This chapter considers population dynamics where the population changes over time, owing to environmental noise, fishing, or both. It first derives the population growth rate with various analytic and numeric approximations. Next, the chapter develops a full numerical solution to the McKendrick–von Foerster equations and uses it to create stylized recovery plans. Last, the chapter describes how a fish stock responds to fluctuations in the recruitment. From there, the chapter develops a general understanding of how a fish stock responds to idealized perturbations: a press perturbation and a continuously varying perturbation. It then makes general expectations of the responses to perturbations in general, citing three rules: lag, averaging, and nonmetabolic scaling of population growth rate.
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