time scales only when $K$ is relatively small. More realistic models have to take into account other types of noise (including environmental variations, attacks by pathogens etc.) that may lead to extinction, and the Wilson-MacArthur model will then be relevant even for higher values of $K$.

The symmetry line and the Hubbell point
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On the $x$ axis, the $\sigma = 0$ line, species do interact with each other but the interaction is symmetric; i.e., no change in community dynamics occurs upon switching the species labels of any two given populations. $C$ measures the strength of interspecific competition: if $C<1$, the intraspecific competition is stronger than the interspecific (reflecting mechanisms like resource partitioning or frequency dependent predation) and a low-density species may invade the system. On the other hand, for any $C>1$ the intraspecific competition is weaker than the interspecific, resulting in competitive exclusion [@chesson2000mechanisms]. At the boundary between these regimes one finds the Hubbell point $C=1$ (see Figure \[fig1\]). At the Hubbell point the model is *neutral*: any individual competes equally with any other individual and the strength of each pair competition is fixed and independent of species affiliation.

Without immigration, the deterministic GCLV supports, to the left of 