Species segregation in a model of interacting populations

Coarsening underlies numerous natural processes including phase separation, grain growth, soap bubbles, and species segregation. It is generally believed that coarsening systems exhibit dynamical scaling [1], i.e., the typical domain size grows algebraically with time, `(t) ∼ t. The exponent α is usually independent of many details of the system such as the spatial dimension. However, little is known on coarsening in systems with more than two equilibrium phases. In this study, we investigate species segregation and reveal the two-length scaling instead of the ordinary single-length scaling. Lotka-Volterra model of interacting populations “living” on a one-dimensional lattice is the simplest system which exhibits species segregation. The case where N species form a food chain is especially well suited for studying species segregation. We assume that every species plays the role of prey and predator simultaneously. The food chain is arranged in a cyclic manner. For example, when N = 3, A eats B, B eats C, and C eats A. “Eating” events involve nearest neighbors and lead to duplication of the winner and elimination of the loser, corresponding to the following reaction scheme