Complex response of a food-web module to symmetric and asymmetric migration between several patches

Author-Highlights
• We analyze the stability of the diamond food web motif on two patches.
• We evaluate robustness (species survival) and dynamical patterns.
• We vary migration rate and migration bias.
• With increasing migration rate, robustness shows two minima.
• Systems with more than two patches show similar results when bias is adjusted.

We investigate the stability of a diamond food-web module on two patches coupled by migration in terms of robustness, which is the proportion of surviving species in the system. The parameters are chosen such that the dynamics on an isolated patch have a periodic attractor with all four species present as well as an attractor where the prey that is preferred by the top predator dies out. The migration rate and the migration bias between the two patches are varied, resulting in a surprisingly complex relation between migration rate and robustness. In particular, while the degree of synchronization usually increases with increasing migration rate, robustness can increase as well as decrease. We find that the main results also hold when the number of patches is larger. Different types of connectivity patterns between patches can lead to different extent of migration bias if the migration rate out of each patch is the same.