From simple rules to cycling in community assembly

Simulation studies of community assembly have frequently observed two related phenomena: (1) the humpty dumpty effect in which communities can not be reconstructed by ‘‘sequential’’ invasions (i.e. single species invasions separated by long intervals of time) and (2) cycling between sub-communities. To better understand the mechanisms underlying these phenomena, we analyze a system consisting of two predators and two prey competing for a shared resource. We show how simple dominance rules (i.e. R and P rules) lead to cycling between sub-communities consisting of predator /prey pairs; predator and prey invasions alternatively lead to prey displacement via apparent competition and predator displacement via exploitative competition. We also show that these cycles are often dynamically unstable in the population phase space. More specifically, while for too slow invasion rates (i.e. ‘‘sequential’’ invasions) the system cycles indefinitely, faster invasion rates lead to coexistence of all species. In the later case, the assembly dynamics exhibit transient cycling between predator-prey subcommunities and the length of these transients decreases with the invasion rate and increases with habitat productivity.