Segregation in a One-Dimensional Model of Interacting Species

We investigate segregation and spatial organization in a one-dimensional system of $N$ competing species forming a cyclic food chain. For $N<\mathrm{}5\mathrm{}$, the system organizes into single-species domains, with an algebraically growing average size. For $N=3\mathrm{}$ and $N=4\mathrm{}$, the domains are correlated and they organize into “superdomains” which are characterized by an additional length scale. We present scaling arguments as well as numerical simulations for the leading asymptotic behavior of the density of interfaces separating neighboring domains. We also discuss statistical properties of the system such as the mutation distribution and present an exact solution for the case $N=3\mathrm{}$.