Instability of harvested populations multiple equilibria

Even with regulation of effort, harvesting near the MSY level may be courting disaster. The recruitment rate may be particularly low in the smallest populations (a pattern known as depensation; Figure 15.11a); for instance, the recruitment of young salmon is low at low densities because of intense predation from larger fish, and the recruitment of young whales may be low at low densities simply because of the reduced chances of males and females meeting to mate. However, depensation is apparently quite rare; Myers et al. (1995) detected it in only three of 128 fish stock the problem of 'depensation'

data sets with 15 or more years available for analysis. Alternatively, harvesting efficiency may increase in small populations (Figure 15.11b). For instance, many clupeids (sardines, anchovies, herring) are especially prone to capture at low densities, because they form a small number of large schools that follow stereotyped migratory paths that the trawlers can intercept. With either depensation or higher harvesting efficiency at low density, small overestimates of Em are liable to lead to overexploitation or even eventual extinction.

Even more important, however, is the fact that these interactions may have crucial 'multiple equilibria' (see Section 10.6). Note the two points where the harvesting line crosses the recruitment curve in Figure 15.11a. The point S is a stable equilibrium but the point U is an unstable 'breakpoint'. If the population is driven slightly below the MSY density, or even to a level slightly above Nu, a breakpoint, it returns to the MSY density (Figure 15.11a). But a marginally increased depression in density, to a level slightly below Nu, perhaps resulting from only a very small increase in effort, would make the harvesting rate greater than the recruitment rate. The population would be en route to extinction. Moreover, once the population is on this slippery slope, much more than a marginal reduction in effort is required to reverse the process. This is the crucial, practical point about multiple equilibria: a very slight change in behavior can lead to a wholly disproportionate change in outcome as the point of attraction in the system shifts from one stable state to another. Drastic changes in stock abundance can result from only small changes in harvesting strategy or small changes in the environment.

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