A dynamic scholastic model of a fish population - Formacion, Sonia
By considering a milkfish population growing in a well-managed pond where no births occur and where in-migration of fish are not allowed, a dynamic stochastic mortality model of a biological population is developed which may also apply to biological populations other than a fish population. The process occurring in the pond is described in two equivalent ways: I) In terms of the basic differential equations q (t) = A (t) q (t) where q (t) is a vector of probabilities associated with the size of the population, q(t) is a vector of first derivatives with respect to time of these probabilities, and A (t) is a matrix involving the parameters used to describe the process. II) In terms of the kologorov forward differential equations Ṗ (ℸ, t) = P (ℸ , t) A ' (t) where A(t) is the same matrix as in i) and ( ℸ , t) is a matrix of transition probabilities. When the parameters defining the process are taken at a fixed time, a recursive solution to the system of differential equations are obtained under more simplifying assumptions on the parameters. maximum likelihood estimators of the parameters are also derived under certain assumptions regarding the times of entrance of the diseased states and the healthy states.