Abstract
There have been few documented extinctions of fished species, but many bioeconomic models predict that open‐access incentives make extinction possible. Open‐access multi‐species fisheries can cause species' extinction if other, faster‐growing species maintain profits at fatal effort levels. Even target species can be profitably harvested to extinction if their prices rise sufficiently as they are depleted. Here, we explore interactions between these potential extinction mechanisms by modelling an open‐access multi‐species fishery with one or multiple fleets exploiting two species, each with different growth rates, ex‐vessel prices, and price dynamics. Increases in the strong stock's (the stock with higher productivity relative to fishing susceptibility) price as it is depleted increase the range of conditions under which the weak stock can be driven extinct and shrinks the range of bioeconomic parameters in which both species can coexist under open‐access. Catch hyperstability – whereby species become easier to catch as they are depleted – makes the weak stock weaker as it is depleted and further narrows the scope for coexistence. Fleet diversity in targeting ability can prevent weak stock extinction, as competition or switching balances species abundances. With few documented global fished‐species extinctions, our results raise important questions, which we discuss. Is the apparent lack of extinctions largely due to management? Are more species in lightly‐managed fisheries threatened with extinction than previously acknowledged? Have more extinctions than we realize already happened in data‐ and management‐poor fisheries? Or have fishes' high fecundity and the oceans' vastness provided protection against extinction that is uncaptured by existing theoretical models?