The Overfishing Metaphor
Dr. Brian J. Rothschild

NOTE: This paper was originally published by the American Institute of Fishery Research Biologists in their January-February 2011 newsletter. Dr. Rothschild is Dean Emeritus of the University of Massachusetts School for Marine Science and Technology.

The term “overfishing” seems to have first been used in 1854 at a meeting of the British Association for the Advancement of Science (Rozwadowski, 2002). The determination of whether or not a stock is overfished preoccupied fishery scientists for the next several decades. During this time no precise definition of overfishing could be developed, despite a prestigious inquiry by the International Council for Exploration of the Sea (ICES) (Petersen, 1903).

Progress seemed evident in the 1940s and 1950s with the development of quantitative theories of fishing. The theories created the belief that practical and concrete overfishing definitions could be developed from mathematical models linking fishing mortality and population abundance. These models could generate optimal values (maxima) of production, yield-perrecruit, and recruitment as functions of stock size or fishing mortality. Thus, if optimal values were exceeded — the stock size was too low, or fishing mortality was too high — the stock could be declared overfished.

However, the promise one-half century ago has dissipated. The connection between the theories and real fish populations has been disappointing for several reasons. The theoretical models:

do not in general correspond with real data;
do not exhibit well-defined optima or maxima for extensive portions of their parameter space (Rothschild et al., 1997). As a consequence, generally arbitrary substitutes (so-called “proxies”) are contrived to replace the optimization target;
are equivocal and generally not consistent with one another (e.g., growth overfishing and stock overfishing) (see Cushing, 1973);
focus on populations in equilibrium despite the fact that real populations are generally not in equilibrium (see, however, Rothschild and Jiao, 2009; Prager, 1994);
ignore critical sources of variability in fish-stock population dynamics, such as interactions with associated species and effects of the ocean environment (Cushing, 1995).

Taken together, these deficiencies result in applications that do not describe the dynamics of fish populations. A consequence of this is that stock abundance and fishing mortality are not always tightly coupled, reflecting that the theories of fishing can only be considered to be metaphorical representations of the relationship between fishing mortality and fish population abundance and, as such, associated definitions of “overfished/overfishing” are also metaphorical. The fact that there is no unique definition of overfishing (except in the Schaefer model sense), and different overfishing standards are applied to different stocks, make it difficult to interpret overarching “mission accomplished” claims about the success or lack of success of fisheries management. Furthermore, the lack of environmental information in the overfishing calculus prevents any meaningful claim that overfished stocks will increase in abundance, if fishing mortality is reduced or terminated.

The spectacular collapse of the cod stock complex in the northwest Atlantic, which has been widely attributed to overfishing, is an interesting, somewhat typical case study (for reviews, see: Rothschild, 2007; Rice, 2002; Lilly et al., 2008; Hilborn and Litzinger, 2009; Halliday and Pinhorn, 2009). The assertion that overfishing is the main cause of the collapse is not supported by the data. Five stanzas in the northwest Atlantic cod-population complex dynamics can be discerned (Figure 1). In the first stanza, the complex is stable despite increasing fishing mortality. In the second stanza, biomass decreases sharply under high fishing mortality. Note however that this major increase in fishing mortality occurs after the stock complex has declined in abundance. In the third stanza, the cod complex rebuilds at low fishing mortality. In the fourth stanza, the biomass declines sharply at low fishing mortality. In the fifth stanza, fishing mortality rises sharply after the complex has declined. In the second and most dramatic collapse from 1984-1994 (stanzas 4 and 5), the cod complex begins to decline at relatively low levels of fishing mortality. Counter-indicating fishing intensity as a primary cause of the cod decline during this decade are observations that reflect a widespread deterioration of environmental productivity. These observations include: 1) a fishing moratorium imposed subsequent to the cod collapse did not result in a recovery; 2) the natural mortality rate (i.e., mortality independent of fishing) of cod increased by a factor of four; 3) cod growth rates declined substantially; 4) individual cod condition factors declined; 5) changes in the typical food of the cod were evident; 6) associated species exhibited declines in abundance, growth, and condition; and 7) abnormal quantities of cold, relatively fresh water were evident throughout the region. Altogether these observations point to a major environmental change as the primary cause generating and sustaining the 1984-1994 decline of the cod in the northwest Atlantic.

