A Cellular Automaton Model for Two Competitive Populations with Allee Effect and Overcrowding Effect

Abstract

Cellular automata (CA) have shown to be a valuable approach in ecological modeling, in particular when dealing with local interactions between species and their environment. In CA model, a global spatial pattern emerges through the evolution of interaction at a local scale. A cellular automata model for two competitive populations with overcrowding effect and Allee effect in a patchy environment has been developed. Having discussed the influence of the two effects on spatial pattern and dynamical complexity of two competitors, five primary results are given. First, overcrowding effect can produce the cricoids waves in space and chaos in time as well as single population model. And suitable increasing the colonization parameter of population produced the wave may shorten period of the spatial wave availably, also can vary its shape and is conducive to self-organization of system; Second, overcrowding effect of a competitor not only change complexity of two competitors but also influence their persistence in competitive system. But when its intensity exceeds some threshold, the complexity of two populations disappears suddenly and system will become stable. Third, the period of the wave caused by the overcrowding effect of the superior competitor is longer than the period of the wave caused by the overcrowding effect of the inferior. Fourth, Allee effect may not vary complexity of two populations until its intensity exceeds some threshold. In addition, extinction or invasion of some competitor may affect the dynamical complexity of original system significantly.