the South Pacific

    J. Ichtyol.

    (1993)
  • S.A. Evseenko

    On the reproduction of the Peruvian jack mackerel, Trachurus symmetricus murphyi (Nichols), in the southern part of the Pacific Ocean

    Voprosy Ikhtiol.

    (1987)
  • R.I.C.C. Francis

    Use of risk analysis to assess fishery management strategies: a case of study using orange roughly (Hoplostethus atlanticus) on the Chatham Rise, New Zealand

    Can. J. Fish. Aquat. Sci.

    (1992)
  • Francis, R.I.C.C., 1993. Monte Carlo evaluation of risks for biological reference points used in New Zealand fishery...
  • Getz, W.M., 1980. Harvesting models and stock recruitment curves in fisheries management. In: Getz, W.M. (Ed.),...
  • Grechina, A.S., 1998. Historia de investigaciones y aspectos básicos de la ecologı́a del jurel (Trachurus symmetricus...
  • Grechina, A.S., Núñez, S., Arcos, D., 1998. Biologı́a reproductiva del jurel (Trachurus symmetricus murphyi) en el...
  • Gulland, J.A., 1983. Fish Stock Assessment: A Manual of Basic Methods. Wiley, New York, 223...
  • Hilborn, R., Walters, C.J., 1992. Quantitative Fisheries Stock Assessment, Choice, Dynamics and Uncertainty. Chapman &...
  • ICES, 1997. Report of the comprehensive fishery evaluation working group. ICES CM 1997/Assess:...
  • Cited by (3)

    View full text