Fig. 2.

Bifurcation diagram showing how the equilibrium values, $N_e$, of (2) and their stability vary as the parameter $\alpha$ (corresponding to the growth in colony size) increases. For small $\alpha$ the colony cannot be maintained; once the critical threshold $\alpha =2\mu A$ is exceeded, the colony exhibits bistable dynamics. The solid line corresponds to locally stable equilibria, $N_e=0$ and $N_e={\widehat{N}}_2$ while the dotted line represents an unstable equilibrium, $N_e={\widehat{N}}_1$