General types of population models include surplus production, delay-difference, age-based, and length-based models (see Chapter 5 for specific references and more detailed descriptions of the models used in this study). They rely on rates of change in biomass and productivity that can be calculated based on information about yield from fisheries, recruitment, and natural deaths. Detailed presentations of these models are given in Ricker (1975), Getz and Haight (1989), Hilborn and Walters (1992), and Quinn and Deriso (in press). Models of population change can be written as a differential equation

or, in words, the rate of change in biomass () equals productivity () minus yield (). The productivity of a population depends on the recruitment of progeny () and the growth () and death () of existing individuals. Barring time-dependent processes in Equation (3.1), equilibrium biomass and yield result only if some of the rates in Equation (3.1) are regulated by population densities; otherwise, the population can either increase or decrease without limit.

This type of model can be implemented with an instantaneous response (no lags) or 1-year difference equation approximation. These models have simple productivity parameters embedded and require no age or length data (Schaefer, 1954; Fletcher, 1978; Prager, 1994). Estimation is accomplished by fitting nonlinear model predictions of exploitable biomass to some indices of exploitable population abundance (usually standardized catch per unit effort, CPUE). The primary advantages of surplus production models are that (1) model parameters can be estimated with simple statistics on aggregate abundance and (2) the models provide a simple response between changes in abundance and changes in productivity. The primary disadvantages of such models are that (1) they lack biological realism (i.e., they require that fishing have an effect on the population within 1 year) and (2) they cannot make use of age- or size-specific information available from many fisheries. However, in some circumstances, surplus production models may provide better answers than age-structured models (Ludwig and Walters, 1985, 1989).

These models incorporate age structure and provide a method for fitting an age- or size-structured population model to data aggregated by age (Deriso, 1980; Schnute, 1985; Horbowy, 1992). Estimation can be accomplished by fitting nonlinear model predictions of aggregate quantities to CPUE, biomass indices, and/or recruitment indices. Delay-difference models are a special-case solution to a more general aggregate-matrix model made possible by the assumption of a particular age-specific growth model (the von Bertalanffy equation [Ricker, 1975]). These types of models share the advantages of surplus production models; additionally, the functional relationship between productivity and abundance accounts for both yield-per-recruit and recruit-spawner effects. Unlike production models, the parameters of delay-difference or aggregate-matrix models have direct biological interpretations, but they cannot make full use of age- or size-specific information. In addition, these models require the estimation of more initial conditions than production models, unless a simplifying assumption, such as an initial equilibrium condition, is made.

Age-based models use recursion equations to determine abundance of year classes as a function of several parameters (Fournier and Archibald, 1982; Deriso et al., 1985; Megrey, 1989; Methot, 1989, 1990; Gavaris, 1993). Relationships between spawning stock biomass and recruitment are not required but can be used. Because of the

Front Matter (R1-R10)

Executive Summary (1-6)

1 Introduction (7-12)

2 Data (13-26)

3 Assessment Methods (27-36)

4 Harvest Strategies (37-58)

5 Simulations (59-110)

6 Findings and Recommendations (111-118)

References (119-128)

Appendix A (129-132)

Appendix B (133-134)

Appendix C (135-136)

Appendix D (137-140)

Appendix E (141-146)

Appendix F (147-148)

Appendix G (149-152)

Appendix H (153-160)

Appendix I (161-172)

Appendix J (173-174)

Appendix K (175-177)