Stochastic Differential Equation Models of Fisheries in an Uncertain World: Extinction Probabilities, Optimal Fishing Effort, and Parameter Estimation
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.
Unable to display preview. Download preview PDF.
- Abramowitz, M. and I. A. Stegun, eds. (1965). A handbook of mathematical functions. Dover, N.Y.Google Scholar
- Braumann, C.A. (1979). Population growth in random environments. Ph. D. thesis-, S.U. N.Y., Stony Brook, N.Y.Google Scholar
- Braumann, C.A. (1980). Time-average methods for estimation of parameters and prediction for some stochastic differential equation models. Invited talk at the Int. Summer School on S tatistical Distributions in Scientific Work, Ms. 93, Trieste.Google Scholar
- Braumann, C.A. (1981). Pescar num mundo aleatório: um modelo usando equações. diferenciais estocásticas. Proceedings of the XII Congresso Luso-Espanhol de Matemàtica, pp. 301–308, CoimbraGoogle Scholar
- Braumann, C.A. (1983 a). Population extinction probabilities and methods of estimation for population stochastic differential equation models. In Nonlinear Stochastic Problems, K.S. Bucy and J.M.F. Moura (eds.), pp. 553–559, D. Reidei Publ. Co.Google Scholar
- Dennis, B. and G.P. Patii (1983). The gamma distribution and weighted multimodal gamma distributions as models of population abundance, (submited)Google Scholar
- Gleit, A. (.1978). Optimal harvesting in continuous time with stochastic growth. Math. Biosc. 41.Google Scholar