the small external flux will reintroduce it and it will then grow in abundance. Increasing $C$ further, things continue on in this fashion, losing and regaining species. The main characteristic of the partial exclusion phase, the distinction between semi-resident species that admit a finite population and $\cal{O}(\lambda)$ transients that cannot invade, still holds.

An example of the stochastic version of this partial coexistence phase can be seen in the second and third panels of Fig. \[fig all\]. For this realization of the $c_{i,j}$, with $Q=20$, the May transition point is at approximately $C_1 \approx 0.169$. We show in Fig. \[figdetvsmean\] the time averaged abundances of the species for an extended version of the run presented in the second panel of Fig. \[fig all\], with $C=0.25$, past the May point. We see that the deterministic solution is essentially missing 3 species, $\{4,\,11,\, 16\}$. The stochastic run shows that the overall structure of the abundance vs. species of the deterministic model is preserved. The smaller species are, as might be expected, more severely impacted by the demographic noise, to the benefit of the larger species, which do not have to suffer as much competition from these small species. As $C$ increases, not 