Dependence of Exploitation Rates for Maximum Yield and Stock Collapse on Age and Sex Structure of Chinook Salmon (Oncorhynchus tshawytscha) Stocks

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Abstract
In this paper we investigate the equilibrium behavior of an age- and sex-structured version of the Ricker stock–recruitment model specifically tailored to the complex nature of chinook salmon (Oncorhynchus tshawytscha) biology and fisheries. Conclusions from our analysis include the following. (1) Exploitation rates for maximum yield (umsy) and stock collapse (umax) depend strongly on a stock's maturity schedule, being lowest for a late-maturing stock and greatest for an early maturing stock. (2) Values of exploitation rates for umax overlap considerably with those for umsy, emphasizing the probability of stock collapse in fully exploited mixed stock fisheries. (3) Values of umsy and umax are independent of the value of the Ricker β parameter but depend directly on the Ricker α parameter, indicating that management research should focus on obtaining better estimates of α, contrary to recent suggestions in the literature. (4) Because they mature at older ages, female chinook suffer greater cumulative fishery removal rates than males and decline in abundance more rapidly as exploitation increases. Consequently, the use of sex-independent maturity schedules can give misleading estimates for umsy and umax. (5) Maximum changes in mean age of stocks that can be attributed to fishing up effects ranged from 0.32 to 0.81 yr. Many stocks appear already to have declined in mean age by this amount, further emphasizing the probability of impending collapse of some stocks.

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