Fig. 1. The fitness of a species as a function of Φ.

Fig. 2. (a) Schematic representation of the three dynamical phases of community-driven dispersal: I, disordered; II, complex and III, organized domains (equivalent to Fig. 5a between c = 0.05 and 0.1). (b) Snapshot of the spatial prey density D_v at p_motion = 0.3. (c) Snapshot of the spatial predator density D_p at p_motion = 0.3. (d) Temporal evolution of the average density for the prey ρ_v (gray) and for the predator ρ_p (black) at p_motion = 0.3. (e) Log–log plot of the structure factor of the spatial prey density at p_motion = 0.3 (the structure factor for the predator is not shown since it is very similar to that of the prey). (f–i) Same as (b–e) but at p_motion = 0.7. (j–m) Same as (b–e) but at p_motion = 1.0. All figures are obtained with c = 0.06.

Fig. 3. Log–log representation of the structure factor for the model with community-driven dispersal for three different lattice sizes: L = 256 (diamond), L = 128 (dot) and L = 64 (square), for p_motion = 0.7.

Fig. 4. Standard deviation of the average population density ρ for the model with community-driven dispersal as a function of p_motion for the prey (square) and for the predator (dot). Three ratio-dependent functional responses are represented: (a) Holling type II, (b) Holling type III (sigmoidal) and (c) exponential.

Fig. 5. Dynamical regimes for (a) community-driven dispersal and (b) density-independent dispersal. The phase diagrams are expressed as functions of the level of fitness sensitivity (effect of scaling parameter c) and the dispersal probability (p_motion in the community-driven case and p_ind in the density-independent case). Points drawn on the diagram have been computed through simulations while the position of the phase boundaries has been deduced. Estimated 0.05 and 0.1 errors on the dispersal probability should be considered in (a) and (b), respectively. As before, regime I, II and III correspond, respectively, to the disordered, complex and organized regime.

Fig. 6. (a) Schematic representation of the two dominant dynamical phases for density-independent dispersal: I, disordered and III, organized domain (equivalent to Fig. 5b between c = 0.05 and 0.1). (b) Snapshot of the spatial prey density D_v at p_ind = 0.1. (c) Snapshot of the spatial predator density D_p at p_ind = 0.1. (d) Temporal evolution of the average density for the prey ρ_v (gray) and for the predator ρ_p (black) at p_ind = 0.1. (e) Log–log plot of the structure factor of the spatial prey density at p_ind = 0.1. (f–i) Same as (b–e) but at p_ind = 0.7. (j–m) Same as (b–e) but at p_ind = 1.0. All figures are obtained at c = 0.06.

Fig. 7. Standard deviation of the average population density ρ for the model with density-independent dispersal as a function of p_ind for the prey (square) and for the predator (dot). Note the different vertical scale from Fig. 4.

Exponent of the power law for the structure factor as a function of p_motion in the model with community-driven dispersal

Every exponent is obtained by finding the slope of a linear fit on a log–log graph of the structure factor (averaged over time and over 100 simulation runs), all give r² > 0.99.

Exponent of the power law for the structure factor as a function of p_ind in the model with density-independent dispersal

Every exponent is obtained by finding the slope of a linear fit on a log–log graph of the structure factor (averaged over time and over 100 simulation runs), all give r² > 0.99.