The fishery system

It helps to think broadly about the fishery system (Cole-King 1993, Okey 2003). The recent books of Jennings et al. (2001) and Hart and Reynolds (2002) are great starting points. Some other entry points include Gulland (1977, 1988), Wooster (1988), Norse (1993), King (1995), Olver et al. (1995), Pikitch et al. (1997), McAllister et al. (1999), Cochrane (2000), Corkett (2002), and Rosenberg (2003). Zabel et al. (2003) introduced the notion of ecologically sustainable yield (ESY), defined as the maximum yield of fish that an ecosystem can sustain without shifting states in the sense of a system with multiple steady states. Other community-level metrics such as species richness, evenness, or community resiliency could also be used as ESY targets. However, because communities change in response to natural processes in ways that we do not fully understand, and we can never predict the behavior of communities with absolute certainty, we can and should improve our understanding of the bounds of expected community behavior and define ESY within the limits of their predictability. Smith (1994) provides a history of fishery science before 1955. It is also helpful to learn about some particular fishery systems, such as the Northeast Pacific (Trumble 1998), or the Atlantic groundfish fishery (Boreman et al. 1997). For more quantitative approaches to the subject, the classic work is Beverton and Holt (1957); updates are Quinn and Deriso (1999) and Walters and Martell (2004). Some years ago, the Marine Fisheries Section of the American Fisheries Society republished Ray Beverton's 1951 lectures on the use of theoretical models in the study of the dynamics of exploited fish (Beverton 1994).

Models and data

In thinking about the issues of fishery management, Don Ludwig (Ludwig 1995) recognized that we will have to use models for management, and that the data associated with the fishery system will have both process uncertainty and observation error. This caused him to raise two paradoxes:

(1) management for sustained yield cannot be optimal;

(2) effective management models cannot be realistic.

Each paradox is caused by the interaction of data and models and we still lack complete resolution of those paradoxes (see Mangel et al. (2001) for some thoughts about resolution).

Fisherman behavior

Models of the behavior of fishermen are important to know about. I have not included them here because most of what I would write is contained in Chapter 7 of Clark and Mangel (2000). I especially like the work of Abrahams and Healey (1993), Gillis et al. (1995), Gillis (1999, 2003), and Babcock and Pitcher (2000); other nice papers include Healey (1985), Healey and Morris (1992), Holland and Sutinen (1999), Vestergaard (1996) and Vestergaard et al. (2003). One of the most important reasons for understanding behavior, as Gillis and his colleagues and Vestergaard argue, is to get a sense of the nature of discarding, which causes additional and often unreported mortality on stock (Perkins and Edwards 1995, Crowder and Murawski 1998, Harris and Dean 1998, Stratoudakis et al. 1998). Gillis and Peterman (1998) discuss how the behavior of fishing vessels affects the interpretation of CPUE. Anderson (1991a, b) discusses individual transferable quotas. When most broadly interpreted, behavior should also include that of scientists (Starr et al. 1998).

