other values of migration and $K$. The different phases in the $\sigma-C$ plane are sketched in Figure \[fig1\]. In the following we intend to discuss each phase in detail; before doing that, let us focus on two very interesting limits that correspond to the $x$ and the $y$ axes of Figure \[fig1\].

![A schematic sketch of the $C-\sigma^2$ plane, showing the different phases of the generalized competitive Lotka-Volterra system, as will be discussed below. On the $C=0$ line there is no competition, all species have the same carrying capacity and the extinction-recolonization dynamics is described by the Wilson-MacArthur theory. At the Hubbell point, $C=1$ and $\sigma = 0$, all individuals are equivalent and the system supports a marginally stable manifold on which the dynamics is governs only by the noise. In the weak competition region (small $C$) all the mainland species are still semi-resident on the island, but with heterogeneous abundance and extinction times. Above $C_2$, some species are transients, with ${\cal O} \lambda$ abundance. Another increase in the strength of competition takes the system to the chaotic/intermittent phase, where the community structure changes dramatically over time and the instantaneous assembly is usually invadable. Finally in the glass-like phase a 