Bibliography

This bibliography is not intended to be comprehensive, only to provide a quick introduction.

  • May and Leonard 1975, “Nonlinear Aspects of Competition Between Three Species”, SIAM Journal on Applied Mathematics, Vol. 29 No. 2, pp. 243-253. A predecessor of recent work on explicit graphs, this paper discusses non-transitive (rock-paper-scissors) competition in a well-mixed system.

  • Durrett and Levin 1994, “Stochastic Spatial Models: A User’s Guide to Ecological Applications”, Philosophical Transactions of the Royal Society B, Vol. 343 No. 1305. This library is based on the models discussed in Section 6 of this survey.

  • Durrett and Levin 1996, “Allelopathy in Spatially Distributed Populations”, Journal of Theoretical Biology, Vol. 185, pp. 165-171. Models non-transitive competition between three strains of E. Coli bacteria on a lattice graph.

  • Reichenbach, Mobilia, and Frey 2007, “Mobility Promotes and Jeopardizes Biodiversity in Rock-Paper-Scissors Games”, Nature, Vol. 448, pp. 1046-1049. The first example I am aware of of running May-Leonard symmetric non-transitive competition on a lattice graph, demonstrating the formation of spirals with the addition of a diffusion term, and demonstrating connections between the continuous-time, discrete-space system and the Complex Ginzburg-Landau Equation (CGLE).

  • Roman, Dasgupta, and Pleimling 2013, “Interplay Between Formation and Competition in Generalized May-Leonard Games.” Physical Review E, Vol. 87 No. 3, March 2013. Introduces the \((n, r)\) notation for May-Leonard models and demonstrates the formation of multilevel domains, with superdomains containing subdomains of competing species.

  • Szabo and Sznaider 2004, “Phase Transition and Selection in a Four-Species Cyclic Predator-Prey Model.” Physical Review E, Vol. 69, 2004. Demonstrates the formation of alliances between different species.

  • Szolnoki et al 2014, “Cyclic Dominance in Evolutionary Games: A Review”, Journal of the Royal Society Interface, Vol. 11 No. 100. Recent survey paper on continuous-time graph models.