56, 2553 (1986).

L. H. Tang and H. Leschhorn, Phys. Rev. A 45, R8309(1992).

M. S. Bartlett, [*Stochastic Population Models in Ecology and Epidemiology*]{} (Methuen, London, 1960).

A. Vespignani, R. Dickman, M. A. Muñoz, and S. Zapperi, Phys. Rev. Lett. [**81**]{}, 5676 (1998).

R. Dickman, M. A. Muñoz, A. Vespignani, and S. Zapperi, Braz. J. Phys. [**30**]{}, 27 (2000).

K. A. Takeuchi, M. Kuroda, H. Chaté, and M. Sano, Phys. Rev. Lett. [**99**]{}, 234503 (2007).

L. Corté, P. M. Chaikin, J. P. Gollub, and D. J. Pine, Nature Physics [**4**]{}, 420 (2008).

S. Okuma, Y. Tsugawa, and A. Motohashi, Phys. Rev. B[**83**]{}, 012503 (2011).

M. M. de Oliveira and R. Dickman, Phys. Rev. E [**84**]{}, 011125 (2011)

Similar conclusions apply to a related model, the CP with creation at second-neighbor sites, in which each species inhabits a distinct sublattice [@cpsl] with enhanced survival at first neighbors.

H. K. Janssen, Z. Phys. B [**42**]{}, 151 (1981).

P. Grassberger, Z. Phys. B [**47**]{}, 365 (1982).

R. Dickman, Phys. Rev. A [**34**]{}, 4246 (1986).

D. [ben-Avraham]{} and J. Köhler, Phys. Rev. [**A**]{} 45, 8358 (1992).

A well known example is the triplet-creation model; see G. Ódor and R. Dickman, J. Stat. Mech. [**2009**]{} 