deterministic dynamics (without immigration) no longer supports a steady state with all the $Q$ mainland species coexisting. In the heterogeneous coexistence phase, as discussed above, the $\lambda=0$ steady-state system admits a solution, Eq. (\[steady\]), which is both feasible ($N_i >0$) and stable (the real part of all the eigenvalues of the community matrix are negative). As follows from the work of May [@may1972will], the chance for the system to fulfill these requisites, for fixed heterogeneity $\sigma$, decreases exponentially with $Q$. In fact, for the GCLV in the coexistence phase, the main obstacle is feasibility [@rozdilsky2001complexity]. Eq. (\[steady\]) suggests that the solution will be feasible when the sum of all the rows of $B^{-1}$ is positive. As the average sum of a row approaches zero with $C$, the chance to pick only positive values for $N_i$ decreases exponentially with $Q$.

In Figure \[fig2\] one observes that, for the particular realization of the $c_{i,j}$ being simulated here, with $Q=10$, the abundance of the weakest species reaches zero around $C=0.28$. This point marks the transition from the heterogeneous coexistence phase to the partial coexistence phase. In this phase the island species richness, $S$, is smaller that the mainland richness $Q$, as some populations 