  In this note, we study the long time behavior of Lotka-Volterra systems whose
coefficients vary randomly. Benam and Lobry established that randomly switching
between two environments that are both favorable to the same species may lead
to four different regimes: almost sure extinction of one of the two species,
random extinction of one species or the other and persistence of both species.
Our purpose here is to provide a complete description of the model. In
particular, we show that any couple of environments may lead to the four
different behaviours of the stochastic process depending on the jump rates.