Stock, recruitment, and catchability

As mentioned in the text, there are many other stock-recruitment relationships (a recent review - with both diagnosis and prognosis -is by Needle (2002)). In the alpha-logistic or z-logistic, we find N(t + 1) = N(t)+ rN(t)(1 — (N(t)/K)z), where typically z> 1 for mammals and z < 1 for small fish. As an exercise, you might want to make sketches of the biological production in each of these cases. One can build more complicated density dependence into stock-recruitment relationships (Bjorksted 2000) given the appropriate life history information. Schnute and Kronland (1996) describe a management oriented approach to stock-recruitment relationships. Some of my favorite papers deal with stock-recruitment models for Pacific sardine Sardinops sagax (see Jacobson and MacCall (1995), and Jacobson et al. (2001)), and swordfish (Prager 2002). Amazingly, there is actually still argument from some quarters that there is no relationship between spawning stock size and recruitment (e.g. that the main factors driving recruitment are abiotic, such as climate, or non-autotrophic, such as food web interactions) or that the relationship is extremely weak (Marshall et al. 1998); also see Hennemuth et al. (1980), Leggett and Deblois (1994), Rickman et al. (2000), and Chen et al. (2002). Brodziak et al. (2001) give a nice summary of the debate and a very convincing reply to the charges. In recent years, stock-recruitment relationships have been parametrized by the biomass in the absence of fishing (B0) and the "steepness," defined to be the fraction of the maximum number of recruits when the spawning stock biomass is 0.2B0. One generalization of the Beverton-Holt stock recruitment curve is the "hockey-stick:'' a piece-wise linear relationship that rises linearly until it flattens as a horizontal line (Barrowman and Myers 2000). Another involves "depensation," in which the line R = S intersects the stock-recruitment relationship R = f(S) at more than one point, so that there is an unstable steady state between the origin and a high stable steady state (or even more steady states). Depensation has been proposed as a possible cause for the lack of recovery of the northern cod Gadus morhua (Shelton and Healey 1999). The obituary of Ricker (Beamish 2002) is very interesting. Age-structured models are commonly used in fishery management as means of estimating stock abundances and setting management levels; an example is found in Matsuda and Nishimori (2003). A good starting point for more general approaches is the extended survivors analysis described by John Shepherd (Shepherd 1999). Jacobson et al. (2002) describe ways to estimate the fishing mortality that generates MSY in any stock assessment model. There is a growing literature applying life history concepts more directly to fishery related problems. Good entry points are Jennings et al. (1998), Denney et al. (2002), Frisk et al. (2001), King and McFarlane (2003). We have assumed that catch per unit effort is proportional to abundance, but there are both theoretical and empirical reasons that it might not be (Harley et al. 2001). For example, if the catch is constrained by operational considerations to be a fixed amount (say 10 mt) and we recognize that in a small amount of time the fraction of the stock taken is 1 — e—qEAt then it becomes clear that it will appear that q depends upon the total stock size (taking 10 mt from a stock with biomass of 100,1000, or 1 000 000 mt represents very different fractions). Ray Beverton discusses this issue in depth with excellent examples in his lecture series BevertonLectures1994. In his new book (Clark 2006), Colin Clark argues that we would be more conservative to assume that catch were independent of N, so that C = qE. An alternative, which to my knowledge has not been investigated, is to think of catch as a functional response so that C(N) = cmaxqEN/(qEN + C0). Williams (2002) discusses the effects of unaccounted discard and incorrectly specified natural mortality on estimates of spawners per recruit and on the harvest policies based on spawners per recruit. We have ignored spatial aspects of stock, recruitment and harvesting, but the reaction diffusion models that we discussed in Chapter 2 apply; an excellent starting point is MacCall (1990). Schnute and Richards (2001) have an interesting discussion on the role of models (and the abuse of models) in stock assessment; whether we want to become fishmeticians doing fishmetic is a different question; also see Mangel et a/. (2001).

Targets, thresholds, and reference points

Perhaps a generation ago, MSY was viewed as a "target for management." We are much wiser than that now (Maunder 2002). Whether or not MSY should be viewed as a target, reference point or limit for management is a topic that can be addressed by quantitative means; some entry points are Thompson (1993), Nakken et a/. (1996), Schnute and Richards (1998), Overholtz (1999), Bradford et a/. (2000), Caddy

(2002), Hilborn et a/. (2002), Ulrich and Marchal (2002), Koeller

(2003) and Prager et a/. (2003). A recent issue of the BuZZet/n of Marine Sc/ence (70(2), 2002) is focussed on targets and thresholds.


We have just barely touched on bioeconomics, through our introduction of the discount rate, bionomic equilibrium and Exercises 6.8 and 6.9. The subject is very important. Corkett (2002) argues that bioeconomics is essential for making fishery stock assessment a falsifiable science; the problem of excess capacity for catching fish is perhaps the most significant factor leading to overfishing (Figure 6.16). The classic text in bioeconomics (and indeed, the one that got the field going) is Clark (1990; this is the second edition; the first published in the mid 1970s). Clark (1985) is also superb. As with understanding the specifics of fishery systems, it is also good to understand specific bioeconomic models of fishery systems such as New England groundfish (Overholtz et a/. 1995), the southern bluefin tuna fishery (McDonald et a/. 2002), US silver hake fisheries (Helser et a/. 1996), English channel artisinal fisheries (Ulrich et a/. 2002a), North Sea flatfish fishery (Ulrich et a/. 2002b), traditionally managed Fijian fisheries (Jennings and Polunin 1996), the Gulf of Mexico red snapper fishery (Gillig et a/. 2001), or the role of individual transferable quotas (McGarvey 2003).

The role of Bayesian methods

For even the simplest model of the fishery, we have seen that parameters are confounded (e.g. MSY = rK/4) and Bayesian methods provide the natural way for dealing with problems in which parameters are confounded and there is prior information (in fisheries, for example on similar stocks elsewhere). There is an excellent and growing literature

Figure 6.16. The overcapacity ratio, defined as the actual capacity of the fishery divided by the estimated long-run sustainable capacity, of various historical fisheries (data from Clark 1990) and of the USA as a whole in 2002 (D. Fluharty, personal communication).

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