Gause’s principle in interspecific competition of the cyclic predator–prey system

• We model the interspecific competition based on the cyclic predator–prey system.
• We consider the average individual ability to prey and the aggregation degree.
• We prove the validity of Gause’s Competitive Exclusion Principle.
• We provide a suitable explanation for the biological phenomenon of competition.

In this paper, we study the law of survival for species in interspecific competition in the cyclic and predator–prey system. In our model, the successful rate for a predator to prey depends on the individual ability to prey and the two interacting clusters sizes, and the size of a cluster is determined by the aggregation degree between individuals. Experimental results show that only one species can survive when competition occurs on one niche. And which species can survive ultimately depends on the relative relationship between the average individual ability to prey and the aggregation degree between it and its competing species. If competing species have identical values for the average individual ability to prey and the aggregation degree, the species that can survive is determined at random. Therefore, Gause’s Competitive Exclusion Principle is correct, but the causes of competing species to survive are different.