  In this paper, we formulate a stochastic logistic fish growth model driven by
both white noise and non-Gaussian noise. We focus our study on the mean time to
extinction, escape probability to measure the noise-induced extinction
probability and the Fokker-Planck equation for fish population X(t). In the
Gaussian case, these quantities satisfy local partial differential equations
while in the non-Gaussian case, they satisfy nonlocal partial differential
equations. Following a discussion of existence, uniqueness, and stability, we
calculate numerical approximations of the solutions of those equations. For
each noise model we then compare the behaviors of the mean time to extinction
and the solution of the Fokker-Planck equation as growth rate r, carrying
capacity K, the intensity of Gaussian noise ${\lambda}$, noise intensity
${\sigma}$ and stability index ${\alpha}$ vary. The MET from the interval (0,1)
at the right boundary is finite if ${\lambda} <{\sqrt2}$. For ${\lambda} >
{\sqrt2}$, the MET from (0,1) at this boundary is infinite. A larger stability
index ${\alpha}$ is less likely to lead to the extinction of the fish
population.
