Competitive Exclusion

Recent developments in the mathematical theory of competitive exclusion are discussed and placed in historical perspective. The models which have been used in theoretical investigations of competitive exclusion are classified into two groups: those in which the resources regenerate according to an algebraic relationship (abiotic resource models), and those in which resource regeneration is governed by differential equations (biotic resource models). We then propose a mathematical framework for considering problems of competitive exclusion, and provide examples in which n competitors can coexist on k < n resources (both biotic and abiotic). These systems persist because of internally generated cyclic behavior. We conclude that the competitive exclusion principle applies in general only to coexistence at fixed densities.