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Optimizing Metapopulation Sustainability through a Checkerboard Strategy

Figure 2

Coupled Logistic map, four-patch system with periodic boundary conditions.

Here the deterministic () orbit diagram (A) shows two stable regions that correspond to alternating (up-down-up-down, green, and up-up-down-down, black) spatial configurations. Panel (B) shows the Lyapunov exponent of the orbit: while the chaotic regions are characterized by a positive exponent indicating that the trajectories are unstable, for the periodic orbits, is negative. Yet, although the UUDD orbits are more attractive (more negative ), the lifetime of the stochastic system () peaks in the UDUD region, as shown in panel (C). The vertical arrow shows where the time to extinction is maximal; the horizontal arrow points to a representative snapshot of the agent-based system in that optimal migration, while the colors represent density. Clearly, the maximal sustainability (smallest chance for extinction) occurs in the checkerboard (UDUD) phase.

doi: https://doi.org/10.1371/journal.pcbi.1000643.g002