extinct a total of four times over a period of $24,000$ snapshots.

![**Abundance vs. competition**. The abundance of $Q=10$ species on the island is plotted vs. the competition parameter $C$, for a deterministic GCLV model with $K=100$ and $\sigma = 0.5$, without immigration ($\lambda=0$). In the non-interacting limit $C=0$ the abundance of all species is identical and equal to $K$. At $C_1
\approx 0.28$ the abundance of the “weakest" species reaches zero - this is the May transition, where the system enters the competitive exclusion phase. Upon increasing $C$, more and more species go extinct until (here, around $C=0.78$) a species comes back to life, as the competitors that suppressed it were themselves suppressed. []{data-label="fig2"}](N10nvsC){width="45.00000%"}

In such a scenario one expects deviations from the Wilson-MacArthur formula. When the abundance of the species are different from each other, the chance of extinction $e$ becomes species dependent, so once $C>0$ the sojourn times will reflect a convolution of exponents with different timescales. When the community heterogeneity increases, the Wilson-MacArthur extinction-recolonization dynamics is most relevant for the smaller species, again with heterogeneous statistics of extinction times.

The May transition and Phase II: the partial coexistence phase
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As $C$ increases even more, the 