Two forms of decoupling are apparent. In the first, decoupling appears to be associated with a fish population reaching its “carrying capacity”—either because the size of the stock exceeded the capacity of the environment, or because the capacity of the environment deteriorated. This type of decoupling is evidenced by the not uncommon situation where a stock “crashes” at relatively low fishing mortality. The second form of decoupling relates to the unorthodox concept that declines in fish-stock abundance cause increases in fishing mortality, rather than the conventional view that increases in fishing mortality cause decreases in fish stock. This is easy to explain inasmuch as nominal fishing mortality (e.g., the number of fishing vessels) tends to decrease more slowly than the number of individuals in a rapidly declining population, generating a sharp post population-crash increase in fishing mortality.

A more plausible model is that fish stock abundance is often coupled with fishing intensity. However, exceptional abundance of a fish stock or decadal transients in ocean productivity (e.g., Steele, 2004) generate a decoupling between fishing intensity and stock abundance. In cases where the stock declines, the slower dynamics of fishing effort causes fishing mortality to increase rapidly, and it is reasonable to argue that this can impede the stock from recovering. Nevertheless, for recovery to take place, both a reduction of fishing mortality and a restoration of ecological productivity must take place.

An underlying theme to all of this is that we have been attempting to smash a 19th century concept into a 21st century mold, apparently forgetting basic scientific principles of constraining the complexity of theory by the information content of the data. It would be interesting to test the notion or hypothesis that it would be simpler and less expensive (particularly in multiplespecies fisheries) to target on sustained yield rather than ephemeral maximum sustained yield by tracking catches and correcting nominal effort when catches exceeded or did not meet control bounds. This would obviate the need to define stocks as subject to overfishing or overfished while concentrating on obtaining a socio-economic acceptable sustained yield from either single stocks or from a mixture of stocks in a mixed species fishery.

D. H. Cushing, Population Production and Regulation in the Sea: A Fisheries Perspective (Cambridge University Press, 1995), xii, 354p.

D. H. Cushing, Dependence of recruitment on parent stock. J. Fish. Res. Board Can. 30, 1965-1976 (1973).

R. B. Halliday, A. T. Pinhorn, The roles of fishing and environmental change in the decline of Northwest Atlantic groundfish populations in the early 1990s. Fisheries Research 97, 163-182 (2009).

R. Hilborn, E. Litzinger, Causes of decline and potential for recovery of Atlantic cod populations. The Open Fish Science Journal 2, 32-38 (2009).

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M. H. Prager, A suite of extensions to a non-equilibrium surplus production model. U.S. Fishery Bulletin. 92, 374-389 (1994).

J. Rice, Changes to the large marine ecosystem of the Newfoundland–Labrador Shelf. Pages 51–104 in K. Sherman and H. R. Skjoldal, editors. Large marine ecosystems of the North Atlantic: changing states and sustainability. Elsevier, Amsterdam (2002).

B. J. Rothschild, A. F. Sharov, M. Lambert, Single-species and multispecies management. In Northwest Atlantic Groundfish: Prospectives on a Fishery Collapse. Edited by J. Boreman, B. S. Nakashima, J. A. Wilson and R. L. Kendall. American Fisheries Society, Bethesda, MD. 141-152 (1997).

B. J. Rothschild, Coherence of Atlantic cod stock dynamics in the northwest Atlantic Ocean. Trans. Am. Fish. Soc. 136, 858-874 (2007).

B. J. Rothschild, Y. Jiao, The structure of complex biological reference points and the theory of replacement. Trans. Am. Fish. Soc. 138, 949-965 (2009).

H. M. Rozwadowski, The Sea Knows No Boundaries: A Century of Marine Science under ICES (ICES in Association with Univ. of Washington Press, 2002) pp. 448.

J. H. Steele, Regime shifts in the ocean: reconciling observations and theory. Progress in Oceanography 60, 135-141.