Fig 2. Spatial dynamics for the four types of directed migration.

Each of the four panels (A)-(D) shows snapshots of the spatial distributions at time t = 2000 as a function of the multiplication factor r when varying one of the four modes of migration. The bottom row shows the dynamics of purely diffusive migration in the proximity of r_Hopf ≈ 2.365 as a reference. (A) Aggregating cooperators oppose the effects of diffusion and hence slow down the population expansion. The positive feedback between cooperator densities and aggregation can cause discontinuous distributions and discretization-dependent numerical results. (B) Hunting defectors increase competition in areas where cooperators concentrate. This allows cooperators to escape into unpopulated terrain but also increases the risk of extinction. (C) Fleeing cooperators avoid defectors and hence readily explore vacant space but with the defectors at their tails also tend to spread themselves too thin and risk extinction. (D) Spreading defectors reduce exploitation on cooperator aggregates and consequently promote pattern formation as well as population survival. Parameters as in Fig 1 unless otherwise indicated.