An important application involving two-species reaction-diffusion systems relates to the problem of finding the best statistical strategy for optimizing the encounter rate between organisms. We investigate the general problem of how the encounter rate depends on whether organisms move in Lévy or Brownian random walks. By simulating a limiting generalized searcher-target model (e.g., predator-prey, mating partner, pollinator-flower), we find that Lévy walks confer a significant advantage for increasing encounter rates when the searcher is larger or moves rapidly relative to the target, and when the target density is low.

Axis labels appear incorrectly in Fig. 2. The axis labels should appear exchanged as in the correct Fig. 2 shown below. The main results reported in our Letter are not affected by this error, but some secondary conclusions are incorrect. Figure 2(a) is approximately symmetrical with respect to the r v line; therefore, the error in the figure ends up not being important. However, in the case of Fig. 2(b), there is no such symmetry, and some conclusions require modification. Specifically, for Lévy targets it is v rather than r that determines whether Lévy searches confer advantages relative to Brownian searches.We thank E. P. Raposo and M. G. E. da Luz for helpful comments. FIG. 2. Gray-scale graph showing as a function of r and v for (a) Browning targets and (b) Lévy targets. Each set of 4 graphs corresponds to increasing system size L 25, L 50, L 75, and L 100 from top-left to bottom-right.

The stationary critical properties of the isotropic majority vote model on random lattices with quenched connectivity disorder are calculated by using Monte Carlo simulations and finite size analysis. The critical exponents γ and β are found to be different from those of the Ising and majority vote on the square lattice model and the critical noise parameter is found to be qc = 0.117 ± 0.005.

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