  In this paper, we use a stochastic partial differential equation (SPDE) as a
model for the density of a population under the influence of random external
forces/stimuli given by the environment. We study statistical properties for
two crucial parameters of the SPDE that describe the dynamic of the system. To
do that we use the Galerkin projection to transform the problem, passing from
the SPDE to a system of independent SDEs; in this manner, we are able to find
the Maximum likelihood estimator of the parameters. We validate the method by
using simulations of the SDEs. We prove consistency and asymptotic normality of
the estimators; the latter is showed using the Malliavin-Stein method. We
illustrate our results with numerical experiments.
