Abstract:
Abstract
We formulate a mathematical fishery model with over-fishing induced Allee effect and stock dependent
harvesting, since fish populations when reduced to low densities experience reduced rates of survival and
reproduction. The model takes the form of a set of differential equations in which the population growth
equation
1 1 qnE,
K
n
T
n
n rn
has a depensation term. The other two equations describe the
evolution of the fishing mortality E and the market price p. Aggregation is performed to reduce the model
from a system of three equations to a system of two equations. Analysis of the model yields four points
of equilibria. Local stability analysis is done for the equilibria points with zero harvesting.
Keywords: Depensation, allee effect, fishing mortality
