Ecological graph theory: Simulating competition and coexistence on graphs

Since its inception, the evolutionary graph theory (EGT) has been extensively used to study the fixation probability, the rate of evolution, game‐theoretical topics and related questions in a spatially structured framework. However, few attempts have been made to use this framework in ecology. We develop an ecological extension of EGT, dubbed the ecological graph theory (EcoGT), to construct a graph‐based equivalent to the classic Lotka‐Volterra (LV) model. Firstly, we apply EcoGT to simple topologies, specifically a regular dodecahedron and a King's graph, to illustrate how such extreme topologies result in deviation from the LV model. Secondly, we explore how various graph families, for example, complete graphs, random graphs, small‐world graphs, affect the competitive outcome between species. Finally, we explore species competition in EcoGT on graphs with dynamic topologies. Our results illustrate the suitability of the EcoGT approach to investigate fundamental questions related to species competition and coexistence at community and metacommunity levels without neglecting spatial structure across these scales.