  We discuss a model of a system of interacting populations for the case when:
(i) the growth rates and the coefficients of interaction among the populations
depend on the populations densities: and (ii) the environment influences the
growth rates and this influence can be modelled by a Gaussian white noise. The
system of model equations for this case is a system of stochastic differential
equations with: (i) deterministic part in the form of polynomial
nonlinearities; and (ii) state-dependent stochastic part in the form of
multiplicative Gaussian white noise. We discuss both the cases when the formal
integration of the stochastic differential equations leads: (i) to integrals of
Ito kind; or (ii) to integrals of Stratonovich kind. The systems of stochastic
differential equations are reduced to the corresponding Fokker-Planck
equations. For the Ito case and for the case of 1 population am analytic
results is obtained for the stationary PDF of the the population density. For
the case of more than one population and for the both Ito case and Stratonovich
case the detailed balance conditions are not satisfied and because of this
exact analytic solutions of the corresponding Fokker-Plank equations for the
stationary PDFs for the population densities are not known. We obtain
approximate solutions for this case by the methodology of the adiabatic
elimination.
