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Many natural resource stocks have collapsed under exploitation. There is a need for management methods that are less prone to failure. Here I compare various management strategies for stocks with complicated stochastic dynamics. The complications include \"critical depensation\" where the stock tends to collapse if brought below a critical size, catastrophes where the stock suddenly decreases in size, and heavy-tailed distribution of fluctuations in net reproduction. The results indicate that these complications are all influential in determining the probability of early collapse and in determining the expected sum of discounted harvests of the stock. A strategy involving abrupt changes in harvest size in response to fluctuations in the stock abundance produces a lower probability of early collapse and a higher expected sum of discounted harvests than other strategies.