Mathematics in Biology and Medicine pp 201-206 | Cite as

# Stochastic Differential Equation Models of Fisheries in an Uncertain World: Extinction Probabilities, Optimal Fishing Effort, and Parameter Estimation

## Abstract

Logistic and Gompertz models of population growth, with, an extra terato allow for fishing under constant quotas, constant effort, and mixed policies, are considered Stochastic fluctuations of environmental and fishing conditions are added as noise terms. Ultimate extinction occurs with probability one for constant quotas or mixed policies, but not for constant moderate effort policies. For constant effort policies, we show that the fishing efforts that maximize the expected yield are close to the ones obtained in the deterministic models if the noise fluctuations are small. Conditions on the effort in order to control the probability of the population size dropping below some critical threshold are studied. Maximum likelihood techniques of parameter estimation based on yield data are developed for constant effort models.

### Keywords

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