Coexistence for a multitype contact process with seasons. (English) Zbl 1206.60090

The paper deals with a multitype contact process with temporal heterogeneity involving two species competing for space on the \(d\)-dimensional integer lattice. Time is divided into two alternative seasons. The authors prove that there is an open set of the parameters, for which species can coexist when their dispersal range is large enough. Numerical simulations also suggest that three species can coexist in the presence of two seasons. This contrasts with the long-term behavior of the time-homogeneous multitype contact process for which the species with the higher birth rate outcompetes the other species when the death rates are equal.


60K35 Interacting random processes; statistical mechanics type models; percolation theory
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[1] Armstrong, R. A. and McGehee, R. (1976). Coexistence of species competing for shared resources. Theoret. Popul. Biol. 9 317-328. · Zbl 0349.92030
[2] Chan, B. and Durrett, R. (2006). A new coexistence result for competing contact processes. Ann. Appl. Probab. 16 1155-1165. · Zbl 1110.60089
[3] Durrett, R. (1991). A new method for proving the existence of phase transitions. In Spatial Stochastic Processes. Progress in Probability 19 141-169. Birkhäuser, Boston, MA. · Zbl 0825.60052
[4] Durrett, R. (1995). Ten lectures on particle systems. In Lectures on Probability Theory ( Saint-Flour , 1993). Lecture Notes in Math. 1608 97-201. Springer, Berlin. · Zbl 0840.60088
[5] Durrett, R. (2002). Mutual invadability implies coexistence in spatial models. Mem. Amer. Math. Soc. 156 viii+118. · Zbl 0992.60092
[6] Durrett, R. and Lanchier, N. (2008). Coexistence in host-pathogen systems. Stochastic Process. Appl. 118 1004-1021. · Zbl 1141.60384
[7] Griffeath, D. (1979). Additive and Cancellative Interacting Particle Systems. Lecture Notes in Math. 724 . Springer, Berlin. · Zbl 0412.60095
[8] Harris, T. E. (1972). Nearest-neighbor Markov interaction processes on multidimensional lattices. Adv. in Math. 9 66-89. · Zbl 0267.60107
[9] Lanchier, N. and Neuhauser, C. (2006). Stochastic spatial models of host-pathogen and host-mutualist interactions. I. Ann. Appl. Probab. 16 448-474. · Zbl 1096.92046
[10] Lanchier, N. and Neuhauser, C. (2006). A spatially explicit model for competition among specialists and generalists in a heterogeneous environment. Ann. Appl. Probab. 16 1385-1410. · Zbl 1109.60084
[11] Lanchier, N. and Neuhauser, C. (2009). Spatially explicit non-Mendelian diploid model. · Zbl 1195.60125
[12] Lotka, A. J. (1925). Elements of Physical Biology . Williams & Wilkins, Baltimore. · JFM 51.0416.06
[13] Neuhauser, C. (1992). Ergodic theorems for the multitype contact process. Probab. Theory Related Fields 91 467-506. · Zbl 0739.60100
[14] Neuhauser, C. (1994). A long range sexual reproduction process. Stochastic Process. Appl. 53 193-220. · Zbl 0810.60097
[15] Neuhauser, C. and Pacala, S. W. (1999). An explicitly spatial version of the Lotka-Volterra model with interspecific competition. Ann. Appl. Probab. 9 1226-1259. · Zbl 0948.92022
[16] Volterra, V. (1928). Variations and fluctuations of the number of individuals in animal species living together. J. Cons. Int. Explor. Mer. 3 3-51.
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