  In this note, we study the long time behavior of Lotka-Volterra systems whose
coefficients vary randomly. Bena{\"i}m and Lobry (2015) recently established
that randomly switching between two environments that are both favorable to the
same species may lead to different regimes: extinction of one species or the
other, or persistence of both species. Our purpose here is to describe more
accurately the range of parameters leading to these regimes, and the support of
the invariant probability measure in case of persistence.
